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 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 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 interactions 
[2], so weak intermolecular interactions have been of 

particular interest in chemistry [3-20], 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 
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, 23]. Hydrogen bonding 
is a frequent weak intermolecular interaction, similar to 
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, dipole-dipole. The 
formation of hydrogen bonds involves electron donors 
and electron acceptors, where the electron acceptors 

Mu R et al., Mong. J. Chem., 23(49), 2022, 19-26

https://doi.org/10.5564/mjc.v23i49.1407

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

Mu Ren1, Ao Rigele2, Na Shun3, Narantsogt Natsagdorj1*

1Department of Chemistry School of Mathematics and Natural Sciences, 
Mongolian National University of Education, Ulaanbaatar, 14191, Mongolia

2Academic Affairs, Hulunbuir University, Hulunbuir, 021108, China
3Agilent Technologies China Co., Ltd., Beijing, 100102, China

 * Corresponding author: Narantsogt@msue.edu.mn; ORCID ID: 0000-0002-1040-1276

Received: 23 March 2022; revised: 11 May; accepted: 19 May 2022   

ABSTRACT

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 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 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 
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 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. 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.

Keywords: Quantum chemistry, hydrogen bonding natures, acetic acid, dimethylsulfoxide 

Mongolian Journal of Chemistry 
www.mongoliajol.info/index.php/MJC

© The Author(s). 2022 Open access. This article is distributed under the terms of the Creative Commons Attribution 4.0 International License 
(http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give 
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19

https://doi.org/10.5564/mjc.v23i49.1407
https://orcid.org/0000-0002-1040-1276


Mu R et al., Mong. J. Chem., 23(49), 2022, 19-26

must be positively charged hydrogen atoms [5]. A more 
accurate calculation of hydrogen bonding from theory 
is an obvious way to understand hydrogen bonding, 
since experiments can be a complicating factor. 
Liu et al. performed AIMD calculations on the structure 
of hydrogen bonds in liquid water [24], Dereka et al. 
investigated (HF)2 hydrogen bonding using quantum 
chemical calculations combined with experimental 
methods [25], and Alkorta et al. described non-
covalent interactions in detail using quantum chemical 
calculations [26]. However, the definition of hydrogen 
bonding still seems to be vague.
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 (BSSE) [27] of DFT-D3(BJ) 
empirical dispersion correction [28]. 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 (MO) [29, 
30]; 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)-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.

EXPERIMENTAL
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 the theoretical basis of 
quantum chemical calculations [31, 32]. 
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 equation [33] or the DFT 
method [34-36] both seek approximations to solve the 
Schrödinger equation.
Molecular modeling: Molecular modeling is simply 
the theoretical methods and computational techniques 

used to model or simulate the behavior of molecules 
[37]. Each model is an approximate solution of the 
Schrödinger equation, which includes theoretical 
approaches and basis sets. The rapid development of 
computer technology and rapid advances in density 
general function theory and molecular dynamics theory 
have made theoretical calculations a powerful tool 
for studying intermolecular forces. In 1998, the Nobel 
Prize in Chemistry honored quantum chemists Pople 
and Kohn for their contributions to quantum chemistry. 
Pople’s approach to quantum chemical calculations 
and Kohn’s density functional theory are significant 
milestones in computational chemistry. Mhamad 
Chrayteh et al. used second-order perturbation theory 
(MP2), where aldehyde hydrogen atoms strongly 
interact with water oxygen atoms, in the case of di- and 
tri-hydrates [38]. Chen Jun et al. used density flooding 
theory (DFT) and molecular dynamics (MD) simulations 
to study the hydration mechanism of kaolinite surfaces 
[39]. Bilonda and Mammino performed calculations 
of intramolecular hydrogen bonding in matter using 
different theoretical approaches and basis sets [40]. 
Quantum chemical calculations played an essential 
role in all these studies.
Theoretically, the use of higher-level theoretical 
methods and more sophisticated basis sets can 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 qualitative forecast of hydrogen bonding in the 
AA-DMSO hydrogen-bonded dimer complex was found 
using the Gaussian16 quantum chemistry package 
[41] in the DFT calculations because the quantitative 
structure is not predicted.

RESULTS AND DISCUSSION
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 polarity, high electronegativity, and 
weak acidity. These functional groups are capable of 
hydrogen bonding by providing and accepting protons 
[42] and will produce strong hydrogen bonds with the 
polar non-protic solvent DMSO. 
Quantum chemical computations provide a good 
characterization of the intermolecular interactions and 
the sites of action. In this paper, structure-optimization 
and frequency calculations were performed separately 
for the AA molecule and the DMSO molecule using the 
M062X/6-311++G(3d,2p) [43, 44] method and the DFT-
D3BJ [28] dispersion correction, which includes NBO 
[45] analysis and characterization of the hydrogen 
bonding sites between the solvent AA molecule and the 
DMSO molecule. 

20

Ĥ Ψ = E Ψ #                               (1)



Mu R et al., Mong. J. Chem., 23(49), 2022, 19-26

The absence of imaginary frequencies is the end of the 
structural optimization-stable structure.
In Fig. 1, the different colors on the molecular surface 
correspond to the qualitative size of the surface 
electrostatic potential (ESP). Regions colored in red 
indicate the ESP is negative: electrons concentrate 
more in these locations and positively charged 
particles have stronger interactions. Regions colored in 
blue indicate the ESP is positive: negatively charged 
particles more favorably interact in these locations [46]. 
The maximum positive ESP value of the AA molecule 
concentrates in the upper portion of the carboxyl 
functional group (-OH), while the upper region of the 
S=O in the DMSO molecule has a negative ESP value; 
these two regions produce hydrogen bonding [47]. 
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 [48]. 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 concordance with the results 
of Rohmann’s study [49]. We also performed ESP 
calculations for hydrogen-bonded dimer complexes 
of AA with N-methyl-pyrrolidone (NMP) and AA- 
dimethylformamide (DMF) (Fig. 2), both of which are 
polar, non-protic solvents with similar dipole moments 
to DMSO [50]. The results and hydrogen bonding 
interaction sites are consistent with the results of Mu 
[51] and Safonova [52] et al. ESP accurately shows the 
hydrogen bonding action sites and effectively illustrates 
the electrostatic nature of hydrogen bonding.

Covalent nature of hydrogen bonds: 
HOMO/LUMO Interaction: HF is a typical hydrogen 
bonding system, and the structure-optimized geometry 
of the (HF)2 hydrogen bonding system according to 
previous reports [53-55] and using the computations of 
section 0 is shown in Fig. 3(b). The angles of F-H...F-H 
are θ1 = 113° and θ2 = 7.6°, and the four atoms not 
in a straight line, which matches the action site 
characterized by the ESP results of HF. However, the 
angle of action does not follow the results of the ESP 
(Fig. 3 (a)), and our computations are consistent with 
the studies of Řezac [55] and Howard [56]. 

Frontier molecular orbital theory, which incorporates 
highest occupied molecular orbital (HOMO) and lowest 
unoccupied molecular orbital (LUMO) calculations, 
is an important indicator for chemical reactions [57]. 
The formation of covalent bonds is the redistribution 
of electrons in the orbitals of frontier molecules when 
satisfying certain conditions [58, 59]. Following the 
arrangement of the AA-DMSO hydrogen-bonded dimer 
complex according to the hydrogen bonding sites, we 
used the calculation method in section 0 for structure 
optimization and frequency calculations. During the 
mapping of its molecular orbitals, we were able to 
determine the covalent natures of the AA-DMSO 
hydrogen bonding: the redistribution of electrons in 
the AA molecule LUMO+3 (Fig. 4(a)) and the DMSO 
molecule HOMO-1 (Fig. 4(c)) forms HOMO-4 in the AA-
DMSO hydrogen-bonded dimer complex (Fig. 4(b)).

According to the above results, we cannot explain the 
hydrogen bonding energy by van der Waals gravity and 

21

Fig. 1.  The hydrogen bonding site of AA with DMSO

Fig. 2. Hydrogen bonding sites for similar hydrogen-bonded 
dimer complex of AA and DMSO

Fig. 3.  Hydrogen bonding of (HF)2 (a) Site and direction of
(HF)2 interaction presumed by ESP, (b) Hydrogen 
bonding angle of (HF)2

Fig. 4.  Hydrogen bonding associated molecular 
orbials of the AA-DMSO hydr gen-bon ed dimer 
complex (a) LUMO+3 of the AA molecule, 
(b) HOMO-4 of the AA-DSO hydrogen-bonded 
dimer complex 



Mu R et al., Mong. J. Chem., 23(49), 2022, 19-26

chemical bonding gravity alone [60], 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. The results of Wolters [61] for hydrogen 
bonding between compounds containing halogens 
and our quantum chemical calculations indicate the 
involvement of covalent bonds in the hydrogen bonding 
interaction.
Directionality of hydrogen bonding: Potential energy 
surface (PES) determination is one of the central 
concepts in quantum chemical calculations. According 
to the Born-Oppenheimer approximation, a PES is a 
mathematical or graphical relationship between the 
energy of a molecule (or collection of molecules) and 
its geometry [62], and we can represent the energy of 
a system as a function of geometric coordinates. We 
performed a PES scan of the AA-DMSO hydrogen-
bonded dimer complex using the calculation method 
in Section 0. In order to obtain the surface in 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.

Fig. 5(b) shows the 3D PES of the system energy 
variation with hydrogen bond length L and angle θ. 
When the angle θ tends to 180° and the bond length L 
tends to 1.6 Å, the energy of the AA-DMSO hydrogen-
bonded dimer complex decreases, indicating that the 
AA-DMSO hydrogen-bonded dimer complex is more 
stable and the hydrogen bond strength is stronger [63-
66], further indicating the hydrogen bond is directional.
Directionality is an essential indicator of covalent 
bonds. The strength of covalent bonds between atoms 
is strongly dependent on an angle [67]. The three-
dimensional PES of the AA-DMSO hydrogen-bonded 
dimer complex demonstrate the directionality of 
hydrogen bonds and also indicate that hydrogen bonds 
have covalent nature.

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 (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 [68]. For 
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 [69].

In this section, the geometries of all three hydrogen-
bonded dimer complexes (Table 1) were fully optimized 
using the M06-2X exchange-correlation functional with 
DFT-D3(BJ) empirical dispersion correction. 

22

Fig. 5. Hydrogen bonding and three-dimensional PES 
of the AA-DMSO hydrogen-bonded dimer complex
(a) Hydrogen bond length L and angle θ of the 
AA-DMSO hydrogen-bonded dimer complex
(b) Hydrogen bonding PES of the AA-DMSO hy-
drogen-bonded dimer complex

Fig. 6. ESP for FA, AA, and TFA and the NPA charge of 
the hydrogen atoms of  FA, AA, and TFA involved in 
hydrogen bonding

Fig. 7.  Hydrogen bond lengths of FA-DMAO, AA-DMSO, 
and TFA-DMSO

Project FA-DMSO AA-DMSO TFA-DMSO

NPA charge (H atom)* 0.490 0.492 0.502

NPA charge (O atom)* -1.015 -1.015 -1.015

Hydrogen bond length (Å) 1.587 1.618 1.490

Hydrogen bond BE (kJ/mol) -61.743 -59.079 -73.955

Table 1. NPA charges of hydrogen bond atoms, hydrogen bond 
length, and energy

Notice: * NPA charge (H atom) is the NPA charge of the hydrogen 
atoms of FA, AA and TFA involved in hydrogen bonding.

* NPA charge (O atom) is the NPA charge of the oxygen 
atoms of DMSO involved in hydrogen bonding.



Mu R et al., Mong. J. Chem., 23(49), 2022, 19-26

For fully characterizing hydrogen bond interactions, 
we have utilized many other quantum chemical 
calculations in addition to BEs, such as the hydrogen 
bond length, the NPA charges of the atoms at the ends 
of the hydrogen bonds, and ESP.
Using correlations between various well-known 
hydrogen bond-related quantum chemical calculations 
and estimated BE values, we have shown that each 
of these quantum chemical calculations has its own 
ability to characterize the strength of hydrogen bond 
interactions. Our calculations have revealed that the 
higher the NPA charge difference of the hydrogen 
bond terminal atoms, the shorter the bond length.  
Additionally, larger hydrogen bond energy is observed 
with lower electron density of the electron acceptor 
as determined by ESP. We found from the strong 
hydrogen-bonded dimeric complexes that the electron 
acceptor of the hydrogen atom all contain atoms or 
groups of atoms with high electronegativity.

CONCLUSIONS
In the work presented here, we have performed DFT 
calculations for the AA-DMSO hydrogen-bonded 
dimer complex using ESP, HOMO/LUMO, PES, and 
estimated and compared the energy of hydrogen bonds 
of four related hydrogen-bonded dimer complexes. 
The quantum chemical calculations have revealed the 
natures of hydrogen bonding in the AA-DMSO hydrogen-
bonded dimer complex: electrostatic interaction is the 
main factor in the generation of hydrogen bonds, and 
the ESP can characterize the site of action of hydrogen 
bonds; the redistribution of electrons in molecular 
orbitals provides hydrogen bonding with a significant 
degree of chemical bonding character, which is one 
of the reasons why the hydrogen bonding energy is 
between chemical bonding and van der Waals forces, 
and the directionality of hydrogen bonding revealed 
by PES, and estimates of the energy of intermolecular 
hydrogen bonds is also consistent with this finding. 
Different interactions link the atoms in a compound, and 
these links do not have a clear demarcation line, but 
can be considered a mixture of multiple interactions. 
Therefore, on the premise that hydrogen bonding is 
a mixture of electrostatic interactions and covalent 
character, further in-depth study of the percentage of 
each interaction force is of more practical research 
significance than classifying hydrogen bonds.

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