A quantum chemical study of the interaction of carboxylic acids with DMSO

12 Quantum chemical computational methods, which use quantum mechanics and molecular dynamics theory, have developed rapidly in the past few decades, and quantum chemical computation has penetrated almost all fields of chemistry. Hydrogen bonds are ubiquitously 15 common weak intermolecular interactions. Moreover, the bonding mechanism of hydrogen bonds is considered to be different from that of chemical bonding. Because of the difficulty of experimental studies, a more accurate calculation of hydrogen bonding from theory is a more 18 convenient and direct method to understand hydrogen bonding. Density functional theory (DFT) is the most widely used general function in quantum chemical calculations, giving accurate results for most chemical systems. In this paper, the geometries of the hydrogen-bonded dimer complex 21 of acetic acid and DMSO was structurally optimized and potential energy surface was determined. The geometries of four related hydrogen-bonded dimer complexes were fully optimized using the M06-2X/6-311++G (3d, 2p) exchange-correlation functional with DFT-D3(BJ) empirical 24 dispersion correction. We found that hydrogen bonding is a mixture of electrostatic interactions and covalent bonding, and that hydrogen bonding is a kind of force with different percentages of electrostatic and covalent character, rather than a special force independent of chemical bonding. 27 Thus, more clearly defining our inherent classification of forces between substances provides a new perspective for our future study of weak interactions such as hydrogen bonding.


INTRODUCTION
Today's high-performance computers allow for the ground-state DFT geometry optimization of molecules with about 100 atoms in a single day. According to Moore's law, in 25 years the 33 computing power will increase by a factor of 106 [1], and algorithms will improve, so advances in experimental chemistry will not be comparable to advances in computing power. Quantum chemical computing will become an essential tool for studying chemical problems, even 36 surpassing experimental observations, and by 2050, chemical research methods will be very different. Therefore, it is crucial to focus current research and future efforts on theory development.
Many chemical processes and biological systems operate based on weak intermolecular 39 interactions [2], so weak intermolecular interactions have been of particular interest in chemistry [3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20], for example, in the field of gas chromatographic separations using capillary columns, where weak intermolecular interactions play an irreplaceable role [21], We found that hydrogen 42 bonding plays a critical role in the retention time of acetic acid(AA) when using gas chromatography to analyze short-chain fatty acids (SCFAs) dissolved in dimethyl sulfoxide (DMSO) [22]. Hydrogen bonding is a frequent weak intermolecular interaction, similar to 45 chemical bonding in that it is directional and saturated, while the bond energy of hydrogen bonding is much smaller than that of chemical bonding. The bonding mechanism of hydrogen bonds is different from chemical bonds in that hydrogen bonds are a special type of the intermolecular force, 48 dipole-dipole. The formation of hydrogen bonds involves electron donors and electron acceptors, where the electron acceptors must be positively charged hydrogen atoms [5]. A more accurate calculation of hydrogen bonding from theory is an obvious way to understand hydrogen bonding, 51 since experiments can be a complicating factor.  54 with experimental methods [24], and Alkorta et al. described non-covalent interactions in detail using quantum chemical calculations [25]. However, the definition of hydrogen bonding still seems to be vague. 57 The focus of this paper is to present the research methods of quantum chemistry and its utility for studying hydrogen bonds. The hydrogen-bonded dimer complexes were fully optimized using the M06-2X/6-311++G (3d, 2p) exchange-correlation function with Basis set superposition error 60 (BSSE) [26] of DFT-D3(BJ) empirical dispersion correction [27]. The hydrogen bonding in the active site was determined using the electrostatic potential (ESP) results of the molecule; a quantum-chemical explanation of hydrogen bonding was derived using molecular orbital theory 63 (MO) [28,29]; confirmation of the directionality of hydrogen bonding was determined using a potential energy surface scan； estimates and comparisons of the energy of intermolecular hydrogen bonds in the geometries of the related 2 hydrogen-bonded dimer complexes (Formic Acid(FA)- 66 DMSO and Trifluoroacetic acid (TFA)-DMSO) were determined using the M06-2X/6-311++G (3d, 2p) exchange-correlation function with DFT-D3(BJ) empirical dispersion correction. Based on the above calculations, we propose a supplement to the traditional understanding of hydrogen bonding. 69

METHODS OF QUANTUM CHEMISTRY
In classical mechanics, Newton's second law describes the motion of macroscopic objects. In quantum mechanics, Schrödinger proposed the fluctuation equation to describe the state of motion of microscopic particles, which became the most fundamental equation of quantum mechanics and 72 the theoretical basis of quantum chemical calculations [30,31]. The time-independent Schrödinger equation can be written as: Where Ĥ is a Hamiltonian operator and includes all possible interactions within that system. Ψ is the wave function of the system containing all measurable information. E is the energy of the system and the eigenvalue of the Schrödinger equation. On this basis, the traditional Hartree-Fock 78 equation [32] or the DFT method [33][34][35] both seek approximations to solve the Schrödinger equation. simulations to study the hydration mechanism of kaolinite surfaces [38]. Bilonda and Mammino performed calculations of intramolecular hydrogen bonding in matter using different theoretical 93 approaches and basis sets [39]. Quantum chemical calculations played an essential role in all these studies.

Molecular modeling:
Theoretically, the use of higher-level theoretical methods and more sophisticated basis sets can 96 lead to more accurate computational results. However, this can also make the computation costly or even unattainable. Ultimately, a trade-off between computational cost and computational accuracy needs to be made when choosing molecular simulations. In this paper, the trend or 99 qualitative forecast of hydrogen bonding in the AA-DMSO hydrogen-bonded dimer complex was found using the Gaussian16 quantum chemistry package [40] in the DFT calculations because the quantitative structure is not predicted.

Hydrogen bonding sites -Electrostatic natures:
The carboxyl group in AA is a combination of two functional groups connected to a single carbon atom, the hydroxyl group (-OH) and the carbonyl group (=O). This combination imparts unique natures to each functional group, including 105 polarity, high electronegativity, and weak acidity. These functional groups are capable of hydrogen bonding by providing and accepting protons [41] and will produce strong hydrogen bonds with the polar non-protic solvent DMSO. Quantum chemical computations provide a good 108 characterization of the intermolecular interactions and the sites of action. In this paper, structureoptimization and frequency calculations were performed separately for the AA molecule and the DMSO molecule using the M062X/6-311++G(3d,2p) [42,43] method and the DFT-D3BJ [27] 111 dispersion correction, which includes NBO [44] analysis and characterization of the hydrogen bonding sites between the solvent AA molecule and the DMSO molecule. The absence of imaginary frequencies is the end of the structural optimization-stable structure. the DMSO molecule has a negative ESP value; these two regions produce hydrogen bonding [46].
Using the ESP results, the AA molecule and DMSO molecule follow the placement of Fig. 1. ESP has been a popular function for revealing electrostatic interactions between substances [47].
We chose the FA-DMSO hydrogen-bonded dimer complex, which is similar to the AA-DMSO hydrogen-bonded dimer complex. We performed ESP computations, and the results were in 129 concordance with the results of Rohmann's study [48]. We also performed ESP calculations for hydrogen-bonded dimer complexes of AA with N-methyl-pyrrolidone (NMP) and AAdimethylformamide (DMF) (Fig. 2), both of which are polar, non-protic solvents with similar 132 dipole moments to DMSO [49]. The results and hydrogen bonding interaction sites are consistent with the results of Mu [50] and Safonova [51] et al. ESP accurately shows the hydrogen bonding action sites and effectively illustrates the electrostatic nature of hydrogen bonding.  According to the above results, we cannot explain the hydrogen bonding energy by van der Waals 165 gravity and chemical bonding gravity alone [59], nor can we explain the hydrogen bonding angle of (HF)2 by electrostatic interactions alone, since the van der Waals force is also an electrostatic interaction, and electrostatic interactions will only place the four atoms of (HF)2 in a straight line. 168 The results of Wolters [60] for hydrogen bonding between compounds containing halogens and (or collection of molecules) and its geometry [61], and we can represent the energy of a system as a function of geometric coordinates. We performed a PES scan of the AA-DMSO hydrogenbonded dimer complex using the calculation method in Section 0. In order to obtain the surface in 177 three-dimensional space to identify the directionality of the hydrogen bonds, the quantum chemical calculation selects only two variables: the hydrogen bond length L and its angle θ (Fig. 5(a)), so the energy E of the system is a function of L and θ.

Estimates of the Energy of Intermolecular Hydrogen Bonds:
Estimates of the energy of intermolecular hydrogen bonds can be characterized in several ways, of which the binding energy 195 (BE) is one of the most important quantities. The BE, as used herein, is equivalent to the "interaction energy" between two monomers in complex geometry. Quantum chemistry has become a routine and reliable method for estimating the BE of various hydrogen bonds [67]. For 198 example, a study evaluated the performance of DFT generalized functions in calculating the binding energy of furan clusters. The results showed that the functionals M05-2X and M06 are recommended for further affordable investigations of the furan clusters [68]. 201 In this section, the geometries of all three hydrogen-bonded dimer complexes (   Table 1)

CONCLUSION
In the work presented here, we have performed DFT calculations for the AA-DMSO hydrogen-