Research introduction
Economic development and industrialization have led to a significant rise in air pollution, primarily due to increased carbon dioxide (CO2) emissions, which greatly contribute to the greenhouse effect The use of supercritical CO2 (scCO2) in manufacturing offers a promising solution to mitigate emissions while conserving resources, as it is more environmentally friendly compared to toxic organic solvents ScCO2 is widely utilized as a solvent for extraction, in purification processes, and as an antisolvent in polymerization and polymer precipitation To discover new materials and solvents that favor CO2, it is crucial to understand the interactions between CO2 and functional organic compounds, as well as their electronic properties at the molecular level This understanding necessitates a systematic approach that combines experimental methods with modeling, particularly through quantum computational techniques.
Recent experimental studies have focused on understanding the interactions between solutes and supercritical carbon dioxide (scCO2) to enhance solubility Functional organic compounds such as hydroxyl, carbonyl, thiocarbonyl, carboxyl, sulfonyl, and amine are identified as CO2-philic Additionally, the incorporation of polar compounds like water and small alcohols (methanol and ethanol) as cosolvents has been shown to influence both the thermodynamic and kinetic properties of CO2-involved reactions Notably, adding water to scCO2 increases the solubility and extraction yield of organic compounds Therefore, systematic research into the interactions among CO2, water, and organic functional compounds is essential for understanding the nature of these interactions and the impact of cooperativity within the solvent-cosolvent-solute system.
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The achieved results are hopefully to provide a more comprehensive look at scCO 2 application and also contribute to the understanding of the intrinsic characteristics of weak noncovalent interactions.
Object and scope of the research
- Research object: Geometrical structure, stability of complexes involving CO 2 ; nature and role of noncovalent interactions including tetrel bond, hydrogen bond.
- Scopes: complexes of functional organic compounds including dimethyl sulfoxide, acetone, thioacetone, methanol, ethanol, ethanethiol, dimethyl ether and its halogen/methyl substitution with some molecules of CO 2 and/or H 2 O.
Novelty and scientific significance
This study explores the geometries, stability, and properties of noncovalent interactions in complexes formed by dimethyl sulfoxide, acetone, thioacetone, dimethyl ether and its di-halogen/methyl derivative, dimethyl sulfide, methanol, ethanol, and ethanethiol with CO2 and/or H2O High-level ab initio calculations reveal a general trend in the interactions of these organic compounds with CO2 and H2O The analysis highlights that the presence of H2O significantly enhances stability and promotes positive cooperativity compared to complexes with only CO2 Key interactions such as O−H∙∙∙O hydrogen bonds (HBs), along with other weak interactions like C∙∙∙O/S TtBs, C−H∙∙∙O HBs, and O∙∙∙O charge-based interactions (ChBs), contribute to this cooperativity Notably, the study identifies a growth pattern in ethanol complexes with 1-5 CO2 molecules, providing insights into ethanol solvation in supercritical CO2 (scCO2) A comprehensive investigation of the stability of these complexes and the strength of noncovalent interactions is also conducted.
The systematically theoretical investigation on complexes between functional organic molecules and a number of CO 2 and/or H 2 O ones could provide useful information for the development of promising functionalized materials for
CO 2 capture/sequestration and increase knowledge in noncovalent interactions. These obtained results can play as the valuable references for future works on
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This dissertation aims to serve as a valuable resource for educators, researchers, and students interested in computational chemistry at the molecular level, with a particular focus on noncovalent interactions and complexes involving CO2.
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DISSERTATION OVERVIEW
Overview of the research
Human emissions of CO2 and other greenhouse gases are the main drivers of climate change, a critical global challenge The correlation between cumulative CO2 emissions and rising global temperatures highlights the importance of CO2 as a key atmospheric gas influencing the greenhouse effect Innovating CO2 usage is essential for reducing its atmospheric concentration, as CO2 is abundant, reusable, and non-toxic, reaching supercritical conditions at manageable temperatures and pressures Supercritical CO2 (scCO2) serves as an effective solvent for green chemical reactions, replacing conventional toxic solvents, with applications in nanomaterials, food science, and pharmaceuticals Despite its advantages, scCO2 faces challenges in dissolving polar organic compounds and high molecular-mass solutes Research is ongoing to identify effective thermodynamic conditions and interacting species to improve solubility in scCO2 Carbonyl-based compounds, recognized as CO2-philic functional groups, are gaining attention due to their simple synthesis and cost-effectiveness, while efforts to enhance scCO2 applicability continue through various experimental and theoretical studies.
Dimethyl sulfoxide (DMSO) is a widely utilized solvent in biological and physicochemical research, particularly in supercritical antisolvent processes Its applications are extensive, including the micronization of pharmaceutical compounds, polymers, catalysts, superconductors, and coloring materials The combination of DMSO and CO2 plays a significant role in precipitation processes, enhancing the efficiency and effectiveness of these applications.
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The Compressed Antisolvent process for precipitating proteins and polar polymers faces challenges at both lower and upper critical pressures of the DMSO-CO2 mixture Recent experimental studies indicate that incorporating water as a cosolvent with DMSO can effectively alter the phase behavior of the DMSO-CO2 system.
Water molecules play a crucial role in shaping particle morphology and enhancing the limitations of the PCA process by altering the mechanism of particle formation Experimental data on phase equilibrium for binary mixtures of DMSO-CO2 and ternary mixtures of DMSO-CO2-H2O have been collected Research by Wallen et al indicates that DMSO exhibits strong interactions with CO2, with the interaction strength arising from both S=O∙∙∙C Lewis acid-base interactions and C–H∙∙∙O hydrogen bonds, where the former is deemed more significant according to Trung et al Additionally, the intermolecular interactions between DMSO and H2O have been categorized into O−H∙∙∙O red-shifting and C−H∙∙∙O blue-shifting hydrogen bonds, as classified by Kirchner.
Reiher 23 Lei et al revealed that the weak C−H∙∙∙O and strong O−H∙∙∙O contacts represent a consistent concentration dependence in interaction between DMSO and
The phase behavior of binary and ternary mixtures can be effectively managed by understanding the molecular interactions and stability of DMSO with both water (H2O) and carbon dioxide (CO2) This highlights the cooperative effects between different types of hydrogen bonding.
Experimental studies indicate that adding small amounts of cosolvents to supercritical carbon dioxide (scCO₂) enhances solute solubility Specifically, alkanes are effective for dissolving nonpolar compounds, while polar compounds benefit from the addition of functional organic compounds or water Alcohols such as methanol, ethanol, and propanol are commonly used as cosolvents to improve solubility and selectivity Research by Hosseini et al highlights that alcohols influence the structure of complexes formed, with varying effects on the aggregation of CO₂ around the drugs Notably, the solubility of Disperse Red 82 and modified Disperse Yellow 119 significantly increases with these cosolvents.
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The addition of 5% ethanol cosolvent to supercritical CO2 (scCO2) resulted in a 25-fold increase in vapor-liquid equilibria The critical properties of the CO2-ethanol binary mixture were thoroughly examined through various experimental techniques and equipment.
Becker et al found that incorporating CO2 into pure ethanol decreases interfacial tension in the liquid phase Additionally, the introduction of water into supercritical CO2 solvent enhances the solubility and extraction yield of organic compounds.
Understanding the interactions, stability, and structures of complexes between organic compounds and CO2, both with and without H2O, is crucial for elucidating CO2 capture mechanisms Investigating these CO2 complexes reveals that the intrinsic strength of noncovalent interactions between CO2 and adsorbents plays a vital role in their capture capabilities A systematic theoretical analysis of these complexes is essential for advancing our knowledge in this field.
H 2 O at molecular level could give information for solvent-solute and solvent- cosolvent interactions in systems involving CO 2
Molecules containing the carbonyl group have been a subject of extensive research, with numerous experimental and theoretical studies examining their structures and intermolecular interactions Specifically, the complexes formed between CO2 and various organic compounds, such as simple alcohols, formamide, and isopropyl amine, have been widely investigated Ab initio calculations have revealed three possible geometries for these complexes, with the conventional structure being the most supported by theoretical and experimental data In contrast, the parallel geometry, also known as the non-conventional structure, is less favored but has been observed in certain systems, such as methyl acetate-CO2 complexes, and is similar to carbonyl-carbonyl arrangements found in crystallographic structures.
6 download by : skknchat@gmail.com complexes, CãããO tetrel bond (previously called Lewis acid-base interaction) was addressed as the bonding feature.
Figure 1.1 Three types of CO 2 complexes
In 2002, Raveendran and Wallen explored the cooperative effect of C-H···O hydrogen bonding in CO2 interactions with various organic molecules, including formaldehyde, acetaldehyde, acetic acid, and methyl acetate, as well as dimethyl sulfoxide as a model for sulfonyl groups Their research revealed that the hydrogen atom from the carbonyl carbon or α-carbon interacts directly with one of the oxygen atoms in CO2 However, a combination of ab initio calculations and experimental infrared spectra indicated that the complex formed between dimethyl ether and CO2 is primarily stabilized by a C···O tetrel bond, characterized by C_s symmetry, without the significant contribution of C-H···O hydrogen bonding.
Stable geometries of complexes involving CO₂ highlight the significant role of the C–O tetrel bond in interactions with various molecules such as CO, HCN, H₂O, and alcohols like C₂H₅OH and CH₃OH In systems containing formamide and CO₂, the C∙∙∙O interaction is the key stabilizing factor compared to the C∙∙∙N tetrel bond Numerous rotational data have been documented to elucidate the nature of these interactions.
Non-conventional structures downloaded from skknchat@gmail.com involve the interactions between CO2 and partner molecules, influenced by solvent or lattice effects High-resolution Fourier transform microwave (FTMW) spectroscopy provides insights into intermolecular interactions and geometric configurations, allowing for a comparison with results derived from theoretical calculations.
Research on the complexes of simple alcohols with CO2 highlights the significant role of C–C tetrel bonds, complemented by C–H–O hydrogen bonds Molecular dynamics simulations of the ethanol∙∙∙CO2 system under supercritical conditions indicate a higher likelihood of CO2 clustering around the lone pairs of the oxygen atom in ethanol Additionally, a 2017 study examining the structures of ethanol in conjunction with 1-4 and 6 CO2 molecules corroborates these findings, revealing that CO2 molecules preferentially position themselves around the oxygen atom of ethanol.
Comparing the properties of oxygen and sulfur-containing compounds reveals significant differences in stability and interactions A study indicated that (CH₃)₂(S=O)∙∙∙CO₂ complexes exhibit greater stability than (CH₃)₂(S=S)∙∙∙CO₂ complexes, attributed to the stronger electrostatic interactions of the >S=O group Additionally, CO₂ complexes with thioformaldehyde and its derivatives are slightly less stable than those with substituted formaldehydes While carbonyl compounds have garnered substantial research attention, thiocarbonyl compounds remain underexplored as effective cosolvents in supercritical CO₂ (scCO₂) despite their unique reactivity and lower polarity Furthermore, compounds featuring the >C=S group are anticipated to play crucial roles in molecular materials and biologically relevant applications Therefore, investigating the interactions of thioacetone with common solvents and cosolvents, such as scCO₂ and water, is vital for advancing synthesis and extraction processes.
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Objectives of the research
This work has four main objectives detailed as follows:
1) To determine stable structures and to compare the strength of the complexes formed by interaction of basic organic compounds functionalized by various groups with CO 2 and H 2 O molecules, and also to find out functional groups that interact strongly with CO 2 as valuable candidates in searching of novel materials to adsorb CO 2 gas phase.
2) To specify the existence and the role of noncovalent interactions in stabilizing the complexes, to unravel their cooperativity, especially the cooperativity of hydrogen bonds and tetrel bonds; and also to gain further insights into the origin of noncovalent interaction Furthermore, this research was investigated to clarify role of H 2 O in stabilization of noncovalent interactions and complexes, which leads to a clearer understanding of importance of H 2 O as cosolvent in supercritical CO 2
3) To investigate the effect of different substitution groups including halogen and methyl on the geometry and stability of complexes formed by interaction of functional organic compounds with CO 2 and/or H 2 O.
4) To discover the trend of geometrical structures and characteristic of noncovalent interactions when increasing number of CO 2 /H 2 O molecules.This gives information of the aggregation of CO2 around organic compounds,with/without H 2 O.
Research content
In order to obtain the aims of research project, the complexes of functional organic molecules including (CH 3 ) 2 SO, (CH 3 ) 2 CO, (CH 3 ) 2 CS, (CH 3 ) 2 O, (CH 3 ) 2 S,
CH 3 OH, C 2 H 5 OH, C 2 H 5 SH with nCO 2 and/or nH 2 O (n=1-2) were investigated. Additionally, the effect of methyl and halogen substitution is also examined.
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With those systems, the following contents were performed:
- Choosing the computational methods along with basis sets which are suitable for both monomers and complexes based on available experimental data, or reliable results reported in the literature.
- Simulating the structures of monomers and complexes, and then optimizing these structures to obtain stable geometries with minima of energy on potential energy surfaces.
This study focuses on calculating the infrared spectra of monomers and their complexes to analyze changes in C(O)−H bond lengths By examining the stretching vibrational frequencies and infrared intensities of these complexes in comparison to the corresponding monomers, we aim to classify the types of hydrogen bonds formed.
The interaction energy of complexes was calculated and compared to assess their strength Various electronic analysis tools, such as MEP, AIM, NBO, and NCIplot, were employed to identify the presence and stability of noncovalent interactions within the complexes Additionally, the study examined the deprotonation energy (DPE) and its role in understanding the cooperativity contributing to the stability of these complexes Furthermore, the SAPT2+ approach was utilized to estimate the individual energy components involved in complex stabilization, providing a clearer insight into the interaction cooperativity.
- Estimating cooperative energy of ternary complexes to evaluate the cooperation between noncovalent interactions in complexes The effect of addition another CO 2 or H 2 O molecule into complexes will be explored.
This study explores how the presence of DPE and PA influences the formation of blue-shifting hydrogen bonds (HB) associated with C−H covalent bonds By focusing on the proton acceptor's (PA) role and the DPE of the C−H bond in isolated monomers, we aim to provide a clearer understanding of the origins of blue-shifting hydrogen bonds.
Research methodology
Investigation into complexes of functional organic molecules and CO 2 with/without H 2 O at molecular level was carried out using high level computational chemical methods Optimization calculations were done at MP2/6-6-
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The study utilized the highly reliable MP2/6-311++G(2d,2p) level for vibrational frequency analyses to determine minimum structures and estimate zero-point energy Single point energies were calculated using either CCSD(T)/6-311++G(2d,2p) or MP2/aug-cc-pVTZ, depending on the size of the complexes examined Interaction and cooperative energies were corrected for zero-point energy (ZPE) and basis set superposition error (BSSE) The depth of intermolecular interactions was analyzed through wave function calculations at the MP2/6-311++G(2d,2p) level or MP2/aug-cc-pVTZ Natural Bond Orbital (NBO) analyses employing ωB97X-D or MP2 methods were conducted to quantitatively assess charge-transfer effects and noncovalent interaction characteristics To further explore noncovalent behaviors, interactions between carbon dioxide and ethanol were evaluated using NCIplot at the MP2/6-311++G(2d,2p) level Additionally, the molecular electrostatic potential (MEP) of isolated monomers was plotted at MP2/aug-cc-pVTZ, with all quantum calculations performed using the Gaussian09 software package.
The SAPT2+ analysis conducted using the PSI4 program decomposes interaction energy into key components: electrostatic, induction, dispersion, and exchange terms This analysis utilizes density-fitted integrals along with the standard aug-cc-pVDZ basis set for accurate calculations.
In the upcoming chapter, we will delve into the research methodology and techniques tailored to each specific issue, while also utilizing software tools like Molden, Gaussview, Origin, and Excel for effective analysis of the calculated results.
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THEORETICAL BACKGROUNDS AND
Theoretical background of computational chemistry
The Hartree-Fock (HF) method originated shortly after the formulation of Schrödinger's equation in 1926 In 1928, Douglas Hartree introduced the self-consistent field (SCF) method, which aimed to approximate wave functions and energies for atoms and ions Hartree's approach involved assuming that the effective potential for a core electron encompassed both the nucleus and the entire electronic charge distribution Additionally, he posited that the charge distribution for closed shell electron configurations is centrally symmetrical, resulting in a spherically symmetric field created by the nucleus and electrons.
Hartree's approach utilizes the 79 SCF method to solve Schrödinger's equation for systems with distinct electrons, denoted as 1, 2, 3, etc., each represented by their respective states χ 1, χ 2, χ 3, and so on The electronic wave function of the system is expressed as a product of the individual electrons' wave functions, known as the Hartree product When incorporating the complete set of coordinates, the Hartree product is represented as Φ el.
In 1930, Slater and Fock independently modified a method that gained significant attention The Hartree product, which assumes electron independence, fails to meet the anti-symmetry requirement of wave functions However, this anti-symmetry can be achieved by constructing the wave function using Slater determinants.
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To derive the HF equation, it is essential to describe the energy expression of a single Slater determinant Utilizing the Born-Oppenheimer approximation, we can treat the wave functions of atomic nuclei and electrons in a molecule independently The Hamiltonian representing the system of N electrons surrounding the nuclei is then defined accordingly.
The equation consists of several terms: the first represents the kinetic energies of electrons, while the second reflects the attraction of electrons to the nuclei The initial two terms depend solely on a single electron coordinate The third term accounts for the repulsion between electrons, which relies on the interactions of two electrons Additionally, the repulsion among nuclei is included in the energy calculation at the equation's conclusion The final term is a constant related to a specific nuclear geometry and does not depend on electron coordinates These operators can be organized based on the number of electron indices, utilizing atomic units to simplify the equation.
The energy is now written in terms of the permutation operator as:
= ∑ Φ el h i Φ el + ∑∑ Φ el vˆ(i, j) Φ el +V nn i
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According to variational theorem, the idea of HF method is to find out the minimum of E el when χ
The method simplifies the complex many-electron Schrödinger equation by breaking it down into multiple one-electron equations Each of these equations produces a single-electron wave function, known as an orbital, along with its corresponding energy, referred to as orbital energy The orbital effectively describes the behavior of an electron within the collective field created by all other electrons.
Where f is Fock operator, χ i (x i ) is a set of one-electron wave functions, called the HF molecular orbitals.
The Hartree-Fock (HF) method in computational chemistry involves a simplified algorithmic flowchart, as illustrated in Fig 2.1 This algorithm generates the optimal single-determinant electronic configuration for a given set of nuclear coordinates It constructs and diagonalizes the Fock matrix, subsequently solving the eigenvalue problem associated with it A new density matrix is then created, and this iterative process continues until the convergence criteria are met.
Figure 2.1 The flowchart illustrating Hartree–Fock method
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The primary limitation of the Hartree-Fock (HF) method lies in its inadequate treatment of electron correlation In this approach, each electron is assumed to move within an electrostatic field created by the average positions of other electrons However, electrons tend to avoid each other more effectively than this model suggests, as they interact as moving particles and adjust their motions to reduce interaction energy Post-HF methods offer improved treatment of electron correlation, addressing this shortcoming more effectively.
2.1.2 The post–Hartree-Fock method
Post-Hartree-Fock methods extend beyond HF calculations by incorporating electron correlation, offering a more precise representation of electron repulsions compared to the averaged approach of the HF method Among these methods, perturbation theory is one of the most commonly utilized techniques for enhancing accuracy in electronic structure calculations.
In perturbation theory, the Hartree-Fock (HF) solution serves as the initial term in a Taylor series, with Mứller and Plesset being pioneers in developing one of the most widely used perturbation methods Mứller-Plesset (MP) theory allows for the incorporation of various orders in the perturbation series, making it a versatile approach for analyzing quantum systems, particularly when considering second-order perturbations.
MP theory (MP2) is often used for geometry optimizations and fourth order (MP4) for refining calculated energies The second order perturbation was utilized in the present work.
The MP perturbation theory considers an unperturbed Hamiltonian operator ˆ , to which a small perturbation V is added.
Here, λ is an arbitrary real parameter Expanding the exact wave function and energy in term of HF wave function and energy yields:
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Substituting these expansions into the Schrửdinger equation and collecting terms according to powers of λ yields
After a number of transformations, the n th -order MP energy is expressed as:
Thus, the HF energy is the sum of zero- and first- order energy
The correlation energy can then be written as
Various techniques for incorporating electron correlation can yield highly accurate results, although these methods are often time-consuming and primarily applied to small molecules In this study, such labor-intensive calculations are utilized to determine single-point energy for specific small complexes.
The Couple Cluster (CC) method enhances the basic Hartree-Fock (HF) molecular orbital technique by utilizing an exponential cluster operator to effectively model multi-electron wave functions and account for electron correlation In coupled-cluster theory, the wave function is expressed using an exponential ansatz, represented as Ψ = ˆ Φ.
Where Φ 0 is the reference wave function which constructed from HF molecular orbitals, and ˆ
T operator is written in the Taylor expansion form:
(2.1) is typically a Slater determinant is cluster operator The cluster
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Where ˆ is the operator of all single excitations,
T 1 excitations, and so forth For the determination of the amplitudes, the wave function
(2.1) is inserted in the Schrửdinger equation: ˆ
The exponential operator can be written as a Taylor expansion The correlation energy is obtained by subtraction of the HF energy on both sides of the equation:
The H ˆ N is introduced the first time and called the normal order Hamiltonian, which consists of the one-electron ( f N ) and two-electron (W N ) contributions; the
Ecor, or electron correlation energy, is a complex concept that typically involves significant computational effort, making a variational solution to the coupled-cluster problem uncommon The approach involves projecting the equation onto the reference determinant and all excited determinants by multiplying from the left, allowing for a clearer understanding of electron interactions.
The couple cluster energy is thus considered as the expectation value of a similarity transformed Hamiltonian.
The classification of traditional coupled-cluster methods rests on the highest number of excitations allowed coupled-cluster methods usually begin with the letters "CC" and follow by:
S – for single excitations (shortened to singles in coupled-cluster terminology),
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Terms in round brackets indicate that these terms are calculated based on perturbation theory For example, the CCSD(T) method means:
- Coupled cluster with a full treatment singles and doubles.
- An estimate to the connected triples contribution is calculated non-iteratively using many-body perturbation theory arguments.
The CCSD(T) method is often called the “gold standard” of computational chemistry, because it is one of the most accurate methods applicable to reasonably large molecules.
Configuration interaction (CI) addresses electron correlation by allowing multiple occupancy schemes for molecular orbitals (MOs) and mixing microstates derived from electron occupancy permutations A typical CI calculation begins with a self-consistent field (SCF) calculation to establish the MOs, which remain fixed for the duration of the analysis Microstates are generated by transferring electrons between occupied and vacant orbitals based on specific schemes However, full CI, which considers every possible electron arrangement across all MOs, leads to prohibitively large calculations, especially for moderate-sized molecules with extensive basis sets To manage this complexity, restrictions are applied, such as limiting the number of MOs and the types of electron rearrangements allowed The most efficient approach involves promoting a single electron from the ground state to a virtual orbital, known as single excitations (CIS), commonly used for spectral calculations Incorporating all double excitations, where two electrons are promoted, results in CISD, and further extensions can be made.
In conclusion, ab initio calculations typically provide excellent qualitative insights and can achieve more precise quantitative results as the size of the molecules decreases The key benefit of ab initio methods lies in their ability to converge towards the exact solution as the approximations are refined.
20 download by : skknchat@gmail.com small in magnitude In general, the relative accuracy of results is:
HF