DISSERTATION OVERVIEW 4
Human emissions of CO2 and other greenhouse gases are the primary drivers of climate change, making it one of the most pressing global challenges today The correlation between cumulative CO2 emissions and rising global temperatures has been well established, highlighting CO2's crucial role in the greenhouse effect Innovating methods to utilize CO2 is urgent for reducing its atmospheric concentration, as it is abundant, reusable, and non-toxic, with a manageable supercritical state Supercritical CO2 (scCO2) serves as an effective solvent for green chemical reactions, replacing harmful organic solvents in various applications, including nanomaterials, food science, and pharmaceuticals Despite its advantages, scCO2 struggles with polar organic compounds and high molecular-mass solutes, prompting research into enhancing solubility through CO2-philic functional groups like carbonyl-based compounds, which are favored for their cost-effectiveness and ease of synthesis Ongoing experimental and theoretical studies aim to improve the applicability of scCO2 by optimizing its interactions with these functional groups.
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 Additionally, the combination of DMSO and CO2 plays a significant role in precipitation processes, enhancing its utility in various scientific fields.
The Compressed Antisolvent process for precipitating proteins and polar polymers faces challenges at both subcritical and supercritical pressures of the DMSO-CO2 mixture Experimental studies have indicated that incorporating water as a cosolvent with DMSO can effectively alter the phase behavior of the DMSO-CO2 system.
The study explores the role of water molecules in influencing particle morphology during the PCA process, highlighting how they alter particle formation mechanisms Experimental phase equilibrium data were obtained for binary DMSO-CO2 and ternary DMSO-CO2-H2O mixtures Research by Wallen et al indicates a strong interaction between DMSO and CO2, driven by Lewis acid-base interactions and hydrogen bonding, with Trung et al suggesting that the Lewis acid-base interaction plays a more significant role Additionally, the intermolecular interactions between DMSO and H2O have been categorized accordingly.
O−H∙∙∙O red-shifting and C−H∙∙∙O blue-shifting hydrogen bonds by Kirchner and
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 controlled by understanding the molecular interactions and stability of DMSO with both water (H2O) and carbon dioxide (CO2) This cooperative effect between the two types of hydrogen bonding plays a crucial role in determining the overall stability of these mixtures.
Experimental studies have demonstrated that adding small amounts of cosolvents to supercritical carbon dioxide (scCO2) enhances the solubility of various solutes 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 both solubility and selectivity in processes involving scCO2 Research by Hosseini et al indicates that the presence of alcohols influences the formation of complexes, with each type of alcohol uniquely affecting the aggregation of CO2 around the solutes.
Disperse Red 82 and modified Disperse Yellow 119 increases substantially up to
The vapor-liquid equilibria and critical properties of the carbon dioxide-ethanol binary mixture were experimentally studied, revealing a significant 25-fold increase when 5% ethanol cosolvent was added to supercritical CO2 Various experimental techniques and equipment were employed to obtain these results.
Becker et al found that incorporating CO2 into pure ethanol decreases the interfacial tension in the liquid phase Additionally, the introduction of H2O into supercritical CO2 (scCO2) solvent has been shown to enhance the solubility and extraction yield of organic compounds.
Understanding the molecular interactions, stability, and structures of complexes formed between organic compounds and CO2, both in the presence and absence of H2O, is essential for elucidating CO2 capture mechanisms Investigating these CO2 complexes reveals that the intrinsic strength of noncovalent interactions between CO2 and adsorbents is crucial for effective capture capabilities A systematic theoretical analysis of these complexes enhances our understanding of CO2 capture processes.
H2O at molecular level could give information for solvent-solute and solvent- cosolvent interactions in systems involving CO 2
Recent studies have highlighted the significance of carbonyl group-containing molecules, prompting extensive experimental and theoretical investigations Research has focused on the structures and intermolecular interactions of complexes formed with CO2 and various organic compounds, including simple alcohols and formamide Ab initio calculations have identified three geometrical configurations, with the conventional structure being the most supported by data The parallel geometry, akin to the (CO2)2 dimer, is less common and has only been observed in specific cases like methyl acetate-CO2 complexes Notably, the CãããO tetrel bond, previously referred to as a Lewis acid-base interaction, has been recognized as a key bonding feature in carbonyl complexes.
Conventional structures T-shaped structures Non-conventional structures Figure 1 1 Three types of CO 2 complexes
In 2002, Raveendran and Wallen explored the cooperative effect of C-H···O hydrogen bonds in CO2 systems with various organic molecules, including formaldehyde, acetaldehyde, acetic acid, and methyl acetate, alongside dimethyl sulfoxide as a sulfonyl model Their study revealed that the hydrogen atom interacts with either the carbonyl carbon or the α-carbon of these compounds and CO2 However, subsequent investigations combining ab initio calculations with experimental infrared spectra indicated that the dimethyl ether and CO2 complex is primarily stabilized by a C···O tetrel bond with C_s symmetry, without the contribution of C-H···O hydrogen bonds.
The principal role of the CãããO tetrel bond has been observed in various complexes involving CO2, including those with CO, HCN, H2O, and alcohols such as ethanol and methanol In systems with formamide and CO2, the C∙∙∙O interaction over the C∙∙∙N tetrel bond is crucial for stabilizing the complexes High-resolution Fourier transform microwave (FTMW) rotational spectra provide insights into the intermolecular interactions and geometrical structures, which are compared with theoretical calculations Research indicates that in simple alcohol-CO2 complexes, the CãããO tetrel bond plays a dominant role, complemented by C−HãããO hydrogen bonding Additionally, molecular dynamics simulations under supercritical conditions reveal a higher likelihood of CO2 clustering around the lone pairs of the oxygen atom in ethanol, consistent with findings from a 2017 study that showed CO2 molecules preferentially locating near the oxygen atom of ethanol.
Comparative studies have shown that complexes formed between CO2 and compounds featuring >S=O groups exhibit greater stability than those with >S=S groups, primarily due to stronger electrostatic interactions While CO2 complexes with thioformaldehyde and its derivatives are slightly less stable than those with substituted formaldehydes, thiocarbonyl compounds have garnered less attention than carbonyl compounds in the search for effective cosolvents in supercritical CO2 Despite this, thiocarbonyl compounds are valuable in synthesis and organocatalyst development due to their higher reactivity and lower polarity Furthermore, compounds containing >C=S groups are anticipated to play significant roles in molecular materials and biologically relevant applications Therefore, it is crucial to understand the interactions of thioacetone with common solvents and cosolvents, such as supercritical CO2 and water, in various chemical processes.
Most studies have focused on the geometries, stability, and interactions of binary complexes involving CO2 However, the aggregation and growth mechanisms of complexes with multiple CO2 molecules, crucial for understanding absorption processes and their properties, remain unexplored Additionally, the solvation structures and stability of complexes formed by interactions of organic compounds with limited CO2 and H2O molecules have yet to be investigated.
Noncovalent interactions, including hydrogen, tetrel, chalcogen, and halogen bonds, significantly influence crystal packing, material structures, and biological systems Among these, blue-shifting hydrogen bonds (HB) have garnered attention for their importance in crystal engineering and biochemical processes, prompting ongoing theoretical and experimental research to uncover their origins The C−H⋯O interaction, a typical example of blue-shifting HB, has been shown to stabilize complexes between CO2 and organic molecules through IR spectra and ab initio calculations However, other noncovalent interactions, such as tetrel and chalcogen bonds, are relatively new and lack comprehensive theoretical frameworks and molecular-level characterization Understanding the mutual influence of multiple noncovalent interactions is crucial, particularly the well-documented cooperativity effects of hydrogen bonds in biological systems For instance, significant cooperativity has been observed in water clusters, with interaction energies in DMSO and water complexes increasing by 53% and 58% for O−H⋯O and C−H⋯O hydrogen bonds, respectively This cooperative behavior extends beyond hydrogen-bonded complexes to include cation-π, π-π, and other noncovalent interactions.
THEORETICAL BACKGROUNDS AND
2 1 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 calculate approximate wave functions and energies for atoms and ions Hartree's approach involved assuming that the potential experienced by a core electron is the combined potential of 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 formed by the nucleus and electrons The SCF method is succinctly illustrated in the accompanying diagram.
Initial Field Solutions of Initial Field corrected for each core
Distribution of Charge Final Field electron electrons
According to Hartree's approach,79 SCF method gives solutions to
Schrödinger's equation describes systems with individual electrons in distinct states, represented by the electronic wave function as a Hartree product, which is expressed as Φ_el = χ_1(x_1)χ_2(x_2) χ_N(x_N) This approach gained significant attention and was independently refined by Slater and Fock in the 1930s However, the Hartree product, which assumes electron independence, fails to meet the anti-symmetry requirement essential for fermions To address this, the wave function can be constructed using Slater determinants, formulated as Φ_el = χ_i(x_1)χ_j(x_2) χ_k(x_N).
To derive the HF equation, it is essential to express the energy of a single Slater determinant According to the Born-Oppenheimer approximation, the wave functions of atomic nuclei and electrons in a molecule can be treated independently, represented as Ψ total = Φ el Φ nu The Hamiltonian for a system of N electrons surrounding the nuclei is then utilized to describe the interactions within the molecule.
The first term in the equation represents the kinetic energies of electrons, while the second term accounts for the attraction of electrons to nuclei Both of these terms depend solely on a single electron coordinate The third term, which involves the repulsion between electrons, relies on the interactions of two electrons Additionally, the repulsion between nuclei is incorporated into the energy calculation at the end of the equation The final term is a constant that does not depend on electron coordinates and is specific to a given nuclear geometry 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 i Φ el + Φ el ∑ ∑ vˆ(i, j) Φ i j >i el + V nn
= ∑ Φ el hˆ i Φ el + ∑ ∑ Φ el vˆ(i, j) Φ el + V nn i i j >i
According to variational theorem, the idea of HF method is to find out the minimum of E el when χ i → χ i + δχ j (is handled by means of Lagrange multipliers)
One of the advantages of the method is that it breaks the many-electron
The Schrödinger equation can be simplified into multiple one-electron equations, each yielding a single-electron wave function known as an orbital, along with its corresponding energy termed orbital energy These orbitals represent the behavior of an electron within the collective field created by all other electrons The relationship is expressed as fˆ χ i (x 1 ) = εχ i (x 1 ), where f denotes the Fock operator and χ i (x i ) signifies a set of one-electron wave functions referred to as Hartree-Fock (HF) molecular orbitals.
The Hartree-Fock (HF) method in computational chemistry involves a simplified algorithmic flowchart that outlines its key steps This method generates the optimal single-determinant electronic configuration for a given set of nuclear coordinates Subsequently, a Fock matrix is constructed and diagonalized, allowing for the resolution of the eigenvalue problem associated with the Fock matrix 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
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, this model fails to account for the reality that electrons tend to avoid one another more effectively than predicted, as each electron perceives others as moving particles, leading to mutual adjustments in their behavior.
(correlate) their motions to minimize their interaction energy The electron correlation is treated better in post-HF methods, which are represented in the following section
2 1 2 The post–Hartree-Fock method
Post-Hartree-Fock methods enhance traditional HF calculations by incorporating electron correlation, offering a more precise representation of electron repulsions Unlike the HF method, which averages these interactions, post-Hartree-Fock approaches, such as perturbation theory, provide improved accuracy in quantum chemistry calculations.
In perturbation theory, the HF solution is treated as the first term in a
The Taylor series, notably advanced by Műller and Plesset in 1980, is a widely used perturbational approach in quantum chemistry Műller-Plesset (MP) theory allows for the inclusion of various terms in the perturbation series, enabling calculations at different orders Specifically, second-order MP theory (MP2) is frequently employed for geometry optimizations, while fourth-order (MP4) is used to refine calculated energies In this study, the second-order perturbation method was utilized to achieve accurate results.
The MP perturbation theory considers an unperturbed Hamiltonian operator
Hˆ 0 , 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:
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:
E (2) = ψ 0 | V | ψ (1) 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, but these methods are often time-consuming and primarily applied to small molecules In this study, such time-intensive calculations are utilized to determine single-point energy in specific small complexes.
The Couple Cluster (CC) method enhances the basic Hartree-Fock (HF) molecular orbital approach by utilizing an exponential cluster operator to construct multi-electron wave functions, effectively capturing electron correlation In coupled-cluster theory, the wave function is expressed using an exponential ansatz, allowing for a more accurate representation of electronic interactions in molecular systems.
The reference wave function, denoted as Φ 0, is commonly represented by a Slater determinant derived from Hartree-Fock (HF) molecular orbitals The cluster operator, Tˆ, is expressed in the form of a Taylor expansion, allowing for a systematic approach to account for electron correlation effects in quantum many-body systems.
Where Tˆ 1 is the operator of all single excitations, Tˆ2 is the operator of all double excitations, and so forth For the determination of the amplitudes, the wave function
(2 1) is inserted in the Schrửdinger equation: ˆ 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 Hˆ N is introduced the first time and called the normal order Hamiltonian, which consists of the one-electron ( fˆ N ) and two-electron (Wˆ N ) contributions; the
Electron correlation energy, abbreviated as E coor, is a complex concept that typically requires significant computational effort to analyze The coupled-cluster problem is generally not addressed through a variational approach By applying a left multiplication to equation (2.2), the problem is projected onto the reference determinant as well as all excited determinants.
The couple cluster energy is thus considered as the expectation value of a similarity transformed Hamiltonian ˆ ˆ
Traditional coupled-cluster methods are classified based on the maximum number of excitations permitted in the operator Tˆ These methods are commonly abbreviated with "CC" followed by specific designations.
S – for single excitations (shortened to singles in coupled-cluster terminology),
Thus, the T operator in CCSDT has the form: T = T 1 + T 2 + T 3
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 considering multiple occupancy schemes for molecular orbitals (MOs) and mixing microstates derived from permuting electron occupancies A typical CI calculation begins with a self-consistent field (SCF) calculation to determine the MOs, which remain unchanged throughout the process Microstates are formed by transferring electrons from occupied to vacant orbitals based on specific schemes However, performing a full CI calculation that accounts for all possible electron arrangements in MOs can lead to impractically large computations, even for moderately sized molecules To manage this complexity, restrictions are applied, including limiting the number of MOs involved and specifying certain types of electron excitations The most efficient method involves promoting a single electron from the ground state to a virtual orbital, known as single excitations (CIS), which is commonly used for spectral calculations Incorporating double excitations, where two electrons are promoted, results in the CISD method, and further extensions can be applied as needed.