Small gold clusters are used as simple models to simulate the surface of gold nanoparticles.. 10Figure 2.2 Surface plasmon resonance in gold nanoparticles .... Recent studies [49-51] by
INTRODUCTION
Motivation
The use of drugs in cancer treatment often causes several side effects such as increased risk of infection, anemia, fatigue, nausea, constipation, diarrhea, loss of appetite, and hair loss [1] Therefore, many studies have been carried out to find appropriate methods to reduce drug dosage and thereby limit such negative effects One of the most popular approaches is using carriers to deliver drugs to necessary locations to improve the treatment effectiveness Recently, nanotechnology has been widely used in disease diagnosis and treatment [2] Nanomaterials used in drug delivery containing gold are of particular interest due to their unique properties including high durability, easy synthesis and can be prepared in many different shapes and sizes [3] Gold nanoparticles (AuNPs) have the ability to bind with various biomolecules and exhibit low toxicity [4] Their presence in drugs could improve the treatment effectiveness [5], allowing effective drug delivery thanks to the action of metal nanoparticle carriers, which can release the drug when needed [6] and increase treatment retention time in the circulation [7] Many experimental efforts have been conducted to evaluate the role of these nanoparticles in disease treatment, especially related to inflammation and tumors [8]
In addition to experimental methodologies [9], computational techniques are more and more widely used to examine the properties of AuNPs and their interactions with drug molecules and biological molecules In general, these studies can be conducted at many different levels of theory If precise information about structure, energy, and spectra is required, quantum chemical calculations would be the most appropriate choice Lee and Ytreberg [10] examined the effect of AuNPs on the structure and flexibility of peptides using molecular dynamics modeling They found that conjugation of peptides with AuNPs causes the peptides to lose interaction with cellular components For drug delivery purposes, this suggests that peptides have a secondary structure in solution suitable for peptide-AuNPs conjugation In contrast, peptides with little or no secondary structure in solution will adsorb on the nanoparticle surface The interaction between ubiquitin protein and AuNPs has also been probed at different levels of theory including density functional theory (DFT), molecular dynamics (MD) calculations and Brown kinetic simulations [11] Accordingly, a model brings together the structures constituting the ubiquitin complex on the gold surface and insights into the kinetics of ubiquitin binding to AuNPs, as well as the role of surfactants such as citrate in the process Nanoparticle binding and the origin of perturbation in chemical shift NMR spectra
2 The adsorption of the cecropin-melittin (CM) peptide with cysteine (CM-SH) and without cysteine (CM) at the C-terminus on gold surfaces was also investigated by Ferreira et al [12] They found that the inclusion of cysteine facilitates the structural stability The finding could serve as a foundation for comprehensive elucidation at the atomic level regarding the experimental findings of AuNPs immobilization facilitated by CM-SH and
CM Further investigation on the adsorption behavior of the anticancer medication Tamoxifen on the gold surface was also conducted through the utilization of surface- enhanced Raman scattering (SERS) spectroscopy and density functional theory (DFT) calculations [13] Both experimental and theoretical evidences indicate that the protein environment significantly alters the nanocluster characteristics The adsorption of amino acids on gold surfaces is a subject of significant interest due to its potential implications in drug administration and bio-sensing A recent study [14] demonstrated that the interaction between gold and these biological compounds exhibits a combination of electrostatic and covalent characteristics The stability of the covalent bond is attributed to the interaction between the nonbonding electron pair of sulfur, oxygen, and nitrogen and the antibonding orbitals of gold metal In contrast, the nonconventional hydrogen bond is distinguished by the transfer of electrons from gold to the H atom of N−H and O−H bonds
In an up-to-date study [15], DFT calculations are employed in conjunction with molecular dynamics simulations to clarify the intricate interplay between the Au32 fullerene cluster and certain amino acids Amino acids have been found to exhibit a robust binding affinity to the external surface of the cluster in gas phase, mostly through the N atoms of amino acids The interaction is in addition significantly strengthened in aqueous solution, leading to an enhanced stability of resultant complexes The findings on the interaction between Au32 and biomolecules provide valuable insights into its potential utilization as a novel drug delivery system Numerous efforts have also been devoted to the interaction between noble metal nanoparticles and deoxyribonucleic acid bases due to the presence of nucleobases in various anticancer, antiviral, and antibacterial medications [16]
In recent decades, nanomaterials have become more and more widely used in biomedical fields as a promising approach for design of drug delivery systems, diagnosis agents, imaging and biosensors [17,18] Numerous nanostructures are applicable in medicine thanks to their peculiar properties that much differ from those observed in fine particles or bulk materials Generally, nanomaterials relevant for biomedical applications can be categorized as either organic origins including liposomes [19], dendrimers [20], and polymers [21] or inorganic backgrounds such as noble nanoparticles [22], iron oxide NPs [23], and other inorganic compounds [24,25] In terms of chemical stability, environmental compatibility and high mechanical strength, the inorganic groups are likely to prevail over
3 the organic counterparts [26] Of the common inorganic nanostructures, those consisting of gold have peaked much interest as they exhibit valuable impacts and clear-cut advantages [27] Firstly, AuNPs are highly compatible to a variety of bimolecular systems and exhibit a much lower inherent toxicity to human than many others [28] They also pose a remarkable stability and are willing to be functionalized by a number of biological systems, such as drugs, genes and targeting ligands [29] Moreover, AuNPs with various sizes/shapes, i.e spherical, rod-like, cage-like forms and so on, can be easily synthesized [3] Such particles enhance optical properties, distinctive surface and macroscopic quantum tunneling effects, along with SPR phenomenon [30], and are able to penetrate through the cell membrane without creating pores on the cell membrane [31] As a result, AuNPs become one of the most efficient materials for various biomedical applications including bio-sensing, molecular imaging, drug delivery [32] The presence of gold particles in drugs results in several beneficial outcomes, i.e enhancing the therapeutic effect of the drug [33], allowing an effective drug delivery [6] in increasing the therapeutic retention time in the circulation [7], and improving the target specificity of treatments [28,33]
Gold is one of the first metals to have been discovered [19] Gold salts and molten glass were combined to create gold colloids with a beautiful ruby color Many of these variations were used extensively in the medieval era by artists to color glass and pottery The scientific community has expressed a significant amount of interest in clusters formed in the gas phase, particularly since the discovery of C60 [34,35] The surface atoms are typically very reactive in gas phase clusters because their valences are not fulfilled Clusters should be created in situ in experimental apparatuses where the qualities are to be studied because they can not be kept in a free condition Gas phase clusters are typically produced using a number of cluster sources, including liquid metal ions, pulsed arc cluster ions, laser vaporization ions, laser ablation ions, and cluster ion sources [36] After such discoveries, the concepts of electron shell closing based on the Jellium model [37] and superatoms [38] were developed
Besides, the gold clusters undergo a rather short recovery time and a large change of energy gap, which could be conducive to electrical signaling conversion for selective detection of the drugs In addition, gold nanoclusters typically provide a suitable surface for loading various therapeutic agents, such as small biomolecules, peptides, proteins, and nucleic acids [25] El-Mageed [39] also examined the interactions of D-penicillamine with some small gold clusters (Aun, n = 2, 4, and 6) and observed rather strong interactions between them which are governed by the anchoring Au–O/S/N bond, unconventional hydrogen AuãããH–S bonding, and electrostatic AuãããH–C coupling Likewise, a variety of drugs and biomolecules such as methimazole [40], tamoxifen [13], amino acids [15], DNA
4 bases [41], curcumin [42], pectin [43], and others [44] have also been found to strongly be adsorbed on the surface of gold nanoclusters with significant electronic responses
In another study by Salvatore et al [45], cyclic voltammetry and electrochemical scanning tunneling microscopy were combined with DFT calculations to investigate the adenine binding to some larger Aun clusters (n = 32, 44, 56) It has been shown that the adsorption at the N7/N10 position is vertical in the gas phase and almost parallel in low pH environment Nevertheless, it has been widely hypothesized that the adsorption mechanism involves the attachment of adenine to the gold surface via the N3/N9 position This is mostly due to the fact that the N7H tautomer is observed under the majority of the experimental circumstances [41] Farrokhpour [46] also examined the adsorption behavior of adenine (ADE) and cytosine (CYT) on Au(111), Au(100), and Au(110) surfaces It was found that the orientation of the chosen base on the nanoparticle is contingent upon the specific plane The ADE molecule exhibits an inclined geometry when adsorbed on the Au(111) surface, while CYT adopts a vertical orientation on the same surface The Au(110) surface exhibits a pronounced propensity for the adsorption in both gaseous and aqueous phases A comprehensive information on the interaction between DNA bases and the nanocluster surface is essential for elucidating experimental findings pertaining to the adsorption of DNA, single-stranded DNA, RNA, and oligonucleotides on metallic surfaces Nevertheless, there is ongoing debate regarding the arrangement of DNA bases on the surface of gold nanoparticles Hence, it is imperative to conduct additional investigations in this particular domain
Throughout history, sulfur element has been employed for its therapeutic properties in the treatment of various ailments [47] The utilization of magnesium sulfate in the treatment of various diseases has been authorized by the United States Food and Drug Administration (FDA) since its inception This pharmaceutical compound represents the initial iteration of drugs including sulfur atoms To date, FDA has compiled statistical data on medicinal medications that incorporate sulfur atoms [47,48] Typically, pharmaceutical compounds containing sulfur can be categorized into many groups, including sulfonamide, β-lactam, thioether, thiazole, thiophene, phenothiazine, sulfoxide, S=C and S=P, thionucleotide, sulfone, sulfate, macrocyclic disulfide, and medicines with acyclic and cyclic groups [47], as depicted in Figure 1.1
Figure 1.1 Classification of drugs containing sulfur atoms licensed by the FDA
Numerous theoretical and experimental studies have been carried out to validate the advantages of NPs by exploring the nature of their interactions with drugs and biomolecules, as well as to elucidate inherent physicochemical properties [44] At the molecular scale, metallic cluster models are commonly used to examine the adsorption/desorption mechanism of a molecule on the nanoparticle surface Recent studies [49-51] by employing small Aun clusters as simple models to represent the gold nanostructured surface, have demonstrated that AuNPs exhibit promising characteristics of bio-sensing and targeted delivery of several anticancer drugs
Sulfur-containing compounds with a C=S functional group often exhibit a variety of biological activities and play vital roles in pharmaceutical applications The family of drugs containing a C=S functional group exhibits either a thiourea or an artificial DNA base [47] 6-Mercaptopurine (6MP), a purine analogue with antineoplastic and immunosuppressant properties, is non-enzymatically converted to 6-MP in tissues [52] Since its 1953 FDA approval as an antitumour drug [53], it has been widely used to treat acute lymphoblastic leukemia, rheumatological disorders, organ transplant rejection, and inflammatory diseases [54] 6MP can be combined with other drugs to treat systemic lupus erythematosus, non-Hodgkin-lymphoma, polycythemia vera, Crohn’s syndrome and ulcerative colitis [55] 6MP is a nucleobase analogue having a C=S double bond acting as a surrogate for the natural carbonyl compounds (Figure 1.2) It is commonly used to treat cancers by interfering with DNA replication [56] Recently, 6MP has gained significant interest as an antineoplastic agent due to its favorable coordination properties resulting from its nitrogen and sulfur donor sites These sites can form bonds at N1, N3, N7, and N9 Furthermore, it exhibits chemotherapeutic properties The efficacy of 6MP in cancer cells is thought to be attributed to its capacity to convert the nitrogen donor sites into the corresponding ribosides [57] This drug is one of the mosr commonly utilized antitumor medication and
6 immunosuppressant that has been proven effective in treating childhood acute lymphoblastic leukemia in clinical practice It can be used either on its own or in conjunction with other medications during the initial and ongoing stages [58,59] Nevertheless, the oral bioavailability of 6MP is limited to a range of 16% to 50% because it is insoluble (0.22 mg/mL) and has a short half-life of 0.5 to 1.5 hours Furthermore, there is a significant amount of variation between individuals in their clinical response The indiscriminate distribution of 6-MP and genetic variations can lead to severe adverse effects, such as liver toxicity and myelosuppression, which significantly impact the effectiveness of 6-MP in clinical applications [59]
Figure 1.2 Chemical structures of MP and PPX drugs
Parkinson’s disease (PD) typically manifests in individuals who are 50 years of age or older Juvenile PD, also known as Parkinson’s disease, accounts for approximately 5% of cases and primarily affects individuals under the age of 20 The disease prevalence is 0.2–0.3% in the general population, but it rises to 1% among individuals aged 55 and above While L-DOPA is currently considered the most effective treatment for Parkinson’s disease, its efficacy diminishes quickly and its administration often leads to significant motor fluctuations, such as on-off periods, wearing off, freezing, and involuntary movements, in the majority of Parkinson's disease patients Pramipexole is a dopamine agonist that belongs to the aminothiazole class It selectively targets dopamine receptors in the D2 subfamily and exhibits full activity comparable to dopamine [60] Pramipexole (PPX) is a highly favored medication for treating Parkinson’s disease due to its numerous benefits, including the ability to delay the occurrence of motor fluctuations and dyskinesia that are commonly seen with other drugs used to treat the condition
Objectives of the research
(i) To clarify the nature of the interactions between the gold nanostructures and some S-containing drugs such as binding sites, adsorption energies, charge transfer, change of energy gap, and electronic band structures
(ii) To elucidate the drug release mechanism due to internal stimuli (operated within a biologically controlled manner).
Research contents
Chapter 1 is an overview of the thesis In Chapter 2, some important results from prior research studies relevant to the research scope and content will be presented Chapter
3 introduces some quantum chemical methodologies employed in this research Then the applications of these methodologies on the study of interactions between gold clusters and some anti-cancer S-containing drugs are discussed thoroughly in Chapter 4 Finally, we summarize in Chapter 5 the main results obtained in the thesis and suggest some related works in the future.
Methodology
The density functional theory is employed to determine the structure and energetics of the systems considered with the aid of available computational packages such as Gaussian 16 [76] The optimizations are accelerated by making use of an effective core potential (ECP) for the Au atoms [77], which also includes relativistic effects that are very crucial in treatment of gold compounds Time-dependent DFT are employed to predict the vertical electron transitions between the ground state and several excited states The effect of solvent (aqueous solution) is simulated using the popular continuum model known as the Integral Equation Formalism-Polarizable Continuum Model (IEF-PCM) [78]
Harmonic vibrational frequencies are calculated at the same level of theory as the optimization procedures to confirm the character of optimized geometries as local minima on the potential energy surface and to estimate the zero-point vibrational energy (ZPE)
9 corrections Zero-point and thermal enthalpies corrections are then employed to obtain free energies using the following equation:
∆G 0 (298K) = ∆E + ∆ZPE + ∆TCG (1.1) where ΔE is the relative electronic energy at 0 K, ΔZPE is the relative vibrational energy at 0 K, while ΔTCG is relative changes in Gibbs free energy in going from 0 to 298 K The adsorption energy is computed as the difference between the energy of Aun- drug/biomolecule complexes and the sum of the energies of the corresponding moieties, namely:
E ads = E complex − (E Au n + E drug/bio ) (1.2) where E X , is the lowest electronic energy of the X species As for a convention, a negative value of E ads corresponds to a stabilizing complexation Similarly, the energy for drug release is computed as follows:
E des = (E Au n −bio + E drug ) − (E Au n −drug + E bio ) (1.3)
The greater the computed value of the adsorption/desorption energy, the stronger the affinity of gold particles binding to the drug/biomolecules is In order to evaluate the effect of interacting species on each other, the electronic properties such as the HOMO-LUMO energy gap (Eg), the density of states (DOS) will be examined The Eg is a useful factor for determining the kinetic reactivity of materials [79], and also its change upon the adsorption process indicates the sensitivity of an adsorbent to an adsorbate based on the following equation: σ = AT 3/2 e −E g /2𝑘 𝐵 T (1.4) where 𝑘 𝐵 is the Boltzmann’s constant and A is a constant The change of Eg of adsorbent can help one to recognize the presence and attachment of the drug to the carrier.
Creativeness and innovativeness
(i) Method of simulating the absorption process of biomolecules on the Au nanoparticle surfaces using the small clusters as reactant models; (ii) The nature of interactions between S-containing anticancer drugs and gold nanoparticles, such as binding energies, bonding characteristics, and electronic responses; (iii) Mechanism of the SERS chemical enhancement of S-containing drugs adsorbed on gold nanostructured surfaces (iv) The drug release mechanism due to internal stimuli The novelty of this work has been demonstrated by the papers published in peer-reviewed journals such as RSC Advances, Journal of Molecular Modeling, Symmetry, Journal of Computational Chemistry
LITERATURE OVERVIEW
Introduction to gold nanoparticles
Michael Faraday discovered that the “fine particles” produced from the aqueous reduction of gold chloride by phosphorus could be stabilized by the addition of carbon disulfide, resulting in a “beautiful ruby fluid” This discovery was reported in the first scientific report describing the production of colloidal gold nanoparticles in 1857 [80] These days, the majority of colloidal synthetic techniques for producing gold nanoparticles (Figure 2.1) use a similar approach, in which solvated gold salt is reduced in the presence of surface capping ligands that stop the particles from aggregating due to physical or electrical repulsion The ratio gold ion/reducing agent or gold ion/stabilizer ratio can be changed to the size of the particles; larger (and usually less monodisperse) sizes are obtained from greater ratios
Figure 2.1 Gold nanoparticles of various size and shape with potential applications [81]
Small (a) and large (b) nanospheres, (c) nanorods, (d) sharpened nanorods, (e) nanoshells, (f) nanocages/frames, (g) hollow nanospheres, (h) tetrahedra/octahedra/cubes/icosahedra, (i) rhombic dodecahedra, (j) octahedra, (k) concave nanocubes, (l) tetrahexahedra, (m) rhombic dodecahedra, (n) obtuse triangular bipyramids, (o) trisoctahedra, and (p) nanoprisms
11 Turkevich et al [82] conducted the first structural studies of gold nanoparticles formed under various synthetic conditions in 1975, derived from systematic studies of Frens in
1973, resulting in monodisperse spherical gold nanoparticles with a diameter ranging from 16–150 nm These studies came about after Knoll and Ruska introduced the electron microscope in 1932 [83] However, Pong et al [84] suggested that the tiny (about 5 nm in diameter) nuclei created by citrate-mediated thermal reduction of chloroauric acid first self- assemble into a web of linked chains The typical nano-sphere outcome of this synthesis is formed when spherical particles break off from these structures as the diameter of these chains increases with increased Au deposition Such a “necklace-breaking” mechanism is much different from other multi-particle mechanisms like oriented attachment (where small crystalline particles fuse with one another along a crystalline face) or classic Ostwald ripening (where larger particles consume smaller particles) Gold nanospheres up to 430 nm in size have been produced by similar techniques (Figure 2.1b) [85]
Schmid et al [86] demonstrated that reducing PPh3AuCl with diborane in benzene could result in the production of substantially smaller (1.4±0.4 nm diameter) phosphine- stabilized gold particles, Au55(PPh3)12Cl6 Unlike the colloidal gold solutions covered in the preceding paragraph, this cluster is a real molecule with a precisely defined formula weight Weare et al [87] subsequently reported that ligand exchange could be used to create gold clusters with a diameter of 1.4–10 nm These particles could be produced in a similar manner in ambient settings without the use of diborane gas Using a two-phase system in which gold chloride was solvated in toluene by means of a phase-transfer reagent (tetraoctylammonium bromide), Brust et al [88] studied the synthesis of thiol-stabilized gold clusters Here, reducing sodium borohydride was introduced to the aqueous phase, and gold clusters that formed in the organic phase were stabilized using dodecanethiol Due to their molecule-like characteristics and ease of conjugation, these and similar clusters have drawn great attention [89] However, because of their reported toxicity, biomedical applications such as immune labeling [90], and as contrast agents for radiation therapy and X-ray imaging [28]are somewhat limited [91]
Around the beginning of the 1990s, when Masuda et al [92] and Martin et al [93] established methods to prepare gold nanorods by electrochemical reduction into nanoporous aluminum oxide membranes, interest in the shape-controlled synthesis of gold nanostructures started to take root These techniques resulted in comparatively monodisperse structures, but at the time, it was difficult to distinguish the optical response from these nanorods because of their low yield and somewhat large diameter (>100 nm) This was primarily due to the multipolar plasmon resonance modes that dominate the incident field’s phase retardation, leading to a non-symmetric plasmon field density
12 distribution [94] Later, Yu et al [95] introduced a method to create much smaller gold nanorods (~ 10 nm in diameter) by electrochemically oxidizing an Au plate-electrode using cationic quaternary ammonium surfactants (tetraoctylammonium bromide, TOAB, and cetyltrimethylammonium bromide, CTAB) The nanorod solutions that demonstrated plasmon resonance modes for both transverse and longitudinal axis polarizations
Recently, gold nanoshells, also known as silica-gold core-shell nanoparticles (Figure 2.1e), have garnered significant interest because of their various biological uses and intriguing optical characteristics The tunable plasmon resonance of a concentric spherical particle, which varies according to the ratio of shell thickness to core radius, was predicted by Aden et al [96] In 1998, Oldenburg et al [97] demonstrated that it was possible to create near-infrared absorption gold nanoshells by electrostatically attaching tiny gold particles to the silica nanoparticle surfaces, then reducing more gold onto the structures to create a conformal shell Typically, base-catalyzed condensation of orthosilicate (also known as Stửber hydrolysis) [98] is used to create silica nanoparticle cores, which are then functionalized with an amine-terminal silane The aqueous reduction of chloroauric acid by tetrakis(hydroxymethyl)phosphonium chloride yields small, anionic gold nanoparticles, which are then electrostatically adsorbed onto the surfaces of the silica cores and mixed with a solution of moderately reduced chloroauric acid The adsorbed gold particles act as nucleation sites for the further reduction of gold surrounding the silica core, which forms a conformal nanoshell when formaldehyde is added to the solution Subsequent findings have demonstrated that thinner and more uniform nanoshells are produced during reduction using carbon monoxide as opposed to formaldehyde [99] There have also been other comparable structures created with unique optical characteristics, like quadruply concentric
Recent studies by Skrabalak et al [101] of gold nanocages and nanoframes also offer promise for a range of biomedical applications because of their favorable optical characteristics and perhaps cargo-holding hollow shapes (Figure 2.1f) These structures are created by a process called galvanic replacement, in which ions of more noble metals (like
Au, Pt) spontaneously oxidize the surface atoms of ions of less noble metals (like Ag, Cu), reducing the more noble metal in the process [101] In this instance, Au(III) reacts with silver nanocubes made from the polyol reduction of silver nitrate to form gold nanocages or frames The density of the resulting structure is greatly reduced because the reduction of one Au(III) ion necessitates surface oxidation to three Ag(I) ions In the case of a single- crystal cube, this results in the initial formation of hollow Au/Ag alloy “nanoboxes”, which subsequently react to form porous Au nanocages and eventually faceless Au “nanoframes” [102]
13 Kim et al [103] demonstrated that a modified polyol technique could be used to create more geometrically complicated gold nanostructures, with sizes ranging from 100 to
300 nm (Figure 2.1h) Poly(vinylpyrrolidone) was used as a particle stabilizer and ethylene glycol as a solvent/reducing agent to produce tetrahedra, cubes, octahedra, and icosahedra in high yield and good monodispersity The amount of gold present in the reaction solution had a significant impact on the morphology of the resulting nanoparticles with tetrahedra forming at high concentrations and icosahedra (along with a few octahedra) at lower concentrations Gold nanocubes were also created by introducing a little amount of silver nitrate during the reaction procedure It was proposed that poly(vinylpyrrolidone)’s crystallographically preferential adsorption led to increased [100] growth and decreased [111] growth, producing tetrahedral and icosahedral that are {111}-dominant Moreover, {100}-dominant cubes could arise as a result of silver ions’ preferential adsorption on {111} facets Later, Sau et al [104] suggested a method to synthesize equally complicated gold nanostructures at high yield using seed-mediated growth techniques that are roughly akin to those employed to create colloidal nanorods Rectangular, hexagonal, cubic, triangular, and star-like nanoparticles were produced by adjusting the amounts of Au(III), ascorbic acid, and silver nitrate in the growth fluid as well as the number of additional seeds supplied An comparable seed-less, modified polyol synthesis was created in 2006 by Seo et al [105]
In summary, the reduction of chloroauric acid was achieved in the presence of poly(vinylpyrrolidone) stabilizer by 1,5-pentanediol The morphology varied from Au octahedra, truncated octahedra, cuboctahedra, cubes, to higher polygons as the concentration of AgNO3 increased Later research by Niu et al [106] shown that a similar seeded growth technique may be used to generate additional complex gold nanostructures in high yield (>96%) In this case, rhombic dodecahedral, octahedral, and cubic gold nanocrystals from Au(I) were grown from CTAB-capped gold nanorods that were amplified in an Au(III)/CTAB solution and functionalized with cetylpyridinium chloride (CPC) The seeds were single-crystalline and had a diameter of around 40 nm Remarkably, the authors discovered that, contrary to their normally observed surface free energies (i.e., {110} > {100} > {111}), the CPC surfactant preferentially stabilized {100} > {110} > {111} facets When the CPC-Au{100} (and to a lesser extent, Au{110}) association was found to be prominent, a rhombic dodecahedral morphology (Figure 2.1i) was observed, and when the CPC-Au{111} association was found to be dominant, octahedral geometries (Figure 2.1j) were detected When Br − ions were added, it was discovered that cubic gold nanoparticles formed The authors explained this phenomenon by stating that Br − adsorption increased the stabilization of {100} facets, which in turn led to the electrostatic connection of CP +
A method for producing monodisperse gold nanocubes in high yield has also been recently established by Zhang et al (Figure 2.1k) [107] This process uses a seeded growth procedure similar to that used to make nanorods, but instead of employing CTAB’s bromide counterpart, cetyltrimethylammonium chloride (CTAC) The researchers discovered that adjusting the quantity of seeds introduced to the growing medium allowed them to control the size of the nanocubes, producing cubes with edge lengths ranging from 38±7 nm to 269±18 nm with a 95% yield The nanocubes are anticipated to display new catalytic capabilities because of their concavity, which caused them to show a surface plasmon resonance that was about 80 nm red-shifted from their {100}-faced counterparts According to the authors’ hypothesis, surface-bound Ag created by underpotential deposition (UPD) and its growing stabilization by a Cl − adlayer may be the cause of the creation of high-index {720} facets Previously, Ming et al [108] used a similar synthetic technique employing CTAB (>95% yield) to create structurally-related, near-infrared absorbent tetrahexahedral gold nanoparticles surrounded by 24 {037} facets (Figure 2.1l) Personick et al [109] demonstrated that obtuse triangular bipyramids (Figure 2.1n) and rhombic dodecahedra (Figure 2.1m) could be created by a seeded growth (7 nm diameter) involving CTAC and diluted Ag + concentrations This resulted in the only known {110}-faceted bipyrimidal gold nanostructures (31±5 nm and 270±26 nm edge length, respectively) [109]
According to crystallographic research, the near-infrared absorbing triangular bipyrimads comprised two triangular prisms separated by bridging (111) planes, whereas the rhombic dodecahedra contained twelve identical {110} facets Subsequent investigation revealed that the usage of a combination of seeds containing both single-crystals and twin- defected particles was the source of these structural variations, and that size-selective filtration was an easy way to separate the product particles It is interesting to note that they also discovered that, when the Au(III):seed ratio was raised, deposition progressively favored development on twinned bipyramidal particles They speculated that this was because Ag UPD growth-directing effects predominated due to Cl − ’s low(er) binding affinity for Au A straightforward aqueous reduction of chloroauric acid has been used to create even more unusual structures, such as gold trisoctahedra (Figure 2.1o) [110] Ma et al [110] demonstrated that the formation of these nanostructures, which have a diameter of 100–200 nm and are surrounded by 24 {221} facets, occurs through the reduction of chloroauric acid with ascorbic acid in the presence of CTAC (around 85% yield) The authors also discovered that CTA + and Cl − were required for the production of trisoctahedra, albeit the exact mechanism for their synthesis is still unknown They further proposed that ascorbic acid or its oxidation products may stabilize high-energy concave faces
15 Triangular or prismatic nanoparticles have been synthesized using several techniques such as photo-reduction, seed-mediated growth, plasmon-driven synthesis, and biosynthesis Shankar et al [111] initially achieved gold nanoprismatic structures with a reasonable yield (about 200−500 nm in size, 45% yield) through the reduction of chloroauric acid using lemongrass extract in an aqueous solution The scientists ascribed this change to the plant extract’s ability to reduce aldose sugars, resulting in the creation of a specific shape due to the selective adsorption of aldehydes/ketones found in the extract Millstone et al [112] subsequently demonstrated that gold nanoprisms with similar dimensions (144±30 nm edge length) could be efficiently manufactured using a seeded growth technique (Figure 2.1p) The synthesis process involves the reduction of chloroauric acid using borohydride, resulting in the formation of spherical seeds with a diameter of 5.2±0.6 nm These seeds are then further enhanced by progressively adding chloroauric acid, sodium hydroxide, ascorbic acid, and CTAB to the solution The nanoprisms were separated through the process of filtration, utilizing a commercially-accessible membrane made of aluminum oxide with a nominal pore size of 100 nm Subsequently, the isolated nanoprisms were subjected to analysis using optical spectroscopy and computational techniques
The functionalization of gold nanoparticles for biomedical purposes builds upon the research conducted by Nuzzo and Whitesides, who initially investigated the creation of self-assembled monolayers (SAMs) of molecules on flat gold surfaces This work was further expanded upon by Bard [113] and Sardar [114], who studied the behavior and structures of these assemblies using electrochemical, scanning probe, and mass spectrometric techniques Currently, a diverse range of functional molecular linkers and passivating agents are used to attach gold nanoparticles in biomedical applications The anchoring groups commonly employed for attaching these molecules to the gold surface include thiolate [115], dithiolate [116], dithiocarbamate [117], amine [118], carboxylate [119], selenide [120], isothiocyanate [121], or phosphine [122] moieties Recent research [123] indicates that the production of a direct bond between gold and carbon can potentially be accomplished using a trimethyl tin leaving group However, its effectiveness in biomedical or nanoparticle-based applications has not been evaluated yet The selection of a certain molecular anchor is normally determined by the required level of molecular instability for a particular application, with bonding strength trends generally aligning with Pearson’s hard-soft acid-base (HSAB) theory for a soft Au(I) surface Thiol-based anchoring groups are commonly used in non-labile applications, whereas labile applications typically utilize amine or carboxylate surface anchors Cheng et al [124] have demonstrated that the effectiveness of therapeutic outcomes in photodynamic therapy, when delivered using gold nanoparticles, is significantly improved by using amino linkers
Biomedical applications of gold nanoparticles
Photodynamic therapy has become widely accepted as a significant therapeutic approach for the management of oncological conditions Additionally, it is employed in the treatment of specific skin disorders and infectious diseases, utilizing photosensitizers as agents that sensitize to light, in conjunction with a laser that emits light at a wavelength that is associated with the peak absorption of the dye Tumor cells undergo apoptosis or necrosis as a result of singlet oxygen and highly active free radicals produced through the utilization of photosensitizers [138,139] The application of AuNPs in photodynamic therapy has been facilitated by their notable characteristics, namely effective fluorescence quenching and SPR absorption Moreover, the conjugation of gold serves to enhance the intracellular penetration, as it exhibits a propensity to interact with thiols, disulfides, and amines [138]
Figure 2.4 The application of plasmonic photothermal therapy for the treatment of cancer cells through the active delivery of AuNPs [138]
Photothermal therapy, also referred to as thermal ablation [139] or optical hyperthermia [140] is a widely utilized approach in the field of cancer therapy due to its minimal invasiveness [141] This technique has garnered significant interest in recent times [142] AuNPs that exhibit a peak absorption in the visible or near-infrared (NIR) region have the ability to absorb light and subsequently convert it into heat The elevated temperature leads to the demise of cancerous tumors [143] Spherical solid gold nanoparticles that possess a diameter exceeding 50 nm, primarily owing to their pronounced near-infrared absorption capabilities, are frequently observed in the context of photothermal therapy [141] Figure 2.4 illustrates the schematic depiction of the application of gold nanoparticles within the framework of photothermal therapy It has been proposed to refer to this particular approach as plasmonic photothermal therapy Additionally, the utilization of AuNPs-antibody conjugates can be employed for both diagnostic purposes and plasmonic photothermal therapy, encompassing the combined approach known as theranostics The intracellular transfer process is significantly influenced by the binding properties of AuNPs, similar to the impact observed in photodynamic therapy [138]
AuNPs have garnered significant interest as a potential X-ray contrast agent due to their high X-ray absorption coefficient, synthetic manipulability, lack of toxicity, ability to be surface-functionalized for colloidal stability, and potential for targeted delivery Vascular contrast agents commonly employed in medical imaging, such as iodinated molecules, possess a low molecular weight The iodinated aromatics exhibit a high degree of water solubility, which is suggestive of their low toxicity However, it should be noted that the duration of blood circulation is relatively brief and the elimination of blood occurs rapidly via the renal system Therefore, a limited imaging time frame may necessitate the administration of multiple injections, thereby increasing the potential for the development of thyroid dysfunction AuNPs have been the primary focus in addressing the challenges [144] The longer vascular retention time of AuNPs compared to common agents has led to the development of an imaging window, which can be attributed to the significant properties of AuNPs [144]
As previously mentioned, AuNPs possess notable characteristics including distinct optical and physicochemical properties, biocompatibility, functional adaptability, adjustable monolayers, controlled dispersity, a large surface area for drug loading, stability, and lack of toxicity These attributes collectively establish AuNPs as an effective nanocarrier in drug delivery systems [145] The nano-carriers discussed in this study have demonstrated efficacy in the delivery of a wide range of drugs, including peptides [146], proteins [147], plasmid DNAs, small interfering RNAs, and chemotherapeutic agents [148]
The unique optical properties, ease of synthesis, and chemical stability of AuNPs have garnered significant attention in the field of technology The utilization of particles in biomedical contexts encompasses a range of applications, including but not limited to cancer therapy, biological imaging, chemical detection, and pharmaceutical transport [149,150] Sun et al [149] extensively discussed two distinct approaches for achieving controlled drug release using nanoparticles These approaches encompassed (i) sustained release mechanisms, specifically diffusion-controlled and erosion-controlled release, and (ii) stimuli-responsive release mechanisms, including pH-sensitive, enzyme-sensitive, thermos-responsive, and photosensitive release Figure 2.5 depicts the mechanism by which NPs function as a means of delivering medications specifically to cancer cells (Figure 2.5A) and delivering therapeutic genes to facilitate the synthesis of desired proteins in targeted cells (Figure 2.5B) Nanoparticles have the capability to transport therapeutic agents to precise anatomical regions within the body, resulting in enhanced precision and efficacy of medical interventions [151] For instance, AuNPs have been extensively investigated as
20 potential carriers for drug delivery owing to their inherent stability and capacity to selectively accumulate in specific cancerous tumors [151] The utilization of ZnO nanoparticles for drug delivery has been investigated in light of their capacity to specifically target cancer cells [152] Copper nanoparticles have demonstrated antimicrobial characteristics and are currently being investigated as a potential drug delivery system for the treatment of bacterial infections [153] AuNPs possess distinctive optical, electrical, and catalytic characteristics, making them a subject of investigation for drug delivery applications This is primarily attributed to their capacity to accumulate selectively in specific cancerous tumors
Figure 2.5 The usage of nanoparticles in the field of medicine encompasses two key areas: targeted drug delivery (A) and the generation of therapeutic proteins (B) [137]
In addition to spherical nanoparticles, recent studies have suggested that stable colloidal gold nanorods may serve as a suitable vehicle for drug delivery The utilization of PEGylated gold nanorods has demonstrated effective drug delivery capabilities through the evasion of reticular-endothelial system clearance The other candidates are gold nanocages Targeted drug delivery occurs through the binding of cancer cell receptors to the surface of nanocages that are conjugated with bioactive molecules, such as antibodies Verigene, an FDA-approved gold-based nanomaterial, and Aurimmune, currently in Phase II clinical trials, are both utilized for therapeutic purposes [154]
21 Numerous studies have documented the utilization of gold nanoparticles as carriers for drug delivery purposes Tumor necrosis factor-alpha (TNF-α), a cytokine known for its potent anticancer properties, has been hindered in its therapeutic applications due to its systemic toxicity [155] A nanoparticle delivery system was developed, comprising of gold nanoparticles coated with polyethylene glycol and loaded with TNF-α The purpose of this system was to optimize the destruction of tumors while minimizing the adverse effects of TNF-α on the entire body [156] The concurrent utilization of localized heating and nanoparticle-mediated administration of TNF-α demonstrated superior therapeutic effectiveness compared to either treatment in isolation The application of the nanoparticle via intravenous administration at the appropriate dosage and timing resulted in an augmentation of the delay in tumor growth induced by thermal means The inhibition of tumor blood flow, along with the presence of defects in tumor perfusion, indicates that the killing of tumor cells may be attributed to vascular damage Furthermore, the utilization of this nanoparticle conjugate has been observed in the eradication of the tumor encapsulated within an iceball, demonstrating minimal adverse effects on the overall physiological system [157] The ongoing Phase I clinical trials of the conjugate, referred to as “CYT- 6091” [158], aim to assess its safety, pharmacokinetics, and clinical efficacy
In recent times, a multitude of research endeavors have been undertaken with the aim of discovering novel and inventive approaches to enhance the efficacy and replicability of fluorescent contrast agents, specifically designed for the purpose of targeting specific cells [159] The utilization of gold nano-carriers has been shown to improve the loading capacity of platinum (II) and platinum (IV) drugs on the surface of these nano-carriers Furthermore, the release of these drugs is contingent upon the pH conditions of the surrounding environment The study implemented a novel system utilizing platinum drugs based on AuNPs Within this system, Aminoanthraquinone was integrated into the unit, serving as both fluoroprobes and DNA intercalators The unit exhibits unique, atypical, and noteworthy DNA binding characteristics [160] AuNPs are also employed in the application of ocular treatments, specifically targeting deeper regions of the eye, including the retina
A research study was conducted to examine the potential of AuNPs as a means of delivering drugs and biomacromolecules to the eye, as well as their efficacy as active therapeutic agents [161] The implementation of a cell membrane coating strategy has presented novel prospects for the development of versatile drug delivery platforms A proposed system utilizing AuNPs in conjunction with blood cell membranes has been suggested for potential application in the field of cancer therapy, specifically targeting melanoma The study assessed the potential enhancement of the anticancer efficacy of R/P-cGNS through the utilization of platelet membrane-coated Au nano-stars conjugated with curcumin
22 The red blood cell coating possesses self-antigens, which enables it to evade clearance by macrophages On the other hand, the platelet membrane coating provides targetability The findings indicate that the system has the potential to be efficacious in cancer treatment [162] Conversely, a study was undertaken to propose a novel approach involving the utilization of doxorubicin-loaded oligonucleotides bound to AuNPs as carriers in the context of prostate cancer chemotherapy The findings indicate that this approach is a feasible technique with considerable prospects [163] In addition, the carrier capability and biomarkers of three mercaptopropionic acid-capped AuNPs were examined in resistant leukemia K562/ADM cells The experimental findings exhibit promise as well [164]
Nanoshells have undergone experimental evaluation for the purpose of drug delivery A previous investigation involved the development of composites comprising hydrogels and gold nanoshells for the purpose of photothermally-modulated drug delivery [165] The absorption of irradiation at a wavelength of 1064 nm by the nanoshells resulted in the conversion of energy to heat This thermal effect caused the hydrogel to collapse, thereby greatly improving the release of the drug The authors were able to achieve modulated drug delivery of methylene blue, insulin, and lysozyme by subjecting the drug- loaded nanoshell-hydrogel composites to irradiation The rate at which the drugs were released was found to be dependent on the molecular weight of the therapeutic molecule, as indicated in reference [166] Hollow gold nanoshells have the capability to encapsulate enzymes, including horseradish peroxidase These enzymes have been observed to retain their activity when enclosed within the nanoshells, but this effect is limited to small substrate molecules rather than larger ones [167] As expected, the enzymatic activity of horseradish peroxidase was not observed when it was encapsulated within solid gold nanoparticles
The exploration of drug delivery utilizing gold nanoparticles, in conjunction with their inherent capacity for photothermal therapy, warrants further investigation in subsequent studies The suitability of different types of gold nanoparticles for drug delivery applications remains a topic of ongoing debate The study revealed that the cellular absorption of gold nanoparticles of varying sizes and shapes is significantly influenced by their physical dimensions [168] The calculation of absorption/scattering efficiency and determination of optical resonance wavelengths have been conducted for three frequently employed categories of gold nanoparticles, namely nanospheres, nanoshells, and nanorods [169] The limited range of the SPR peaks observed in nanospheres, approximately ranging from 520 to 550 nm, has restricted their potential for in vivo applications The surface plasmon resonance peaks of gold nanoshells are predominantly located in the near-infrared
23 region The complete eradication of nanoshells exhibits a linear correlation with the overall size, regardless of the ratio between the core and shell radii The contribution of scattering to the overall extinction can be significantly enhanced by increasing the size of the nanoshell or reducing the ratio of the core radius to the shell radius The optical properties of gold nanorods were discovered to be similar to those of nanoshells and nanospheres, but with a significantly smaller effective size Additionally, the absorption and scattering coefficients of gold nanorods were found to be approximately ten times higher than those of nanoshells and nanospheres Nanorods with a higher aspect ratio and a smaller effective radius exhibit enhanced photoabsorption properties, rendering them more suitable for therapeutic applications Conversely, nanorods with a larger effective radius are more advantageous for imaging purposes
Research has indicated that the application of femtosecond pulse excitation, specifically at a wavelength of 400 nm, to DNA-modified nanoparticles can result in the detachment of thiolated DNA strands from the surface of the nanoparticles This detachment is achieved by breaking the gold-sulfur bond [170] The potential of this property to be utilized in the future for the purpose of controlled drug release should be acknowledged The characterization of the stability of bioconjugates of gold nanoparticles in high ionic strength media has been conducted, taking into account the variables of nanoparticle size, polyethylene glycol (PEG) length, and monolayer composition [170] The study revealed that the stability of nanoparticles exhibited an upward trend as the length of PEG increased, the diameter of the nanoparticles decreased, and the mole fraction of PEG increased Significantly, gold nanoparticles that were modified with PEG chains of molecular weight (MW) 5000 exhibited comparable levels of internalization to those conjugates that possessed PEG chains of MW 900 According to this discovery, gold nanoparticles that have been modified with PEG chains of an optimal size (preferably with a molecular weight of at least 5000 to effectively evade the reticuloendothelial system) and possess a circulation half-life of several hours, could potentially be the most effective for the treatment of cancer
Brief overview of the two drug structures
The drugs 6MP and its prodrug azathioprineare currently utilized in the treatment of various diseases, such as childhood acute lymphoblastic leukaemia and inflammatory bowel disease These medications are both cytotoxic and immunosuppressive Both compounds are prodrugs that are not active until they are activated by hypoxanthine guanine phosphoribosyltransferase inside cells This activation process converts them into thioinosine monophosphate and then into thioguanine nucleotides, which are the active and cytotoxic metabolites [184] (Figure 2.6) There are two additional reactions that are in competition with this process Xanthine oxidase converts 6MP to 6-thioxanthine and then to 6-thiouric acid through oxidation Furthermore, thiopurine S-methyltransferase is responsible for transforming 6MP into inactive 6-methyl-MP It also metabolizes thioinosine monophosphate into 6-methylmercaptopurine nucleotides, which are highly effective at inhibiting the production of new purines through a biochemical process known as de novo purine synthesis [185]
6MP is a commonly utilized antineoplastic agent for the treatment of leukemia in children The Food and Drug Administration granted approval to this compound, which is derived from purine, in 1953 as a treatment for leukemia [53] It also has other uses as an immunosuppressant and in the treatment of inflammatory bowel diseases [186] The structure of 6MP consists of sulfur and nitrogen atoms that act as donor sites and can be converted into ribosides [57] The molecule’s antitumor properties are enhanced by the coordination of these sites with other ions Therefore, the scientific community is interested in 6MP and its complexes with various metal ions
Figure 2.6 Metabolism of 6-mercaptopurine [187] Note: 6MP, 6-mercaptopurine; IMP, inosine monophosphate; IDP, ioinosine diphosphate; ITP, ioinosine triphosphate; GMP, guanosine monophosphate; GDP, guanosine diphosphate; GTP, guanosine triphosphate;
XO, xanthine oxidase; HPRT, hypoxanthine phosphoribosyltransferase; TPMT, thiopurine methyltransferase; IMPD, inosine monophosphate dehydrogenase; GMPS, guanosine monophosphate synthetase; ITPA, inosine triphosphate pyrophosphatase
Several metal-based 6MP complexes, including Pt(II), Pd(II), and Au(I), have been reported [188] The compounds exhibit greater anticancer efficacy compared to the unbound 6-MP medication Furthermore, the antimicrobial efficacy of Ag(I) and certain Au(I) 6MP complexes has been examined [189] The literature has described the reaction of a divalent transition metal with a 6MP ligand using the formulas [M II (6-MP)2X2] or [M II (6-MP)n]X2 [190] In these formulas, the 6MP ligand is coordinated to the metal through S and N7 donor atoms
28 Inflammatory bowel disease (IBD), a chronic inflammatory disorder, is thought to be caused by genetically predisposed immune dysregulation IBD includes Crohn's disease and ulcerative colitis Since the immune system is so important in IBD, immune modulation is the main treatment [191] 6MP and its prodrug azathioprine are effective treatments for IBD, including steroid-dependent and refractory IBD and active Crohn's fistulous disease Mark Lửwenberg et al demonstrates that 6MP is more effective than placebo in achieving both clinical remission and endoscopic improvement, as well as histological remission, in patients with ulcerative colitis who have undergone corticosteroid treatment for remission induction Interestingly, a remarkable 87.5% of these patients achieved both clinical remission and endoscopic improvement Thus, it can deduce that mercaptopurine is a beneficial therapeutic choice for patients with ulcerative colitis who are able to tolerate it [192]
The chemical characteristics of 6MP are determined by important factors such as the partition coefficient (logP) and the solubility in water 6MP exhibit pK a values of 3.0 and 11.1 The pK a value of mercaptopurine at pH 7.4 is −0.12 Moreover, the aqueous solubility of mercaptopurine at pH 7.4 is 0.09 mg/ml The low aqueous solubility of thiopurines continues to pose a difficulty for the administration of these drugs orally Nevertheless, the degree of absorption is mainly influenced by the amount of its non-ionized form at the absorption site [193] This explains why 6MP is absorbed despite low gastrointestinal tract solubility More specifically, the dissolution rate and extent of drugs in the gastrointestinal tract control 6MP absorption Since stomach pH is low (~ pH 1–2), all 6MP dosages should dissolve quickly in gastric fluids The majority of 6MP species are protonated, which significantly increases their solubility (~ 1 to 100 mg/ml at pH 1–2) Increasing pH in the gastrointestinal tract shifts 6MP from protonated to unionized species in the small and large intestines, where pH is > 5.0 The pH-partition hypothesis states that protonated drugs cannot pass through the gastrointestinal epithelium's lipid bilayer, but unionized forms can [193]
The coprecipitation method was used to prepare iron oxide coated with chitosan containing 6MP, which has the potential to be utilized as a controlled-release formulation These nanoparticles could function as an alternative method of delivering drugs for cancer treatment, while also having the benefit of not harming nearby healthy cells and tissue [194] To prolong drug release and improve bioavailability, mucoadhesive polymer, chitosan, and polyvinylpyrrolidone were used to make oral thin films of 6MP [195] Smooth, translucent, flexible film formulations were all made Thin films have pH- dependent release profiles that are better than pure drugs in in vitro drug release The study
29 found that solvent cast technology can easily and effectively deliver drugs to achieve therapeutic compliance in 6MP oral thin film
The nanocarriers currently used for 6MP are primarily created through the chemical bonding of 6MP or 6MP derivatives with polymers such as chitosan, carboxymethyl chitosan (CMCS), and dendrimer [196,197] This process unavoidably involves the use of crosslinking agents Furthermore, specialists have employed metal vector, mesoporous silica, and magnetic substances like iron oxide to fabricate 6MP nanoparticles Researchers have additionally altered these nanoparticles by incorporating hyaluronic acid and folate in order to enhance the nanomedicine’s capacity to specifically target tumors and cells [59] Although nanotechnology has improved the solubility of 6MP, the methods used to prepare it are intricate Additionally, safety concerns arise from the presence of toxic crosslinkers, surfactants, or organic solvents The in vitro release profile demonstrated that nanomedicines loaded with 6MP initially experienced a rapid release, followed by a sustained release phase [59] The apoptosis assay revealed that 6MP nanomedicines enhanced the in vitro cytotoxicity in Jurkat cells The pharmacokinetics profiles demonstrated that 6MP nanomedicines exhibited enhanced oral bioavailability and increased absorption of 6MP in the duodenum, while also showing minimal accumulation of the toxic metabolites of 6MP The in vivo pharmacodynamics study demonstrated that the administration of 6MP nanomedicines resulted in a significant increase in the survival time of the mice with acute lymphoblastic leukemia
Pramipexole’s (PPX) specific affinity for the D3 receptor subtype may contribute to its effectiveness in treating both the motor and psychiatric symptoms of Parkinson’s disease Both laboratory studies conducted on cells and studies conducted on living animals indicate that PPX has several neuroprotective properties [60] These properties include acting as an agonist for dopamine autoreceptors, having antioxidant effects, blocking the mitochondrial permeability transition pore, and stimulating the release of trophic factors PPX has been shown in clinical studies to possess favorable pharmacokinetic characteristics It is proven to be efficacious as a standalone treatment for early-stage Parkinson’s disease and as a supplementary therapy alongside L-DOPA for advanced-stage Parkinson’s disease Furthermore, PPX has exhibited effectiveness in a clinical trial for the management of major depression It demonstrated the ability to delay the requirement for
L-DOPA treatment for a significant duration during the initial stages of the disease Therefore, it is now conceivable to establish a novel approach, known as the “L-DOPA- sparing” paradigm, for managing Parkinson’s disease This approach involves initially administering PPX to patients and only introducing L-DOPA when it becomes essential
30 PPX is a newly developed compound belonging to the aminobenzothiazole class, which acts as a strong stimulator at the D2 subtype of dopamine receptors [60] It exhibits minimal activity at receptor families other than D2, and among the D2 subfamily, it has the strongest binding affinity to D receptors Furthermore, unlike the ergot dopamine agonists typically employed for Parkinson’s disease treatment, pramipexole completely activates the dopamine receptors it attaches to, while the ergots only partially activate these receptors [25] The preclinical pharmacology of PPX indicated that it is likely to be effective in treating symptoms of Parkinson’s disease, with minimal risk of side effects resulting from interactions with dopamine receptors outside of the D2 subfamily
PPX is a pharmacological compound with a low molecular weight and a solubility of 3.9 mg/mL in water This molecule has the potential to be delivered through the skin due to its low molecular weight of 211.33 g/mol and a suitable logP value of 2.3 However, the highly polar structure of the drug may have an impact on its ability to permeate the skin [198] Emerging drug delivery systems, such as microspheres, liposomes, niosomes, nanogels, nanoemulsions, iontophoresis, and implants, have the ability to deliver drugs through the skin and address the limitations of current dosage forms while enhancing treatment effectiveness Prior research has developed traditional liposomes containing PPX determine the effectiveness of efficiently trapping PPX in the water-filled center of the liposomes [199] Several cutting-edge methods, such as microneedle technology and nanocrystals, have been documented as enhancing the transdermal administration of medications An evaluation of taking advantage of pramipexole extended-release in individuals diagnosed with Parkinson’s disease in Refs [200,201]
THEORETICAL BACKGROUND AND COMPUTATIONAL
Schrửdinger equation
The ultimate goal of most quantum chemical approaches is the approximate solution of the time-independent, nonrelativistic Schrửdinger equation
ĤΨ 𝑖 (𝑥⃗ 1 , 𝑥⃗ 2 , … , 𝑥⃗ 𝑁 ; 𝑅⃗⃗ 1 , 𝑅⃗⃗ 2 , … , 𝑅⃗⃗ 𝑀 ) = 𝐸 𝑖 Ψ 𝑖 (𝑥⃗ 1 , 𝑥⃗ 2 , … , 𝑥⃗ 𝑁 ; 𝑅⃗⃗ 1 , 𝑅⃗⃗ 2 , … , 𝑅⃗⃗ 𝑀 ) (3.1) where Ĥ is the Hamilton operator for a molecular system consisting of 𝑀 nuclei and 𝑁 electrons in the absence of magnetic or electric fields Operator Ĥ is a differential operator representing the total energy
(3.2) here, 𝐴 and 𝐵 run over the 𝑀 nuclei while 𝑖 and 𝑗 denote the 𝑁 electrons in the system The first two terms describe the kinetic energy of the electrons and nuclei, respectively
The Laplacian operator ∇ 2 is defined as a sum of differential operators in cartesian coordinates)
𝜕𝑧 2 (3.3) and 𝑀 𝐴 is the mass of nucleus 𝐴 in multiples of the mass of an electron (atomic units)
The remaining three terms define the potential part of the Hamiltonian and represent the attractive electrostatic interaction between the nuclei and the electrons and the repulsive potential due to the electron-electron and nucleus-nucleus interactions, respectively 𝑅 𝑝𝑞 |𝑟⃗ 𝑝 − 𝑟⃗ 𝑞 | is the distance between the particles 𝑝 and 𝑞; Ψ 𝑖 (𝑥⃗ 1 , 𝑥⃗ 2 , … , 𝑥⃗ 𝑁 ; 𝑅⃗⃗ 1 , 𝑅⃗⃗ 2 , … , 𝑅⃗⃗ 𝑀 ) stands for the wave function of the i’th state of the system, which depends on the 3𝑁 spatial coordinates 𝑟⃗ 𝑖 , and the 𝑁 spin coordinates 𝑠 𝑖 of the electrons, which are collective termed 𝑥⃗ 𝑖 and the 3𝑀 spatial coordinates of the nuclei 𝑅⃗⃗ 𝐼 The wave function Ψ 𝑖 contains all information that can possibly be known about the quantum system at hand Finally, 𝐸 𝑖 is the numberial value of the energy of the state described by Ψ 𝑖
Born−Oppenheimer approximation and Pauli’s exclusion principle
The simplification of the Schrửdinger equation can be achieved by exploiting the substantial disparities in mass between nuclei and electrons The proton, which is the lightest nucleus, has a mass around 1800 times greater than that of an electron In the case of a typical nucleus like carbon, the mass ratio surpasses 20000 Consequently, the nuclei exhibit significantly slower movement in comparison to the electrons The practical implication of this is that, to a reasonable degree of accuracy, we can adopt an extreme perspective and regard the electrons as being in motion inside the presence of stationary nuclei The Born-Oppenheimer approximation is a well-known concept in the field Certainly, in the scenario where the nuclei are immobilized and devoid of any motion, their kinetic energy is rendered null, while the potential energy arising from the repulsion between the nuclei is reduced to a fixed value Therefore, the Hamiltonian expressed in Eq (3.2) can be simplified to the electronic Hamiltonian, as commonly referred to
The wave function Ψ elec and the electronic energy Ĥ elec are obtained as the solution to the Schrửdinger equation with the Hamiltonian operator Ĥ elec The wave function Ψ elec is contingent upon the electron coordinates, but the nuclear coordinates are only included in a parametric manner and are not directly manifested in Ψ elec The aggregate energy, denoted as 𝐸 tot , is obtained by adding the energies 𝐸 elec and 𝐸 nuc , where 𝐸 nuc represents the constant nuclear repulsion term
Ĥ elec Ψ elec = 𝐸 elec Ψ elec (3.5) and
The exterior potential, referred to as 𝑣 ext in density functional theory, is the expected value of the 𝑉̂ ne operator in Eq (3.4) This potential arises from the attractive force exerted on the electrons by the nuclei Henceforth, our focus will be solely on the electronic problem described by Eqs (3.4) – (3.6), and we will omit the subscript “elec”
33 The wave function Ψ is not directly measurable The square of the wave function is the sole aspect that can be attributed to a physical interpretation
The given expression denotes the likelihood of electrons 1, 2, … , 𝑁 being present concurrently within volume elements 𝑑𝑥⃗ 1 𝑑𝑥⃗ 2 … 𝑑𝑥⃗ 𝑁 Given the indistinguishability of electrons, it follows that the probability un question remains invariant when the coordinates of any two electrons are interchanged
Hence, it can be observed that the two wave functions can exhibit a maximum discrepancy of a unimodular complex number It can be demonstrated that in natural phenomena, there exist two possibilities: either the two functions are identical, resulting in a symmetric wave function This property applies to particles known as bosons, which possess integer spin, including zero Alternatively, the interchange of the functions results in a sign change, leading to an antisymmetric wave function This characteristic applies to fermions; whose spin is half-integral Electrons are classified as fermions due to their intrinsic spin value of −1/2 Consequently, the wavefunction Ψ associated with electrons must exhibit antisymmetry when the spatial and spin coordinates of any two electrons are interchanged Ψ(𝑥⃗ 1 , 𝑥⃗ 2 , … , 𝑥⃗ 𝑖 , 𝑥⃗ 𝑗 , … , 𝑥⃗ 𝑁 ) = −Ψ(𝑥⃗ 1 , 𝑥⃗ 2 , … , 𝑥⃗ 𝑗 , 𝑥⃗ 𝑖 , … , 𝑥⃗ 𝑁 ) (3.9)
In the near future, we are poised to confront the profound ramifications of the antisymmetric principle, which serves as a quantum mechanical extension of Pauli’s exclusion principle, wherein the occupation of a single state by two electrons is prohibited
One logical implication arising from the probability interpretation of the wave function is that the integral of Eq (3.7) over the whole range of all variables is equal to one Stated otherwise, it is imperative that the probability of locating the 𝑁 electrons in any region of space is precisely equal to one
A wave function that meets Eq (3.10) is referred to as being normalized
Variational principle
In order to solve the Schrửdinger Eq (3.5) for an arbitrary molecule, the initial step involves establishing the Hamilton operator that is particular to the system under consideration In order to achieve this objective, it is imperative to ascertain the components of the Hamiltonian operator Ĥ that are unique to the particular system under consideration Nevertheless, it is currently unattainable to find a solution to the Schrửdinger equation that accurately describes atomic and molecular systems, and no known approach exists to do this A systematic approach exists for determining the wave function of the ground state, denoted as Ψ 0 , which corresponds to the state with the lowest energy, 𝐸 0 The variational principle occupies a major position in all quantum chemical applications The operator Ô, which is suitable for use with any wave functions Ψ trial , even those that may be complex, and which are normalized according to Eq (3.10), can be expressed as follows
The bracket notation for integrals, which is highly practical and frequently employed in the field of quantum chemistry, is initially introduced The asterisk symbol in Ψ trial ∗ denotes the complex conjugate of Ψ trial The current formulation of the variational principle asserts that the energy, which is calculated using Eq (3.11) as the expected value of the Hamilton operator Ĥ based on a given trial wavefunction Ψ trial , will serve as an upper limit on the actual energy of the ground state
The condition for equality to hold is that Ψ trial is identical to Ψ 0 A functional, referred to as a rule denoted by Eqs (3.11) or (3.12), assigns a numerical value, 𝐸 trial , to a function, Ψ trial This concept can be juxtaposed with the more commonly encountered notion of a function, which involves the mapping of a single numerical value to another numerical value In alternative terms, it can be stated that a functional is a mathematical entity that takes a function as its input In written discourse, the differentiation between a functional and a function is commonly achieved by the utilization of square brackets to enclose the argument Therefore, the function 𝑓(𝑥) is dependent on the variable 𝑥, but 𝐹[𝑓(𝑥)] is a functional that operates on the function 𝑓(𝑥) It is important to note that a function requires a numerical value as its input and produces a numerical value as its output
35 For example, 𝑓(𝑥) = 𝑥 2 + 1 Then, for 𝑥 = 2, the function delivers 𝑦 = 5 Conversely, a functional requires a function as its input, however it yields a numerical output
For example, if we define 𝐹[𝑓(𝑥)] = ∫ [𝑓(𝑥)] 0 1 2 𝑑𝑥 and use 𝑓(𝑥) as defined above as input, this functional delivers 𝐹[𝑓(𝑥)] = 28/15 If, instead we choose 𝑓(𝑥) = 2𝑥 2 + 1, the result is 𝐹[𝑓(𝑥)] = 47/15
The approach to determining the ground state energy and wave function should now be evident: it is necessary to minimize the functional𝐸[Ψ] by systematically exploring all admissible N-electron wave functions In this particular context, “acceptable” refers to the trial functions meeting specific criteria that guarantee their physical validity To illustrate, in order to meet the criteria for being considered a wave function, the function Ψ must exhibit continuity throughout its domain and possess the property of being integrable in a quadratic manner If the aforementioned conditions are not met, it would be unfeasible to normalize Eq (3.10) The function denoted as Ψ 0 corresponds to the state with the lowest energy, whereas the energy associated with this state is referred to as the genuine ground state energy, denoted as 𝐸 0 The recipe can be succinctly articulated as
𝐸 0 = min Ψ→𝑁𝐸[Ψ] = min Ψ→𝑁⟨Ψ|𝑇̂ ne + 𝑉̂ ne + 𝑉̂ ee |Ψ⟩ (3.13)
The notation Ψ → 𝑁 signifies that Ψ represents a permissible wave function for a system with 𝑁-electrons Although conducting a comprehensive search of all eligible functions is clearly unattainable, we can nevertheless employ the variational principle to subsets of the entire set of viable functions Typically, these subsets are selected in a manner that allows for the minimization process described in Eq (3.13) to be carried out inside an algebraic framework The outcome will yield the most accurate estimation of the precise wave function that can be derived from this specific subgroup It is crucial to acknowledge that when limiting the search to a subset, it becomes challenging to identify the precise wave function, unless the exact wave function happens to be contained in the subset, which is highly unlikely An illustrative instance is the Hartree-Fock approximation, which will be further upon in the subsequent discussion In this approximation, the subset is comprised of all antisymmetric products, namely Slater determinants, that are formed by 𝑁 spin orbitals
In summary, the information presented thus far can be summarized as follows: Once the values of 𝑁 and 𝑣 𝑒𝑥𝑡 are found, which are uniquely determined by 𝑍 𝐴 and 𝑅 𝐴 , we are
36 able to construct Ĥ By utilizing the prescription provided in Eq (3.13), it is theoretically possible to derive the wave function of the ground state This, in turn, facilitates the calculation of the ground state energy and all other characteristics of the system Visually, this can be represented as {𝑁, 𝑍 𝐴 , 𝑅 𝐴 } ⇒ Ĥ ⇒ Ψ 0 ⇒ 𝐸 0
Therefore, the values of𝑁 and 𝑣 𝑒𝑥𝑡 fully and exclusively establish the values of Ψ 0 and 𝐸 0 The ground state energy can be described as a functional dependent on the number of electrons, denoted as 𝑁, and the nuclear potential, represented as 𝑣 𝑒𝑥𝑡
Hartree−Fock approximation
The Hartree−Fock approximation is not only corner stone of almost all conventional, i.e., wave function based quantum chemical methods, it is also of great conceptual importance An understanding of the physical behind this approximation will thus be of great help in our later analysis of various aspects of density functional theory As discussed above, it is impossible to solve Eq (3.13) by searching through all acceptable 𝑁-electron wave functions We need to define a suitable subset, which offers a physically reasonable approximation to the exact wave function without being unmanageable in practice In the Hartree−Fock scheme the simplest, yet physically sound approximation to the complicated many-electron wave function is utilized It consists of approximating the 𝑁-electron wave function by an anti-symmetrized product of 𝑁 one-electron wave function 𝜓 𝑖 (𝑥⃗ 𝑖 ) This product is usually referred to as a Slater determinant, Φ SD
The Hartree-Fock approximation holds significant relevance both as a fundamental component in nearly all traditional quantum chemistry approaches that rely on wave functions, and as a conceptually significant framework Therefore, acquiring knowledge about the fundamental principles underlying this approximation will greatly assist us in our subsequent examination of many facets of density functional theory As previously mentioned, the resolution of Eq (3.13) cannot be achieved by exhaustively examining all admissible 𝑁-electron wave functions It is imperative to establish a viable subset that provides a physiologically plausible approximation of the precise wave function while being feasible to handle in practical applications The Hartree-Fock technique employs the most basic approximation to the intricate many-electron wave function, while still maintaining scientific validity The approach involves the approximation of the wave function of 𝑁 electrons by employing an antisymmetrized product of 𝑁 one-electron wave functions, denoted as 𝜓 𝑖 (𝑥⃗ 𝑖 ) The phrase commonly used to denote this particular product is the Slater determinant, denoted as Φ SD
Alternatively, a concise shorthand notation can be employed, wherein only the diagonal elements are provided Φ SD = 1
The spin orbitals, denoted as 𝜓 𝑖 (𝑥⃗ 𝑖 ), are single-electron functions that consist of a spatial orbital 𝜒 𝑖 (𝑟⃗) and one of the two spin state functions, 𝛼(𝑚 s ) or 𝛽(𝑚 s )
The spin functions possess a significant characteristic known as orthonormality, which may be expressed as ⟨𝛼|𝛼⟩ = ⟨𝛽|𝛽⟩ = 1 and ⟨𝛼|𝛽⟩ = ⟨𝛽|𝛼⟩ = 0 In order to facilitate computational efficiency, it is customary to select spin orbitals that are mutually orthogonal
The mathematical symbol 𝛿 𝑖𝑗 is commonly referred to as the Kronecker delta in academic literature The value of the expression is 1 when the indices 𝑖 and 𝑗 are equal, and it is 0 when they are unequal
After determining the desired form of the wave function, the subsequent task involves employing the variational principle to identify the optimal Slater determinant, denoted as Φ SD , that produces the minimum energy The sole source of flexibility within a Slater determinant is in the spin orbitals In the Hartree-Fock method, the spin orbitals 𝜒 𝑖 are subject to variation while maintaining their orthonormality, with the objective of minimizing the energy derived from the appropriate Slater determinant
The Hartree-Fock energy, denoted as 𝐸 HF , can be expressed using the variation theorem
𝐸 HF = ⟨Φ SD |Ĥ + 𝑉̂ nn |Φ SD ⟩ (3.20) Given that the internuclear repulsion operator, denoted as 𝑉̂ nn , does not depend on electronic coordinates and the wavefunction Φ SD is normalized, we may deduce that
⟨Φ SD |𝑉̂ nn |Φ SD ⟩ = 𝑉̂ nn ⟨Φ SD |Φ SD ⟩ = 𝑉̂ nn The operator Ĥ can be expressed as the summation of one-electron operators 𝑓̂ 𝑖 and two-electron operators 𝑔̂ 𝑖𝑗 The present study encompasses
Hence, the Hartree-Fock energy of a diatomic or polyatomic molecule comprising solely of closed shells is
𝑟 12 |𝜓 𝑗 (𝑥⃗ 1 )𝜓 𝑖 (𝑥⃗ 2 )⟩ (3.25) where the one-electron core Hamiltonian 𝐻̂ 𝑐𝑜𝑟𝑒 (1)
The sum of the kinetic energy operator for electron 1 and the potential energy operators for the attractions between electron 1 and the nuclei can be determined The operator 𝐻̂ 𝑐𝑜𝑟𝑒 (1) neglects the electron-electron interactions between electron 1 and the remaining electrons The summation of the 𝑛/2 occupied spatial orbitals 𝜓 𝑖 of the 𝑁-electron molecule over 𝑖 and 𝑗 The Coulomb integrals 𝐽 𝑖𝑗 and the exchange integrals 𝐾 𝑖𝑗 involve the integration across the spatial coordinates of electron 1 and electron 2
The derivation of the equation that finds the orthonormal 𝜓 𝑖 ’s that minimize the Hartree-Fock energy (𝐸 HF ) is complex and has been excluded from the discussion It has been observed that the closed-shell orthogonal Hartree-Fock molecular orbitals adhere to a certain condition
39 where 𝜀 𝑖 is the orbital energy and the Fock operator 𝐹̂ is
The Coulomb operator 𝐽̂ 𝑗 (1) and the exchange operator 𝐾̂ 𝑗 (1) for a single electron can be defined as follows
Let 𝑓 represent an arbitrary function, and let the integrals be definite integrals over the entire space The presence of the factor 2 in Eq (3.28) can be attributed to the existence of two electrons occupying each spatial orbital The Hamiltonian operator and wave function incorporate the spatial coordinates of all 𝑁-electrons The Fock operator, denoted as 𝐹̂, is classified as a one-electron operator The concept pertains to the coordinates of a single electron, and Eq (3.27) represents a differential equation for a solitary electron The operator 𝐹̂ exhibits a unique characteristic in that it relies on its own eigenfunctions, which are not initially known Therefore, it is necessary to employ an iterative approach to solve the Hartree-Fock equations, commencing with an initial estimation of the molecular orbitals
In order to derive the equation for the orbital energies 𝜀 𝑖 , we perform a multiplication of Eq (3.27) by the complex conjugate of 𝜓 𝑖 ∗ (1) and subsequently integrate over the entire space By utilizing the information that 𝜓 𝑖 is normalized and taking into consideration the given data, we can deduce that
The quantities 𝐻 𝑖𝑖 𝑐𝑜𝑟𝑒 , 𝐽 𝑖𝑗 and 𝐾 𝑖𝑗 are defined by Eqs (3.23), (3.24), and (3.25), respectively The summation of Eq (3.31) over the 𝑁/2 occupied orbitals yields
By solving the equation for the summation of the diagonal elements of the core Hamiltonian matrix, denoted as ∑ 𝐻 𝑖 𝑖𝑖 𝑐𝑜𝑟𝑒 , and subsequently substituting this result into Eq (3.22), we are able to derive the Hartree-Fock energy:
One significant advancement that enabled the computation of precise molecular SCF wave functions was the suggestion to expand the spatial orbitals 𝜓 𝑖 as linear combinations of a collection of one electron basis functions 𝜒 𝑠
To exactly represent the MOs 𝜓 𝑖 , the basis functions 𝜒 𝑠 should form a complete set This requires an infinite number of basis functions In practice, one must use a finite number
𝑏 of basis functions If 𝑏 is large enough and the functions 𝜒 𝑠 are well chosen, one can represent the MOs with negligible error
In order to accurately represent the MOs 𝜓 𝑖 , it is necessary for the basis functions
𝜒 𝑠 to constitute a comprehensive set The task at hand necessitates the utilization of an unbounded set of basis functions In practical applications, it is necessary to employ a limited number, denoted as 𝑏, of basis functions If the value of 𝑏 is sufficiently large and the functions 𝜒 𝑠 are appropriately selected, it is possible to represent the MOs with minimal error.
Density functional theory
Density functional theory (DFT) employs the electron density 𝜌(𝑟) as the fundamental quantity for describing an atom, molecule, or solid, in contrast to the wavefunction Ψ typically used in wavefunction-based quantum chemistry [202] The statement in question is derived from the well-known Hohenberg-Kohn theorems [203] The initial theorem asserts that the external potential, denoted as 𝑣(𝑟), which applies to a system (in the case of an isolated system, this refers to the potential originating from the nuclei), can be determined by the electron density, with the exception of an inconsequential, supplementary constant Consequently, the energy of the system, denoted as 𝐸, can be expressed as a functional of the density 𝜌(𝑟) This is analogous to the representation of 𝐸
41 as a functional of the wave function Ψ in wave function theory To be more precise, the expression for the ground state energy can be formulated as follows
𝐸[𝜌(𝑟)] = 𝑉 ne [𝜌(𝑟)] + 𝑇[𝜌(𝑟)] + 𝑉 ee [𝜌(𝑟)] = 𝑉 ne [𝜌(𝑟)] + 𝐹 HK [𝜌(𝑟)] (3.35) with 𝑇[𝜌(𝑟)] – the kinetic energy,
𝑉 ne [𝜌(𝑟)] – the nucleus-electron attraction energy,
𝑉 ee [𝜌(𝑟)] – the electron-electron repulsion
As can be seen, in the second part of Eq (3.35), 𝑇[𝜌(𝑟)] and 𝑉 ee [𝜌(𝑟)] have been grouple in the so-called Hohenberg–Kohn functional 𝐹 HK [𝜌(𝑟)]
The 𝑉 ne [𝜌(𝑟)] is exactly expressed as
The second theorem of Hohenberg-Kohn establishes the variational principle within the framework of density functional theory (DFT) Assuming a trial density function 𝜌′(𝑟) that satisfies 𝜌′(𝑟) ≥ 0 for all values of 𝑟 and ∫ 𝜌′(𝑟) 𝑑𝑟 = 𝑁, where 𝑁 represents the total number of electrons in the system, it can be inferred that the ground state energy 𝐸 0 of the system is lower than or equal to the expectation value 𝐸[𝜌′(𝑟)] The minimization of the energy (as denoted by Eq (3.35)) is performed by considering variations in the electron density, while ensuring that the density remains integrated to the total number of electrons
𝛿 𝛿𝜌(𝑟)[𝐸 − 𝜇 (∫ 𝜌(𝑟) 𝑑𝑟 − 𝑁)] = 0 (3.37) where 𝜇 represents the Lagrange multiplier associated with the aforementioned constraint Upon conducting the minimization process, the following results are obtained
The equation referred to as the Euler equation is occasionally recognized as the Discrete Fourier Transform (DFT) analogue of the Schrửdinger equation This suggests that for every point in space, the total of the local quantities 𝑣(𝑟) and 𝛿𝐹 HK
𝛿𝜌(𝑟) should remain constant and be equivalent to 𝜇 The Hohenberg-Kohn functional, denoted as 𝐹 HK , is presently unknown and encompasses a substantial magnitude Hence, even a minor deviation in its approximation will result in a significant effect
To address this issue, Kohn and Sham proposed the inclusion of orbitals within the minimization problem of Density Functional Theory (DFT) This approach involves the utilization of a noninteracting reference system, where the density precisely corresponds to the ground state density of the interacting system The use of a single Slater determinant as a wavefunction is a precise representation for a system of non-interacting electrons that are independent of each other It is assumed that this expression for density encompasses all potential 𝑁-electron densities, regardless of whether they interact or not The electron density of the non-interacting system can be expressed as
(3.39) where 𝜓 𝑖 (𝑟) are the spin-orbitals in the Slater determinant
For this non-interacting system, the kinetic energy, denoted 𝑇 S is excactly given as
The term “ kinetic energy density ” can be employed to describe a specific concept, although it is important to note that this definition is not universally agreed upon An alternative term for this mathematical expression is provided as
The local temperature 𝑇(𝑟) is then introduced as
The Boltzmann constant, denoted as 𝑘 𝐵 , is a fundamental constant in physics The aforementioned quantity was introduced as a metric for quantifying the proximity of an electron pair and was also suggested as an indicator of reactivity The time-dependent variant of this metric was employed to calculate the time-dependent entropy in collision
43 phenomena, leading to the development of a principle known as the maximum entropy principle
It can be reasonably postulated that the kinetic energy 𝑇 S serves as a suitable approximation to the total kinetic energy 𝑇 within the framework of the Hohenberg-Kohn energy functional It is also justifiable to estimate 𝑉 ee [𝜌(𝑟)] using the classical Coulomb self-repulsion 𝐽[𝜌(𝑟)], which is defined as
The aforementioned approximations, despite their relatively small magnitude compared to the other precisely determined factors, resulted in an error known as the exchange-correlation energy 𝐸 XC
The Kohn-Sham total energy functional is expressed as such
Once again, by minimizing the energy while considering the electron density, subject to the constraint that the density must always integrate to the total number of electrons, we obtain
The exchange-correlation potential, denoted as 𝑣 XC (𝑟), is being introduced
The effective Kohn-Sham potential is denoted as 𝑣 KS (𝑟) Upon comparing Eq (3.47) to Equation (3.38), it is evident that we are able to validate the Kohn-Sham representation of non-interacting systems (𝑉 ee = 0), wherein the electrons exhibit motion within an effective potential denoted as 𝑣 KS (𝑟)
The classic KS equations are obtained by minimizing the energy with respect to the occupied Kohn-Sham orbitals
The symbol 𝜀 𝑖 represents the orbital energies of the KS orbitals Numerous scholarly articles have been published that delve into the examination of orbital energies within finite systems (molecules) and extended systems (solids), exploring their respective quantities [204]
DFT calculations employ a range of approximate functionals, denoted as 𝐸 XC , to evaluate the exchange-correlation energy In order to assess the precision of an approximate exchange-correlation energy functional (𝐸 XC ), researchers employ it in DFT calculations and subsequently compare the computed molecular properties with their corresponding experimental values The primary limitation of the DFT method lies in the absence of a structured methodology for enhancing 𝐸 XC , thereby impeding the enhancement of computed molecular properties The Eq (3.45) for the exchange-correlation energy 𝐸 XC encompasses various components, including the kinetic correlation energy, the exchange energy, the Coulombic correlation energy, and a self-interaction correction (SIC) The SIC is a consequence of the classical charge-cloud electrostatic-repulsion model, which mistakenly allows the interaction between the charge contributions of a specific electron and the portion of the charge density (𝜌) in a differential volume element (𝑑𝑟) that originates from the electron’s spread-out region
Hohenberg and Kohn demonstrated that in the case of a significantly slow variation of the electron density 𝜌 with respect to position, the exchange-correlation energy 𝐸 XC [𝜌] can be reliably determined as
The integral is taken over the entire spatial domain, where 𝑑𝑟 represents the differential volume element 𝑑𝑥𝑑𝑦𝑑𝑧 The symbol 𝜀 XC (𝜌) denotes the exchange and correlation energy per electron in a uniform electron gas with an electron density𝜌
Jellium refers to a theoretical system that is characterized by being electrically neutral and possessing an infinite volume This system is composed of an unlimited number of electrons that interact with each other, while moving within a space that contains a continuous and uniform distribution of positive charge The jellium exhibits a non-zero constant value, denoted as 𝜌, for the electron density per unit volume The electrons within the jellium system form a homogeneous electron gas, exhibiting uniform characteristics throughout When the functional derivative of 𝐸 XC LDA is taken, it is found
Kohn and Sham proposed employing Eqs (3.19) and (3.48) as approximations for
𝐸 XC and 𝜐 XC , respectively, which is commonly referred to as the local density approximation (LDA) technique The expression for 𝜀 XC can be represented as the aggregate of its exchange and correlation components
The correlation component 𝜀 C (𝜌) has been computed and subsequently represented as a complex function 𝜀 C VWN of 𝜌 We obtain
Dispersion corrections
One significant limitation observed in the majority of the functionals that have been examined thus far is their inadequate ability to effectively account for intramolecular and intermolecular London dispersion interactions Such weak interactions play a crucial role in the context of macromolecules, particularly biomolecules Numerous approaches have been suggested to address this issue [206] One approach is to simply add on a correction term for dispersion after the usual KS DFT energy calculation has been executed This procedure is called the DFT-D method The simplest form of correction term is described as:
(3.70) where the sum goes over all pairs of atoms A and B, 𝐶 AB is a constant, 𝑅 AB is the distance between A and B, and 𝑓(𝑅 AB ) is a damping function that makes 𝐸 disp go to zero as 𝑅 AB →
0 In practice, more complicated forms of 𝐸 disp are used The most successful DFT-D method is the DFT-D3; the number 3 here indicates the third version This approach includes three empirically determined parameters in 𝐸 disp , computing the 𝐶 AB coefficients theoretically, and including a 1/𝑅 AB 8 term The values of the three parameters depend on which functional the dispersion correction is being used with The DFT-D energy is defined as follows:
Several functionals with high degree of parameterization, which do not explicitly account for dispersion, also perform quite well for non-bonded interactions One illustrative instance is the M06-2X functional Vydrov and Van Voorhis proposed the development of a two-parameter correlation functional, denoted as 𝐸 C VV10 , which can be incorporated into any pre-existing exchange-correlation (𝐸 XC ) functional that lacks substantial binding capabilities in van der Waals complexes This integration results in the creation of a functional that effectively accounts for dispersion effects [207] The performance of VV10 was evaluated using different standard hybrid functionals, revealing satisfactory results for the energies of noncovalent interactions with an error range of 5 to 10% Additionally, the VV10 model demonstrated accurate predictions for the intramolecular and intermolecular distances in the complexes of the S22 and S66 test sets [207] The performance exhibited by VV10 was comparable to that of DFT-D3 However, DFT-D3 was found to have a higher computational efficiency than VV10, although the latter exhibits a broader range of applicability
Relativistic effects
In the context of a nonrelativistic hydrogen-like atom, it can be observed that the root-mean-square speed of the 1𝑠 electron is given by the expression (𝑍 × 𝑐)/137, where 𝑍 represents the nuclear charge and 𝑐 denotes the speed of light Therefore, in the case of atoms with a large atomic number, the average velocity of electrons in the inner shell is a considerable portion of the speed of light Consequently, relativistic adjustments to inner- shell orbitals and orbital energies are significant for atoms with high-𝑍 values The valence electrons within an atom or molecule experience effective shielding from the nuclei, resulting in their average velocities being significantly lower than the speed of light, even in the case of heavy atoms Therefore, it was previously postulated that the inclusion of relativistic corrections in molecules containing high-𝑍 atoms was unnecessary It has been recognized that the relativistic effects on the properties of molecules containing heavy atoms can be significantly significant
The average radius of a hydrogen-like atom exhibits a direct relationship with the Bohr radius (𝑎 0 ), while 𝑎 0 demonstrates an inverse relationship with the mass of the electron Therefore, the phenomenon of relativistic mass increase due to velocity causes a contraction of the inner 𝑠 orbitals in a heavy atom In order to preserve their orthogonality with the inner s orbitals, the outer 𝑠 orbitals must undergo a reduction in size as well The phenomenon of relativistic mass increase also results in a contraction of the p orbitals, albeit to a lesser degree compared to the 𝑠 orbitals The effective screening of the nucleus in relativistic atoms is attributed to the contraction of the s and p orbitals, resulting in a greater degree of screening compared to nonrelativistic atoms Consequently, there is an observed expansion of the 𝑑 and 𝑓 orbitals The relativistic contractions of the average radius of the 6𝑠 orbital in certain atoms have been determined to be 4% for 55Cs, 7% for 70Yb, 12% for
75Re, 18% for 79Au, and 12% for 86Rn [208] Because of relativistic contraction, the atomic radius of Fr is less than that of Cs, which lies above Fr in the periodic table.The Dirac equation is the relativistic formulation of the Schrửdinger equation for a single electron Relativistic Hartree-Fock calculations can be performed by employing the Dirac equation to modify the Fock operator, resulting in a computational approach known as Dirac-Fock (or Dirac-Hartree-Fock) Similarly, it is possible to employ a relativistic version of the Kohn-Sham equations in order to perform calculations based on relativistic density- functional theory
All-electron Dirac–Fock relativistic calculations on molecules containing heavy atoms such as Au or U are very time-consuming A commonly used approach is to do an all electron atomic Dirac–Fock calculation on each type of atom in the molecule and use the result to derive a relativistic effective core potential (RECP) or pseudopotential for
51 that atom Since the smallest parts of the relativistic effects are neglected in deriving RECPs, RECPs are sometimes called quasi-relativistic ECPs One then does a molecular Hartree–Fock calculation in which only the valence electrons are treated explicitly The valence electrons are treated non-relativistically, and the effects of the core electrons are represented by adding the operator ∑ 𝑈 𝛼 ̂ 𝛼 to the Fock operator 𝐹̂, where 𝑈̂ 𝛼 is a relativistic ECP for atom 𝛼, and the sum goes over the atoms of the molecule Here, it is assumed that the inner-shell AOs are not significantly changed on going from isolated atoms to the molecule The results of the SCF calculation can be improved using CI or MP perturbation theory MCSCF and MCSCF-CI calculations with RECPs are also done RECPs can also be used in KS DFT calculations
The subsequent examples illustrate the impact of relativistic effects on molecular properties as determined through Hartree-Fock calculations employing relativistic effective core potentials (RECPs) The numerical values are presented in the specified sequence: The non-relativistic ECP calculated value, the relativistic ECP calculated value, and the experimental value are the three quantities under consideration Additionally, the values obtained from nonrelativistic KS DFT calculations and relativistic perturbation-theory KS DFT calculations using the B88P86 functional and a contracted Gaussian basis set are provided in parentheses, including the calculated nonrelativistic, calculated relativistic, and experimental values Equilibrium bond lengths: 2.80, 2.73, 2.48 Å in Ag2; 1.73, 1.71, 1.70 Å in SnH4; 1.76, 1.51, 1.52 Å (1.73, 1.56, 1.52 Å) in AuH; 2.83, 2.48, 2.47 Å (2.77, 2.58, 2.47 Å) in Au2; 2.81, 2.53, 2.50 Å in Hg2 2+; (2.10, 2.06, 2.06 Å) for the W–C length in W(CO)6 Bond angle: 98.6, 98.2, 98 in PbCl 2 Dipole moments: 1.02, 0.92, 0.83 D for HBr, 0.71, 0.52, 0.45 D for HI Harmonic vibrational wavenumber: 77, 163, 191 cm −1 (121,
165, 191 cm −1 for Au 2 Equilibrium dissociation energies: (52.3, 69.1, 77.4 kcal/mol) for AuH; (33.0, 47.1, 53.1 kcal/mol) for Au2 Relativistic effects are substantial for these heavy- atom molecules
Relativistic all-electron calculations on F2, Cl2, Br2, I2, and At2 using various correlation methods found that the relativistic corrections were approximately independent of the level of theory used, except for At2.For example, with a valence triple-zeta polarized basis set, the changes in 𝐷 𝑒 on going from a nonrelativistic to a relativistic calculation were
−8, −7, −7, −7, −7 kcal/mol for Br2using the HF, MP2, CISD, CCSD, CCSD(T) methods, respectively; for I2, these changes were −15, −13, −12.5, −13, −13 kcal/mol; for At2, they were −30, −27, −24, −25, −24 kcal/mol This effect is significant not only for the innermost electrons, but it also strongly affects electrons in 𝑠 orbitals (and lesser extent p orbitals) in outer shells The higher angular momentum 𝑑, 𝑓, and 𝑔 orbitals are farther from the nucleus and experience stronger screening of the nuclear attraction by 𝑠 and 𝑝 shells and hence are
52 less affected by relativistic contraction Therefore both 𝑑 and 𝑓 shells will undergo a relativistic expansion and destabilization These relativistic effects scale roughly with 𝑍 2 and become important for elements heavier than the lanthanides
Gold, with an atomic number of 79, is the final element in the periodic table that is stable, alongside other stable elements such as mercury, thallium, lead, and bismuth The gold atom’s electrons undergo a strong electrostatic attraction as a result of the existence of
79 protons within its nucleus The characteristic yellow color of bulk gold is ascribed to the pronounced relativistic effects it displays The energy levels of 𝑠 orbitals in gold experience a contraction as a result of relativistic effects, causing them to shift towards the 𝑑 orbitals This shift is attributed to the relatively lower influence of relativity on the d orbitals This phenomenon causes a shift in the absorption of light, specifically the transition from the 5𝑑 to 6𝑠 energy level, resulting in a move from the ultraviolet region to the lower frequency range within the blue visual spectrum Consequently, gold exhibits a higher propensity for absorbing blue light in comparison to other wavelengths within the visible spectrum As a result, when exposed to white light, gold manifests a yellow appearance to the human visual system In the absence of relativistic effects, gold would exhibit a white coloration In the field of Ag, a similar transition takes place However, due to the influence of relativistic effects, the distance between the 4𝑑 and 5𝑠 orbitals in Ag is significantly larger compared to the distance between the 5𝑑 and 6𝑠 orbitals in Au As a result, silver exhibits a white appearance The relativistic effect has resulted in an upward shift of the 5𝑑 orbital and a downward shift of the 6𝑠 orbital
Another important impact of a relativistic effect is the initial resistance of gold towards oxidation Due to the relativistic contraction of 6𝑠 orbital toward the nucleus and stronger electrostatic attraction of the 79 protons in the nucleus, the “atomic radius” of gold reduces considerably Only the strongly reactive substances can tug gold’s 6𝑠 1 electron out from where it’s place The importance of relativistic effects in gold has been a topic of theoretical and experimental research for a long time.
Computational details
In this research work, most quantum chemical calculations for both structures, energies and related properties are performed with the aid of the Gaussian 16 program package [76] Geometries of all systems studied are located with revTPSS [209] and PBE [210] functionals, in combination with a mixed basis set, i.e the effective core potential
(ECP) cc-pVDZ-PP [77] for gold and cc-pVTZ for other non-metals Such approaches have been shown to describe relatively well the molecular geometries, spectroscopic properties, and some thermodynamic parameters for gold-containing compounds [211,212].Its use
53 greatly facilitates a direct comparison with previous results In the cc-pVDZ-PP basis set, the inner electrons along with the nucleus are considered as an inert core, and those on 5s, 5p, 5d, and 6s orbitals of the Au atom are taken as valence electrons The interaction between valence electrons and inert core is included in the pseudopotential This allows us to reduce greatly the number of electrons to be treated, and thereby computing times, but still describe properly the interactions between gold atoms and biomolecules [49,213]
Initial structures of the gold cluster-organic complexes for geometry optimizations are generated by attaching the drug molecule via electron-rich centers, i.e the S, N, O atoms, to the most stable forms of gold clusters [74] Harmonic vibrational frequencies are subsequently calculated at the same level as the optimization procedure to confirm the character of optimized geometries as local minima on the potential energy surface, and estimate the zero-point energy (ZPE) corrections The Gibbs (free) energy of reaction is calculated by the following equation (Eq 3.72):
∆G 0 (298) = ∑(𝜀 0 + 𝐺 𝑐𝑜𝑟𝑟 ) 𝑓𝑖𝑛𝑎𝑙 − ∑(𝜀 0 + 𝐺 𝑐𝑜𝑟𝑟 ) 𝑖𝑛𝑖𝑡𝑖𝑎𝑙 (3.72) where (𝜀 0 + 𝐺 𝑐𝑜𝑟𝑟 ) is the sum of electronic and thermal free energies [214]
The binding energy E b of the complexes is computed as the absolute value of the total energy difference (Eq 3.73):
E b = E Au n ∙drug − (E Au n + E drug ) (3.73) where E X is the sum of electronic and zero-point energies of the X species Hence, a negative value of E b indicates a favorable adsorption The more negative the computed value of the binding energy, the stronger the affinity of drug binding to the gold cluster is This parameter can also be used to evaluate the relative stability of the complexes
As both the Aun clusters and all adsorbed species have a closed electron shell in their ground state, we consider only the singlet state The effect of the solvent, an aqueous solution considered in this study, is simulated using the continuum model, namely, the integral equation formalism-polarizable continuum model (IEF-PCM) [78] This model has been proved to properly describe both electrostatic and non-electrostatic interactions, and thus could provide us with a sufficient physical description of the solvent environment [215] To carry out the density of state (DOS) calculations, the GaussSum program [216] has been used
To obtain deeper insights into the binding mechanism, we further examine the energy levels of frontier orbitals (HOMO and LUMO) in the drug, gold clusters and the resulting complexes The change of HOMO-LUMO energy gap (ΔE g ) is then calculated as follows (Eq 4.3): ΔE g =|E g 2 − E g 1 |
E g 1 × 100% (3.74) where E g 1 and E g 2 are the energy gaps for the bare gold clusters and Aun∙ drug complexes, respectively The energies of frontier orbitals are among the most relevant characteristics to probe the electronic structure of metal clusters and their chemical reactivity as well The difference between these two levels, i.e HOMO–LUMO energy gap (E g ), can be used to qualitatively examine the kinetic stability, chemical stability, and electrical conductivity of the metal clusters [217]
The changes in E g can also help us to recognize the presence and attachment of the drug to the clusters [218] Indeed, the electric conductivity of a material before and after adsorption of a molecule can be described by the following formula (Eq 3.75) [219]: σ = AT 3/2 e −E g /2k B T (3.75) where 𝑘 𝐵 and 𝑇 are the Boltzman’s constant and thermodynamic temperature, respectively, and A is a constant
RESULTS AND DISCUSSION
An overview on the structural evolution of small gold clusters
The equilibrium structures of gold clusters will be examined and presented in this section The above structures are typically referred to as Aun-X, where n = 2−20 and X = I, II are isomers with increasing relative energy (eV) As a result, Aun-I is the size n isomer that is the most stable
Figure 4.1 The lowest-energy isomers for Aun, n = 3 – 6, clusters with point groups and electronic states
Benchmark calculations for the Au2 dimer have been performed using a series of DFT and MO methods The calculated Au−Au bond length of Au2 (2.51 Å) is close to the measured value (2.47 Å) [220] This result is in good agreement with the CCSD(T)/cc- pVTZ-PP method (2.49 Å) [221] Many DFT functionals such as the GGA (PBE, BPW91, BP86), hybrid GGA (PBE0, B3LYP, B3P86, B3PW91), meta-GGA (HCTH, M06-L), hybrid meta-GGA (TPSSh, M05, M06) and long-range hybrid (CAM-B3LYP, LC-wPBE,
B97X) tend to overestimate the bond length of Au2 A recent study [222] showed that the revTPSS functional has a good performance for calculating both the structural and energy properties of small gold clusters However, the revTPSS functional exhibits a small deviation on the vibrational frequency, being smaller by 10 cm −1 than that of experimentally predicted vibrational frequencies, 181 vs 191 cm −1 [220,223]
In the ground state, small gold clusters prefer planar structures (2D) up to n = 6 (Figure 4.1) The lowest-energy Au3 trimer (C 2v) is a distorted structure due to a Jahn-Teller effect Its electronic state is a 2 B2 state because of electron occupancy in the 𝑏 2 singly occupied molecular orbital (SOMO), which causes a degradation of 𝑒" orbital (D 3h) into 𝑏 2 and 𝑎 1 orbitals in the resulting C 2v structure (Figure 4.2) The most stable structure of the
Au4 cluster has a D 2h rhombic form (Figure 4.1), which is consistent with higher level calculations such as CCSD(T)/cc-pVTZ and CCSD(T)/cc-pVQZ [224] Its other Y-shaped isomer (not shown here) is less stable by 0.12 eV than the D 2h Au4-I structure at the CCSD(T)/cc-pVQZ
Figure 4.2 Frontier molecular orbitals of Au3 (C 2v)
Next, the energy minimum of the Au5 cluster is in the form of W-type (C 2v) which originates from adding an Au atom to the Au4 (D 2h) So far, for the Au6 (Figure 4.1), the equilateral triangle structure (D 3h) is assigned as the most stable structure In general, each small Aun isomer in the size range of n = 2−6 is formed by adding another Au atom to the lowest-lying structure Aun−1 Figure 4.3 displays the lowest-energy isomers for Aun with n
= 7 to 9 The most stable isomer C s Au7-I is again developed upon addition of an Au atom to the Au6-I isomer (Figure 4.1), followed by a D 5h pentagonal bipyramid Au7-II structure The energy of the latter is 0.1 eV higher than that of the former The Au7-III is about 0.18 eV less stable than Au7-I Only 0.01 eV separates the two structures Au8-I (T d) and Au8-II (D 2h), making them energetically degenerate The planar D 2h Au8-II structure was also reported as the lowest energy isomer when CCSD(T) computations with the correlation consistent basis sets are employed [225]
Figure 4.3 The lowest-energy isomers for Aun, n = 7 – 9, with relative energy (eV), symmetry point group and electronic state
Addition of an extra Au atom to the structure D 2h Au8-II results in the formation of the global minimum C 2v Au9-I The second stable isomer C 2v Au9-II, however, exhibits a reverse pattern The calculated energy of this isomer is slightly higher at 0.02 eV Previous DFT calculations [226,227] also reported both Au 8 -II and Au 9 -I as the best equilibrium geometries At last, the C 4v Au9-III structure is 0.16 eV higher than its Au9-I isomer (Figure 4.3) Previous studies discovered that strong relativistic effects control not only the structural characteristics and chemical bonding of gold clusters but also their unique behavior [227].They, thereby, exhibit a number of unusual physiognomies Although small pure Aun clusters naturally favor a planar shape, depending on their charge state, a transition from a 2D to a 3D shape could occur at n = 8−13 [228,229] Although both 2D and 3D
58 conformations were typically predicted to be energetically quasi-degenerate at the size of
Au11 for the neutral series, a consensus has emerged that such a conversion is likely to begin there [227,230] This suggests that a planar or quasi-planar structure still exists for the Au10 size
In fact, in the case of Au10 (Figure 4.4), the planar D 2h Au10-I is marginally favored, by 0.09 eV, over the 3D D 2d Au 10 -II [231] This result is consistent with some previous studies [226,231,232] According to single reference second-order perturbation theory results [233], however, the lowest-energy structure of Au10 has a 3D D 2d Au10-II conformation A careful comparison of the calculated vibrational spectra of Au10 isomers with the experimental spectrum obtained by the far-IR multiple photo-dissociation investigation, which represents the most satisfactory spectrometric analysis to date [231], indicates an agreement Recent theoretical findings using CCSD(T) computations [232] allow us to reach a conclusion that the vibrational spectrum of the planar Au10-I isomer is the closest to experiment [231,232] Overall, results on structures and energetics [232]point out that both planar and non-planar isomers of Au10 likely coexist at the beginning of a 2D−3D structural transition in pure neutral gold clusters.
Figure 4.4 The lowest-energy isomers for Au10 with relative energy (eV), symmetry point group and electronic state
59 Following such a trend, the 3D Au11-I is confirmed to be the global minimum for
Au11 (Figure 4.5) The second stable structure Au11-II, with only an energy of 0.1 eV higher than Au11-I; it is consistent with previous reports [226,227] Let us note that the most stable
Au10-I is the starting point for the 2D Au11-III
Figure 4.5 The lowest-energy isomers for Au11 clusters with relative energy (eV), symmetry point group and electronic state
Regarding Au12 cluster (Figure 4.6), previous literature has indicated the emergence of a variety of structural motifs as its lowest-lying equilibrium structure, depending on the computational methods employed [231] The 3D Au12-I which was typically considered as the global energy minimum in recent literature [231] as well as the 2D Au12-II which is believed to have the lowest energy in some other studies [231,234], can be seen in Figure 4.6 According in another study [235], the Au12-III is the most stable one Our most recent study showed that vibrational spectrum of the Au12-I isomer matches the experimental findings from the far-IR (FIR) spectrum best [212]
Figure 4.6 The lowest-energy isomers for Au12 with relative energy (eV), symmetry point group and electronic state
We now examine in some detail the experimental spectra [231] as the vibrational fingerprints of the lower-lying Au12 isomers This cluster was created by laser ablation, heated to about 100 K, and then its FIR spectra were recorded with messenger Kr atoms present (Figure 4.7) Our calculated results show that the experimental vibrational signals [236] were not carried by the 2D Au12-II but rather the 3D Au12-I which can effectively be referred to as the primary carrier of the observed spectra in this situation As a matter of fact, the strongest signal experimentally observed close to ~180 cm −1 matches well the strongest peak in the simulated spectrum of Au12-I, which is also centered at 180 cm −1 (Figure 4.7) Additionally, this isomer exhibits an empirically detected shoulder peak at
~187 cm −1 , as well as a signal of a lower strength at ~140 cm −1
Figure 4.7 Theoretical and experimental IR spectra of Au12 isomers (revTPSS/aug-cc- pVDZ-PP) The experimental IR spectra are taken from Ref [231]
Figure 4.8 illustrates a few stable isomers of the 13-gold atom cluster [237] The most stable structure in this case was, and still is, the subject of considerable debate [231] The 3D structures are demonstrably more stable for Au13 than the 2D ones The two lowest- lying structures are all 3D and degenerate in energy (0.02 eV) [230] However, previous DFT studies suggested the flake-like nonplanar C 2v Au13-I as the most stable isomer [230,238]
Figure 4.8 The lowest-energy isomers for Au13 with relative energy (eV), symmetry point group and electronic state
Both Au14-I and Au14-II isomers are now considered as the most stable isomers [235,239] shown in Figure 4.9 For the Au15 size (Figure 4.9), the non-planar C s shape Au 15 -
I is obtained in a similar way by adding an Au atom to one side of Au 14 -II About 0.33 eV separates Au 15 -I from the second most stable C s Au 15 -II Previous studies [227,240] also indicated that the Au14-II and Au15-I seen here represent the global minima for Au14 and
Au15, respectively The lowest-lying Au16-I (Figure 4.9) has a C 2v symmetry, which is in agreement with previous analyses [241] According to previous reports [74,242], the T d
Au16-III is expected to have an energy of ~0.5 eV higher than the C 2v Au16-II [243]
Figure 4.9 The lowest-energy isomers for Aun, n = 14−16 with relative energy (eV), symmetry point group and electronic state
Binding mechanism of MP, PPX drugs toward Au n clusters
This section evaluates the interaction between small gold clusters Aun (n = 6, 8, 20) and two medication structures, namely 6-Mercaptopurine (6MP) and Pramipexole (PPX) The selection of these gold cluster structures was based on their demonstrated great temperature stability in previous studies [49,51,74]
Interaction of 6MP with small Au n clusters
As described in the previous sections, numerous experimental and theoretical studies have been devoted to small gold clusters [74] Energetic data point out the higher thermodynamic stability of the Aun systems with n = 6, 8 and 20 In their ground state, both
Au6 and Au8 clusters prefer planar structures, i.e the regular triangle and square planar shapes, respectively, while the tetrahedron with a T d symmetry (Figure 4.18) is univocally assigned as the most stable form of Au20 The Au20 pyramid is also well-known as an outstanding indicator in cluster science for its exceptional stability and peculiar 20-electron superatom shell structure [61,252]
Equilibrium structure of Au20 NBO charge distribution in Au20
Figure 4.18 Geometry and NBO charge distribution in the tetrahedral Au20 cluster Au color range: green, more positive than 0.06 au; red, more negative than −0.06 au
Regarding the molecular structure of a 6-mercaptopurine (6MP) drug, out of several stable configurations [267,268], two planar tautomers 6MP-7 and 6MP-9 presented in Figure 4.19 tend to dominate its ground state population with a large quantity in both the gaseous phase and aqueous environments, as reported in recent literature [269] In a vacuum, 6MP-7 lies ~3 kcal/mol above 6MP-9, but this energy difference is significantly reduced to ~1 kcal/mol in an aqueous solution (PBE/cc-pVTZ value) Henceforth, both
6MP-7 and 6MP-9 tautomers are considered in the following calculations and discussion
Figure 4.19 Equilibrium structures of two 6MP lowest-energy conformations Values in brackets are their relative energies (kcal/mol) in gas phase (PBE/cc-pVTZ)
As shown in Figure 4.19, the 6MP molecule exhibits several positions available for binding to the Au20 cluster, i.e., the thione head and the nitrogen atoms unbound to hydrogen During the interaction, the unoccupied anti-bonding orbitals of 6MP can accept electron density from the Au20 HOMO The drug is also able to donate electrons localized on its lone pairs (HOMO) back to the metal LUMO Moreover, the cluster can play the role of a proton acceptor and thereby form nonconventional AuãããH–N hydrogen bonds in which a net charge is transferred from the gold lone pair to the σ * (NH) orbitals [270] Such an interaction is expected to be an additional factor determining the stability of the resulting products NBO charges for the Au20 cluster (Figure 4.18) indicated that the corner Au atoms are positively charged, and thus, they are more suitable for a nucleophile attack Previous NBO charge computations [213] for Au6, Au8 clusters also confirmed that the corner Au atoms are positively charged
Optimized geometries and relative energies of the Aun∙6MP complexes with n = 6 and 8 are located and presented in Figure 4.20 As for a convention, these structures are denoted as Au n ∙6MP_X in which X = 1, 2,… indicating isomers with increasing relative energy (kcal/mol) The most preferred binding site of 6MP is found to be the sulfur (S) atom, giving rise to the most stable form Au 6 ∙6MP_1 with a binding energy of −34 kcal/mol
(Figure 4.20) This can be understood on the basis of the hard – soft acid – base (HSAB) theory [271] The softer head (S atom) of mercaptopurine is more willing to establish strong bonds with a soft element such as gold than a harder head (N atom) Moreover, consistent with the analysis of the NBO charges discussed above, coordination involving the corner
Au atoms with positive charges is more energetically favorable for the drug adsorption The next low-lying isomer, i.e Au 6 ∙6MP_2 in Figure 4.20, which is also formed by anchoring
76 the Au6 ring on the thiocarbonyl group, is around 7 kcal/mol above Au 6 ∙6MP_1 The former is thus more stable than the latter due to the presence of nonconventional N–H⋯Au hydrogen bond The remaining structure Au 6 ∙6MP_3 constructed by directly binding a nitrogen atom of the imidazole ring to Au6, is computed to be 15 kcal/mol higher in energy
Au 6 ∙6MP_1 (0.00) Au 6 ∙6MP_2 (7.3) Au 6 ∙6MP_3 (15.4)
Au 8 ∙6MP_1 (0.00) Au 8 ∙6MP_2 (7.8) Au 8 ∙6MP_3 (8.6)
Figure 4.20 Lower-lying structures of the Au6∙6MP and Au8∙6MP complexes in the gas phase Values given in parentheses are their relative energies in kcal/mol from PBE computations
Similarly, the most stable conformation of Au8∙MP complex, i.e Au 8 ∙6MP_1 in Figure 4.20, is formed by anchoring the sulfur atom on the Au8 ring with a binding energy of −38 kcal/mol The next isomer Au 8 ∙6MP_2, which is also constructed by binding the sulfur atom to Au8, is about 8 kcal/mol higher in energy than ground state As in
Au 6 ∙6MP_2, Au 8 ∙6MP_2 is less stabilized because a nonconventional N–H⋯Au hydrogen bond is not present Another isomer Au 8 ∙6MP_3 with an Au8−N bond is computed to be 9 kcal/mol higher in energy than the ground state The Au−S bond lengths in Au 6 ∙6MP_1 and Au 8 ∙6MP_1 are around 2.37 and 2.35 Å, respectively, which are rather shorter than the sum of covalent radii 2.46 Å of Au (1.44 Å) and S (1.02 Å) [272] The distances of 2.18 and 2.14 Å for the anchoring bonds Au−N (Au 6 ∙6MP_3 and Au 8 ∙6MP_3), respectively, are comparable to the sum of the covalent radii of nitrogen (0.75 Å) and gold (1.44 Å)
Au 20 ∙6MP_1 (0.0) Au 20 ∙6MP_2 (3.2) Au 20 ∙6MP_3 (3.3)
Au 20 ∙6MP_4 (4.7) Au 20 ∙6MP_5 (5.2) Au 20 ∙6MP_6 (12.0)
Figure 4.21 Lower-lying structures of the Au20∙6MP complex in the gas phase Values given in parentheses are their relative energies in kcal/mol from PBE computations
The six stable configurations of the complex formed following binding of 6MP to
Au20 are presented in Figure 4.21 They were denoted as Au 20 ∙6MP_X with X = 1, 2, 3… corresponding to an increasing ordering of relative energy (kcal/mol) In general, 6MP prefers to anchor on the vertex of the pyramid, forming a single coordination between the drug and gold cluster (Figure 4.21) In particular, conformations containing an Au−S bond and a nonconventional hydrogen AuãããH−N interaction obviously dominate the lowest- lying population of the resulting Au20∙6MP complexes Such structural motifs, i.e., the
Au 20 ∙6MP_1, Au 20 ∙6MP_2, and Au 20 ∙6MP_3 isomers in Figure 4.22, strongly compete with each other to be the global minimum structure In the gas phase, Au 20 ∙6MP_1 is considered the most stable form, lying only about 3 kcal/mol below Au 20 ∙6MP_2 and
Au 20 ∙6MP_3 Hence, within the expected error margin of the DFT computations, ±3
78 kcal/mol on relative energies, they can coexist in subtle experimental conditions, and the adsorbed molecule is likely to rotate around in axing on the C−S bond
The next lower-energy isomers Au 20 ∙6MP_4 and Au 20 ∙6MP_5 are formed by anchoring the drug on Au20 via the S atom of the pyrimidine ring and the N7 atom of the imidazole moiety Previously, it was suggested that such interactions are the preferred adsorption modes of 6MP on the gold surface [273] However, these complexes were computed at the PBE/cc-pVTZ/cc-pVDZ-PP level to be ~5.0 kcal/mol less stable than
Au 20 ∙6MP_1 since an N–H⋯Au hydrogen bond was not present, as shown in Figure 4.21
The remaining structure Au 20 ∙MP_6, which is constructed by directly binding Au20 to a nitrogen atom of the imidazole ring, was computed at 12 kcal/mol less stable These forms may thus only exist in very small quantities because of their high relative energies Typically, the S atom is the preferred binding site for 6MP, a finding that can be explained by the HSAB theory [271] As a result, the S head of 6MP, which possesses a softer nature, exhibits a greater propensity for interacting with malleable elements such as gold compared to the N head, which is comparatively harder
The surface-enhanced Raman scattering phenomenon
Surface-enhanced Raman scattering (SERS) is a phenomena that was first reported in 1973 for pyridine adsorption on a rough surface silver electrode [282] and was successfully characterized in 1977 [283] When SERS was first developed, it was used by a small group of researchers with knowledge in both electrochemistry and Raman spectroscopy, the latter of which at the time necessary in-depth information of optics and lasers The last 50 years have seen the rapid development of SERS, and both advances in
91 nanofabrication and Raman equipment were significant Even now, scientists from a wide range of fields, particularly chemistry, physics, and the life and material sciences, are deepening our understanding of SERS and are just beginning to understand fully its huge potential in both uni- and multi-disciplinary techniques SERS, in contrast to conventional Raman spectroscopy, also needs the occurrence of metallic nanostructures as a fundamental element Accordingly, in addition to considering how light interacts with molecules and other matter, we also need to understand about how light interacts with metal nanostructures in order to fully understand SERS [284-286]
Raman spectroscopy has one significant disadvantage due to the tiny cross-section of Raman scattering, which frequently results in low spectrum resolution The analyte therefore has to be present at a high concentration The SERS results demonstrate that a high local field resulting from the plasmon excitation in conjunction with direct chemical interactions between the molecule and the metal surface can increase the spectral signal by a ratio up to 10 10 − 10 15 The above SERS characteristics have been explained by a variety of different SERS mechanisms But no single mechanism can account for all the observed behaviors Two generally acknowledged processes that have recently contributed to the SERS effect are electromagnetic enhancement (EM) and chemical enhancement (CE)
As illustrated in Figure 4.29, EM mechanism involves the creation of a surface plasmon on the substrate surface, which transfers energy through an electric field to the target molecules allowing otherwise inaccessible vibrational structure to be determined Because of the fact that the local field enhancement carried on by plasmon excitation is commonly very considerable in comparison to the enhancement factor of those other mechanisms, the EM is typically regarded as the primary component to the observed SERS signal Strong fields produce the electrodynamic enhancement mechanism, and it is usually claimed that the SERS intensities are enhanced by a factor equal to the 4-fold of the electric field enhancement [287] The EM enhancement factor can range from 10 10 to 10 11 depending on the surface of the material, such as gold, silver, and copper nanoparticles The EM does not include chemical interactions and charge transfer process between both molecule and metallic surface.
Figure 4.29 Enhancement mechanisms of surface-enhanced Raman scattering
CE mechanism is also referred as charge transfer and resonance effect A molecule’s electronic states are changed during chemisorption when it is adsorbed on a metal surface The novel electronic states might function in Raman scattering as resonance intermediate states Due to the charge transfer between the adsorbed molecule and the metallic nanoparticles, which is in resonance with the wavelength of transmitted light, a CE mechanism can reach an enhancement factor of up to 10 3 Evaluating a CE process that had occurred during a SERS experiment continues to remain challenging Following interactions with electrons in the conduction band, adsorbate molecular orbitals transmitted into resonances While resonances at levels with energies close to the Fermi energy are only partially filled, those at levels with energies considerably lower are fully filled There are two possibilities that new excitations can be created: by transferring metal electrons to the half-filled adsorbate affinity level (metal → molecule charge transfer) or by moving electrons from full adsorbate orbitals to unfilled metal orbitals above the Fermi level (molecule → metal charge transfer) There are various published documents that discuss great detail about these mechanisms [287,288]
Overall, for an interpretation of the SERS phenomenon, two operational mechanisms, i.e., the electromagnetic and the chemical enhancements, are frequently taken into consideration [289,290] The former mechanism is controlled by the molecular symmetry and orientation with respect to the metal surface [291] Certain Raman signals of molecules near the metallic surface become remarkably enhanced as their intensity is proportional to the squared local electromagnetic field intensity On the contrary, the enhancement does not occur for vibrations parallel to the metal surface [292] Moreover, the Raman-scattered light results in an extra enhancement when the Raman mode overlaps with a plasmonic resonance [293] The latter mechanism, in contrast, mostly refers to the
93 chemical interaction and charge transfer between the nanoparticles and adsorbed molecules [294]
Recently, quantum chemical computations have been widely employed for probing the SERS behaviors including the Raman activities and tensor properties that could provide us with valuable information about the interacting centers and the binding mechanism between adsorbed molecules and the metal surface [295] For example, the Raman enhancements of pyridine on an Ag electrode were measured and then analyzed with the aid of DFT calculations using the tetrahedral Ag20 cluster as a model representing the silver nanoparticles [283] More recently, similar approaches were also applied to probe the SERS phenomenon of the chlorpyrifos, which is a pesticide using the Ag20 cluster as a model for the silver surface [296] Likewise, the tetrahedral gold Au20 cluster was also used as a model to validate the SERS spectrum of pramipexole molecules adsorbed on the gold surfaces [297] Previous reports are also available on the Raman characteristics of 6MP as well as its SERS phenomenon on gold surface [292] The molecule is well suited for SERS detection, owing to its high affinity for Ag/Au substrates More importantly, previous studies have revealed for 6MP as well as for other relevant biochemical species that several proposed hypotheses conflict with each other, and numerous interpretative approaches are needed to address the observations
Normal Raman signatures of 6MP simulated in an aqueous solution are presented in Figure 4.30 As reported experimentally [268], several important signals of the free molecule appeared in the region above 3100 and below 1600 cm −1 In particular, the N−H stretching mode of the imidazole ring is predicted to vibrate at 3532 cm −1 , which a rather strong peak at 3541 cm −1 in the measured spectrum could be assigned to [268] However, the corresponding mode of the pyrimidine ring, which is located around 3482 cm −1 , is not observed in experimental data The C−H stretching mode of the imidazole ring is computed to occur at 3185 cm −1 , while that of the pyrimidine emerges at around 3124 cm −1 , which appears comparable to the measured result of 3104 cm −1 [268] Nonetheless, it seems rather difficult to unambiguously assign the intense peaks present in the energy region of 1200–
1600 cm −1 as they typically resulted from a combination of several vibrations, such as C−X stretching and X−H (X = S, N, C) bending modes For example, strong signals located around 1360 and 1500 cm −1 likely result from a coupling of in-plane ring stretching modes with X−H and C−H in-plane bending vibrations Experimentally, these modes were observed at 1376 and 1540 cm −1 [268] Also in line with experimental observations, some weak bands in the lower energy region were likely to arise from a coupling of ring breathing with the N−H and C−H out-of-plane bending modes
Figure 4.30 Computed Raman signatures of 6MP (above) and its SERS spectra absorbed on the Au20 cluster (below) Simulations are performed in both neutral (left) and acidic
(right) conditions Typical signals are marked by the symbol “*”
The simulated Raman signatures for the 6MP thiol formed in acidic solution also agree well with experimental data acquired in HCl solution [273] Several strong signals in the fingerprint region peaked at 578, 662, 1017, 1304, 1364 and 1450 cm −1 , that are comparable to corresponding measured values at 588, 675, 1023, 1330, 1377 and 1449 cm −1 In particular, the appearance of the band at 2570 cm −1 is due to the thiol (S−H) group [298] The tetrahedron Au20 on the contrary exhibit obvious Raman signals in a narrow frequency range of below 180 cm −1 , that are much lower in energy than those of the adsorbed molecules
The normal Raman and SERS spectra of 6MP adsorbed on the Au20 cluster surface are compared in Figure 4.31; those simulations are performed in both neutral and acidic conditions For the neutral environment, the 6MP species binding to Au metals through the
S head contains a major contribution to the SERS phenomenon From the simulated spectra, we saw an extraordinary enhancement of vibrations in the energy region of 1250–1500 cm −1 In particular, the strongest enhanced peak at ~1280 cm −1 is mostly produced from the N−H bending mode coupled with the C−H deformation and ring breathing In the experimental SERS spectrum of 6MP on the gold surface recorded in a KCl solution [273], a very strong band at 1257 cm −1 is also detected Another noteworthy aspect is the
95 appearance of a prominent band around 3200 cm −1 related to the N−H stretching mode, which is negligible and emerged at higher wavenumbers (3500 cm −1 ) in the normal Raman spectrum of free 6MP
Fiugre 4.31 Comparison of 6MP SERS spectra adsorbed on small Aun clusters with n 6, 8, 20 Simulations are performed in an aqueous solution Typical signals are marked by the symbol “*”
In our present calculations, the most enhanced peak is located at 1278 cm −1 and the AuH−S coupling turned out to be a predominant factor leading to the SERS enhancement, rather than an aromatic ring–gold surface π overlap As a result of this nonconventional hydrogen bond, a charge redistribution emerged, giving rise to a SERS chemical enhancement of the thiol form A further noteworthy feature is found in the high energy
96 region of the spectrum, where the N/C−H stretching vibrations were located The SERS spectrum, presented in Figure 4.31, exhibited a complete absence of signals in the 3000–
4000 cm −1 range, which totally agreed with previous experimental observation [292]
A comparison of SERS spectra adsorbed on some small gold clusters is presented in Figure 4.31 At first glance, we notice that the spectral positions are almost comparable to each other, while the signal intensity is greatly modified with respect to the cluster size Small Au6 and Au8 systems resulted in higher SERS signals than the larger Au20 counterpart In particular, the most enhanced SERS signals of 6MP adsorbed on Au8 were primarily related to its lowest HOMO–LUMO energy gap as compared to that of Au6 and
Au20 [74].To simulate the surface of gold nanoparticles, the use of Au20 cluster is expected to provide more reliable results than the smaller sizes Au6 and Au8 as it had a larger number of gold atoms and a more sphere-like structure Typically, an icosahedral Au nanoparticle with a diameter of 2–10 nm contains several hundreds to thousands of gold atoms [299] Overall, in considering their characteristics, these small gold clusters behaved quite well as the simplest models for the gold nanoparticles The smaller sizes Au6 and Au8 allowed us to investigate much larger bio-molecular targets having well-defined functional groups
The drug release in target cells
4.4.1 The effect of hydrogen ions on the stability of the Au n ∙drug interactions
We now examine the ability to detach the drug from the gold cluster in target cells, which is considered as the decisive step in a drug delivery process [49,297] In a human body, the drug can be segregated from the carrier by either external stimuli or internal stimuli operated within a biologically controlled manner such as the pH and glutathione [300] Because of an exhaustive lactic production, tumor cells are often more acidic than the normal ones Indeed, the pH of cancer cells is typically below 6 as compared to values above 7 in blood [301] In an acidic environment, protons can attack any rich-electron site of the drug molecule, but the interaction with the binding atom may affect the drug release more significantly Hence, we inspect the effects of protons on the stability of Au20∙6MP complexes by protonation of the thione group, and then determine the geometrical forms of the resulting Au20∙6MPH + products
In an acidic environment, the drug binding to gold metals becomes much more breakable The interaction is now characterized by a weaker hydrogen bond AuH−X (X
= S, N), as demonstrated in Figure 4.33, instead of a covalent Au−S bond as in Au20∙6MP Correspondingly, the binding energy of 6MPH + ions on the Au20 surface is substantially reduced to 11 kcal/mol, which is much smaller than the corresponding value of 22 kcal/mol in the neutral solution This obviously indicates that under acidic conditions, the 6MP binding to a gold surface is getting weaker, resulting in a faster release
Figure 4.33 Lower-lying structures of the Au20∙6MP complexes in an acidic environment Values in parentheses are binding energies (kcal/mol, PBE/cc-pVTZ/pVDZ-PP + ZPE)
Similarly, with the presence of protons, interactions between the PPX drug and gold metals becomes more easily breakable as it is now characterized by weaker H-bonds as illustrated in Figure 4.34 rather than the covalent bond as in Aun∙PPX The binding energies of PPX on gold clusters are substantially reduced to −9 kcal/mol, as compared to the value from −23 to −28 kcal/mol in neutral condition Therefore, it is expected that in an acidic environment the PPX drug molecule binding to the carrier is getting weaker, thereby able to be released faster
Figure 4.34 Optimized structures of Aun∙PPXH + complexes Values in parentheses are binding energies (kcal/mol)
Table 4.6 Binding energy (Eb) and Gibbs energy (ΔG) of Aun binding to drugs and cysteine in different environments The results are obtained at the theoretical level PBE/cc- pVTZ/cc-pVDZ-PP
Species Eb (kcal/mol) G (kcal/mol)
Au6 Au8 Au20 Au6 Au8 Au20
4.4.2 Interactions with thiol-containing residues in the protein matrices
Another force that may result in a drug release is an internal inducement related to amino acids in proteins Such residues containing sulfur like cysteine and methionine are predicted to be the energetically favorable binding sites for noble metals [302,303] The dissociation constants of cysteine are pK1 = 1.71 and pK2 = 8.33 [304] indicating that in biological systems or aqueous solution the molecules mostly exist as the deprotonated forms, which are shown in Figure 4.35 To examine more thoroughly the drug release from the gold complexes, we further consider the following ligand-exchange process:
Aun∙Drug(aq) + CYSa(aq) → Aun∙CYSa (aq) + Drug(aq)
Au 6 -PPXH + (−9.1) Au 8 -PPXH + (−9.0) Au 20 -PPXH + (−8.9)
Au 20 ∙CYS (−16.0) Au 20 ∙CYSa (−35.0) Figure 4.35 Global minima located for the deprotonated cysteine and its resulting complexes with Au20 Two deprotonated forms of cysteine are quasi-degenerate with a tiny energy gap of 2.0 kcal/mol competing for the ground state Values in parentheses are binding energies (kcal/mol, PBE/cc-pVTZ/cc-pVDZ-PP + ZPE)
Table 4.7 Ligand exchange energy (ET, kcal/mol) and Gibbs free energy (ΔG, kcal/mol) of Aun∙drug complexes with CYSa
The most stable forms of Au20 with cysteine (CYS) and its deprotonated form, denoted as CYSa, are presented in Figure 4.35 As recently reported [297], these species tend to adsorb on the gold surface via the S-atom of the thiol group In an aqueous solution, the binding energies to Aun were −39, −43, and −35 kcal/mol for n = 6, 8, and 20,
103 respectively These values are much larger than the corresponding values obtained for 6MP adsorption In fact, the largest binding energy of 6MP to Au20 amounts to ~22 kcal/mol in neutral condition, and it is substantially dropped to ~11 kcal/mol in acidic solution Such values are also much more negative than the binding energies of PPX on gold clusters, being in the range of −18 to −25 kcal/mol (Table 4.7)
GENERAL CONCLUSIONS AND OUTLOOK
General conclusions
This thesis provides a concise analysis of the structural evolution, stability trends, and energetic characteristics of small gold clusters ranging from two to twenty atoms Next we present a thorough investigation on the adsorption and desorption behaviors of certain anti-cancer drugs on a gold nanostructured surface, as well as the chemical enhancement of surface-enhanced Raman spectroscopy (SERS) Small Aun clusters are utilized as reactant models to simulate the surface of gold nanoparticles The impact of an aqueous solution on the structural, energetic, and spectroscopic characteristics of the resulting complexes is evaluated using the IEF-PCM model
The 6MP molecule prefers to bind with Au metals via the S-atom of the thione group and is further stabilized by the N−H∙∙∙Au contact However, in an acidic solution when the drug mainly exists in the thiol form, the interaction was mostly dominated by the weak AuH−S interaction, rather than the stronger covalent Au−S bond Binding energies are substantially reduced from −29 kcal/mol in a vacuum to −22 and −11 kcal/mol in neutral and acidic solutions, respectively Investigation into the frontier MOs also revealed that the forward donation from HOMO(6MP) to LUMO(Au20) is a main ingredient for the 6MP−Au chemical bonding A comparison of current computed results with previously measured SERS spectra allowed the preferable orientation of drug molecules on the gold surface to be verified In a neutral solution, both N−H bending and stretching modes are the predominant factors leading to the SERS enhancement as they are directly oriented to the gold surface In an acidic environment, the most enhanced peak is found in the fingerprint region and mainly arises from the AuH−S bond rather than the aromatic ring-gold surface π overlap as previously assumed
For the PPX binding to gold metals, the most favored state is the interaction between the nitrogen of the thiazole ring and the positively charged atoms of gold clusters Adsorption processes occur spontaneously with rather negative Gibbs energies, ca −13 to
−18 kcal/mol in gas phase and ca −4 to −14 kcal/mol in water, respectively In the resulting complexes, the Au−Nthiazole bond length gets shorter, while the Au−S bonds are somewhat longer than the sum of covalent radii of binding atoms, indicating the elevated interactive effectiveness regarding the former Analysis based on frontier orbitals suggests the forward donation from the HOMO of PPX to LUMO of Aun as primary contribution for PPX-Au bonding formation While the normal Raman spectrum of PPX exhibits several main peaks
100 related to C−H stretching vibrations, C−X stretching and XH2 (X = N, C) bending modes, a significantly enhanced shaped peak of SERS spectrum of PPX on Au20 corresponds to the stretching vibrations of N−H bonds
The desorption of drug molecules from the gold surface occurs due to the acidic environment in cancerous tissues or the presence of cysteine residues in protein matrices This highlights the potential of gold nanostructures as effective drug carriers and detectors, especially in physiological conditions Methodologically, using small gold clusters Aun with n as 6, 8, or 20) as models for nanoparticle surfaces yields consistent results for complex characteristics and spectra, with minor variations in spectral intensities The efficacy of small clusters as surface models encourages more systematic theoretical investigations into larger bio-molecular targets Further experimental validation of the gold nanocluster model is hoped for in the near future.
Outlook
A deeper understanding of metal cluster structures, stability, and energetics is crucial for advancing science and technology While the thesis findings can aid future studies on nanostructured materials, unresolved issues and challenging perspectives remain Therefore, further exploration of various metal cluster classes, including transition metals beyond gold, is essential to gain a comprehensive understanding of their properties Although first-principle methods like DFT offer valuable insights into ground state properties, their computational demands limit studies to small atom systems, hindering effective calculations of excited states Anticipated breakthroughs in methodology and computational power are expected to facilitate theoretical exploration of larger metal and semiconductor clusters The rise of machine learning applications is also predicted to aid in this advancement Validation of predictions awaits spectroscopic data from experimental groups, enabling further investigations into larger systems
The present and future applications of nanostructured materials in biomedical sciences, catalysis, and electronic industries hold significant promise and warrant further exploration Open issues exist regarding the use of metal clusters in assembling materials as catalysts or drug carriers, emphasizing the need for computational studies on their electronic, optical, and aggregate properties Understanding interactions with organic and bio-molecular compounds is crucial for confidently interpreting and predicting chemical phenomena
LIST OF PUBLICATIONS CONTRIBUTES TO THIS THESIS
1 Nguyen Thanh Si, Pham Vu Nhat and Minh Tho Nguyen, Small gold clusters: Structure, energetics and biomedical applications, Comprehensive Computational
Chemistry 2024, Volume 2, Pages 523−567, doi: https://doi.org/10.1016/B978-0-12- 821978-2.00148-3 (A book chapter)
2 Duong Thi Huyen, Thanh Q Bui, Nguyen Thanh Si, Pham Vu Nhat, Phan Tu Quy, and Nguyen Thi Ai Nhung, Theoretical study of the binding mechanism between anticancerous drug mercaptopurine and gold nanoparticles using a cluster model,
3 Nguyen Thanh Si, Pham Vu Nhat and Minh Tho Nguyen, Binding mechanism and SERS spectra of 5-fluorouracil on gold clusters, Frontiers in Chemistry 10, 1050423,
4 Pham Vu Nhat, Nguyen Thanh Si, Nguyen Ngoc Khanh Anh, Long Van Duong and Minh Tho Nguyen, The Au 12 gold cluster: Preference for a non-planar structure,
5 Nguyen Thanh Si, Nguyen Thi Ai Nhung, Thanh Q Bui, Minh Tho Nguyen and Pham
Vu Nhat, Gold nanoclusters as prospective carriers and detectors of pramipexole, RSC Advances 11, 16619-16632, 2021
6 Nguyễn Thanh Sĩ, Dương Thị Huyền, Phạm Thị Bích Thảo, Trần Ni Kha, Phạm Vũ
Nhật, Nghiên cứu tính toán khả năng gắn kết với cluster vàng Au n (n = 3, 4) của mercaptopurine và thioguanine Tạp chí xúc tác và hấp phụ Việt Nam (2021), 10, 3
7 Pham Vu Nhat, Nguyen Thanh Si, Nguyen Thi Thu Tram, Long Van Duong and Minh Tho Nguyen, Elucidating the binding mechanism of thione-containing mercaptopurine and thioguanine drugs to small gold clusters, Journal of Computational Chemistry 41
8 Nguyễn Thanh Sĩ, Nguyễn Khánh Ngọc và Phạm Vũ Nhật, Cấu trúc và tính chất điện tử của cluster vàng Au n (n = 2-20), Tạp chí Khoa học Đại học Cần Thơ 56(CĐ Tự nhiên), 10-17, 2020
9 Nguyen Thanh Si and Pham Vu Nhat, A computational study of cysteine and glutathione binding to small gold cluster Au 8 , Journal of Science and Technology Development 23 (1), 430-438, 2020
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