Complexation of cyclodextrins with benzoic acid in water-organic solvents: A solvation-thermodynamic approach

Article abstract of DOI:10.3390/molecules26154408

The aim of this research is to obtain new data about the complexation between β-cyclodextrin (β-CD) and benzoic acid (BA) as a model reaction of the complex formation of hydrophobic molecules with cyclodextrins (CDs) in various media. This research may he

Full text of DOI:10.3390/molecules26154408

molecules
Article
Complexation of Cyclodextrins with
Benzoic Acid in Water-Organic Solvents:
A Solvation-Thermodynamic Approach
1
,
2
2
2
3
Tatyana R. Usacheva *, Vitaly A. Volynkin
, Viktor T. Panyushkin , Dmitry A. Lindt , Thi Lan Pham ,
4
3
1
1,5
1
Thi Thu Ha Nguyen
, Thi My Hanh Le , Diana A. Alister , Dzhovidon N. Kabirov
, Natalya N. Kuranova ,
George A. Gamov 1 , Roman A. Kushnir , Marco Biondi , Concetta Giancola
1
6
6
and Valentin A. Sharnin
1
1
Department of Inorganic Chemistry and Technology, Ivanovo State University of Chemistry and Technology,
53000 Ivanovo, Russia; matchoaa@mail.ru (D.A.A.); kabirov93.93@mail.ru (D.N.K.);
1
kuranova_nn@isuct.ru (N.N.K.); ggamov@isuct.ru (G.A.G.); oxt705@isuct.ru (R.A.K.); sharn@isuct.ru (V.A.S.)
Department of Chemistry and High Technologies, Kuban State University, 350040 Krasnodar, Russia;
vva@chem.kubsu.ru (V.A.V.); panyushkin@chem.kubsu.ru (V.T.P.); chem.lindt_d.a@mail.ru (D.A.L.)
Laboratory of Applied Research and Technology, Institute for Tropical Technology, Vietnam Academy of
Science and Technology, Hanoi 100000, Vietnam; ptlan@itt.vast.vn (T.L.P.); hanhltm76@gmail.com (T.M.H.L.)
Faculty of Chemistry, Hanoi National University of Education, Hanoi 100000, Vietnam; ntt.ha@hnue.edu.vn
Department of Pharmaceutical and Toxicological Chemistry, Avicenna Tajik State Medical University,
Dushanbe 734003, Tajikistan
2
3
4
5
6
Department of Pharmacy, University of Naples Federico II, 80131 Naples, Italy; mabiondi@unina.it (M.B.);
giancola@unina.it (C.G.)
ꢀ
ꢁꢂꢀꢃꢄꢅꢆꢇ
ꢀ
ꢁꢂꢃꢄꢅꢆ
*
Correspondence: oxt@isuct.ru
Citation: Usacheva, T.R.; Volynkin,
V.A.; Panyushkin, V.T.; Lindt, D.A.;
Pham, T.L.; Nguyen, T.T.H.; Le,
Abstract: The aim of this research is to obtain new data about the complexation between
β-
cyclodextrin ( -CD) and benzoic acid (BA) as a model reaction of the complex formation of hy-
β
T.M.H.; Alister, D.A.; Kabirov, D.N.;
Kuranova, N.N.; et al. Complexation
of Cyclodextrins with Benzoic Acid in
Water-Organic Solvents: A
drophobic molecules with cyclodextrins (CDs) in various media. This research may help developing
cyclodextrin-based pharmaceutical formulations through the choice of the appropriate solvent mix-
ture that may be employed in the industrial application aiming to control the reactions/processes in
liquid phase. In this paper, NMR results for the molecular complex formation between BA and
β-CD
Solvation-Thermodynamic Approach.
Molecules 2021, 26, 4408. https://
doi.org/10.3390/molecules26154408
(
[BA⊂β-CD]) in D O-DMSO-d and in D O-EtOH have shown that the stability of the complex in
2
6
2
the H O-DMSO-d varies within the experimental error, while decreases in H O-EtOH. Changes
2
6
2
in the Gibbs energy of BA resolvation in water and water–dimethylsulfoxide mixtures have been
obtained and have been used in the analysis of the reagent solvation contributions into the Gibbs
energy changes of the [BA⊂β-CD] molecular complex formation. Quantum chemical calculations of
Academic Editor: Georgia N. Valsami
the interaction energy between
and the energy of
β
-CD and BA as well as the structure of the [BA⊂β-CD] complex
Received: 11 June 2021
Accepted: 13 July 2021
Published: 21 July 2021
β
-CD and BA interaction in vacuum and in the medium of water, methanol and
dimethylsulfoxide solvents are carried out. The stability of [BA⊂β-CD] complex in H
O-EtOH and
2
H O-DMSO solvents, obtained by different methods, are compared. The thermodynamic param-
2
Publisher’s Note: MDPI stays neutral
with regard to jurisdictional claims in
published maps and institutional affil-
iations.
eters of the [BA⊂β-CD] molecular complexation as well as the reagent solvation contributions in
H O-EtOH and H O-DMSO mixtures were analyzed by the solvation-thermodynamic approach.
2
2
Keywords: benzoic acid; binary solvents; β-cyclodextrin; quantum chemical calculations; inclusion
complexes; NMR spectroscopy; stability constant; solvation-thermodynamic approach; thermody-
namic parameters
Copyright: © 2021 by the authors.
Licensee MDPI, Basel, Switzerland.
This article is an open access article
distributed under the terms and
conditions of the Creative Commons
Attribution (CC BY) license (https://
creativecommons.org/licenses/by/
1
. Introduction
Solvation plays a key role in all chemical and physico-chemical properties of solutions
as well as virtually all processes occurring in solution.
In the recent book Scientific Schools of Ivanovo Chemtech: Through the Prism of History [1],
O.I. Koifman et al. pointed that it is necessary to significantly expand the experimental
4
.0/).
Molecules 2021, 26, 4408. https://doi.org/10.3390/molecules26154408
https://www.mdpi.com/journal/molecules

Molecules 2021, 26, 4408
2 of 25
possibilities of thermodynamic and molecular-kinetic approaches to the study of solvate-
thermodynamic effects in liquid systems.
In recent studies [2,3], we have reported on the effect of reagents solvation on amine
stability, the effect of reagents solvation on changes in the stability of amine, carboxylate,
and coronate complexes of d-metal ions, as well as the thermodynamic characteristics of
complexation reactions in water–organic solvents. General demonstrated trends in the
changes of the thermodynamic characteristics of reactions allow us to predict modifications
in the stability and the energy of coordination compounds that, in turn, depend on the
solvation of reagents. Furthermore, the analysis of data on the thermodynamics of complex-
ation reactions of the “metals of life” (e.g., silver (I), copper (II), iron (III), etc.) with selected
members of class B vitamins (nicotinamide, nicotinic acid) allows for the isolation of the
solvation contribution of the ligand reaction centers [4,5]. The use of results for binary mix-
tures of non-aqueous solvents allows to move away from water and its unique properties,
thereby showing which solvation contributions determine the changes in the stability of
the coordination compound and the energy of the reaction during the transition from one
organic solvent to another [6,7]. The analysis of molecular complexation reactions of crown
ethers and cryptands with amino acids and peptides shows that the solvation contributions
of the host and guest molecules play a different role on the change of the coordination
compound and the energy of the reactions [8,9]. To predict the shift of equilibrium in the
reactions of biologically active molecules, it is necessary to extend the knowledge of solvent
influence on these processes. In this context, the aim of this research is to obtain new data
of the complexation between β-cyclodextrin (β-CD) and benzoic acid (BA) as a model
reaction of the complex formation of hydrophobic molecules with cyclodextrins (CDs) in
various media. CDs are cyclic oligosaccharides with a lipophilic internal molecular cavity
and a hydrophilic external surface bearing hydroxyl group. Due to their structure, CDs
can form water-soluble inclusion complexes with various hydrophobic molecules. The
different influence of water and non-aqueous media on molecular complexation suggests
the possibility to improve CDs ability to enhance the apparent solubility of hydrophobic
molecules by changing the solvent as a medium of occurring processes.
Thus, this research may help developing CD-based pharmaceutical formulations
through the modulation of the appropriate solvent mixture that would thus be employed
in the industrial field as a means to control the reactions/processes carried out in liquid
phases.
The formation of [BA⊂β-CD] molecular complex in solution is described by the
following pseudo-chemical equation:
BAsolv + β-CDsolv ↔ [BA⊂β-CD]solv
The set of new data obtained for the reaction (1) and reported in this paper includes:
NMR data for the complexation of benzoic acid with -cyclodextrin in D O-DMSO-
(1)
-
-
-
β
2
d and in D O-EtOH, the stability constants of [BA⊂β-CD] molecular complexes
6
2
calculated from NMR results;
Changes in the Gibbs energy of benzoic acid resolvation at the transfer from water to
water–dimethylsulfoxide solvents obtained by a method of interfacial distribution of
the substance between two immiscible phases;
Quantum chemical calculations of the interaction energy between
β-CD and BA
and the structure characteristics of the benzoic acid complex with
vacuum and in water, methanol and DMSO.
β-cyclodextrin in
The stability of the [BA⊂β-CD] complex in water–ethanol and water–DMSO, obtained
by different methods are compared. The thermodynamic parameters of the [BA⊂β-CD]
molecular complexation as well as the reagent solvation contributions to the equilibrium of
[
BA⊂β-CD] complexation in water–ethanol and water–DMSO solvents have been analyzed
by using the solvation/thermodynamic approach.

Molecules 2021, 26, 4408
3 of 25
2. Results
1
2
.1. H NMR Studies of Inclusion Complex Formation of Benzoic Acid with β-Cyclodextrin in
D O, D O-DMSO-d and D O-EtOH
2
2
6
2
NMR spectroscopy is one of the most important and useful methods to investigate
the structure, stability and stoichiometry of host–guest complexes. It provides direct and
detailed observation of individual nuclei relevant to the structure and dynamics of the
system. The inclusion complexes are formed mainly due to weak interactions (hydrogen
bonds, van der Waals forces, etc.), therefore complexation induces relatively small chemical
shifts. The most shifted signals in NMR spectrum of complex usually correspond to
“
interacting” atoms in “host” and “guest” molecules that are close in space. For example,
in -cyclodextrin protons H4 and H2 of the glucopyranose residues are located on the
β
outer side, and protons H3 and H5 on the inner side of the macrocyclic cavity (Figure 1).
Therefore, the predominant shifts of H3 and H5 protons (Figure 2) suggest the inclusion of
1
13
a “guest” molecule into β-CD cavity. By treating the dependencies of observed H (or C)
chemical shifts from the “host” to “guest” ratio it is possible to obtain the data for stability
and stoichiometry of the complexes formed.
Figure 1. Schematic representation of the β-CD molecule and atom numbering in a single glucopyranose unit.
1
Figure 2. H NMR spectrum of β-CD.

Molecules 2021, 26, 4408
4 of 25
Prior to the studies on the formation of inclusion complexes in mixed solvents, a
reference experiment was carried out in D O solution. It consisted of a series of seven
2
points with the different
chemical shifts of -CD are given in Table 1 and Figure 3. Labels H1, H2, H3, H4, H5 and
H6 refer to the proton position in a glucopyranose unit of -CD molecule (Figures 1 and 2).
µ = CBA/Cβ-CD ranging from 0 to 1.4. The observed relative
β
β
Table 1. The observed chemical shifts of
different “host”–“guest” ratio (relative to the β-CD).
β
-CD protons for the [BA⊂β-CD] system in D O at the
2
∆
, ppm
CBA/Cβ-CD
H1
H5
H6
H3
H2
H4
0
0
0
.4
.6
.8
−0.017
−0.025
−0.028
−0.032
−0.038
−0.04
−0.082
−0.091
−0.1071
−0.1245
−0.145
−0.147
−0.014
−0.027
−0.0273
−0.0307
−0.027
−0.029
−0.065
−0.1
−0.019
−0.028
−0.031
−0.037
−0.044
−0.045
−0.01
−0.015
−0.016
−0.019
−0.022
−0.024
−0.118
−0.137
−0.159
−0.162
1
1
1
.2
.4
As shown in Figure 3, the inner protons H5 and H3 are the most affected among all
the β-CD protons. This confirms the inclusion of a “guest” molecule into the β-CD cavity.
Figure 3. NMR titration curves of the β-CD by BA in D O.
2
The proximity of the BA aromatic ring to the inner side of β-CD cavity contributes to
magnetic anisotropy and shielding effect leading to the upfield shift for H5 and H3 protons
of β-CD.
In turn, aromatic protons of BA show perceptible downfield shift, which can be
explained by the de-shielding effect of nearby electronegative oxygen atoms arranged
inside
evidence of the guest positioning into the cavity of
chemical shifts are usually interpreted as the almost full inclusion of the benzene ring of BA
molecule into -CD cavity, while BA carboxylic group is located outside the cavity [11 13].
β-CD cavity. Such a simultaneous chemical shift change could be considered as an
β-CD [10]. Close values of H5 and H3
β
–
These observations are in satisfactory agreement with the results of our calculations.
The pattern in the observable chemical shifts changes for the different host to guest ratio
assumes the formation of a 1:1 complex. To prove this hypothesis, an additional experi-
ment using Job’s method of continuous variation was carried out. It is the simplest and
most intuitive method to prove the stoichiometry when only one type of the complex is

Molecules 2021, 26, 4408
5 of 25
formed [14
–
16]. The Job’s plot for the [BA⊂β-CD] system is shown on Figure 4. Maximum
at the point [H]/([H] + [G]) = 0.5 confirms the 1:1 complex formation.
Figure 4. 1H NMR Job’s plot for the [BA⊂β-CD] system in D O (Shifts refer to
β-CD H5 chemical
2
shifts).
The next part of the work is devoted to the study of the inclusion complex formation
between β-cyclodextrin and benzoic acid in D O-DMSO-d .
2
6
A preliminary series for X(DMSO-d6) = 0.24 mol. fr. showed no changes of protons
chemical shifts both for -CD and BA. The maximum change observed for H5 was 0.01 ppm
β
that is within the experimental error. In a series with a molar fraction of 0.15 the statistically
significant changes of chemical shifts were observed, but the processing of this data gave
unreliable results. Therefore, this series was excluded from further investigation and only
series with molar fractions of DMSO-d equal to 0.05, 0.075 and 0.10 were included. The
6
series with X(DMSO-d6) = 0.075 mol. fr. was carried out in an extended range of BA-
β
-CD
1
ratio from 0.2 to 2.5. All the raw data on H chemical shifts for all treated series are given
in the Supplementary Materials except for the NMR titration curves for X(DMSO-d6) = 0.05
mol. fr. presented below (Figure 5).
These data clearly indicate that with an increase of X(DMSO-d6) in the solvent, the
observed chemical shifts tend to decrease (mostly H3 and H5 of β-CD, and to a lesser
extent BA protons). We assume that this is due to an increased BA solvation in DMSO-d6
and competition between solvation and inclusion complex formation processes.
In order to determine the parameters of inclusion complex formation process (the
binding constants and the complexation-induced chemical shifts), the data obtained for all
the series (in water and mixed solvents) were fitted by the nonlinear least squares method
assuming the one-stage complexation model according to the following equation:

s

ꢀ
ꢁ
2
∆GH
2
1
1


∆obs
=
· 1 + µ +
−
1 + µ +
− 4µ
(2)
K·CH
K·CH
where ∆obs is the observable chemical shift, ∆GH the complexation induced chemical shift
of -CD proton, C the concentration of -CD and = CBA/Cβ-CD. To improve the fitting
results, accuracy chemical shift dependencies for both H5 and H3 protons of -CD were
treated simultaneously. Figure 6 shows the fitting results for the treatment of NMR titration
curves of the BA -CD system in D O-DMSO-d (X = 0.05 mol. fr.). Pearson’s
correlation coefficient for H3 and H5 is 0.996 and 0.997, respectively.
β
β
µ
H
β
β
2
6
(DMSO-d6)

Molecules 2021, 26, 4408
6 of 25
Figure 5. NMR titration curves for BA-β-CD system in D O-DMSO-d (X
= 0.05 mol. fr.).
2
6
(DMSO-d6)
Figure 6. Fitting results for NMR titration curve for BA-β-CD system in D O-DMSO-d6
2
(
X(DMSO-d6) = 0.05 mol. fr.).
Calculation results for D O and D O-DMSO-d are summarized in Table 2. The
2
2
6
increase of DMSO molar fraction leads to a monotonic decrease of the induced chemical
shifts and binding constants. This may be due to an increase of BA solvation in DMSO-d6
and the competition between solvation and inclusion complex formation processes. These
results are consistent with the assumption made above as well as with the data obtained by
other methods.
The next three series were investigated in D O-EtOH mixed solvent. Due to the use
2
1
of non-deuterated ethanol, the EtOH signals in H NMR spectra were very intensive and,
in most cases, partially overlapped with some β-CD signals. A molar fraction of ethanol
in a mixed solvent was set to 0.05, 0.075 and 0.10. The further increase of EtOH content
prevented accurate measurement of chemical shifts in spectra even when we used various
signal suppression techniques, thus X(EtOH) = 0.10 mol. fr. was set as a practical upper
limit in these series. The observed chemical shifts and NMR titration curves for the BA
and
shows the data for all
highest chemical shifts changes, which is consistent with previous series and confirms the
β-CD in the case (X(EtOH) = 0.075 mol. fr.) are shown in Table 3 and Figure 7. Table 3
β
-CD and BA protons. The H3 and H5 protons of -CD have the
β

Molecules 2021, 26, 4408
7 of 25
inclusion of the “guest” into
β-CD cavity. Benzoic acid protons 2, 6 and 4 have chemical
shifts bigger than protons 3 and 5 that are close to the carboxylic group of BA. The most
likely it would be explained if only “bottom” part of benzene ring is immersed in
cavity while the carboxylic group of BA protrudes from cavity.
β-CD
Table 2. Binding constants and complexation induced chemical shifts for [BA⊂β-CD] inclusion com-
plex in D O solution and in D O-DMSO-d mixed solvent with different molar fractions X(DMSO-d6).
2
2
6
−
1
X(DMSO-d6), mol. fr.
K, M
∆(H5), ppm
∆(H3), ppm
0
388.5
368.6
157.5
30.8
−0.1986
−0.0900
−0.1013
−0.1068
−0.2147
−0.1409
−0.1537
−0.1963
0
0
0
.05
.075
.10
X(DMSO-d6), mol. fr.
K
∆(H5)
∆(H3)
0
388.5
368.6
157.5
30.8
−0.1986
−0.0900
−0.1013
−0.1068
−0.2147
−0.1409
−0.1537
−0.1963
0
0
0
.05
.075
.10
Table 3. The observed complexation induced chemical shifts for the [BA⊂β-CD] solution in D O-
2
EtOH at the X(EtOH) = 0.075 mol. fr. and different “host”–“guest” ratio.
∆
(BA), ppm
4
∆(β-CD), ppm
CBA/Cβ-CD
2
,6
3,5
H1
5H
H6
H3
H2
0
0
0
0
.2
.4
.6
.8
0.0058
0.0118
0.0132
0.0122
0.0116
0.0056
0.0149
0.0101
0.0167
0.0096
0.0604
0.0699
0.0591
0.0589
0.0514
0.0469
0.0460
0.0466
0.0426
0.0337
0.0399
0.0396
0.0339
0.0354
0.0311
0.0318
0.0316
0.0293
0.0319
0.0219
−
−
−
−
−
−
−
−
−
−
0.0113
0.0145
0.0233
0.0246
0.0272
0.0267
0.0236
0.0258
0.0308
0.0304
−
−
−
−
−
−
−
−
−
−
0.0256
0.0421
0.0567
0.0664
0.0722
0.0779
0.0809
0.0837
0.0839
0.0883
−
−
−
−
−
−
−
−
−
−
0.0162
0.0232
0.0329
0.0332
0.0325
0.0386
0.0394
0.0419
0.0358
0.0381
−
−
−
−
−
−
−
−
−
−
0.0172
0.0269
0.0390
0.0479
0.0529
0.0552
0.0549
0.0562
0.0579
0.0629
−
−
−
−
−
−
−
−
−
−
0.0081
0.0089
0.0165
0.0138
0.0154
0.0091
0.0081
0.0120
0.0145
0.0141
1
1
1
1
1
.2
.4
.6
.8
2
Figure 7. NMR titration curves of the β-CD by BA in D O-EtOH (X(EtOH) = 0.075 mol. fr.).
2

Molecules 2021, 26, 4408
8 of 25
The data obtained were used in calculations of the binding constants and complexation-
induced chemical shifts for each D O-EtOH molar ratio using the same procedure as for D O
2
2
and D O-DMSO-d series. Calculations were carried out for a 1:1 complexation model while
2
6
simultaneously treating two protons H3 and H5. A two-stage complexation model with one
BA and two -CD molecules was also tested, but it was proven to be erroneous. The results
β
are displayed in Table 4. The increase of the molar fractions of ethanol in the solvent mixture
leads to decrease of the binding constant as observed for the D O-DMSO-d series.
2
6
Thus, we can conclude that both DMSO-d and EtOH in mixed solvent compete with
6
BA for the β-CD cavity. On the other hand, despite these components decrease the values
of binding constants in solution, we found they could favor the formation of inclusion
complexes as they significantly increase the yields when we prepared the complexes in the
solid state.
Table 4. Binding constants and complexation-induced chemical shifts of
β-CD for the [BA⊂β-CD]
system in O-EtOH with the different molar fractions X(C2H5OH)
.
−
1
X(EtOH), mol. fr.
K, M
∆(H5), ppm
∆(H3), ppm
0
388.5
292.3
249.4
193.1
−0.1986
−0.1341
−0.0750
−0.1201
−0.2147
−0.1851
−0.1179
−0.1499
0
0
0
.05
.075
.10
X(EtOH), mol. fr.
K
∆(H5), ppm
∆(H3), ppm
0
388.5
292.3
249.4
193.1
−0.1986
−0.1341
−0.0750
−0.1201
−0.2147
−0.1851
−0.1179
−0.1499
0
0
0
.05
.075
.10
2
.2. Quantum Calculation Results
.2.1. Geometry Optimization and Properties of β-CD and BA
The optimized structures of -CD and BA obtained with the GFN2-xTB method are
presented in Figure 8. As for the -CD structure, the outer diameters range from 13.33 to
4.36 Å, while the inner diameter was found to be 7.78 Å, which is in good agreement with
the literature [17].
2
β
β
1
Figure 8. Optimized structures of:
white—H; all key distances are in Å.
β-CD (a) and BA (b) calculated by GFN2-xTB method. Colors: grey—C, red—O,
2
.2.2. [BA⊂β-CD] Complex Formation
From iMTD-GC sampling results, we optimized and calculated the interaction energy
for three [BA⊂β-CD] configurations: (i) the “head first” configuration (denoted as HF), in

Molecules 2021, 26, 4408
9 of 25
which the BA molecule is vertically located with the –COOH group pointed towards the CD
cavity (Figure 9a); (ii) the “parallel” configuration (denoted as PR) in which the BA molecule
is parallelly located to the CD (Figure 9b); and (iii) the “tail first” configuration (denoted as
TF), corresponding to the vertical position of BA with the phenyl group pointed towards
the CD cavity (Figure 9c). All xyz coordinate files of the structures shown in Figures 8 and
9
can be found in the Supplementary Materials. Comparison and evaluation of interaction
energy will reveal which interaction configuration is favored. Table 5 shows the calculated
interaction energy for the HF, PR and TF configurations in vacuum and in different solvents
(in water, methanol and DMSO). Methanol has been selected as the simplest representative
of the homologous series of monohydric alcohols.
Figure 9. Three [BA⊂β-CD] interaction configurations: (a) HF, (b) PR and (c) TF.

Molecules 2021, 26, 4408
10 of 25
Table 5. The interaction energy (Eint) corresponding to the formation of three [BA⊂β-CD] interaction
configurations in different solvents.
Configuration
HF
PR
TF
in vacuum
in water
Eint,kJ mol 1
Eint,kJ mol 1
Eint,kJ mol 1
Eint,kJ mol 1
−
−59.09
−44.41
−32.61
−2.54
−60.20
−38.27
−25.44
−8.32
−102.86
−53.29
−33.30
−19.09
−
in methanol
in DMSO
−
−
The results show that the formation of the TF configuration corresponds to the most
negative interaction energy value in the vacuum, as well as in all solvents. In other
words, in all cases, the TF is the most preferred configuration. The increase in Eint in
solvents compared with that in vacuum likely results the solvation effect, which reduces
the interaction between β-CD and BA.
Analysis of the influence of the solvent on the interaction between
shows that the Eint decreases in the order: vacuum > water > methanol > DMSO. This
indicates that -CD and BA interact most strongly in vacuum. The presence of a solvent
considerably reduces the interaction between -CD and BA. Furthermore, among the
β-CD and BA
β
β
investigated solvents, water is the most favorable for the complexation, whereas DMSO is
much less preferable. This finding allows us to predict that in a binary solvent consisting
of water and an organic solvent such as methanol or DMSO, as the organic solvent content
increases the stability of the complex will decrease.
The Eint values for all examined interaction configurations in vacuum and solvents
−
1
are not excessively negative, ranging from
−
2.54 to
−
102.86 kJ mol . As a result, the
interaction between -CD and BA can be considered as a physical interaction, which is
β
mainly governed by non-covalent interactions such as dispersion interaction and hydrogen
bonding (as shown by the dot lines in Figure 9). It should be emphasized that, in the GFN2-
xTB method, the parameters were specifically optimized for non-covalent interactions.
To get further insight into the nature of the host-guest interaction, significant changes
in geometrical parameters and electronic properties of the BA molecule before and after
the interaction with CD have been analyzed. The results are shown in Table 6.
Table 6. Geometrical and electronic properties of the isolated BA and the BA in the TF configurations.
BA in TF
in Vacuum)
BA in TF
(in Water)
BA in TF
(in Methanol)
BA in TF
(in DMSO)
Parameter
BA
(
d(H1-O2), Å
BO(H1-O2)
d(O2-C4), Å
0.969
0.868
1.344
180.00
179.88
0.000
0.988
0.803
1.331
175.96
161.72
−0.021
0.977
0.798
1.326
178.70
174.20
0.007
0.974
0.824
1.330
178.89
179.99
0.008
0.974
0.818
1.334
176.97
177.97
0.004
<
<
H1O2C4C5, degree
O3C4C5C6, degree
q(BA), e
Compared to the non-complexed molecule, the structure of BA slightly changes when
placed in the cavity of -CD. The most significant difference in geometrical structure of BA
before and after interacting with -CD is obtained for H1O2C4C5 and O3C4C5C6 dihedral
β
β
angles and the H1-OH bond length. The COOH group of BA slightly turns away from the
plane of the benzene ring while the H1-OH bond is elongated. As for TF configuration in
vacuum, the H1-O (in the -CH OH group of β-CD) bond length is 1.847 Å, which is quite
2
close to the hydrogen bond lengths in the BA-BA dimer structure (1.66–1.83 Å) [18]. In
this case, the charge transfer from β-CD to the BA molecule is remarkable compared to

Molecules 2021, 26, 4408
11 of 25
that in the presence of solvents. This is ascribable to the formation of the hydrogen bonds
between
bonds between
with the calculated interaction energy for the TF configurations in solvents. The E for the
β-CD and BA in the vacuum. However, in the presence of solvents, the hydrogen
β-CD and BA are not clearly observed. This finding is in good agreement
int
−
19.09 kJ mol in the DMSO solvent, which
is much higher than the Eint in the vacuum (−102.86 kJ mol ).
1
TF configuration was determined to be only
−
−
1
2.3. Interfacial Distribution-Study of Reagents Solvation State
The calculation of the distribution coefficients of benzoic acid between immiscible
phases such as water–dimethylsulfoxide and n-hexane, and the change in the Gibbs en-
ergy during its transfer from water to water–dimethylsulfoxide solvents were carried out
according to the equations:
K = [BA]Hex/[BA]H2O
(3)
(4)
(5)
1
K = [BA]Hex/[BA]H2O-DMSO
2
0
H2O-DMSO
= RTln([BA]H2O/[BA]H2O-DMSO) = RTlnK /K1
2
∆
trG (BA)
The equilibrium concentrations of benzoic acid in aqueous and mixed solutions of
BA]H2O and [BA]
H2O-DMSO
were calculated by KEV software [19] using the corresponding
[
Hex
dissociation constants [20]. In the n-hexane layer ([BA] ) was calculated as the difference
between the total concentration of benzoic acid and the total concentration of benzoic acid
in the aqueous–organic layer after mixing with hexane, assuming that the volume of the
reaction medium remained constant during the experiment.
The errors are reported as the standard deviation for 3–5 parallel experiments. The
0
values of the Gibbs energy of benzoic acid change (∆trG (BA)) were assumed to be stan-
dard values, due to the low concentration conditions and the absence of concentration
dependences of the distribution coefficients of benzoic acid in the experimental conditions.
The concentration conditions of the experiments, the distribution coefficients of BA
in the Hex-H O and Hex-H O-DMSO systems and the Gibbs energy change of benzoic
2
2
0
acid are shown in Table 7. The ∆trG (BA) values have been used in the analysis of the
reagent solvation contributions into the Gibbs energy changes of the [BA⊂β-CD] molecular
complex formation (Section 3.3).
Table 7. Concentration conditions of experiments, distribution coefficients and changes in the Gibbs
0
energy change of benzoic acid (∆trG (BA)) in the Hex-H O and Hex-H O-DMSO systems, T = 298.2 K.
2
2
H2O-DMSO
4
[BA]Hex × 105,
0
[
BA]
∆trG (BA),
XDMSO, mol. fr.
.0
K1
K2
×
10 , mol/L
mol/L
kJ/mol
4
4
.108
.058
6.860
7.078
0
0.17
-
0
5
.422
4.289
4.666
4.470
0
.05
5.380
-
-
0.08
0.07
0.11
0.08
0.10
−1.70
−2.07
−1.12
−1.91
−1.35
5.421
6
.387
4.592
4.905
4.696
0
.1
6.356
6.376
5.320
5.478
5.975
5.875
0
.15
5.271
5.280
5
.371
4.731
4.287
4.176
0
.2
.3
5.415
-
-
5.426
5.410
5.452
6.393
4.262
0
5.316
.529
5

Molecules 2021, 26, 4408
12 of 25
3. Discussion
3
.1. Thermodynamic Parameters of the [BA⊂β-CD] Complexes Formation in H O-DMSO and
2
H O-EtOH Solvents
2
The thermodynamic characteristics of the formation of complexes of inclusion of
cyclodextrins with BA and its derivatives in water and the structure of the resulting
complexes in the crystalline state are presented in numerous literature sources [10 12 21
]. Most of them indicate the formation of complexes with a 1:1 stoichiometric ratio due to
the predominance of van der Waals interactions and H-binding between guest molecules
and CDs. The complexation of native and hydroxypropylated -, - and -cyclodextrins
–
, –
43
α
β
γ
with benzoic acid and its derivatives has been studied in aqueous solution by isothermal
1
calorimetry titration, densimetry, H NMR and UV spectroscopy at 298.15 K [10
,21
–26]. In
1
13
addition, NOE, H NMR and C NMR were used to study the structure of cyclodextrin
inclusion complexes with benzoic acid and its derivatives [11,30,40].
Computational chemistry methods were used to study the structure and stability
of inclusion complexes involving cyclodextrins [39
calculations performed in [38 44] using the AM1 method for the inclusion complexes
of -and -cyclodextrins with benzoic acid and phenol show that the complexes of
cyclodextrin with both “guest” molecules in the “substituent groups” position are more
,40,44]. The results of semi-empirical
,
α
β
α-
stable than in the “benzene ring first” position, while the complex of
phenol in the “benzene ring-first” position is more stable
β-cyclodextrin with
β-CD inclusion complex with benzoic acid was crystallographically characterized [10].
Two
β
-CD co-crystallize with two BA molecules, 0.7 ethanol molecules and 20.65 water
2(C7H6O2) 0.7 (C2H6O) 20.65H2O].
-CD forms dimers O-2(m)_1/O-3(m)_1· · · O-2(n)_2/O-3 (n)_2, stabi-
lized by direct hydrogen bonds (intradimer) and indirect hydrogen bonds O-6(m)_1· · · O-6
n)_2 with one or two water molecules bound together (interdimer).
molecules in the triclinic space group [2(C6H10O5)
In the crystal lattice,
·
7
·
·
·
β
(
The thermodynamic parameters (lgK , ∆rH , ∆rG , T∆rS0) of the complexation of
0
0
0
BA with -CD in the H O-DMSO and H O-EtOH mixtures are displayed in Table 8. The
β
2
2
values of the stability constants of the inclusion complex [BA⊂β-CD] in water obtained
by different methods are in satisfactory agreement with each other and with the literature
data reported for similar experimental conditions.
Thermodynamic parameters of the [BA⊂β-CD] complexes formation in [45] were
calculated by the HEAT program [46]. Mathematical processing of experimental data
by the HEAT was also successfully used in the study of the formation of low stability
molecular and ionic complexes formed by macrocyclic 18-crown-6 ether in water–organic
solvents [47,48].
The ranges of the molar fractions of DMSO and EtOH in water–organic solvents were
limited due to the lowest complex stability in mixed solvents than in water and hence
making it impossible to calculate reliable thermodynamic parameters for [BA⊂β-CD]
molecular complex in mixed solvents with high concentration of DMSO or EtOH. Despite
these limitations, the obtained results allowed to analyze the effect of the cosolvent on the
change in the thermodynamic parameters of the reaction (1).
It was found that from 0.00 to 0.05 mol. fr. Of DMSO the stability of the [BA⊂β-CD]
complex slightly decreases, and a further increase in the DMSO content to 0.10 mol. fr.
0
leads to a change in the values of lgK within the experimental error (Table 8). We also
observe that the formation of the [BA⊂β-CD] complex becomes slightly less exothermic.

Molecules 2021, 26, 4408
13 of 25
Table 8. Thermodynamic parameters for the reaction of formation of [BA⊂β-CD] complexes (lgK0, ∆rH , ∆rG and T∆rS )
0
0
0
in H O-DMSO and H O-EtOH solvents of variable composition at T = 298.15 K.
2
2
–
∆rH0
–∆rG0
–T∆rS0
kJ mol
X, mol. fr.
lgK0
Experimental Method
Reference
–1
–1
–1
kJ mol
kJ mol
13.7 ± 0.6
10.6 ± 0.8
11.3
Isothermal titration
calorimetry (pH 3.6)
UV–Vis spectroscopy
2
.4 ± 0.10 (2)
12.2 ± 0.5
−1.5 ± 0.6
[45]
[45]
[37]
1
.85 ± 0.16 (3)
-
-
-
-
(
pH 3.6)
Solubility method (pH
.9)
1.94 (1)
0
.00
2
Isothermal titration
calorimetry (acidic
medium)
Circular dichroism
spectroscopy
2
.60 ± 0.10 (2)
13.4 ± 0.4
22.3 ± 0.8
14.7 ± 0.7
−1.3 ± 0.8
[21]
[49]
2
.50 (5)
14.4
7.9
1
H NMR (acidic
medium)
1H NMR
2
.50 (4)
.59 (4)
-
-
-
14.2
14.8
-
-
-
[12]
This work
[12]
2
Densitometry (acidic
medium)
Isothermal titration
calorimetry
2
.40 ± 0.2 (6)
.10 ± 0.4 (2)
13.5 ± 1.1
2
32 ± 2.7
12 ± 0.5
H2O-DMSO
9.5 ± 0.36
10.2 ± 0.2
11.07
20
[36]
Isothermal titration
calorimetry (pH 3.6)
UV–Vis spectroscopy
1
.67 ± 0.2 (2)
.78 ± 0.2 (3)
16.8 ± 0.3 *
-
7.3 ± 0.47 *
[45]
[45]
[45]
0
.05
1
-
(pH 3.6)
Isothermal titration
calorimetry (pH 1.65)
1H NMR
(
2)
1
.94 ± 0.45
16.9 ± 1.4
5.2
(
4)
2
.57
-
-
14.7
-
-
-
This work
This work
(
4)
1
0
.075
2.2
H NMR
Isothermal titration
calorimetry (pH 3.6)
UV–Vis spectroscopy
1
1
1
.86 ± 0.41 (2)
.86 ± 0.41 (3)
10.9 ± 0.9 *
10.9 ± 0.9
10.9 ± 0.9
0.3 ± 1.3 *
[45]
[45]
0
.10
-
-
(pH 3.6)
Isothermal titration
calorimetry (pH 1.65)
1H NMR
(
2)
.85 ± 0.32
10.1 ± 0.2
10.6 ± 0.9
8.5
–0.5
-
[45]
(
4)
1
.49
-
This work
H2O-EtOH
(
4)
4)
1
0
.05
2.47
2.40
-
-
-
-
-
-
H NMR
H NMR
This work
This work
(
1
0
.075
Isothermal titration
calorimetry (pH 3.6)
1H NMR
(
2)
1
.90 ± 0.10
36.8 ± 0.2
-
10.8 ± 0.6
-
26.0 ± 0.7
-
[50]
This work
[50]
0
.10
.20
(
4)
2
.29
Isothermal titration
calorimetry (pH 3.6)
(5)
0.70 ± 0.10 (2)
0
44.3 ± 0.6
3.9 ± 0.6
40.4 ± 0.8
(1)
Phase solubility method; Isothermal calorimetry of titration; (3) UV spectroscopy; (4) 1H NMR spectroscopy; Circular dichroism
(2)
spectroscopy; ( Densitometry; * calculated using the HEAT program taking into account the lgK values obtained from the UV-Vis
6)
0
spectroscopy.
An increase in the EtOH content in the H O-EtOH solvent to 0.20 mol. fr. leads to a
2
decrease in the stability of the [BA⊂β-CD] complex. At the same time, the exothermicity
of complexation increases, which is accompanied by an increase in the numerical values of
the entropy component of the change in the Gibbs energy of complexation. With a molar
fraction of ethanol X(EtOH) = 0.20 mol. fr. the enthalpy and entropy contributions to the
change of Gibbs energy compensate each other, which leads to a decrease in the stability of
0
the complex to lgK = 0.70 ± 0.10.

Molecules 2021, 26, 4408
14 of 25
The analysis of the effect of the compositions of the H O-EtOH and H O-DMSO
2
2
solvents on the stability of the molecular complex [BA⊂β-CD] shows that the stability of
the complex in the H O-DMSO varies within the experimental error, while decreases with
2
increasing of ethanol content in H O-EtOH solvents.
2
The changes in the stability of the molecular complexes [BA⊂β-CD] were compared
with those of the molecular complexes of 18-crown-6 ether (18C6) with glycyl–glycyl–
glycine (3Gly), [3Gly18C6] [51
Phe18C6] [55 56] during the transfer from water to water–organic solvents (Figures 10 and
1). These objects were selected for comparison of the “guest–host” molecular complexes
,52], glycine (Gly), [Gly18C6] [53,54] and phenylalanine (Phe)
[
,
1
formation in aqueous-organic solvents. However, we observed a different effect of solvents
on these processes: the increase of EtOH and DMSO concertation leads to increasing of
the stability of the molecular complexes [3Gly18C6], [Gly18C6] and [Phe18C6]. On the
contrary, the stability of [BA⊂β-CD] decreases.
Figure 10. Effect of H O-EtOH solvents on the stability of molecular complexes: 1—[BA⊂β-CD];
2
2
—[3Gly18C6], [51,52]; 3—[Gly18C6], [53]; 4—[Phe18C6], [56].
Figure 11. Effect of H O-DMSO solvents on the stability of molecular complexes: 1—[BA⊂β-CD];
2
2
—[3Gly18C6], [52]; 3—[Gly18C6], [54]; 4—[Phe18C6], [57].
Previous studies [51
,
52
,
56
–
59] showed that the stability of complexes tends to increase
0
as the content of non-aqueous components of solvents increases in line: lgK [Phe18C6] <
0
0
lgK [Gly18C6] < lgK [3Gly18C6].

Molecules 2021, 26, 4408
15 of 25
The changes in the enthalpy of the reactions of the formation of complexes [BA⊂β-CD],
[
3Gly18C6] [51,52], [Gly18C6] [53–55] and [Phe18C6] [56,57] when transferred from water
to water–organic solvents are shown in Figures 12 and 13. In the case of water–ethanol
solvent the increase of the exothermicity of the reaction is observed for all examined
molecular complexes [BA⊂β-CD], [3Gly18C6], [Gly18C6] and [Phe18C6].
Figure 12. Change in the enthalpy of complex formation reactions in H O-EtOH solvents: 1—[BA⊂β
-
2
CD]; 2—[3Gly18C6], [51,52]; 3—[Gly18C6], [53]; 4—[Phe18C6], [56].
Figure 13. Changes in the enthalpy of complex formation reactions in H O-DMSO solvents: 1—
2
[BA⊂β-CD];.2—[3Gly18C6], [54], 3—[Gly18C6], [58]; 4—[Phe18C6], [57].
The highest increase in the exothermicity of the reactions (Figures 12 and 13) has
been observed when passing from water to ethanol, whilst the smaller value is obtained in
DMSO.
The influence of H O-EtOH and H O-DMSO solvents on molecular complex for-
2
2
mation is explained on the base of solvation-thermodynamic approach and is described
below.
3.2. Solvation/Thermodynamic Approach
The nature, composition and structure of the solvent are the fundamental parameters
that determine the stability of a complex, its composition, the rate of complex formation, as
well as the mechanism of the complexation reaction.

Molecules 2021, 26, 4408
16 of 25
A wide body of experimental evidence has been accumulated, showing the extremely
important role of the solvent as a means of controlling the chemical process [2,3,60]. This
has spurred the development of theoretical and experimental studies aimed at studying the
functional behavior of the solvent in chemical reactions and establishing general patterns
of the solvent influence on the thermodynamics of complex formation.
The influence of the solvent on the shift of the chemical equilibrium is so diverse that
a general theory describing the role of the solvent in chemical processes has not yet been
developed, despite a large amount of research. Here, we will focus on the role played
by the solvent without aspiring to be exhaustive owing to the abundance of literature
data [61–70].
From this point of view, solvation approaches to the explanation of the causes of
changes in the thermodynamic characteristics of complexation reactions with varying
solvent composition are of universal importance.
A universal approach based on the thermodynamic characterization of the solvation
of all reagents is more promising for creating a scientific basis for the use of a solvent
as a means of controlling liquid-phase processes. At the same time, the thermodynamic
0
0
0
parameters (∆G , ∆H , ∆S ) of the reaction and solvation (or transfer) of the complexing
ion, ligand, and coordination compound are determined; their contributions to the total
solvent effect have been analyzed to determine which reagent solvation is crucial.
In accordance with the thermodynamic cycle the solvate–thermodynamic effect of the
0
0
0
reaction ∆tr
Y
r
=
∆r
Y
− ∆r
Y W, i.e., the change in the thermodynamic characteristic of
S
the reaction in a non-aqueous solvent (compared to an aqueous one) is the result of three
solvation contributions:
(
6)
0
0
0
0
where: ∆Y = ∆G , ∆H , ∆S .
This relationship is the basis of the solvation approach to the description of the role
of the solvent in complexation reactions, which we will use in the following paragraphs
when analyzing the literature data on the thermodynamics of complexation reactions in
binary mixtures of water–organic and non-aqueous solvents.
3
.3. The Thermodynamic Characteristics of the Molecular Complexation and Solvation of the
Reagents: A Solvation-Thermodynamic Analysis
Changes in the thermodynamic parameters of the reactions of formation of molecular
complexes [BA⊂β-CD] and [Phe18C6] [56
,57] during transfer from water to water–organic
solvents are shown in Figures 14 and 15.

Molecules 2021, 26, 4408
17 of 25
Figure 14. Changes in the thermodynamic parameters of complexation reactions during transfer from
0
0
T
∆trS0; [Phe18C6], 4—∆trH ,
0
water into H O-EtOH solvents: [BA⊂β-CD], 1—∆trH , 2—∆trG , 3—
−
2
0
0
5
—∆trG , 6—−T∆trS [56].
Figure 15. Changes in the thermodynamic parameters of complexation reactions during transfer
0
0
T
∆trS0; [Phe18C6], 4—∆trH ;
0
from water into H O-DMSO: [BA⊂β-CD], 1—∆trH , 2—∆trG , 3—
−
2
0
0
5
—∆trG ; 6—−T∆trS [57].
In H O–EtOH, there is a significant difference in the change in the corresponding
2
thermodynamic transfer functions of complexation [BA⊂β-CD] and [Phe18C6] (Figure 14).
On the contrary, H O–DMSO solutions with a 0.00, 0.10 mol. fr. of DMSO did not show
2
a significant differentiating effect on the change in the thermodynamic parameters of the
reactions of the formation of [BA⊂β-CD] and [Phe18C6] (Figure 15).
There are some differences in complexation between BA and β-CD in water and in a
water–organic solvent: the part of the inner cavity of β-CD in which the BA molecule is
located may be more hydrophobic in water than in the water–organic mixture, and this
may be the reason for the increase in the complexation exothermicity when passing from
water to water–ethanol mixtures. Analysis of the solvation contributions of reagents to the
change in the Gibbs energy and enthalpy of the molecular complex formation reaction can
shed light on this phenomenon.
The relations of the thermodynamic characteristics of the reaction of the formation of
[
BA⊂β-CD] and the solvation of the reagents are shown in Figures 16 and 17.

Molecules 2021, 26, 4408
18 of 25
Figure 16. Influence of water–ethanol solvents on the Gibbs energy change of the reaction of
formation of [BA⊂β-CD] and solvation of reagents during the transition from H O to H O-EtOH:
2
2
0
0
0
0
1
—∆trGr ; 2—∆trG (BA) [71]; 3—∆trG (β-CD) [72]; 4—∆trG [BA⊂β-CD].
Figure 17. The effect of the water–ethanol mixture on the enthalpy of the reaction change of the
formation of [BA⊂β-CD] and the solvation of reagents during the transition from H O to H O-EtOH
2
2
0
0
0
0
solvents: 1—∆trHr ; 2—∆trH (BA) [71]; 3—∆trH (β-CD) [73]; 4—∆trH [BA⊂β-CD].
0
0
The ∆trG (
X(EtOH) = 0.00
β
-CD) and ∆trG [BA⊂β-CD] values are close to zero at concentrations
÷
0.15 mol. fr., indicating that the decrease in the stability of the complex is
0
determined by an increase in the solvation of BA (∆trG (BA)) (Figure 16).
When a small amount of EtOH is added to the solvent (X(EtOH) < 0.12 mol. fr.), the
0
increase in the exothermicity of the complex formation reaction (∆tr
by the de-solvation of both
solvation contributions into the Gibbs energy change of the complexation in water–DMSO
are slightly different from that in H O-EtOH (Figure 18).
H
r
) is determined
β-cyclodextrin and BA (Figure 17). The ratios of reagents
2

Molecules 2021, 26, 4408
19 of 25
Figure 18. Effect of a water–dimethylsulfoxide mixture on the Gibbs energy changes of the benzoic
acid complexation with
β
-cyclodextrin and the solvation of reagents in H O-DMSO: 1—∆tr
G
r
0;
2
0
0
0
2
—∆trG (BA); 3—∆trG (β-CD) [74]; 4—∆trG [BA⊂β-CD].
Solvation increases almost equally for both reagents (BA and β-CD) in the initial stage
of DMSO addition to water. As a consequence, a decrease of [BA⊂β-CD] complex stability
has been observed, but the increase of the solvation of the molecular complex leads to the
decrease of this effect.
4. Materials and Methods
4.1. Materials
The following chemical reagents were used in this work:
-
-
-
Benzoic acid (C H COOH) (“chemically pure” grade), used without additional purifi-
6 5
cation. The purity of reagents was declared by the manufacturer >99% by weight.
-cyclodextrin (C H O ) from Sigma-Aldrich Saint (Louis, MO, USA) with a CD
β
42
70 35
content of ≥99% was used without additional purification;
Dimethylsulfoxide (C H OS) was purified by distillation according to the method [75
]
2
6
before use. The DMSO content was 99.4 wt.%. The residual water content in the
organic solvents used was taken into account when preparing the solutions.
Deuterated water and dimethylsulphoxide (atomic fraction of deuterium more than
-
9
9.9%) were purchased from Sigma-Aldrich USA. Ethyl alcohol (C H OH) (96% by
2 5
vol.) was purified by distillation at the atmospheric pressure.
The solutions were prepared by the weight method according to exact weights. The
analytical scales of the brand AUW220D (SHIMADZU) were used. For the preparation of
solutions, fresh bidistillate water was used.
4.2. Methods
4
.2.1. NMR Spectroscopy
1
All NMR H spectra were recorded on JNM-ECA-400 (400 MHz, «JEOL», Tokyo,
Japan) NMR spectrometer at the temperature 298 K using DSS (Sodium trimethylsilyl-
propanesulfonate) as the external standard.
When studying the inclusion complex formation, three types of series were run. One
series was prepared in pure deuterated water. Four series were done in a D O-DMSO-d
2
6
mixed solvent (with DMSO-d molar fractions 0.05, 0.075, 0.10 and 0.15) and three series
6
in a D O-EtOH mixed solvent (with molar fractions of EtOH 0.05, 0.075, and 0.10). In
2
each series, the
β-CD concentration held constant (0.0135 mol/L), while the benzoic acid
concentration was variable.

Molecules 2021, 26, 4408
20 of 25
4.2.2. Models and Computational Methods
All geometry and energy calculations have been performed by using an accurate and
broadly parametrized self-consistent tight-binding quantum chemical method with multi-
pole electrostatics contribution called GFN2-xTB method (short for “Geometry, Frequency,
Noncovalent, eXtended tight-binding”). The GFN2-xTB method includes hydrogen bond-
ing, halogen bonding as well as dispersion corrections (via D4 London dispersion model).
This method has been parameterized for all spd-block elements and the lanthanides up
to Z = 86 [76
temperature of 300K, integral cutoff of 0.25
–78]. In this work, geometry optimization was performed with an electronic
2
−5
×
10 , SCF convergence of 0.1
×
10 Ha and
−
3
wavefunction convergence of 0.1 × 10 e.
When BA interacts with -CD, there are numerous binding positions. The interaction
between -CD and BA has been studied by the following scheme: First, searching of
β
β
the most preferable configurations was performed using meta-dynamics (MTD) simula-
tions with an additional genetic z-matrix crossing (GC) approach for the generation of
conformer/rotamer ensembles [79]. This method combines forcefield speed with almost
quantum mechanical accuracy [80]. Next, the most favorable (the best) configurations
generated from iMTD-GC algorithm were fully optimized by GFN2-xTB method. The
results obtained by GFN2-xTB method reach an accuracy remarkably close to the DFT
reference, justifying their application for efficient binding site screening [81].
The nature of the interaction between
β-CD and BA was estimated based on interaction
energy (Eint) which is calculated as follows:
Eint = E[BA⊂β-CD] − E(β-CD) − E(BA)
(7)
where E[BA⊂β-CD], E(
β
-CD) and E(BA) are the energy of the [BA⊂β-CD] configuration,
β-CD and BA, respectively.
The interaction energy can be considered as a critical thermodynamic criterion to
estimate the ability and the extent of the process. In addition, a significant change in the
geometrical structures of BA was also analyzed. The population analysis, including charge
transfer and bond orders were reported and discussed for a detailed description of the
interaction process. Furthermore, the influence of the different solvents was also included
via the analytical linearized Poisson–Boltzmann (ALPB) model.
4.2.3. Interfacial Distribution-Study of Reagents Solvation State
The distribution coefficients of benzoic acid in water and its mixtures with DMSO
are determined by the method of interfacial distribution of the substance between two
immiscible phases: an aqueous or water–dimethylsulfoxide solution and n-hexane. The
applicability of this method for similar studies, as well as experimental confirmation of
the immiscibility of a water–dimethylsulfoxide solvent (X(DMSO) = 0.0–0.5 mol. fr.) with
n-hexane are given in [82,83].
During the experiment, equal aliquots of an aqueous organic solution of benzoic
acid and n-hexane were placed in a flask with polished lids. The contents of the flask
were stirred with a magnetic stirrer for 8 hours at a constant temperature (298.2
After settling (15 h), a sample of the lower layer of the heterogeneous system (benzoic
±
0.1 K).
acid + solvent H O–DMSO) was taken, in which the equilibrium concentration of benzoic
2
H2O-DMSO
acid in the water–dimethylsulfoxide layer ([BA]
determined.
) was spectrophotometrically
All measurements were carried out on a two-beam UV spectrophotometer SPECORD
M400 (Shimadzu), at a wavelength of 273.0 nm in cuvettes with a thickness of 10 mm at
−
4
−4
10 mol/L in the optical
a concentration of benzoic acid from 1.133
density range 0.15–0.6.
×
10 to 6.276
×

Molecules 2021, 26, 4408
21 of 25
5
. Conclusions
The experimental results are in accordance with the theoretical calculations performed
for the inclusion studies of BA in -CD and complement each other. Stability constants
β
obtained by NMR agree with those calculated from calorimetric measurements. In turn,
the calorimetric and NMR data for [BA⊂β-CD] stability also confirm that the addition of
DMSO (up to 0.10 mol. fr.) leads to the most significant decrease in the stability of the
complex compared to the same mol. fr. in EtOH. Quantum calculations allowed to evaluate
the effect of individual solvents on BA inclusion into β-CD, which is impossible to obtain
by calorimetric or by NMR experiments. For molecular complexes of BA and
increase in the solvation of BA lead to a decrease of lgK values in water–ethanol mixtures.
β
-CD the
0
In water–DMSO solvent, nearly equal increase of solvation of both BA and β-CD results in
a decrease of [BA⊂β-CD] complex stability.
The data obtained in this work will be contributed to predict the thermodynamic pa-
rameters of the reactions of the formation of complexes of hydrophobic biologically active
molecules with CD in various media. This research may help developing cyclodextrin-
based pharmaceutical formulations through the modulation of the appropriate solvent mix-
ture that would thus be employed industrially as a mean to control the reactions/processes
carried out in liquid phases.
Supplementary Materials: The following are available online. Table S1. Observed chemical shifts
of
β
-CD protons for the [BA⊂β-CD] system in D O. Table S2. Observed chemical shifts of
β-CD
2
protons for the [BA⊂β-CD] system in D O (relative to
β-CD). Table S3. Observed chemical shifts of
2
β
-CD protons for the [BA⊂β-CD] system in the solvent D O-DMSO-d (X
= 0.05 mol. fr.).
(DMSO-d6)
2
6
Table S4. Observed chemical shifts of
β
-CD protons for the [BA⊂β-CD] system (relative to
β
-CD) in
-CD
= 0.075 mol. fr.). Table
(DMSO-d6)
the solvent D O-DMSO-d (X
= 0.05 mol. fr.). Table S5. Observed chemical shifts of
β
2
6
(DMSO-d6)
protons for the [BA⊂β-CD] system in the solvent D O-DMSO-d (X
2
6
S6. Observed chemical shifts of
β
-CD protons for the [BA⊂β-CD] system (relative to
β
-CD) in the
= 0.075 mol. fr.). Table S7. Observed chemical shifts of -CD
= 0.10 mol. fr.). Table
solvent D O-DMSO-d (X
β
2
6
(DMSO-d6)
protons for the [BA⊂β-CD] system in the solvent D O-DMSO-d (X
2
6
(DMSO-d6)
S8. Observed chemical shifts of
β
-CD protons for the [BA⊂β-CD] system (relative to
β
-CD) in the
solvent D O-DMSO-d (X
= 0.10 mol. fr.). SII. xyz coordinate files of the structures shown
2
6
(DMSO-d6)
in Figures 11 and 12.
Author Contributions: Conceptualization, T.R.U.; methodology, T.R.U., V.A.V., T.L.P. and V.A.S.;
formal analysis, T.R.U., V.A.V., V.T.P., T.L.P., T.T.H.N., T.M.H.L., N.N.K., G.A.G. and V.A.S.; investiga-
tion, T.R.U., V.A.V., D.A.L., T.L.P., T.T.H.N., T.M.H.L., D.A.A., D.N.K., N.N.K., G.A.G. and R.A.K.;
resources, T.R.U., V.A.V., V.T.P., D.A.L., T.L.P., T.T.H.N., T.M.H.L., D.A.A., D.N.K., N.N.K., G.A.G.,
R.A.K., M.B. and C.G.; writing—original draft preparation, T.R.U., T.L.P., T.T.H.N., T.M.H.L., D.A.A.,
M.B., C.G. and V.A.S.; writing—review and editing, T.R.U., V.A.V., T.L.P., M.B., C.G. and V.A.S.; visu-
alization, T.R.U., V.A.V., D.A.L., T.L.P., T.T.H.N., T.M.H.L., D.A.A. and D.N.K.; project administration,
T.R.U. All authors have read and agreed to the published version of the manuscript.
Funding: This research was funded by the Ministry of Science and Higher Education of the Russian
Federation (project number FZZW-2020-0009) and by the Vietnam Academy of Science and Technol-
ogy (VAST) under grand number QTRU01.04/19-20 (quantum-chemical calculation). This research
was also conducted under the international agreement between the University of Naples Federico
II and the Ivanovo State University of Chemistry and Technology. The enthalpic characteristics of
molecular complex formations was carried out by use the equipment of the Centre for collective use
of ISUCT.
Data Availability Statement: The data presented in this study are available on request from the
corresponding authors.
Conflicts of Interest: The authors declare no conflict of interest.
Sample Availability: Samples of the compounds are not available from the authors.

Molecules 2021, 26, 4408
22 of 25
References
1.
2.
3.
4.
5.
Koifman, O.I.; Ganyushkina, V.V.; Malyasova, A.S. Scientific Schools of Ivanovo Chemtech: Through the Prism of History; Ivanovo
State University of Chemical Technology: Ivanovo, Russia, 2020; p. 496. (In Russian)
Shormanov, V.A.; Sharnin, V.A. In the monograph Achievements and problems of solvation theory. In Structural and ThermoDy-
namic Aspects; Kutepov, A.M., Ed.; Nauka: Moscow, Russia, 1998; pp. 173–207. (In Russian)
Sharnin, V.A.; Usacheva, T.R.; Kuzmina, I.A.; Gamow, G.A.; Alexandriiskii, V.V. Complexation in Non-Aqueous Media: A Solvation
Approach to Describing the Role of a Solvent; Sharnina, V.A., Ed.; URSS: Moscow, Russia, 2019; p. 304. (In Russian)
Sharnin, V.A.; Aleksandriysky, V.V.; Dushina, S.V.; Gamov, G.A. Stability of H-complexes of nicotinamide nitrogen heteroatom
13
with water and ethanol in mixed solvents by C NMR probing. Magn. Reson. Chem. 2013, 51, 193–198. [CrossRef] [PubMed]
Sharnin, V.A.; Dushina, S.V.; Zevakin, M.A.; Gushchina, A.S.; Grazhdan, K.V. Potentiometric and calorimetric study on stability of
nicotinamid complexes of silver(I) and copper(II) in aqueous ethanol and dimethylsulfoxide. Inorg. Chim. Acta 2009, 362, 437–442.
[CrossRef]
6
.
Sharnin, V.A.; Kuzmina, I.A. Regularities of changes in thermodynamic characteristics of reactions of complexation and solvation
of reagents in the formation of metal coronates in binary mixtures of non-aqueous solvents. J. Gen. Chem. 2013, 83, 375–378.
[CrossRef]
7
.
.
Kuzmina, I.A.; Volkova, M.A.; Kuzmina, K.I.; Usacheva, T.R.; Sharnin, V.A.; Arena, G. Effect of reactant solvation on the stability
of complexes of silver(I) with 18-crown-6 in ethanol-dimethyl sulfoxide mixtures. J. Mol. Liq. 2019, 276, 78–82. [CrossRef]
Usacheva, T.R.; Thi, L.P.; Terekhova, I.V.; Kumeev, R.S.; Sharnin, V.A. Thermodynamics of molecular complexation of glycyl–
glycyl–glycine with cryptand [2.2.2] in water–dimethylsulfoxide solvent at 298.15 K. J. Therm. Anal. Calorim. 2016, 126, 307–314.
8
[CrossRef]
9
.
Usacheva, T.R.; Thi, L.P.; Terekhova, I.V.; Kumeev, R.S.; Sharnin, V.A. Application of isothermal titration calorimetry for evaluation
of water-acetone and water-dimethylsulfoxide solvents influence on the molecular complex formation between 18-crown-6 and
triglycine at 298.15K. J. Therm. Anal. Calorim. 2015, 121, 975–981. [CrossRef]
1
1
1
1
0. Salvatierra, D.; Jaime, C.; Virgili, A.; Sanchez-Ferrando, F. Determination of the inclusion geometry for the β-cyclodextrin/benzoic
acid complex by NMR and molecular modeling. J. Org. Chem. 1996, 61, 9578–9581. [CrossRef]
1. Aree, T.; Chaichit, N. Crystal structure of
CrossRef]
β-cyclodextrin-benzoic acid inclusion complex. Carbohydr. Res. 2003, 338, 439–446.
[
2. Terekhova, I.V.; Ko z´ biał, M.; Kumeev, R.S.; Gierycz, P. Complex formation of native and hydroxypropylated cyclodextrins with
1
benzoic acid in aqueous solution: Volumetric and H NMR study. Chem. Phys. Lett. 2011, 514, 341–346. [CrossRef]
3. Pessine, F.B.T.; Calderini, A.; Alexandrino, G.L. Review: Cyclodextrin Inclusion Complexes Probed by NMR Techniques; Kim, D.-
H., Ed.; InTech: London, UK, 2012; pp. 237–264. Available online: http://www.intechopen.com/books/magneticresonance-
spectroscopy/review-study-of-inclusion-complexes-with-cyclodextrins-by-mrs (accessed on 10 June 2021).
1
4. Ulatowski, F.; Da˛browa, K.; Bałakier, T.; Jurczak, J. Recognizing the Limited Applicability of Job Plots in Studying Host Guest
−
Interactions in Supramolecular Chemistry. J. Org. Chem. 2016, 81, 1746–1756. [CrossRef]
1
5. Hibbert, D.B.; Thordarson, P. The death of the Job plot, transparency, open science and online tools, uncertainty estimation
methods and other developments in supramolecular chemistry data analysis. Chem. Commun. 2016, 52, 12792. [CrossRef]
[PubMed]
1
6. Renny, J.S.; Tomasevich, L.L.; Tallmadge, E.H.; David, B. Collum Method of Continuous Variations: Applications of Job Plots
to the Study of Molecular Associations in Organometallic Chemistry. Angew. Chem. Int. Ed. 2013, 52, 11998–12013. [CrossRef]
[PubMed]
1
1
7. Chankvetadze, B. Capillary Electrophoresis in Chiral Analysis; John Wiley: Chichester, UK, 1997; pp. 71–133, 141–228.
8. Petrovi c´ , I.; Milovanovi c´ , B.; Etinski, M.; Petkovi c´ , M. Theoretical scrutinization of nine benzoic acid dimers: Stability and energy
decomposition analysis. Int. J. Quantum Chem. 2019, 119, e25918. [CrossRef]
1
2
2
2
2
2
2
9. Meshkov, A.N.; Gamov, G.A. KEV: A free software for calculating the equilibrium composition and determining the equilibrium
constants using UV-Vis and potentiometric data. Talanta 2019, 198, 200–205. [CrossRef] [PubMed]
0. Bondarev, N.V. Exploratory Analysis in Thermodynamics of Equilibria. Classification and Prediction of Benzoic Acid Strength in
Aqueous-Organic Solvents. Russ. J. Gen. Chem. 2016, 86, 1221–1228. [CrossRef]
1. Terekhova, I.V. Comparative thermodynamic study on complex formation of native and hydroxypropylated cyclodextrins with
benzoic acid. Thermochim. Acta 2011, 526, 118–121. [CrossRef]
2. Terekhova, I.V.; Kumeev, R.S.; Alper, G.A. Inclusion complex formation of
α
- and
β
-cyclodextrins with aminobenzoic acids in
1
aqueous solution studied by H NMR. J. Incl. Phenom. Macrocycl. Chem. 2007, 59, 301–306. [CrossRef]
3. Terekhova, I.V. Volumetric and calorimetric study on complex formation of cyclodextrins with aminobenzoic acids. Mendeleev
Commun. 2009, 19, 110–112. [CrossRef]
4. Terekhova, I.V.; Obukhova, N.A. Study on inclusion complex formation of m-aminobenzoic acid with native and substituted
β-cyclodextrins. J. Solut. Chem. 2007, 6, 1167–1176. [CrossRef]
5. Zielenkiewicz, W.; Terekhova, I.V.; Wszelaka-Rylik, M.; Kumeev, R.S. Thermodynamics of inclusion complex formation of
hydroxypropylated α- and β-cyclodextrins with aminobenzoic acids in water. J. Therm. Anal. Calorim. 2010, 101, 15–23. [CrossRef]

Molecules 2021, 26, 4408
23 of 25
2
2
2
2
6. Terekhova, I.V. Inclusion Complex Formation of Cyclodextrins with Aminobenzoic Acids in Aqueous Solution. Ch. 8 in Macrocyclic
Chemistry: New Research Developments. Изд-вo; Nova Science Publishers Inc.: New York, NY, USA, 2010; pp. 263–286.
7. Sankaranarayanan, R.K.; Siva, S.; Prabhu, A.A.M.; Rajendiran, N. A study on the inclusion complexation of 3,4,5-
trihydroxybenzoic acid with β-cyclodextrin at different Ph. J. Incl. Phenom. Macrocycl. Chem. 2010, 67, 461–470. [CrossRef]
8. Rajamohan, R.; Nayaki, S.K.; Swaminathan, M. Study on Host–Guest Complexation of 5-Amino-2-Mercaptobenzimidazole with
β-Cyclodextrin. J. Solut. Chem. 2011, 40, 803–817. [CrossRef]
9. Hendrickson, K.; Easton, C.J.; Lincoln, S.F. Cyclodextrin and termethylated cyclodextrin complexation of aromatic carboxylic
acids and their conjugate bases in aqueous solution: The effect of size, hydrophobicity and charge. Aust. J. Chem. 1995, 48,
1
125–1132. [CrossRef]
3
3
3
0. Simova, S.; Schneider, H.-J. NMR analyses of cyclodextrin complexes with substituted benzoic acids and benzoate anions. J. Chem.
Soc. Perkin Trans. 2000, 8, 1717–1722. [CrossRef]
1. Rotich, M.K.; Brown, M.E.; Glass, B.D. Thermal studies on mixture of benzoic and salicylic acids with cyclodextrins. J. Therm.
Anal. Calorim. 2003, 73, 671–686. [CrossRef]
2. Roik, N.V.; Belyakova, L.A. Study of complex formation in the «
9–79.
β-cyclodextrin-p aminobenzoic acid» system. Surface 2009, 15,
6
3
3
3. Stalin, T.; Rajendiran, N. Intramolecular charge transfer effects on 3-aminobenzoic acid. Chem. Phys. 2006, 322, 311–322. [CrossRef]
4. Stalin, T.; Shanthi, B.; Rani, P.V.; Rajendiran, N. Solvatochromism, prototropism and complexation of para-aminobenzoic acid. J.
Incl. Phenom. Macrocycl. Chem. 2006, 55, 21–29. [CrossRef]
3
3
3
3
3
4
5. Rajendiran, N.; Thulasidhasan, J.; Jenita, M.J. Guest-Host Inclusion Complex Formation of 2-, 3-, and 4-Aminobenzoic Acids with
Native and Modified Cyclodextrins, International Letters of Chemistry. Phys. Astron. 2016, 69, 10–21.
6. Lewis, E.A.; Hansen, L.D. Thermodynamics of binding of guest molecules to
973, 2, 2081–2085. [CrossRef]
7. Mendez, S.G.; Espinar, F.J.O.; Alvarez, A.L.; Longhi, M.R.; Quevedo, M.A.; Zoppi, A. Ternary complexation of benzoic acid with
-cyclodextrin and aminoacids. Experimental and theoretical studies. J. Incl. Phenom. Macrocycl. Chem. 2016, 85, 33–48. [CrossRef]
α- and β-cyclodextrins. J. Chem. Soc. Perkin Trans.
1
β
8. Huang, M.-J.; Watts, J.D.; Bodor, N. Theoretical studies of inclusion complexes of α- and β-cyclodextrin with benzoic acid and
phenol. Int. J. Quantum Chem. 1997, 65, 1135–1152. [CrossRef]
9. Liu, L.; Song, K.-S.; Li, X.-S.; Guo, Q.-X. Charge-transfer interaction: A driving force for cyclodextrin inclusion complexation. J.
Incl. Phenom. Macrocycl. Chem. 2001, 40, 35–39. [CrossRef]
0. Lu, C.-S.; Hu, C.-J.; Yu, Y.; Meng, Q.-J. The inclusion compounds of
benzaldehyde drugs studied by proton nuclear magnetic resonance spectroscopy. Chem. Pharm. Bull. 2000, 48, 56–59. [CrossRef]
PubMed]
β-cyclodextrin with 4-substituted benzoic acid and
[
4
4
4
4
4
1. Roik, N.V.; Belyakova, L.A.; Spectroscopy, I.R. X-Ray Diffraction and thermal analysis studies of solid β-cyclodextrin-para-
aminobenzoic acid inclusion complex. Phys. Chem. Solid State 2011, 12, 168–173.
2. Zhang, Y.; Yu, S.; Bao, F. Crystal structure of cyclomaltoheptaose (
o-aminobenzoic acid. Carbohydr. Res. 2008, 343, 2504–2508. [CrossRef]
3. Kacsó, I.; Borodi, G.; Farcas, S.I.; Hernanz, A.; Bratu, I. Host–guest system of Vitamin B10 in
β-cyclodextrin) complexes with p-aminobenzoic acid and
β-cyclodextrin: Characterization of
the interaction in solution and in solid state. J. Incl. Phenom. Macrocycl. Chem. 2010, 68, 175–182. [CrossRef]
4. Lehner, S.J.; Muller, B.W.; Seydel, J.K. Interaction between p-hydroxybenzoic acid esters and hydroxypropyl-
their antimicrobial effect against Candida albicans. Int. J. Pharm. 1993, 93, 201–208. [CrossRef]
β-cyclodextrin and
5. Usacheva, T.R.; Kabirov, D.N.; Alister, D.A.; Zavalishin, M.N.; Gamov, G.A.; Thi, L.P.; Xuan, M.V.; Thuan, Z.N. Thermodynamics
of complexation of benzoic acid with - and -cyclodextrins in a water-dimethyl sulfoxide solvent. Russ. Chem. Bull. 2020, 69,
692–1696. (In Russian) [CrossRef]
β
γ
1
4
4
4
4
5
6. Borodin, V.A. Processing of the results of calorimetric measurements on a digital computer in the study of complex equilibria in
solutions. J. Inorg. Chem. 1982, 27, 2169–2172. (In Russian)
7. Usacheva, T.R.; Ledenkov, S.F.; Sharnin, V.A. Complex formation of Ag+ with polyether 18-crown-6. Calorimetric and potentio-
metric methods. J. Therm. Anal. Calorim. 2002, 70, 379–385. [CrossRef]
8. Usacheva, T.R.; Thi, L.P.; Sharnin, V.A. Calorimetric study of the molecular complex formation of glycyl–glycyl–glycine with
1
8-crown-6 in aqueous organic solvents. Russ. J. Gen. Chem. 2017, 87, 591–599. [CrossRef]
9. Harata, K. Induced circular dichroism of cycloamylose complexes with meta- and para-distributed benzenes. Bioorg. Chem. 1981
0, 255–265. [CrossRef]
0. Usacheva, T.; Pham, L.T.; Nguyen, D.T.; Kabirov, D.; Alister, D.; Minh, X.; Le, T.; Sharnin, V.; Giancola, C. Host–guest inclusion
complex of -cyclodextrin and benzoic acid in water–ethanol solvents: Spectroscopic and thermodynamic characterization of
,
1
β
complex formation. J. Therm. Anal. Calorim. 2020, 142, 2015–2024. [CrossRef]
5
1. Usacheva, T.R.; Thi, L.P.; Sharnin, V.A.; Baranskiy, A. Molecular complexation of some amino acids and triglycine with 18-crown-6
ester in H O–EtOH solvents at 298.15 K. Russ. J. Inorg. Chem. 2013, 58, 1264–1268. [CrossRef]
2

Molecules 2021, 26, 4408
24 of 25
5
2. Usacheva, T.R.; Thi, L.P.; Sharnin, V.A. Influence of the composition of the H O–EtOH solvent on the formation reactions of
2
molecular complexes of triglycine and glycine with the 18-crown-6 ether at T = 298.15 K. J. Phys. Chem. 2014, 88, 602–606.
(In Russian)
5
5
5
3. Matteoli, E.; Lepori, L.; Usacheva, T.R.; Sharnin, V.A. Thermodynamics of complex formation in mixed solvents K and ∆H for the
formation reaction of [Gly18C6] at 298.15 K. J. Therm. Anal. Calorim. 2009, 97, 811–817. [CrossRef]
4. Usacheva, T.R.; Thi, L.P.; Sharnin, V.A. Thermodynamics of formation for the 18-crown-6-triglycine molecular complex in
water-dimethylsulfoxide solvents. Russ. J. Phys. Chem. A 2014, 88, 908–912. [CrossRef]
5. Usacheva, T.R.; Kuzmina, I.A.; Sharnin, V.A.; Chernov, I.V.; Matteoli, E. The influence of the composition of an aqueous-acetone
solvent on the thermodynamic characteristics of complex formation of 18-crown-6 ether with glycine. Russ. J. Phys. Chem. A 2011
,
8
5, 948–951. [CrossRef]
5
5
6. Usacheva, T.R.; Chernov, I.V.; Sharnin, V.A.; Matteoli, E.; Terekhova, I.V.; Kumeev, R.S. The influence of water–ethanol mixture on
the thermodynamics of complex formation between 18-crown-6 ether and L–phenylalanine. Chem. Phys. Lett. 2012, 543, 153–158.
[
CrossRef]
7. Usacheva, T.R.; Chernov, I.V.; Sharnin, V.A.; Voronina, S.I.; Matteoli, E. Molecular complex formation between L-phenylalanine
and 18-crown-6 in H O–DMSO solvents studied by titration calorimetry at T = 298.15 K. J. Therm. Anal. Calorim. 2013, 112,
2
3
99–405. [CrossRef]
5
5
8. Usacheva, T.R.; Sharnin, V.A.; Matteoli, E. Influence of solvation on the thermodynamics of the formation of molecular complexes
of 18-crown-6 ester with glycine in water–dimethyl sulfoxide solutions. J. Phys. Chem. 2011, 85, 2038–2042. (In Russian)
9. Usacheva, T.R. Molecular complexation of glycine by 18-crown-6 in aqueous-organic solvent: A solvation-thermodynamic study.
In Glycine: Biosynthesis, Physiological Functions and Commercial Uses; Usacheva, T.R., Sharnin, V.A., Matteoli, E., Vojak, W., Eds.;
Nova Science Publishers Inc.: New York, NY, USA, 2013; pp. 1–33.
6
6
0. Krestov, G.A. Ionic Solvation; Ellis Horwood: London, UK, 1994; p. 264.
1. Turyan, Y.I.; Shtipelman, R.Y. Polarographic study of thiocyanate complexes of lead in aqueous, water-methanol, methanol,
water-ethanol solvents. J. Inorg. Chem. 1959, 4, 804–812. (In Russian)
6
6
6
2. Turyan, Y.I.; Zhantalay, V.P. Polarographic study of cadmium chloride complexes in aqueous, water-methanol, methanol,
water-ethanol solvents. J. Inorg. Chem. 1960, 5, 1748–1753. (In Russian)
3. Shulman, V.M.; Larionov, S.V.; Kramareva, T.V.; Arykova, E.I.; Yudina, V.V. On the stability of complex compounds of zinc,
cadmium, cobolt and nickel with thiourea in aqueous acetone solutions. J. Inorg. Chem. 1966, 11, 1076–1080. (In Russian)
4. Nazarova, L.V.; Budu, G.I. Stability of nickel and cobalt pyridinates in water-alcohol and water-acetone solutions. J. Inorg. Chem.
1
970, 14, 3072–3075. (In Russian)
6
6
6
5. Mayer, U. Ionic equilibria in donor solvents. Pure Anal. Chem. 1979, 41, 1697–1712. [CrossRef]
6. Beck, M.T.; Nagypal, I. Chemistry of Complex Equilibria; Akademiai Kiado: Budapest, Hungary, 1989; p. 402.
7. Krestov, G.A.; Berezin, B.D. Basic Concepts of Modern Chemistry, 2nd ed.; Chemistry Publishing House: Leningrad, Russia, 1986; p.
1
04. (In Russian)
6
6
8. Quist, A.S.; Marshall, W.L. Ionization equilibria in ammonia-water solutions to 700.deg. and to 4000 bars of pressure. J. Phys.
Chem. 1968, 72, 3122–3128. [CrossRef]
9. Belevantsev, V.I.; Fedorov, V.A. On the change in the equilibrium constants of complexation depending on the composition of the
aqueous-organic solvent. Coord. Chem. 1977, 3, 638–642. (In Russian)
7
7
0. Belevantsev, V.I.; Peschevitsky, B.I. Study of Complex Equilibria in Solutions; Science: Novosibirsk, Russia, 1978; p. 256. (In Russian)
1. Hu, X.G.; Lin, R.S.; Zong, H.X. Enthalpies and entropies of dissolution and dissociation of benzoic acid in EtOH-H O and
2
i-PrOH-H O mixtures. J. Acta Phys.-Chim. Sin. 1999, 15, 838–844.
2
7
7
7
2. Chatjigakis, A.K.; Donze, C.; Coleman, A.W.; Cardot, P. Solubility Behavior of
Chem. 1992, 64, 1632–1634. [CrossRef]
3. Belica, S.; Sadowska, M.; Stepniak, A.; Graca, A.; Palecz, B. Enthalpy of solution of
organic solvents. J. Chem. Thermodyn. 2014, 69, 112–117. [CrossRef]
4. Kuzmina, I.A.; Volkova, M.A.; Marov, A.S.; Thi, L.P.; Usacheva, T.R. Thermodynamics of the solvation of β-cyclodextrin in
β
-Cyciodextrin in Water-Cosolvent Mixtures. Anal.
α
- and -cyclodextrin in water and in some
β
water–dimethylsulfoxide solvents. Russ. J. Phys. Chem. A 2020, 94, 2034–2037. [CrossRef]
7
7
5. Vasiliev, V.P. Thermodynamic Properties of Electrolyte Solutions; Higher School: Moscow, Russia, 1982; p. 262. (In Russian)
6. Grimme, S.; Bannwarth, C.; Shushkov, P. A Robust and Accurate Tight-Binding Quantum Chemical Method for Structures,
Vibrational Frequencies, and Noncovalent Interactions of Large Molecular Systems Parametrized for All spd-Block Elements (Z =
1
–86). J. Chem. Theory Comput. 2017, 13, 1989–2009. [CrossRef]
7. Bannwarth, C.; Ehlert, S.; Grimme, S. GFN2-xTB—An Accurate and Broadly Parametrized Self-Consistent Tight-Binding Quantum
Chemical Method with Multipole Electrostatics and Density-Dependent Dispersion Contributions. J. Chem. Theory Comput. 2019
5, 1652–1671. [CrossRef]
7
,
1
7
7
8. Pracht, P.; Caldeweyher, E.S.; Grimme, S. A Robust Non-Self-Consistent Tight-Binding Quantum Chemistry Method for large
Molecules. ChemRxiv 2019. [CrossRef]
9. Pracht, P.; Bohle, F.; Grimme, S. Automated exploration of the low-energy chemical space with fast quantum chemical methods.
Phys. Chem. Chem. Phys. 2020, 22, 7169–7192. [CrossRef]

Molecules 2021, 26, 4408
25 of 25
8
0. Spicher, S.; Grimme, S. Robust Atomistic Modeling of Materials. Organomet. Biochem. Syst. 2020, 59, 15665–15673. [CrossRef]
8
1. Spicher, S.; Bursch, M.; Grimme, S. Efficient Calculation of Small Molecule Binding in Metal-Organic Frameworks and Porous
Organic Cages. J. Phys. Chem. C 2020, 124, 27529–27541. [CrossRef]
8
2. Thi, L.P.; Usacheva, T.R.; Kuz’mina, I.A.; Nguyen, N.; Thai, H.; Volkova, M.; Le, H.; Nguyen, T.; Volynkin, V.; Tran, D. Effect of
Cyclodextrin types and reagents solvation on the stability of complexes between β-Cyclodextrins and rutin in water-ethanol
solvents. J. Mol. Liq. 2020, 318, 114308. [CrossRef]
8
3. Usacheva, T.R.; Kuz’mina, I.A.; Sharnin, V.A.; Sidorenko, N.S.; Voronina, S. The influence of solvation on the formation of Ag+
complexes with 18-crown-6 ether in water-dimethyl sulfoxide solvents. Russ. J. Phys. Chem. A 2011, 85, 952–954. [CrossRef]