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Current Status of Quantum Chemical Studies of Cyclodextrin Host–Guest Complexes

Department of Physical Chemistry, Chair of Physical Pharmacy and Bioanalysis, Faculty of Pharmacy, Doctoral School, Medical University of Warsaw, Banacha 1 Str., 02-093 Warsaw, Poland
Department of Physical Chemistry, Chair of Physical Pharmacy and Bioanalysis, Faculty of Pharmacy, Medical University of Warsaw, Banacha 1 Str., 02-093 Warsaw, Poland
Author to whom correspondence should be addressed.
Molecules 2022, 27(12), 3874;
Received: 30 May 2022 / Revised: 9 June 2022 / Accepted: 13 June 2022 / Published: 16 June 2022
(This article belongs to the Special Issue Cyclodextrin Chemistry and Toxicology II)


This article aims to review the application of various quantum chemical methods (semi-empirical, density functional theory (DFT), second order Møller–Plesset perturbation theory (MP2)) in the studies of cyclodextrin host–guest complexes. The details of applied approaches such as functionals, basis sets, dispersion corrections or solvent treatment methods are analyzed, pointing to the best possible options for such theoretical studies. Apart from reviewing the ways that the computations are usually performed, the reasons for such studies are presented and discussed. The successful applications of theoretical calculations are not limited to the determination of stable conformations but also include the prediction of thermodynamic properties as well as UV–Vis, IR, and NMR spectra. It has been shown that quantum chemical calculations, when applied to the studies of CD complexes, can provide results unobtainable by any other methods, both experimental and computational.

Graphical Abstract

1. Introduction

Due to their unique structural, physical, and chemical properties, cyclodextrins (CDs) and their derivatives have been of great interest for more than a century [1]. The biodegradability, biocompatibility, and versatility of CDs and CDs-based materials extend their applications to new areas every year; however, the main property that makes CDs so popular is their ability to form host–guest complexes with a variety of compounds [2].
CDs are commonly used in pharmaceutical formulations as they increase the solubility of poorly soluble drugs and protect substances against external factors, such as light, humidity, and heat [3]. CDs can mask unpleasant smells or flavors of drugs, which is especially important in formulations dedicated to children [4]. More than 100 original drugs are currently being manufactured with CDs as excipients [5,6,7].
Interactions between CDs (host) and guest molecules may yield a stable complex with a high equilibrium constant; for example, β-CD forms highly stable inclusion complexes with adamantyl derivatives with a binding constant of ~104–105 M−1 [8,9]. It is not surprising then that the number of newly obtained cyclodextrin host–guest complexes is constantly increasing. However, only a small amount of those complexes is being reported with their crystal structures. This is caused by the fact that most of those complexes are either amorphous or polycrystalline, and even for the crystalline complexes it is usually very hard to obtain a crystal of a size suitable for single crystal X-ray measurements [10,11]. This is probably one of the reasons why a lot of experimental works describing the structure and properties of CDs complexes are supported by theoretical calculations.
To fully understand the behavior and physicochemical properties of a complex, knowledge of its structure is essential. However, it is not just the desire to reveal how the complex looks that makes the application of molecular modeling methods so popular in the studies of CDs complexes. By choosing an appropriate computational approach, it is possible to determine (or explain) the molar stoichiometry of the complex, the differences observed in the spectra (UV–VIS, IR, NMR) of host–guest physical mixtures and their complexes, and also to predict the stability of such structures under various conditions such as different solvents, temperature or pressure.
CDs host–guest complexes are surely very flexible structures, which is the common cause of their polycrystallinity. This is why a lot of the molecular modelling studies devoted to those complexes utilize molecular dynamics simulation at the molecular mechanics level. Those works have been recently reviewed by us [12]. However, the types of intermolecular forces that stabilize such complexes such as hydrogen bonding, van der Waals, and hydrophobic and dipole–dipole interactions, usually cannot be modeled with the required accuracy using the molecular mechanics methods. This is why the number of works in which the calculations of CD complexes at the higher level of theory, namely, quantum chemical (QC), has constantly increased since 2005 (Figure 1). Now, after 20 years of studies, the number of such articles is large enough to draw some general conclusions and trends as well as the advantages and disadvantages of such an approach. Therefore, the aim of this review was to gather and analyze the works in which the CD host–guest complexes have been modeled using QC methods.
There were at least a few reasons behind writing this review. First, it was worth analyzing whether some conclusions can be made on the choice of the most accurate method, including the applied DFT functional, basis set, dispersion correction or solvent model. Those aspects are discussed at the very beginning. Then, it was interesting to check the main reasons behind the QC method chosen by the authors of the reviewed works. Was it solely to predict or suggest the possible structure of the complex, or were the calculations used for something more such as the simulation of the spectra or explanation of the reaction mechanism to support the experimental findings? Further, we wanted to find out what type of CDs and what possible guests were studied in those computational works. Therefore, an informative table presenting the most essential information such as the composition of the complex, applied functional, basis set, and solvent treatment has been prepared to serve as an informative and easy-to-follow guide for future studies. Finally, the chosen examples are described in a more detailed way, suggesting the possible solutions and future indications.
As the authors of this review have been using the QC methods to model the structure and properties of CD complexes and found this approach very useful, it was our hope and desire to convince other researchers to try such solutions in their works.

2. Applied Calculational Methods and Parameters

2.1. Choice of QC Method

The computational methods that were used in the reviewed works nicely correspond with the general increase in the computational power available to researchers worldwide. The earliest (before 2005) QC works studying CD complexes were done using the least demanding semi-empirical methods such as AM1, PM3 and later PM6 or PM7. Subsequently, those methods have been gradually superseded by density functional theory (DFT) calculations, while recently a few works have been published in which the Møller–Plesset perturbation theory (MP) was applied. It is worth noticing that CD complexes are not small objects, in terms of QC calculations, especially when the γ-CD or substituted CDs are the hosts with the large ligand as a guest. Application of QC can also be a problem when studying complexes with a host:guest ratio higher than 1:1. This is why even in the 2020s in some works, semiempirical methods have been applied; however, the ratio of DFT to the semi-empirical ones is constantly increasing (Figure 2).

2.2. General Remarks

  • Calculations of CD other than in the form of typical complexes
As stated in the title of this manuscript, this review focuses on the application of QC methods in the analysis of CD complexes. However, computational studies are also performed for the systems where CDs play different roles, i.e., as nanocarriers, corrosion inhibitors or building blocks for even more complex structures, often with some additives such as gold particles. Those studies have not been listed in Table 1. The selected newest articles on the topic are [13,14,15,16,17,18].
It should be noticed that to increase the accuracy of DFT calculations in solid state, periodic boundary conditions are often applied, using crystal unit cells as simulation boxes. During the computations, only the properties of the original unit cell need to be calculated and then propagated in the chosen dimensions. However, to perform such computations, the crystal structure of the studied object is mandatory. More information on such calculations can be found in a recent review [19] with an example of such calculations for CDs presented in [20].
  • Software
In almost all of the reviewed works presenting the results of the DFT calculations, Gaussian software was used. There are only a few cases when ORCA [21,22,23], VASP [24] or ADF [25] were applied instead. Only for the solid state calculations or those involving adhesion, nanocarriers, etc., is DMol3 also commonly used.
In several works that included CD where DFT was applied, the ONIOM method was presented (see Table 1). ONIOM stands for Our own N-layered Integrated molecular Orbital and Molecular mechanics and is a hybrid method which combines QC (either ab inito or semi-empirical) and molecular mechanics methods in order to reduce the computational cost [26]. On the basis of the ONIOM results, other properties such as thermodynamic ones are calculated. This approach was for years popular in the computation of the CD systems, as CDs are relatively big structures, and for a long time it was not possible to calculate both the CD and a guest using DFT. Therefore, CD was considered an outer layer and there a lower level of theory was applied, and the guest molecule was computed using a higher level of theory. However, with the general increase in computational power available, this approach is currently rarely used in the studies of CD complexes due to its lower accuracy when compared with pure QC calculations.
  • Molecular dynamics
An MD simulation is a well-established technique used for the study of various molecules complexes and mixtures in any state of matter and at almost any temperature and pressure condition. It can be used to determine structural, energetic, and thermodynamic properties as well as a means to scan the potential energy surface of a studied system.
For MD simulations of large molecular complexes, such as ligand–protein, molecular mechanics (MM) methods are commonly used. On the contrary, when MD simulations are performed on relatively small molecules, it is usually at the quantum mechanics (QM) level of theory, which significantly increases the accuracy of calculations, but also their computational costs. In terms of the sizes of the modeled objects, CD complexes are somewhere in between. While geometry optimization calculations on the static structures of CD complexes are, nowadays, performed mostly at the QM level, usually by the means of DFT, the MD simulations are still being performed at the MM level [12].

2.3. Semi-Empirical Methods

Semi-empirical methods are based on the Hartree–Fock equation but simplified by the application of the empirical corrections [27]. Semi-empirical calculations are much faster than their ab initio counterparts, mostly due to the use of the zero differential overlap approximation. Their results, however, can be very wrong if the molecule being computed is not similar enough to the molecules in the database used to parameterize the method. Here, we will concentrate on the most popular semi-empirical methods, that is AM1, PM3, PM6, and PM7.
According to Figure 2, the most popular semi-empirical method applied for the cyclodextrin complexes is PM3. However, it may be argued whether PM3 delivers better results than the newer generations, PM6 and PM7. The reason for wider application of PM3 instead of PM6 and PM7 may be the fact that some researchers got used to PM3 and some software does not support the newer parametrizations (PM6 and PM7). Since 2019, the DFT methods have strongly overtaken the role of a leading quantum chemistry-based calculation method in the cyclodextrin systems. Naturally, DFT is more precise than any semi-empirical approach, which leaves no space for further investigation, and among the semi-empirical methods, seems to be the most reliable in the complexes in question. Below, the application of the semi-empirical methods in the cyclodextrin-including complexes is described based on the examples from 2015–2022. However, it should also be noticed that the PM3, PM6, and PM7 approaches often co-exist with the DFT ones. In those cases, the systems are first optimized with the semiempirical method to obtain the initial structure for the DFT calculations.
The oldest of all here presented semi-empirical methods is the AM1 approach. There are just a few examples of the cyclodextrin complexes calculated using this approach. In some of them, AM1 was applied to perform the geometrical optimization of a whole guest–CD complex [28]; in others, both substrates were calculated by AM1 whereas the complex underwent the DFT treatment [29], and in others, AM1 was applied solely for the CD.
The next generation of semi-empirical methods is PM3. There are studies showing that PM3 predicts the presence and energy of hydrogen bonds better than AM1 [30]. Moreover, it has been reported that after α- and β-CD optimization with AM1 and PM3, the former resulted in badly distorted geometries, whereas the latter reproduced the crystalline structure rather well [31].
Semi-empirical methods are repetitively reported to deliver good insight into the complex formation process as well as reliable order of the configuration stabilities [32,33,34,35]. These methods help to determine global or local minima. However, it is stressed that to obtain reliable complexation energy values, DFT calculations should be performed [36]. Often, the PM3 approach is undertaken along with the ONIOM DFT/PM3 approach [34,37,38,39,40,41,42,43,44].
The most often and standard PM3 application in the cyclodextrin complexes is to move the guest along the selected axis going through the CD cavity. The guest is stopped every 1 Å, usually between −8 Å or −10 Å and respectively +8 Å or +10 Å. Additionally, the guest is rotated from 0°to 360° usually every 20° or 45°. At each such stopping point, the complexation energy is measured with PM3 [37,44,45,46,47].
In the way of their application to the cyclodextrin systems, the PM6 and PM7 approaches follow the same pattern as PM3. Namely, they are used to gain insight into the complex structure [48] and thermodynamic properties [48,49,50,51,52], which allows to determine the most stable complex [52,53,54,55], and, as in case of ofloxacin enantiomers, rank the eluted substances in the order in which they will be eluted [49]. Similarly, as in the case of PM3, FT-IR spectra can be simulated [50,56]. Further, PM6 and PM7 are often combined with the DFT methods in form of the ONIOM approach [42,52,57,58].
In contrast to PM6, in PM7, the description of dispersion interactions and hydrogen bonding has been improved, and consequently the errors associated with modelling large molecules and complexes have been reduced [49]. The description of properties such as heat of formation or height of the reaction barrier has been improved [59]. In turn, it has been reported that PM6, compared with PM3, can yield better agreement with the experimental values [59]. In another study, when compared to the experiment, PM3 provided wrong and at the same time opposite results to those obtained by PM7 [60]. To depict another example, in a study where β-CD, dimethyl-β-CD, and hydroxypropyl-β-CD were analyzed by both PM6 and PM7, in all cases PM7 delivered complexation energies of significantly lower values [58].
A separate topic is ADMP, the Atom Centered Density Matrix Propagation Molecular Dynamics approach, which can be performed with semi-empirical, Hartree–Fock or DFT methods. It provides equivalent functionality to Born–Oppenheimer molecular dynamics at a considerably reduced computational cost. The ADMP method has a number of attractive features. Systems can be simulated by accurately treating all electrons or by using pseudopotentials. Through the use of a tensorial fictitious mass and smaller values of the mass, reasonably large time steps can be employed, and lighter atoms such as hydrogens need not be replaced with heavier isotopes. A wide variety of exchange-correlation functionals can be utilized, including hybrid density functionals [61]. In the last decade, only two cases have been published: β-CD-olsalazine with PM3-ADMP [62] and β-CD-propranolol with PM6-ADMP, ONIOM(DFT/PM3)-ADMP, and DFT-ADMP approaches [63]. ADMP results confirm the importance of the non-bonded interactions in the complex stabilization.
To sum up this part of the review, a relatively new and complex study should be cited. In the article entitled ‘Prediction of correct intermolecular interactions in host–guest systems involving cyclodextrins’ [63] published in 2020, the following approaches were tested: AM1, PM3, PM6, and DFT with the most standard B3LYP/6-31G(d,p), as well as PM6 and DFT with and without dispersion correction. The study involved 15 α-CD and 28 β-CD inclusion complexes in terms of both geometrical parameters and complexation energy values. The results showed that the most accurate was the B3LYP/6-31G(d,p)-D3 approach, followed by PM6-D3. Nevertheless, taking into account the high computational requirements of the DFT methods, the authors suggest that PM6-D3 is the most accurate and cost-effective approach. However, it must be stated that as the availability of the computational power is developing quickly, the DFT approach might shortly be, or already is, the best option for the computational analysis of the structure and energy of CD systems.

2.4. Density Functional Tight Binding (DFTB)

An approach that can be positioned between semi-empirical methods and DFT is the Density Functional Tight Binding Self Consistent Charge method (DFTB-SCC, referred here to as DFTB), which is often described as DFT approximation [64]. According to the Web of Science, just a few articles referring to DFTB and CD complexes have been published. However, those works show a relatively wide spectrum of possible DFTB applications. In the oldest works [64,65], DFTB was applied to verify the experimental NMR results and deliver some additional structural information. In the first case [64], the method’s application confirmed which conformation of spironolactone was preferred in the complex. In the second case [65], DFTB confirmed that in the analyzed peptide, tyrosine was a favored residue to access the CD’s cavity. In this second study, DFTB was applied within the QM/MM approach. In both of the described cases, the authors claimed good agreement of the obtained computation data with the experimental data.
A more complex situation is described in [66], where the topic is self-inclusion (in the own cavity) of the CD’s substituents. Here, DFTB was compared with the DFT approach. DFTB is said to be method of choice as it predicts the stability order of the analyzed complexes properly, delivers the energy data that are close to the DFT data, and is faster than DFT. Both options including dispersion correction and the absence of this correction have been tested in DFTB and in DFT. The results plainly show that in both cases, application of the correction is necessary. In the case of DFTB, the dispersion-corrected version of calculations result in lower complexation energies and the order is maintained. Nevertheless, the authors emphasize that the application of an empirical dispersion correction may significantly overestimate dispersion interactions, and therefore a comparison with a rigorous DFT method should be done.
Some drawbacks of DFTB have been pointed out in the work that targeted the largest CD for which the crystallographic structure is known [67]. The heavy atoms’ RMSD between the optimized structure and the crystallographic one were between 0.89 Å and 1.35 Å for DFT, depending on the parameters applied, with the best results for the B3LYP functional and 0.95 Å for DFTB. However, even if the overall RMSD looks good, large discrepancies in the angles sizes when compared with the experiment have been reported in the case of the DFTB approach as opposed to all DFT methods.
In turn, the article from 2018 utilizes the DFTB approach to analyze the tautomerization process during encapsulation of genistein in CD [68]. The results are clear and deliver important information on the complexation, namely, ‘DFTB-based MD simulations reveal that spontaneous keto-enol tautomerization occurs even within a hundred picoseconds, which suggests that the encapsulated genistein is complexed in the ordinary enol form of the drug molecule’.

2.5. Density Functional Theory (DFT)

  • Functionals
While performing the DFT calculations, the main two parameters that must be decided on are type of functional and a basis set. Functionals mathematically define the electronic energy, which when added to the kinetic and electrostatic energy of the system, sums up to the total system’s energy [68,69]. According to the literature (see Table 1) for the systems that included CD, the hybrid B3LYP [70], semi-empirical GGA (generalized gradient approximation): wB97XD, B97D3 [71] or meta-GGA kinetic energy density incorporating Minnesota [72] functionals have been applied so far. Among the last category, M06-2X, M05-2X, and M06-L are used, with M06-2X being the most common in the analysis of the non-covalent interactions, whereas M05-2X includes 0% Hartree–Fock (HF) exchange, and M06-2X has 54% HF exchange [73]. In one of the studies including CDs, it was concluded that M06-L delivered poor results [74]. This was expected as the analyzed complex was β-CD-alprazolam, whereas M06L has been designed for calculations of the systems including transition metals, inorganic or organometallics [21]. wB97X and 97D3 are comprised of 22% Hartree–Fock exchange in the short range and 100% Hartree–Fock in the long range [75].
  • Dispersion correction
Noncovalent forces, such as hydrogen bonding and van der Waals interactions, are crucial for the formation, stability, and function of most CD complexes. At present, ubiquitous van der Waals interactions can only be accounted for properly by high-level quantum-chemical wavefunctions or by the Quantum Monte Carlo method. In contrast, the correct long-range interaction tail is absent from all popular local-density or gradient corrected exchange-correlation functionals of DFT, as well as from the Hartree–Fock (HF) approximation. A long-range electron correlation effect, known as the London part of the dispersion energy term, is not included in the Kohn–Sham DFT equation [76]. For years this was an issue affecting the accuracy of the DFT calculations. Nowadays, several dispersion correction methods are available. Nevertheless, their inclusion not always improves the calculation effect, hence this should be tested separately for each system in question. The most widely used dispersion corrections are TS (Tkatchenko-Scheffler) [77], GD (Grimme Dispersion, written also as D) [78], and MBD (Many-Body Dispersion) [79]. However, to perform calculations on the systems that included CD, almost solely the semi-empirical Grimme dispersion correction was applied (see the Table 1). It occurs in the D2, D3, D4, and D3(BJ) versions, where BJ indicates Becke Johnson damping. This last one is rarely used in CD-complex calculations. It is claimed that ‘the damping function in DFT-D methods has only a minor impact on the quality of the results’ [80] and even the comparison between D3 and D3 (BJ) published by Stefan Grimme clearly indicates that ‘the differences between the two methods are much smaller than the overall dispersion effect’ [80]. D3 includes less empirical input than D2, can be called a newer D2-version, and is the dispersion correction that is currently the most widely used.
No dispersion correction is applied to the Minnesota functionals that are parametrized for dispersion. The same applies to wB97X (written also as ωB97X), which is the dispersion-incorporating version of B97X. B3LYP is sometimes used as B3LYP-CAM (Cambridge extension) [81], which includes the long-range correction; however, this is not common, and there is no strong evidence that this type of dispersion correction gives better results than application of the Grimme correction.
Sometimes it seems reasonable to perform the same calculations with two chosen functionals as has been done for the β-CD-2,2′-bipyridine complex [82]. The authors’ conclusion is that wB97XD showed reliability in elucidating weak interactions, whereas B3LYP allowed one to achieve a good time–precision compromise.
Another interesting example is comparison of three types of functionals performed for the β-CD-procaine HCl system [83]. According to the authors, B3LYP showed the highest efficiency and quality of results, wB97XD was specifically used to analyze the long-range interactions, and M06-2X was applied to predict the presence of hydrogen bonds. On the other hand, there are works such as [84] (β-CD-8-Anilinonaphthalene-1-sulfonate) where it is claimed that among tested functionals, B3LYP, wB97XD and M06-2X, the overall best results were delivered by wB97XD.
To take one more example, for the β-CD-benzocaine system [53], where B3LYP, CAM-B3LYP, M05-2X, and M06-2X were tested, M06-2X was claimed to deliver excellent results when used to obtain the NMR spectra. In another study, for UV–Vis spectrum simulation, the B3LYP-D3-based results showed the best agreement with the experimental data. The tested functionals were BLYP-D3, B3LYP-D3, and M06-2X-D3 [22]. In the case of β-CD-5-fluorouracil, inclusion of the dispersion correction changed the interaction energy by 15% and by 20% in water and ethanol solvent, respectively [85].
This only allows us to draw three important conclusions. Firstly, a couple of functionals, preferably representing all three groups (hybrid, GGA, Minnesota) should be tested for each system. Secondly, the choice of a functional depends on the goal of the study: geometry optimization, thermodynamic parameters, NMR spectra, etc. Thirdly, this literature review sends a clear message that the three most used and effective functionals are B3LYP-(D3), wB97XD, and M06-2X.
  • Basis set
It should not be forgotten that in the study preparation, the functional and dispersion correction and the basis set choice play a significant role. The basis sets applied for the CD complexes so far are the Pople, correlation-consistent (cc-pVDZ), and Karlsruhe (def-TZVP, def2-SVP) basis sets (see Table 1). However, the Pople ones are definitely the most common and the variety among them is large, for instance, 6-31G(d), 6-31G(d,p), 6-31+G(d,p), 6-311++G(d,p), 6-31G**, where ‘1′ means basis set enlargement, ‘+’ means an additional diffuse function, and ‘*’ means a polarization function. The choice among different Pople basis sets depends partly on the available computational possibilities and partly on the type of studied objects. Inclusion of diffuse functions is needed to properly calculate the long-range interactions, such as hydrogen bonds. In turn, by extending the size of a basis set, the addition of polarization functions is meaningless. This is why, in the works presented in Table 1, the most presented basis sets are 6-31G(d,p) and 6-311G(d,p).
In Table 1, it is noticeable that the ‘6-31+G* for H, N, O and 4-31G for C’ basis set combination is present. However, first of all, several of these works have been published with one affiliation, in other words, there is one laboratory that uses such an approach, and secondly, such a combination of basis sets for one system has been used mainly in the past when insufficient computation possibilities were at hand. In order to perform computation using the limited available tools, it is common practice to perform the geometry optimization in a lower basis set and later, for instance, for single point calculations, a larger basis set is used. An analogical approach applies to the more and less computationally demanding functionals.

2.6. Solvent

The last parameter to decide on refers to the environment of the system. Calculations can be performed in gas or in solvent. To simulate a solvent in DFT, implicit solvent models are typically used. For the CD systems, the most popular is the family of the Polarizable Continuum Models (PCM) [86]. The other possibility is the Solvation Model Based on Density (SMD). IEFPCM [87] is a reformulation of the dielectric PCM, and the C-PCM is a conductor-like PCM, closer to the COSMO model. SMD defines the free energy of solvation via two components: the one is electrostatic contribution arising from the self-consistent reaction field, the other comes from the short-range interactions between the solute and solvent molecules [88].
Both PCM and SMD treat the solvent as a continuum because using Quantum Mechanics, it would not be possible to calculate a system with a large number of explicit solvent molecules. However, this issue can be partly approached as has been done in the study [64]. There, for general calculations, IEFPCM has been applied, but additionally a separate set of calculations has been done on the limited number of water molecules placed inside the CD cavity. Such an approach is useful if there is the probability that the CD–guest interaction is influenced significantly by the solvent’s presence. For example, when it is assumed that the hydrogen bonds between the guest and host molecules are water mediated. Sometimes, inclusion of the solvent effect decreases the complexation energy significantly, as in the case of the dexamethasone and SMD model [89]. However, it must be pointed out that inclusion of a solvent in the calculated system not always results in better (closer to the experimental data) complexation energies.
Taking into account all what has been written above, in order to make a fully justified selection of the parameters for the DFT calculations, a cross-study including different but most commonly used functionals, dispersion corrections (presence or absence), basis sets, and the environment (gas or solvent, type of solvation) should be performed. To the authors’ best knowledge, so far no such study has been undertaken on any system that includes CD. The already published benchmark studies are quite uncommon and usually focus on modification of one of the parameters, i.e., functionals, dispersion correction or the solvation method [67,90,91,92].
Only afterwards, with the parameters chosen carefully for the analyzed system (e.g., CDs+steroidal hormones, CDs+flavonoids etc.), should further calculations be performed.

2.7. Møller–Plesset Perturbation Theory 2 (MP2)

Only a few (five in the period from 2014–2021) articles in which the MP2 method has been applied for CD analysis have been published. The reason is the fact that this technique is computationally more demanding than DFT and since CD complexes are relatively large, as the objects for QC studies, this method is currently not affordable for most of the computational researchers.
The most recent work in this topic was published in 2017 and concerns β-CDs with one large substituent that can either be located in or outside of the CD’s cavity [68]. The geometry optimization has been performed with the B3LYP-D3 functional but single point calculations already with both B3LYP-D3 and MP2 using various basis sets, for MP2: 6-31G* and 6-311G*.
In another study (β-CD-sertraline) [93], MP2/6-31G(d,p) was applied for the single point calculations, although even the authors of the work state that such a small basis set does not allow one to obtain results with the required accuracy.

3. Preparation of Structures, Post-Processing Methods, and Some Examples

3.1. Preparation of the CD Complexes for the QC Calculations

To obtain the structure of the CD complex that can be used for DFT calculations, both the structure of the chosen CD as well as the structure of the guest molecule must be prepared beforehand. The method of in silico complex preparation is also important, as it may have a major influence on the results.
Since the crystal structures of all of the native and also some of the modified CDs can be found in the CCDC [94], they are usually used as the starting points for calculations. The structure of the guest is either simply drawn using one of the multiple available software packages or taken from the CCDC, assuming that its crystal structure has been deposited previously.
Very important, for the accuracy of the results, is the method of preparation of the complex from its components. This must be done unless a crystal structure of the complex has been obtained or deposited previously in the CCDC, which is unfortunately quite uncommon. Usually, one of the two approaches is used. In the first one, molecular docking is applied, treating CD as a macromolecule and the guest as a ligand. In the reviewed works, the authors usually use the popular Auto Dock [95] software for that purpose. However, some other programs are also used such as Schrodinger Maestro [96] or BIOVIA Discovery Studio [97]. Surprisingly, in the reviewed studies, not much attention was being paid to the description of this part, which was justified by the fact that the initial (docked) structures would be optimized at the higher theory level. This may, however, lead to some inaccurate or even wrong results as the energetically lowest conformation obtained from the docking part may not necessarily be close to the global DFT minimum. This is nicely reflected in Figure 3, where the energetically lowest orientation obtained from molecular docking is substantially different from the experimental one, even after optimization using DFT. However, when the other pose from molecular docking was optimized using QC, much better agreement between the experimental and theoretical results was obtained. Therefore, in some studies, the authors decided to optimize not one but a few different complexes from molecular docking. While this approach is reasonable as it increases the likelihood of finding the deep minimum, it should be noticed that the time of calculations increases linearly with the number of initial structures.
Instead of molecular docking based on the molecular mechanics calculations, in some cases, the authors decided to manually dock the guest into the CD. In order to find the best pose within the cavity, the guest molecule is put in different positions along the selected axis, so that the guest has different levels of immersion into the CD’s cavity. For example, in [98], the guest was moved along the Z-axis from +7.5 Å to −7.5 Å with an interval of 0.3 Å. Additionally, in this particular study, the guest was rotated around the Z-axis by 3° from 0° to 360°. In each step, the generated systems underwent geometry optimization calculations. This type of systematic search seems to be the most accurate approach, especially for the ligands with limited conformational space, with the only drawback being the increase in the calculation time.
The other important factor that is usually neglected in the QC studies of CD complexes is the conformational flexibility of the guest molecule. The optimal conformation of the guest found in vacuo is not necessarily the one that it takes in the complex. To increase the likelihood of finding the deep energetical minimum, the conformational space search of the guest molecule should be performed.
Another aspect that must be taken into consideration is the host–guest molar ratio of the complex. When there are some experimental indications for a specific value, the assumption can be tested using QC calculations. Otherwise, it seems reasonable to prepare the complexes of various stoichiometry and confirm their stability via geometry optimization.

3.2. Description of QC Results

After the host, guest, and complex are optimized at the chosen QC level, the interaction and stabilization energies are obtained. Stabilization energy is defined as the difference between the energy of the fully optimized geometry complex and complex components: CD and guest (Equation (1)) [99]. Interaction energy is defined as the corresponding single point energy.
Estb = Ecplx_opt − (ECD_opt − Eguest_opt)
Sometimes the solvation energy is taken into account as well. It is calculated as the difference between the complex energy in water and in gas. Thermodynamic parameters (TD) are often calculated, as they give more insight into the stability of the analyzed systems.
The collected data allow us to draw conclusions, which forces determination of the complex creation: dispersion [100], van der Waals [63] interactions or hydrogen bonds [61]. TD results allow us to determine whether the complexation process is enthalpy driven [51,84,100], which is said to relate to the number and strength of the intermolecular interactions within the system, or entropy driven, which is quite rare for those complexes. Inclusion of the temperature effects allows us to observe if and how the temperature affects the complex stoichiometry, as in the case of β-CD-pentoxifilline [101].
Additionally, often IR or UV–Vis spectra or NMR chemical shifts are calculated (see Table 1) and in the majority of cases, the results are claimed to have very good agreement with the experimental data.
Another common practice is the application of the QTAIM method (Quantum Theory of Atoms In Molecules) for the DFT-optimized complexes in order to analyze weak interactions and therefore obtain a better understanding of the complex’s structure at the molecular level. Several articles about CD complexes including this approach have been published (see Table 1).

3.3. Analyzed CD Complexes

Among the large variety of CDs, in the DFT studies, mainly only β-CD has been applied so far, and a variety of guests in CD complexes has been analyzed, as presented in Table 1. The guests are mainly drugs among which the antidepressants seem to be especially targeted (Table 1A.1) as well as plant derivatives with (potential) medical use (Table 1B). A separate group consists of substances that could be defined as functionalized food (Table 1C). In those cases, CDs serve to protect or even increase the antioxidative capacity of the substances in question, for example (−)-gallocatechin, (−)-catechin gallate and (−)-gallocatechin present in tea [102,103,104], or to reduce the bitter taste of coffee [105,106]. Moreover, CDs can be used as chiral selectors, and this has its reflection in the DFT articles (Table 1D).
Some of the analyzed systems in Table 1 have been already described in the previous paragraphs as examples regarding the applied parameters and computation. Other selected examples showing a particular usefulness and applicability of the DFT methods as well as the obtained results are described below.
The examples that directly show a vast area of DFT applicability for CD systems analysis are studies of the β-CD complexes, with 8-anilinophthalene-sulfonate [84], benzyl isothiocyanthe [23], metheonine [98] or vanillina [107]. In these works, the DFT approach was used to perform geometry optimization, obtain interaction and stabilization energies, calculate thermodynamic properties, use QTAIM and NBO analysis approaches, and simulate NMR and absorption spectra. The obtained data allow the screening of possible conformations, to define the interactions (van der Waals, hydrogen bonds, etc.) determining the CD–guest interaction, rank the complexes according to their stability, complement experimental spectra, and support the signal assignment.
Further, such chemical information happens to be a crucial part of new theses. For instance, DFT calculations revealed that the nicotine forms have considerably stronger binding with β-CD rather than with Mβ-CD in the same orientation with lower complexation energy. This explains why after 21 days the remaining nicotine increased from 65.56% in pure nicotine to 89.32% and 76.22% in β-CD-nicotine and Mβ-CD-nicotine complexes, respectively [34].
Another example is imipramine and desipramine β-CD complexes [108]. DFT calculations revealed an alternative inclusion scenario: via a guest’s side chain and not via the aromatic moiety. Thus, the controversy in the experiments has been explained because such bimodal complexation increased the therapeutic effect of the substances.
For another antidepressant, paroxetine, the DFT calculations helped to confirm the existence of a new CD inclusion polymorph: a new 2:1 stoichiometry complex has been described [109]. It is characterized by a stronger presence of the dispersion interactions and is more energetically favorable than the 1:1 complex, which improves the drug’s bioavailability.
Again, when it comes to structural information, the DFT approach showed that in 1:2 Cu-flavonoid and 1:3 Fe-flavonoid β-CD complexes, in morin and quercetin, the 3-OH site, and in primuletin, the 5-OH site, were utilized as preferable chelation sites [25]. These data are helpful for scientists trying to obtain an effective CD-flavonoid antidiabetic formulation.
Table 1. Selected articles published in the years 2015–2022 on the application of DFT methods for systems that included CD. The functional and basis set information concerns CD complexes, not guests. Abbreviations used in table: DM-CD (2,6-dimethylo-CD), TM-CD (trimetylo-CD), per-M-CD (permethylated-CD), geo. opt. (geometry optimization), SP (single point calculations), NMR (1H NMR spectra simulation), NBO (Natural Bond Orbitals), BJ (Becke Johnson damping function),TD (thermodynamics calculations), n.i.p. (no information provided). In the case where the DFT application in the published research occurs only as an ONIOM component, the article has not been included in the table. The ONIOM approach along with the examples has been described in Section 2.2.
Table 1. Selected articles published in the years 2015–2022 on the application of DFT methods for systems that included CD. The functional and basis set information concerns CD complexes, not guests. Abbreviations used in table: DM-CD (2,6-dimethylo-CD), TM-CD (trimetylo-CD), per-M-CD (permethylated-CD), geo. opt. (geometry optimization), SP (single point calculations), NMR (1H NMR spectra simulation), NBO (Natural Bond Orbitals), BJ (Becke Johnson damping function),TD (thermodynamics calculations), n.i.p. (no information provided). In the case where the DFT application in the published research occurs only as an ONIOM component, the article has not been included in the table. The ONIOM approach along with the examples has been described in Section 2.2.
No.CDGuestFunctionalBasis SetEnvironmentDFT ApplicationRef.
A (potential) drugs
1β(s)-2-Isopropyl-1-(o-nitrophenyl) Sulfonyl) AziridineB3LYP, WB97X-D, B97D36-31G(d)gas, water [110]
2βboron-based aromatic systemsBLYP-D3(BJ)def2-SVPvacuum, CPCMgeo. opt., natural bond orbital calculations (NBO), complexation energy[100]
3α, β, γalprazolamB3LYP, M06Ldef-TZVPvacuumgeo. opt. in gas, NMR spectra[21]
4βlenalidomideB3LYP, M06-2X6-31G(d,p)PCM [111]
5βdexamethasoneBLYP-D4def2-TZVPgas, watergeo. opt., complexation energy[89]
6β2,2′-BipyridineB3LYP, wB97XD6-31G(d)PCM (eight solvents)geo. opt., UV–Vis spectrum, HOMO-LUMO[82]
7β2,2′-DipyridylamineB3LYP6-311++G(d,p)PCM [112]
8 vardenafil hydrochlorideB3LYP6-311G(2d,2p)vacuumgeo. opt., FT-IR[113]
9amino-CDdoxorubicinB3LYP6-31Gvacuumgeo. opt., complexation energy, HOMO-LUMO, dipole moment, chemical potential, electrophilicity[114]
10β5-fluorouracilB3LYP-D36-31+G(d,p)vacuum, PCMgeo. opt., complexation energy, harmonic frequency calculations[85]
11HP-β2-methyl mercapto phenothiazineB97-D3, BP86-D36-31G(d,p)gas, CPCMgeo. opt., vibrational spectra, NBO, QTAIM, HOMO-LUMO[115]
12βvemurafenibωB97XD6-31+G(d)vacuum, PCMGeo. opt., vibrational spectra, MD, NBO, TD, HOMO-LUMO[116]
13βprocaine hydrochlorideB3LYP, M06-2X, WB97XD6-31G(d,p)gas, PCMGeo. opt., NBO[83]
14β, SBE-βfluorometholone, cholesterolM06-2X6-31G**PCMGeo opt., interaction energy[117]
15α, β, γchlordeconeM06-2X-D36-31G(d,p)SMDGeo. opt., QTAIM[118]
16β, methyl-βnicotineM06-2X6-31G(d,p)n.i.p.Geo., opt., complexation enrgy[34]
17β8-Anilinonaphthalene-1-sulfonateB3LYP, M06-2X, WB97X-D6-31G(d)gas, waterGeo. opt., interaction energy, NMR, TD, NBO[84]
18βbenzocaineB3LYP, CAM-B3LYP, M05-2X, M06-2X6-31G(d,p)PCMGeo. opt., QTAIM, NBO, NMR, HOMO-LUMO, TD[53]
19βaryl pentazoleM06-2X6-31+G(d,p)PCMGeo. opt.[119]
20β2,4D, dicamba pesticidesPBE1PBE (PBE0), B97-D, M06-2X6-31G(d,p)gas, SMDGeo. opt.[120]
21Monochlorotriazinyl-βpermethrin, cyppermethrinBLYP (geo. opt.); BLYP-D3, B3LYP-D3, M06-2X-D3 (UV–Vis)def2-SV(P) (geo. opt.); TZVP (UV–Vis)COSMOGeo. opt.[22]
22βdopamineB3LYP, MPW1PW91, M05-2X, M06-2X, ωB97X-D3-21G*CPCMGeo. opt., complexation energy, QTAIM, NBO[61]
23αbenzoate derivativesM06L (geo. opt.); M06-2X//M06-L (SP)6-31+G(d,p)gasGeo. opt.[121]
24α, β, γcholic, deoxycholic acidB97-D, M06-2X, B3LYP6-31G(d)PCMGeo. opt., interaction energy[122]
25αbenzoate derivativesM06-2X//M06-L, M06-2X//BLYP, BLYP, M06-2X6-31+G(d,p)gasGeo. opt., interaction energy[123]
26γcetirizineB3LYPdef-TZVPn.i.p.Geo.opt., interaction energy, HOMO-LUMO, DOS, NMR[124]
27succinyl-βuraniumM06-2X6-31G(d,p)SMDGeo. opt.[125]
28β-CD, DM -βthymidine-carbonateB3LYP-GD26-31G(d,p)PCMGeo. opt., complexation energy, TD, HOMO-LUMO, NMR[126]
29βglycyl-L-phenylalanineB3LYP3-21G(d)PCMGeo. opt., interaction energy, HOMO-LUMO[127]
30βsodium salicylateB3LYP6-31G(d)gas, PCMGeo. opt., solvation energy, relative stabilization energy, complexation energy,
change of volume
31βbenzyl isothiocyantheB97-D3def2-SVPvacuumGeo. opt., complexation energy, HOMO-LUMO, NBO, NMR[23]
32αiodine solutionCAM-B3LYP6-31*GPCMGeo. opt., absorption spectra, HOMO-LUMO[129]
33βmeta-aminophenolM06-2X6-31G(d,p)IEFPCMGeo. opt., complexation energy, HOMO-LUMO, TD, NBO[130]
35βL-glutamineB97-D36-31G(d)n.i.p.Geo. opt., complexation energy, TD, NBO, QTAIM[131]
36βR and S ibuprofenM062X6-31G(d,p) (geo. opt.); 6-311++G(d,p) (SP)gas, SMDGeo. opt., solvation energy[132]
37α, βthioureidesB97-D36–31G(d,p) Geo. opt., interaction energy[133]
38βmepivacaineB97-D36-31G(d,p)gas, SMDGeo. opt., interaction energy, TD[134]
39βL-metheonineWB97-D36-31G(d)PCMgeo. opt., interaction energy, QTAIM, TD, NMR[98]
40βprazosin, losartanB3LYP6–311+G(d,p)gasGeo. opt.[135]
41βolsalazineB3LYP, WB97-D3, CAM-B3LYP (UV-vis)6-31+G(d)PCMGeo. opt., ADMP[62]
42βaspirinB3LYP-D3cc-pVDZgasGeo. opt., qTAIM, NBO[136]
43βquinineB3PW916-311++G(d,p)PCMGeo. opt.[137]
44βerlotinibB3LYP6-31+G*n.i.p.Geo. opt., harmonic frequencies, HOMO-LUMO[138]
45γrocuronium, vecuroniumB3LYP6–31+G(d,p)n.i.p.Geo. opt., NBO, HOMO-LUMO[139]
46α, β, γcathinoneM05-2X6-31G(d)gas, CPCM (water, chloroform, methanol)Geo. opt., QTAIM, NBO, IR spectra, TD[140]
48βflutafemic acidB3LYP, M05-2X6-31G(d)vacuum, waterGeo. opt., complexation energy, TD, NMR[142]
492-HP-βCu (II) and Fe (III) complexes of quercetin, morin, primuletinB3LYP6-311++G**n.i.p.Geo. opt., complexation energy, HOMO-LUMO[25]
50β6-thioguanine, 6-mercaptopurineB3LYP6-31+g(d,p)IEFPCM (DMSO)Geo. opt., interaction energy, TD[37]
51βN-(2-chloroethyl),N -nitroso,N′,N′-dicyclohexylsulfamidB3LYP6-31G(d)PCM (DMSO)Geo. opt., NBO, QTAIM[143]
52βbenzaldehydeB97-D6-31G(d,p) (geo. opt.); 6-311++G(2d,p) (SP)gas, SMDGeo. opt., interaction energy, TD[144]
53αchitibioseM06-2X6-311++G**n.i.p.Geo. opt., NBO, QTAIM[145]
54αhydrated and nonhydrated IIA/IIB group metal cationsM06-2X6-31G(d,p)gas, PCMGeo. opt., interaction energy, TD[146]
55βnabumetoneWB97X-D, B97-D, B3LYP, M05-2X, M06-2X6-31G(d)IEFPCMGeo. opt., NBO, QTAIM[40]
56βpropranololB3LYP, ωB97XB (ONIOM)6-31+G(d)gas, IEFPCM, explicit solvent effect: explicit water molecules inside of the complexGeo. opt., interaction energy, ADMP, TD[59]
57functionalized CDs8-hydroxyquinoline ligandsB3LYP6-31G**n.i.p.Geo. opt.[147]
58βpentoxifillineM06-2X6-31g(d,p)gasGeo. opt., NBO, HOMO-LUMO[101]
59βp-nitropenthyl acetateB3LYP6-31G(d,p)n.i.p.Geo. opt., interaction energy, NBO, HOMO-LUMO[148]
60βnorfloxacinB97D (geo. opt.), B3LYP (SP, NMR)6-31G(d,p)IEFPCMGeo. opt., interaction and stabilization energy, NMR, TD[149]
A1. Antidepressants
61βparoxetineB3LYP (geo. opt.); B97D (SP)6-31+G* for H, N, O and 4-31G for CvacuumGeo. opt., interaction energy, TD[109]
622,6-DM-βmianserinB3LYP-GD2 (geo. opt.); M05-GD3, M06-GD3, M062X-GD3, ωB97XD, mPW1PW91, M11 (SP)6-31G(d,p)PCM, vacuumGeo. opt., interaction energy, NMR[150]
63βsertraline HCl, fluoxetine HClB3LYP6-31+G* for H, N, O and 4-31G for CgasGeo. opt., interaction energy[151]
64βprotriptyline, maprotilineB3LYP6-31+G* for H, N, O and 4-31G for CvacuumGeo. opt., interaction and stabilization energy[152]
65βclomipramine, doxepinB3LYP31+G(d) for H, N, O, Cl, and 4-31G for CgasGeo. opt., interaction energy[153]
66βdesipramine, imipramineB3LYP6-31þG(d) for H, N, O and 4- 31G for Cgas, implicit solvent (water)Geo. opt., interaction and stabilization energy[108]
67βamitryptyline, nortryptilinen.i.p.6-31+G* for H, N, O, Cl and 4-31G for Cvacuum, SMDGeo. opt., interaction and stabilization energy[154]
B. Plant derivatives
68HP-βthymoquinoneB3LYP-D2, B3LYP-D36-31G(d,p)PCMGeo. opt., NBO, QTAIM, HOMO-LUMO, NMR[155]
69αβ-caroteneB3LYPcc-pVDZvacuumGeo. opt., interaction energy, Raman spectra[156]
70γ3-hydroxyflavonePBE0def2-SVPCMGeo. opt., HOMO-LUMO, IT spectra[157]
71βvanillinaB3LYP, ωB97xD, M06- 2X6-311G(d,p)vacuum, CPCMGeo. opt., interaction energy, NMR, HOMO-LUMO, NBO, QTAIM, UV–Vis[107]
72βalfa-terpineolB3LYP (for UV–Vis), B3LYP/CAM, M062X, WB97-D36-311G(d,p)vacuum, CPCMGeo. opt., complexation energy, NBO, QTAIM, TD, UV-vis[158]
73TM-β, βnaringeninB3LYP, M06-2X, wB97X-D6-31G(d)vacuumGeo. opt., interaction energy, NBO, QTAIM, NMR, HOMO-LUMO[159]
742,6-DMβ, 2HP-β, 2,6-DH-β, βeucalyptolM06-2X6-31G(d,p) Geo. opt., interaction energy[160]
75βfisetinM06-2X6-31G(d,p)gas, PCMGeo. opt., interaction energy[161]
76βgallic acidB97-D36-31G*, for GIAO: 6-311++g**gas, solventGeo. opt., HOMO-LUMO, NBO, NMR[162]
77βgabapentinB3LYP-D36- 31G(d)vacuum, PCMGeo. opt., interaction energy, NBO, HOMO-LUMO[163]
78Β, γtropane alkaloidsB3LYP6-31+G(d,p)PCMGeo. opt., interaction energy, NMR[164]
79βcoumarinsEDF26-311G(d,p)PCMGeo. opt.[165]
802-HP-βquercetinB3LYP6-31G* Geo. opt.[166]
81βcarvacrol, thymolB3LYP6-31G, 6-31+G(d)SMDGeo. opt., interaction energy, NBO, HOMO-LUMO[167]
82βthymolB3LYP, PBEPBE, CAM-B3LYP6-31G(d,p)PCMGeo. opt., interaction energy, UV–Vis[168]
83βcarvacrolB3LYP, M05-2X6-31G(d)PCMGeo. opt., HOMO-LUMO, NBO[42]
C. Functionalized food
84β(−)-gallocatechin, (−)-catechin gallate, (−)-gallocatechin gallateB3LYP6-31+G* for H, O and 4-31G for CgasGeo. opt., interaction and stabilization energy[102,103]
85β(−)-epigallocatechin, (−)-epigallocatechin gallateB3PW91cc-pVDZgasGeo. opt., interaction energy[104]
86βcatechol derivatives: protocatechuic aldehyde, protocatechuic acidB3LYP6-31+G* for H, O and 4-31G for Cgas (geo. opt.), implicit solvent (TD)Geo. opt., interaction energy, TD[169]
87βoleuropein, hydroxytyrosol, tyrosoln.i.p.6-31+G* for H, O and 4-31G for CgasGeo. opt., interaction energy, TD[170]
88βchlorogenic, caffeic, quinic acidsB3LYP6-31+G* for H, O and 4-31G for CgasGeo. opt., interaction energy, TD[105,106]
D. CD as a chiral selector
89βD- and L-penicillamineB3LYP-D3 (geo. opt.); M062X-D3, xB97X-D, B3LYP-D3 (interaction energy)6-31G(d, p) (geo. opt.); G-311+G(d,p) (interaction energy)waterGeo. opt., interaction energy[171]
90metal-ion coupled βD- and L-penicillamineDFT, M062X6-31G(d,p)vacuumGeo. opt.[172]
91βR- and S-propranololB3LYP6-311+G(d,p)vacuumGeo. opt., vibrational spectra[173]
92per-M βD- and L-isoleucineB3LYP (geo. opt.), wB97X-D (IR)6-31G*, 6-311G**gasGeo. opt., interaction energy, IR spectra, TD[174]
93per-M βD- and L-alanineB3LYP, wB97X-D, M06-2X6-31G**, 6-311G** Geo. opt., IR spectra[175]
942,3,6-TM-βcis-(2S,4R) and -(2R,4S) ketoconazoleB3LYP6-311G(d,p)gas (geo. opt.), PCM (SP)Geo. opt., interaction energy[36]
952-HP-βabacavir enentiomersPBE6-31G*PCMGeo. opt., interaction energy[176]

4. Conclusions

The number of studies concerning CDs complexes in which the theoretical calculations at the QC level have been used has constantly increased since the beginning of the 21st century. Solely for the DFT-based works in this topic, the number of published articles has already exceeded 300. While this number is still relatively low, when compared to the amount of reported molecular dynamics simulations at the molecular mechanics level [12], the reviewed works reveal that the application of QC calculations in the studies of CD complexes can be essential, providing the results unobtainable by any other method, both experimental and computational.
Initially, for those kind of studies, less computationally demanding semi-empirical methods have been applied (mostly PM3, PM6, and PM7). However, since 2015, each year there have been more papers in which DFT has been chosen instead of the semi-empirical approach. Nevertheless, even in some works published after 2020, the authors have found that the PM6 or PM7, when used with appropriate dispersion correction, can provide results with similar accuracy to those obtained using DFT.
Regarding calculations of geometries and interaction energies with DFT methods, in most of the reviewed works, the inclusion of dispersion correction was found to be crucial to obtain accurate energies, irrespective of the basis set and functional used. As for the functionals, there is no surprise that B3LYP, which is the most commonly applied one in the field of organic molecule calculations, is also the one that is most extensively used for the studies of CD complexes. However, in some works where the authors have used wB97X or M06-2X instead, different results have been obtained both in terms of predicted geometry as well as stability ranking.
When preparing the complexes, some authors prefer to manually dock the molecules, systematically moving the guest towards the CD cavity and rotating it; however, in most of the works, the molecular mechanics docking procedure has been applied, usually employing the popular and freeware Auto Dock. It should be noticed that the best pose from docking was not always the one with the lowest DFT energy; therefore, at least a few different poses should be optimized in order to achieve credible results.
Though in most of the reviewed works the authors have limited their calculations solely to geometry optimization of one or a few conformations, in some of the articles, the complex properties have been computed. Successful application of DFT methods include prediction of UV–Vis, IR, and NMR spectra as well as HOMO-LUMO and NBO calculations.
The major problem with the DFT calculations seems to be the solvent treatment. In the vast majority of the reviewed works, the authors decided to apply an implicit solvation model, usually PCM or SMD. However, other studies have shown that the role of water in the complex formation can be crucial as the water-mediated hydrogen bonds between the host and guest have been observed many times. Further, the role of water release from the cyclodextrin cavity during the complexation significantly affects the thermodynamics of such a process, which can be modeled accurately only using explicit water models.
Finally, it should be emphasized that even when carefully choosing the appropriate DFT method (applied functional, basis set, solvation scheme, dispersion correction, credible initial conformation), the obtained results can still be different from the corresponding experimental ones. This is due to the high flexibility and dynamics of most of CD complexes. Therefore, it seems reasonable to explore the application of ab initio molecular dynamics simulations. While, at this moment, it may be computationally not affordable for many researchers, combining the benefits of molecular dynamics simulations with the accuracy of DFT calculations seems to be the solution to obtain even more accurate results.

Author Contributions

Conceptualization, A.H.M. and Ł.S. writing—original draft preparation, A.H.M., Ł.S.; writing—review and editing, A.H.M., Ł.S.; supervision, Ł.S. All authors have read and agreed to the published version of the manuscript.


This research received no external funding.

Institutional Review Board Statement

Not applicable.

Informed Consent Statement

Not applicable.

Data Availability Statement

Not applicable.

Conflicts of Interest

The authors declare no conflict of interest.


  1. Aiassa, V.; Garnero, C.; Longhi, M.R.; Zoppi, A. Cyclodextrin Multicomponent Complexes: Pharmaceutical Applications. Pharmaceutics 2021, 13, 1099. [Google Scholar] [CrossRef] [PubMed]
  2. Poulson, B.G.; Alsulami, Q.A.; Sharfalddin, A.; El Agammy, E.F.; Mouffouk, F.; Emwas, A.-H.; Jaremko, L.; Jaremko, M. Cyclodextrins: Structural, Chemical, and Physical Properties, and Applications. Polysaccharides 2022, 3, 1. [Google Scholar] [CrossRef]
  3. Hădărugă, N.G.; Bandur, G.N.; David, I.; Hădărugă, D.I. A review on thermal analyses of cyclodextrins and cyclodextrin complexes. Environ. Chem. Lett. 2019, 17, 349–373. [Google Scholar] [CrossRef]
  4. Szejtli, J.; Szente, L. Elimination of bitter, disgusting tastes of drugs and foods by cyclodextrins. Eur. J. Pharm. Biopharm. 2005, 61, 115–125. [Google Scholar] [CrossRef]
  5. European Medicines Agency. Available online: (accessed on 29 May 2022).
  6. U.S. Food & Drug Administration (FDA). Available online: (accessed on 29 May 2022).
  7. Pharmaceutical and Medical Devices Agencty. Available online: (accessed on 29 May 2022).
  8. Tran, D.N.; Colesnic, D.; de Beaumais, S.A.; Pembouong, G.; Portier, F.; Queijo, A.; Tato, J.V.; Zhang, Y.; Ménand, M.; Bouteiller, L.; et al. Cyclodextrin-adamantane conjugates, self-inclusion and aggregation versus supramolecular polymer formation. Org. Chem. Front. 2014, 1, 703–706. [Google Scholar] [CrossRef]
  9. Carrazana, J.; Jover, A.; Meijide, F.; Soto, A.V.H.; Tato, J.V. Complexation of Adamantyl Compounds by β-Cyclodextrin and Monoaminoderivatives. J. Phys. Chem. B 2005, 109, 9719–9726. [Google Scholar] [CrossRef]
  10. Jug, M.; Mura, P.A. Grinding as Solvent-Free Green Chemistry Approach for Cyclodextrin Inclusion Complex Preparation in the Solid State. Pharmaceutics 2018, 10, 189. [Google Scholar] [CrossRef][Green Version]
  11. Wdowiak, K.; Rosiak, N.; Tykarska, E.; Żarowski, M.; Płazińska, A.; Płaziński, W.; Cielecka-Piontek, J. Amorphous Inclusion Complexes: Molecular Interactions of Hesperidin and Hesperetin with HP-Β-CD and Their Biological Effects. Int. J. Mol. Sci. 2022, 23, 4000. [Google Scholar] [CrossRef]
  12. Mazurek, A.H.; Szeleszczuk, Ł.; Gubica, T. Application of Molecular Dynamics Simulations in the Analysis of Cyclodextrin Complexes. Int. J. Mol. Sci. 2021, 22, 9422. [Google Scholar] [CrossRef]
  13. Dehghani, A.; Bahlakeh, G.; Ramezanzadeh, B.; Mofidabadi, A.H.J.; Mostafatabar, A.H. Benzimidazole loaded β-cyclodextrin as a novel anti-corrosion system; Coupled experimental/computational assessments. J. Colloid Interface Sci. 2021, 603, 716–727. [Google Scholar] [CrossRef]
  14. Roschi, E.; Gellini, C.; Ricci, M.; Sanchez-Cortes, S.; Focardi, C.; Neri, B.; Otero, J.C.; López-Tocón, I.; Smulevich, G.; Becucci, M. Surface-Enhanced Raman Spectroscopy for Bisphenols Detection: Toward a Better Understanding of the Analyte–Nanosystem Interactions. Nanomaterials 2021, 11, 881. [Google Scholar] [CrossRef] [PubMed]
  15. Paulino, P.H.S.; Silva, C.F.; De Almeida, B.D.; Guimarães, L.; Nascimento, C.S. A theoretical study of poly(p-phenylenes) and their cyclodextrin-based insulated molecular wires. Comput. Theor. Chem. 2021, 1197, 113157. [Google Scholar] [CrossRef]
  16. Dehghani, A.; Bahlakeh, G.; Ramezanzadeh, B. Synthesis of a non-hazardous/smart anti-corrosion nano-carrier based on beta-cyclodextrin-zinc acetylacetonate inclusion complex decorated graphene oxide (β-CD-ZnA-MGO). J. Hazard. Mater. 2020, 398, 122962. [Google Scholar] [CrossRef] [PubMed]
  17. Tomer, A.; Kusema, B.T.; Paul, J.-F.; Przybylski, C.; Monflier, E.; Pera-Titus, M.; Ponchel, A. Cyclodextrin-assisted low-metal Ni-Pd/Al2O3 bimetallic catalysts for the direct amination of aliphatic alcohols. J. Catal. 2018, 368, 172–189. [Google Scholar] [CrossRef]
  18. Quan, X.; Yi, S.; Wang, X. Theoretical study of an anti-Markovnikov addition reaction catalyzed by β-cyclodextrin. J. Mol. Model. 2018, 24, 77. [Google Scholar] [CrossRef]
  19. Mazurek, A.H.; Szeleszczuk, Ł.; Pisklak, D.M. Periodic DFT Calculations—Review of Applications in the Pharmaceutical Sciences. Pharmaceutics 2020, 12, 415. [Google Scholar] [CrossRef]
  20. Van De Streek, J.; Neumann, A.M. Validation of molecular crystal structures from powder diffraction data with dispersion-corrected density functional theory (DFT-D). Acta Crystallogr. Sect. B Struct. Sci. Cryst. Eng. Mater. 2014, B70, 1020–1032. [Google Scholar] [CrossRef]
  21. Imtiaz, S.; Ali, S.M. Atom accurate structure determination of alprazolam/cyclodextrin inclusion complexes by ROESY and computational approaches. J. Indian Chem. Soc. 2022, 99, 100299. [Google Scholar] [CrossRef]
  22. Lu, H.; Wang, Y.; Xie, X.; Chen, F.; Li, W. Molecular dynamics simulation and TDDFT study of the structures and UV–vis absorption spectra of MCT-β-CD and its inclusion complexes. Spectrochim. Acta Part A Mol. Biomol. Spectrosc. 2015, 149, 564–570. [Google Scholar] [CrossRef]
  23. Bouhadiba, A.; Rahali, S.; Belhocine, Y.; Allal, H.; Nouar, L.; Rahim, M. Structural and energetic investigation on the host/guest inclusion process of benzyl isothiocyanate into β-cyclodextrin using dispersion-corrected DFT calculations. Carbohydr. Res. 2020, 491, 107980. [Google Scholar] [CrossRef]
  24. Wang, J.; Zhang, R.; Lu, Z.; Ai, Y. Experimental and theoretical studies of spherical β-cyclodextrin modified titanium dioxide composites for uranium removal. Ecol. Eng. 2020, 149, 105835. [Google Scholar] [CrossRef]
  25. Jabeen, E.; Janjua, N.K.; Ahmed, S.; Murtaza, I.; Ali, T.; Masood, N.; Rizvi, A.S.; Murtaza, G. DFT predictions, synthesis, stoichiometric structures and anti-diabetic activity of Cu (II) and Fe (III) complexes of quercetin, morin, and primuletin. J. Mol. Struct. 2017, 1150, 459–468. [Google Scholar] [CrossRef]
  26. Yuan, S.; Shi, W.; Li, B.; Wang, J.; Jiao, H.; Li, Y.-W. Theoretical ONIOM2 Study on Pyridine Adsorption in the Channels and Intersection of ZSM-5. J. Phys. Chem. A 2005, 109, 2594–2601. [Google Scholar] [CrossRef]
  27. Christensen, A.; Kubař, T.; Cui, Q.; Elstner, M. Semiempirical Quantum Mechanical Methods for Noncovalent Interactions for Chemical and Biochemical Applications. Chem. Rev. 2016, 116, 5301–5337. [Google Scholar] [CrossRef]
  28. Ferrero, R.; Pantaleone, S.; Delle Piane, M.; Caldera, F.; Corno, M.; Trotta, F.; Brunella, V. On the Interactions of Melatonin/β-Cyclodextrin Inclusion Complex: A Novel Approach Combining Efficient Semiempirical Extended Tight-Binding (xTB) Results with Ab Initio Methods. Molecules 2021, 26, 5881. [Google Scholar] [CrossRef] [PubMed]
  29. Vidal, R.B.P.; Ibañez, G.A.; Escandar, G.M. Spectrofluorimetric study of phenolic endocrine disruptors in cyclodextrin media. RSC Adv. 2015, 5, 20914–20923. [Google Scholar] [CrossRef]
  30. Li, X.-S.; Liu, L.; Mu, T.-W.; Guo, Q.-X. A Systematic Quantum Chemistry Study on Cyclodextrins. Mon. Chem. 2000, 131, 849–855. [Google Scholar] [CrossRef]
  31. Fatiha, M.; Khatmi, D.E.; Largate, L. Theoretical approach in the study of the inclusion processes of sulconazole with β-cyclodextrin. J. Mol. Liq. 2010, 154, 1–5. [Google Scholar] [CrossRef]
  32. Setiadji, S.; Sundari, C.D.D.; Ramdhani, M.A.; Umam, A.B.K.; Ivansyah, A.L. Theoretical Investigation of Inclusion Complex between Omeprazole Enantiomers and Carboxymethyl-β-Cyclodextrin. IOP Conf. Ser. Mater. Sci. Eng. 2018, 288, 012138. [Google Scholar] [CrossRef]
  33. Saroj, M.K.; Payal, R.; Jain, S.; Sharma, N.; Rastogi, R.C. Investigation of indole chalcones encapsulation in β-cyclodextrin: Determination of stoichiometry, binding constants and thermodynamic parameters. J. Incl. Phenom. Macrocycl. Chem. 2018, 90, 306–320. [Google Scholar] [CrossRef]
  34. Nurhidayah, E.S.; Martoprawiro, M.; Zulfikar, M.A. PM3 and ONIOM2 modelling of inclusion complex of ibuprofen enantiomers with dimethyl-β-Cyclodextrin. J. Chem. Tech. Metall. 2019, 54, 673–678. [Google Scholar]
  35. Srihakulung, O.; Triamchaisri, N.; Toochinda, P.; Lawtrakul, L. Theoretical study on ferrocenyl hydrazones inclusion complexes with β-cyclodextrin and its three methylated derivatives. J. Incl. Phenom. Macrocycl. Chem. 2020, 98, 79–91. [Google Scholar] [CrossRef]
  36. Arsad, S.R.; Maarof, H.; Ibrahim, W.A.W.; Aboul-Enein, H.Y. Theoretical and Molecular Docking Study of Ketoconazole on Heptakis(2,3,6-tri-O -methyl)-β-cyclodextrin as Chiral Selector. Chirality 2016, 28, 209–214. [Google Scholar] [CrossRef] [PubMed]
  37. Bensouilah, N.; Fisli, H.; Bensouilah, H.; Zaater, G.; Abdaoui, M.; Boutemeur-Kheddis, B. Host-guest complex of N-(2-chloroethyl), N-nitroso,N′,N′-dicyclohexylsulfamid with β-cyclodextrin: Fluorescence, QTAIM analysis and structure-chemical reactivity. J. Mol. Struct. 2017, 1146, 179–190. [Google Scholar] [CrossRef]
  38. Ivansyah, A.L.; Martoprawiro, M. Buchari Computational modeling of inclusion complex of r/s-omeprazole with β-cyclodextrin using oniom2 method. J. Phys. Conf. Ser. 2017, 812, 012070. [Google Scholar] [CrossRef]
  39. Yang, Z.; Huang, L.; Yao, X.; Ji, H. Host-guest complexes of estragole with β-cyclodextrin: An experimental and theoretical investigation. Flavour Fragr. J. 2017, 32, 102–111. [Google Scholar] [CrossRef]
  40. Bensouilah, N.; Boutemeur-Kheddis, B.; Meddour, I.; Abdaoui, M. Host-guest complex of nabumetone: β-cyclodextrin: Quantum chemical study and QTAIM analysis. J. Incl. Phenom. Macrocycl. Chem. 2017, 87, 191–206. [Google Scholar] [CrossRef]
  41. Reis, V.S.; Santos, E.S.; Bonsolhos, D.N.F.; Guimarães, L.; De Almeida, W.G.; Nascimento, C.S. Theoretical study on the formation process of Cross-Linked β-Cyclodextrin molecular tubes. Chem. Phys. Lett. 2017, 677, 13–18. [Google Scholar] [CrossRef]
  42. Abdelmalek, L.; Fatiha, M.; Leila, N.; Mouna, C.; Nora, M.; Djameleddine, K. Computational study of inclusion complex formation between carvacrol and β-cyclodextrin in vacuum and in water: Charge transfer, electronic transitions and NBO analysis. J. Mol. Liq. 2016, 224, 62–71. [Google Scholar] [CrossRef]
  43. Al Azzam, K.M.; Muhammad, E. Host-guest Inclusion Complexes between Mitiglinide and the Naturally Occurring Cyclodextrins α, β, and γ: A Theoretical Approach. Adv. Pharm. Bull. 2015, 5, 289–291. [Google Scholar] [CrossRef][Green Version]
  44. Yang, Z.; Yao, X.; Xiao, Z.; Chen, H.; Ji, H. Preparation and release behaviour of the inclusion complexes of phenylethanol withβ-cyclodextrin. Flavour Fragr. J. 2016, 31, 206–216. [Google Scholar] [CrossRef]
  45. Nazarov, V.B.; Avakyan, V.G.; Bagrii, E.I.; Vershinnikova, T.G.; Alfimov, M.V. Long-lived phosphorescence of arenes in complexes with cyclodextrins 2. Room-temperature phosphorescence of ternary complexes of naphthalene and phenanthrene with β-cyclodextrin and adamantane derivatives in the presence of oxygen. Russ. Chem. Bull. 2005, 54, 2752–2756. [Google Scholar] [CrossRef]
  46. Bouzit, H.; Stiti, M.; Abdaoui, M. Spectroscopic and molecular modelling investigations of supramolecular complex of β-cyclodextrin with N-[(4-sulfonamidophenyl)ethyl]-5-(1,2-dithiolan-3-yl)pentanamide. J. Incl. Phenom. Macrocycl. Chem. 2016, 86, 121–134. [Google Scholar] [CrossRef]
  47. Laspidou, C.S.; Archimandritis, A.S.; Papadimitriou, T.; Kormas, K.A.; Yannakopoulou, K.; Lazarou, Y.G. Theoretical investigation of microcystin-LR, microcystin-RR and nodularin-R complexation with α-, β-, and γ-cyclodextrin as a starting point for the targeted design of efficient cyanotoxin traps. Sustain. Chem. Pharm. 2016, 3, 25–32. [Google Scholar] [CrossRef]
  48. Suliman, F.O.; Elbashir, A.A.; Schmitz, O.J. Study on the separation of ofloxacin enantiomers by hydroxyl-propyl-β-cyclodextrin as a chiral selector in capillary electrophoresis: A computational approach. J. Incl. Phenom. Macrocycl. Chem. 2015, 83, 119–129. [Google Scholar] [CrossRef]
  49. Mizera, M.; Lewandowska, K.; Miklaszewski, A.; Cielecka-Piontek, J. Machine Learning Approach for Determining the Formation of β-Lactam Antibiotic Complexes with Cyclodextrins Using Multispectral Analysis. Molecules 2019, 24, 743. [Google Scholar] [CrossRef] [PubMed][Green Version]
  50. Djilani, I.; Madi, F.; Nouar, L.; Haiahem, S.; Rahim, M.; Khatmi, D.E.; Bouhadiba, A. Theoretical investigation to characterize the inclusion complex of α-lipoic acid and β-cyclodextrin. Comptes Rendus Chim. 2015, 18, 170–177. [Google Scholar] [CrossRef]
  51. Bouhadiba, A.; Belhocine, Y.; Rahim, M.; Djilani, I.; Nouar, L.; Khatmi, D.E. Host-guest interaction between tyrosine and β-cyclodextrin: Molecular modeling and nuclear studies. J. Mol. Liq. 2017, 233, 358–363. [Google Scholar] [CrossRef]
  52. Sambrook, M.R.; Vincent, J.C.; Ede, J.A.; Gass, I.A.; Cragg, P.I. Experimental and computational study of the inclusion complexes of β-cyclodextrin with the chemical warfare agent soman (GD) and commonly used simulants. RSC Adv. 2017, 7, 38069–38076. [Google Scholar] [CrossRef][Green Version]
  53. Yahia, H.A.; Yahia, O.A.; Khatmi, D.; Belghiche, R.; Bouzitouna, A. Quantum chemical investigations on hydrogen bonding interactions established in the inclusion complex β-cyclodextrin/benzocaine through the DFT, AIM and NBO approaches. J. Incl. Phenom. Macrocycl. Chem. 2017, 89, 353–365. [Google Scholar] [CrossRef]
  54. Ceborska, M.; Kędra-Królik, K.; Kowalska, A.A.; Koźbiał, M. Comparative study of molecular recognition of folic acid subunits with cyclodextrins. Carbohydr. Polym. 2018, 184, 47–56. [Google Scholar] [CrossRef] [PubMed]
  55. Appell, M.; Evans, K.O.; Jackson, M.A.; Compton, D.L. Determination of ochratoxin A in grape juice and wine using nanosponge solid phase extraction clean-up and liquid chromatography with fluorescence detection. J. Liq. Chromatogr. Relat. Technol. 2018, 41, 949–954. [Google Scholar] [CrossRef]
  56. López-Méndez, L.J.; Rojas-Aguirre, Y.; Vázquez-Lima, H.; Cassani, J.; Enríquez, R.G.; Rojo-Domínguez, A.; Guadarrama, P. On the conformational search of a βCD dendritic derivative: NMR and theoretical calculations working together reveal a donut-like amphiphilic structure. J. Mol. Struct. 2020, 1204, 127535. [Google Scholar] [CrossRef]
  57. Sahra, K.; Dinar, K.; Seridi, A.; Kadri, M. Investigation on the inclusion of diclofenac with β-cyclodextrin: A molecular modeling approach. Struct. Chem. 2015, 26, 61–69. [Google Scholar] [CrossRef]
  58. Srihakulung, O.; Maezono, R.; Toochinda, P.; Kongprawechnon, W.; Intarapanich, A.; Lawtrakul, A.L. Host-Guest Interactions of Plumbagin with β-Cyclodextrin, Dimethyl-β-Cyclodextrin and Hydroxypropyl-β-Cyclodextrin: Semi-Empirical Quantum Mechanical PM6 and PM7 Methods. Sci. Pharm. 2018, 86, 20. [Google Scholar] [CrossRef][Green Version]
  59. Bani-Yaseen, A.W. Computational molecular perspectives on the interaction of propranolol with β-cyclodextrin in solution: Towards the drug-receptor mechanism of interaction. J. Mol. Liq. 2017, 227, 280–290. [Google Scholar] [CrossRef]
  60. Prabhu, A.A.M.; Fatiha, M.; Leila, N.; Raj, T.A.; Navarro-González, I.; Periago, M.J.; Yáñez-Gascón, M.J.; Pérez-Sánchez, H. Investigation of 3D Contour Map and Intermolecular Interaction of Dopamine with β-Cyclodextrin and 2-Hydroxypropyl-β-cyclodextrin. J. Solut. Chem. 2018, 47, 409–429. [Google Scholar] [CrossRef]
  61. Iyengar, S.S.; Schlegel, B.H.; Voth, G.A. Atom-Centered Density Matrix Propagation (ADMP): Generalizations Using Bohmian Mechanics. J. Phys. Chem. A 2003, 107, 7269–7277. [Google Scholar] [CrossRef][Green Version]
  62. Al-Jaber, A.S.; Bani-Yaseen, A.D. On the encapsulation of Olsalazine by β-cyclodextrin: A DFT-based computational and spectroscopic investigations. Spectrochim. Acta Part A Mol. Biomol. Spectrosc. 2019, 214, 531–536. [Google Scholar] [CrossRef]
  63. Silva, D.A.; Xavier, M.J.; Dutra, J.D.L.; Gimenez, I.F.; Freire, R.O.; da Costa, N.B. Prediction of correct intermolecular interactions in host-guest systems involving cyclodextrins. J. Mol. Struct. 2020, 1205, 127517. [Google Scholar] [CrossRef]
  64. Lula, I.; Gomes, M.F.; Piló-Veloso, D.; Noronha, A.L.O.; Duarte, H.A.; Santos, R.A.S.; Sinisterra, R.D. Spironolactone and its Complexes with β-cyclodextrin: Modern NMR Characterization and Structural DFTB-SCC Calculations. J. Incl. Phenom. Macrocycl. Chem. 2006, 56, 293–302. [Google Scholar] [CrossRef]
  65. Lula, I.; Denadai, L.; Resende, J.M.; de Sousa, F.B.; de Lima, G.F.; Pilo-Veloso, D.; Heine, T.; Duarte, H.A.; Santos, R.A.; Sinisterra, R.D. Study of angiotensin-(1–7) vasoactive peptide and its β-cyclodextrin inclusion complexes: Complete sequence-specific NMR assignments and structural studies. Peptides 2007, 28, 2199–2210. [Google Scholar] [CrossRef] [PubMed]
  66. Lukin, O.; Dolgonos, G.; Leszczynski, J. A comprehensive test of computational approaches for evaluation of cyclodextrin complexes. Self-inclusion in monosubstituted β-cyclodextrins—A case study. Tetrahedron 2017, 73, 5302–5306. [Google Scholar] [CrossRef]
  67. Schnupf, U.; Momany, F.A. DFT Energy Optimization of a Large Carbohydrate: Cyclomaltohexaicosaose (CA-26). J. Phys. Chem. B 2011, 116, 6618–6627. [Google Scholar] [CrossRef] [PubMed]
  68. Hanpaibool, C.; Chakcharoensap, T.; Hijikata, Y.; Irle, S.; Wolschann, P.; Kungwan, N.; Pongsawasdi, P.; Ounjai, P.; Rungrotmongkol, T. Theoretical analysis of orientations and tautomerization of genistein in β-cyclodextrin. J. Mol. Liq. 2018, 265, 16–23. [Google Scholar] [CrossRef]
  69. Yunta, M. Using Molecular Modelling to Study Interactions between Molecules with Biological Activity. IntechOpen 2012. [Google Scholar] [CrossRef][Green Version]
  70. Lu, L. Can B3LYP be improved by optimization of the proportions of exchange and correlation functionals? Int. J. Quantum Chem. 2015, 115, 502–509. [Google Scholar] [CrossRef]
  71. Ivanov, P. Performance of some DFT functionals with dispersion on modeling of the translational isomers of a solvent-switchable [2]rotaxane. J. Mol. Struct. 2016, 1107, 31–38. [Google Scholar] [CrossRef]
  72. Mardirossian, N.; Head-Gordon, M. How Accurate Are the Minnesota Density Functionals for Noncovalent Interactions, Isomerization Energies, Thermochemistry, and Barrier Heights Involving Molecules Composed of Main-Group Elements? J. Chem. Theory Comput. 2016, 12, 4303–4325. [Google Scholar] [CrossRef][Green Version]
  73. Valero, R.; Costa, R.; Moreira, I.D.P.R.; Truhlar, D.; Illas, F. Performance of the M06 family of exchange-correlation functionals for predicting magnetic coupling in organic and inorganic molecules. J. Chem. Phys. 2008, 128, 114103. [Google Scholar] [CrossRef][Green Version]
  74. Wang, Y.; Jin, X.; Yu, H.S.; Truhlar, D.G.; He, X. Revised M06-L functional for improved accuracy on chemical reaction barrier heights, noncovalent interactions, and solid-state physics. Proc. Natl. Acad. Sci. USA 2017, 114, 8487–8492. [Google Scholar] [CrossRef] [PubMed][Green Version]
  75. Mardirossian, N.; Head-Gordon, M. ωB97X-V: A 10-parameter, range-separated hybrid, generalized gradient approximation density functional with nonlocal correlation, designed by a survival-of-the-fittest strategy. Phys. Chem. Chem. Phys. 2014, 16, 9904–9924. [Google Scholar] [CrossRef] [PubMed][Green Version]
  76. Kohn, W.; Sham, L.J. Self-consistent equations including exchange and correlation effects. Phys. Rev. 1965, 140, A1133–A1138. [Google Scholar] [CrossRef][Green Version]
  77. Bučko, T.; Lebègue, S.; Hafner, J.; Ángyán, J.G. Tkatchenko-Scheffler van der Waals correction method with and without self-consistent screening applied to solids. Phys. Rev. B 2013, 87, 064110. [Google Scholar] [CrossRef]
  78. Grimme, S.; Steinmetz, M. Effects of London dispersion correction in density functional theory on the structures of organic molecules in the gas phase. Phys. Chem. Chem. Phys. 2013, 15, 16031–16042. [Google Scholar] [CrossRef] [PubMed]
  79. Xu, P.; Alkan, M.; Gordon, M.S. Many-Body Dispersion. Chem. Rev. 2020, 120, 12343–12356. [Google Scholar] [CrossRef]
  80. Grimme, S.; Ehrlich, S.; Goerigk, L. Effect of the damping function in dispersion corrected density functional theory. J. Comput. Chem. 2011, 32, 1456–1465. [Google Scholar] [CrossRef]
  81. Yanai, T.; Tew, D.P.; Handy, N.C. A new hybrid exchange–correlation functional using the Coulomb-attenuating method (CAM-B3LYP). Chem. Phys. Lett. 2004, 393, 51–57. [Google Scholar] [CrossRef][Green Version]
  82. Salma, A.; Fatiha, M.; Leila, N. Effect of solvent on absorption and emission spectra of 2,2′-Bipyridine and its inclusion complexinto β-cyclodextrin: DFT and TD-DFT study. Comput. Theor. Chem. 2021, 1206, 113481. [Google Scholar] [CrossRef]
  83. Azayez, M.; Fergoug, T.; Meddah-Araibi, N.; Zelmat, C.; Bouhadda, Y. Theoretical Investigation of the Complexation Reaction of Procaine-hydrochloride by β-cyclodextrin. Phys. Chem. Res. 2020, 8, 155–165. [Google Scholar] [CrossRef]
  84. Safia, H.; Ismahan, L.; Abdelkrim, G.; Mouna, C.; Leila, N.; Fatiha, M. Density functional theories study of the interactions between host β-Cyclodextrin and guest 8-Anilinonaphthalene-1-sulfonate: Molecular structure, HOMO, LUMO, NBO, QTAIM and NMR analyses. J. Mol. Liq. 2019, 280, 218–229. [Google Scholar] [CrossRef]
  85. Buczek, A.; Staś, A.; Hebenstreit, C.; Maller, C.; Broda, M.A.; Kupka, T.; Kelterer, A. Interaction of 5-fluorouracil with β-cyclodextrin: A density functional theory study with dispersion correction. Int. J. Quantum Chem. 2021, 121, e26487. [Google Scholar] [CrossRef]
  86. Cossi, M.; Rega, N.; Scalmani, G.; Barone, V. Energies, structures, and electronic properties of molecules in solution with the C-PCM solvation model. J. Comput. Chem. 2003, 24, 669–681. [Google Scholar] [CrossRef] [PubMed]
  87. Tomasi, J.; Mennucci, B.; Cancès, E. The IEF version of the PCM solvation method: An overview of a new method addressed to study molecular solutes at the QM ab initio level. J. Mol. Struct. 1999, 464, 211–226. [Google Scholar] [CrossRef]
  88. Marenich, A.V.; Cramer, C.J.; Truhlar, D.G. Universal Solvation Model Based on Solute Electron Density and on a Continuum Model of the Solvent Defined by the Bulk Dielectric Constant and Atomic Surface Tensions. J. Phys. Chem. B 2009, 113, 6378–6396. [Google Scholar] [CrossRef]
  89. Belhocine, Y.; Rahali, S.; Allal, H.; Assaba, I.M.; Ghoniem, M.G.; Ali, F.A.M. A Dispersion Corrected DFT Investigation of the Inclusion Complexation of Dexamethasone with β-Cyclodextrin and Molecular Docking Study of Its Potential Activity against COVID-19. Molecules 2021, 26, 7622. [Google Scholar] [CrossRef]
  90. Oqmhula, K.; Hongo, K.; Maezono, R.; Ichibha, T. Ab Initio Evaluation of Complexation Energies for Cyclodextrin-Drug Inclusion Complexes. ACS Omega 2020, 5, 19371–19376. [Google Scholar] [CrossRef]
  91. Sambrook, M.R.; Gass, I.A.; Cragg, P.J. Spectroscopic and inclusion properties of G-series chemical warfare agents and their simulants: A DFT study. Supramol. Chem. 2017, 30, 206–217. [Google Scholar] [CrossRef][Green Version]
  92. Sure, R.; Grimme, S. Comprehensive Benchmark of Association (Free) Energies of Realistic Host–Guest Complexes. J. Chem. Theory Comput. 2015, 11, 3785–3801. [Google Scholar] [CrossRef]
  93. Lopes, J.F.; Nascimento, C.S.; Anconi, C.P.A.; Santos, H.F.; Almeida, W.B. Inclusion complex thermodynamics: The β-cyclodextrin and sertraline complex example. J. Mol. Graph. Model. 2015, 62, 11–17. [Google Scholar] [CrossRef]
  94. CCDC, Cambridge Crystallographic Data Centre. Available online: (accessed on 29 May 2022).
  95. Autodock. Available online: (accessed on 29 May 2022).
  96. Available online: (accessed on 29 May 2022).
  97. Biovia. Available online: (accessed on 29 May 2022).
  98. Nora, M.; Ismahan, L.; Abdelkrim, G.; Mouna, C.; Leila, N.; Fatiha, M.; Nada, B.; Brahim, H. Interactions in inclusion complex of β-cyclodextrin/l-Metheonine: DFT computational studies. J. Incl. Phenom. Macrocycl. Chem. 2020, 96, 43–54. [Google Scholar] [CrossRef]
  99. Pan, A.; Kar, T.; Rakshit, A.K.; Moulik, S.P. Enthalpy–Entropy Compensation (EEC) Effect: Decisive Role of Free Energy. J. Phys. Chem. B 2016, 120, 10531–10539. [Google Scholar] [CrossRef] [PubMed]
  100. Rahali, S.; Belhocine, Y.; Allal, H.; Bouhadiba, A.; Assaba, I.M.; Seydou, M. A DFT Investigation of The Host-Guest Interactions Between Boron-Based Aromatic Systems and β-Cyclodextrin. Res. Sq. 2022, 1–2. [Google Scholar] [CrossRef]
  101. Morais, C.A.S.; Silva, B.L.; Denadai, A.M.L.; Lopes, J.F.; De Sousa, F.B. Structural and thermodynamic investigation of pentoxifylline-cyclodextrin inclusion complex. Chem. Phys. Lett. 2017, 682, 43–48. [Google Scholar] [CrossRef]
  102. Aree, T.; Jongrungruangchok, S. β-Cyclodextrin encapsulation elevates antioxidant capacity of tea: A closing chapter on non-epicatechins, atomistic insights from X-ray analysis, DFT calculation and DPPH assay. Carbohydr. Polym. 2018, 194, 24–33. [Google Scholar] [CrossRef] [PubMed]
  103. Aree, T.; Jongrungruangchok, S. Enhancement of antioxidant activity of green tea epicatechins in β-cyclodextrin cavity: Single-crystal X-ray analysis, DFT calculation and DPPH assay. Carbohydr. Polym. 2016, 20, 1139–1151. [Google Scholar] [CrossRef] [PubMed]
  104. Ikeda, H.; Ohata, T.; Yukawa, M.; Tsutsumi, H.; Fujisawa, M.; Aki, H. Calculation study on complex formation of catechins with β-cyclodextrin using density function theory. J. Incl. Phenom. Macrocycl. Chem. 2021, 100, 99–107. [Google Scholar] [CrossRef]
  105. Aree, T. Understanding structures and thermodynamics of β-cyclodextrin encapsulation of chlorogenic, caffeic and quinic acids: Implications for enriching antioxidant capacity and masking bitterness in coffee. Food Chem. 2019, 293, 550–560. [Google Scholar] [CrossRef]
  106. Aree, T. Inclusion complex of β-cyclodextrin with coffee chlorogenic acid: New insights from a combined crystallographic and theoretical study. Acta Crystallogr. Sect. C Struct. Chem. 2019, 75, 15–21. [Google Scholar] [CrossRef]
  107. Meryem, G.; Rabah, K.; Fatiha, M.; Leila, N.; Aziz, B.A.; Imane, D.; Rachid, M. Computational investigation of vanillin@βéta-cyclodextrin inclusion complex: Electronic and intermolecular analysis. J. Mol. Liq. 2021, 321, 114839. [Google Scholar] [CrossRef]
  108. Aree, T. β-Cyclodextrin Inclusion Complexation With Tricyclic Antidepressants Desipramine and Imipramine: A Structural Chemistry Perspective. J. Pharm. Sci. 2020, 109, 3086–3094. [Google Scholar] [CrossRef] [PubMed]
  109. Aree, T. Inclusion Scenarios and Conformational Flexibility of the SSRI Paroxetine as Perceived from Polymorphism of β-Cyclodextrin–Paroxetine Complex. Pharmaceuticals 2022, 15, 98. [Google Scholar] [CrossRef] [PubMed]
  110. Keniche, A.; Slimani, M.Z.; Miranda, J.I.; Aizpurua, J.M.; Mulengi, J.K. NMR Investigation of the complexation of (S)-2-isopropyl-1-(o-nitrophenyl)sulfonyl)aziridine with β-cyclodextrin. Mediterr. J. Chem. 2013, 2, 620–631. [Google Scholar] [CrossRef]
  111. Harati, H.; Morsali, A.; Bozorgmehr, M.R.; Beyramabadi, S.A. β-cyclodextrin-lenalidomide anticancer drug delivery nanosystem: A quantum chemical approach. J. Mol. Liq. 2021, 344, 117762. [Google Scholar] [CrossRef]
  112. Rohman, M.A.; Phanrang, P.T.; Chamlagai, D.; Mitra, S. Deciphering Spectroscopic and Structural Insights into the Photophysical Behavior of 2,2′-Dipyridylamine: An Efficient Environment Sensitive Fluorescence Probe. J. Phys. Chem. A 2021, 125, 6964–6975. [Google Scholar] [CrossRef]
  113. Wiergowska, G.; Ludowicz, D.; Wdowiak, K.; Miklaszewski, A.; Lewandowska, K.; Cielecka-Piontek, J. Combinations of Freeze-Dried Amorphous Vardenafil Hydrochloride with Saccharides as a Way to Enhance Dissolution Rate and Permeability. Pharmaceuticals 2021, 14, 453. [Google Scholar] [CrossRef]
  114. Akhondi, M.; Jamalizadeh, E.; Mohebbi, A. MD and DFT calculations on the structural variations of amino-cyclodextrin as a pH-sensitive carrier for smart carriage and release of Doxorubicin. J. Mol. Struct. 2021, 1230, 129855. [Google Scholar] [CrossRef]
  115. Mezari, Y.; Nouar, L.; Madi, F.; Guendouzi, A.; Djellala, I.; Lafifi, I.; Merdes, R.; Bouhadiba, A.; Houari, B. Theoretical investigation of inclusion complex of 2-methyl mercapto phenothiazine with hydroxy propyl β-cyclodextrin by DFT approaches. Bulg. Chem. Comm. 2021, 53, 196–210. [Google Scholar] [CrossRef]
  116. Bani-Yaseen, A.D. The supramolecular host-guest complexation of Vemurafenib with β-cyclodextrin and cucurbit[7]uril as drug photoprotecting systems: A DFT/TD-DFT study. Comput. Theor. Chem. 2020, 1191, 113026. [Google Scholar] [CrossRef]
  117. Jafari, G.; Raissi, H.; Hashemzadeh, H. Molecular insight into the interaction of fluorometholone and cholesterol molecules with β-cyclodextrin and sulfobutylether-β-cyclodextrin. Comput. Theor. Chem. 2022, 1208, 113554. [Google Scholar] [CrossRef]
  118. Gamboa-Carballo, J.J.; Ferino-Pérez, A.; Rana, V.K.; Levalois-Grützmacher, J.; Gaspard, S.; Montero-Cabrera, L.A.; Haza, U.J.J. Theoretical Evaluation of the Molecular Inclusion Process between Chlordecone and Cyclodextrins: A New Method for Mitigating the Basis Set Superposition Error in the Case of an Implicit Solvation Model. J. Chem. Inf. Model. 2020, 60, 2115–2125. [Google Scholar] [CrossRef] [PubMed]
  119. Yang, Y.-Z.; Liu, X.-F.; Zhang, R.-B.; Pang, S.-P. Joint experimental and theoretical studies of the surprising stability of the aryl pentazole upon noncovalent binding to β-cyclodextrin. Phys. Chem. Chem. Phys. 2017, 19, 31236–31244. [Google Scholar] [CrossRef] [PubMed]
  120. Pereira, R.A.; Borges, W.M.D.S.; Peraro, C.R.; Anconi, C.P.A. Theoretical inclusion of deprotonated 2,4-D and dicamba pesticides in ß-cyclodextrin. J. Incl. Phenom. Macrocycl. Chem. 2016, 86, 343–349. [Google Scholar] [CrossRef]
  121. Li, Z.; Couzijn, E.P.A.; Zhang, X. Intrinsic Properties of α-Cyclodextrin Complexes with Benzoate Derivatives in the Gas Phase: An Experimental and Theoretical Study. J. Phys. Chem. B 2012, 116, 943–950. [Google Scholar] [CrossRef] [PubMed]
  122. Yao, L.; Mori, Y.; Takano, K. Theoretical Study on Intermolecular Interactions in Complexes of Cyclodextrins with Bile Acids: DFT and Ab Initio Fragment Molecular Orbital Calculations. Bull. Chem. Soc. Jpn. 2014, 87, 258–266. [Google Scholar] [CrossRef]
  123. Li, Z.; Couzijn, E.P.A.; Zhang, X. A quantitative study of intrinsic non-covalent interactions within complexes of α-cyclodextrin and benzoate derivatives. Chem. Commun. 2012, 48, 9864–9866. [Google Scholar] [CrossRef][Green Version]
  124. Muzaffar, S.; Imtiaz, S.; Ali, S.M. Demonstrating accuracy of the proposed protocol for structure elucidation of cyclodextrin inclusion complexes by validation using DFT studies. J. Mol. Struct. 2020, 1217, 128419. [Google Scholar] [CrossRef]
  125. Li, N.; Yang, L.; Ji, X.; Ren, J.; Gao, B.; Deng, W.-Q.; Wang, Z. Bioinspired succinyl-β-cyclodextrin membranes for enhanced uranium extraction and reclamation. Environ. Sci. Nano 2020, 7, 3124–3135. [Google Scholar] [CrossRef]
  126. Ignaczak, A.; Orszański, Ł.; Adamiak, M.; Olejniczak, A.B. Comparative DFT study of inclusion complexes of thymidine-carborane conjugate with β-cyclodextrin and heptakis(2,6-O-dimethyl)-β-cyclodextrin in water. J. Mol. Liq. 2020, 315, 113767. [Google Scholar] [CrossRef]
  127. Ramos, M.L.; Dias, D.C.; Justino, L.L.G.; Verissimo, L.M.P.; Valente, A.J.M.; Esteso, M.A.; Ribeiro, A.C.F.; Leaist, D.G.; Pina, J.; Cabral, A.; et al. Interactions between glycyl-L-phenylalanine and β-cyclodextrin from diffusion, spectroscopic and computational studies. J. Mol. Liq. 2020, 315, 113704. [Google Scholar] [CrossRef]
  128. Deosarkar, S.D.; Sawale, R.T.; Pinjari, R.V.; Kalyankar, T.M. Interactions of sodium salicylate and β-cyclodextrin in water: A volumetric, ultraacoustic and optical study. J. Mol. Liq. 2020, 130, 113151. [Google Scholar] [CrossRef]
  129. Okuda, M.; Hiramatsu, T.; Yasuda, M.; Ishigaki, M.; Ozaki, Y.; Hayashi, M.; Tominaga, K.; Chatani, E. Theoretical Modeling of Electronic Structures of Polyiodide Species Included in α-Cyclodextrin. J. Phys. Chem. B 2020, 124, 4089–4096. [Google Scholar] [CrossRef] [PubMed]
  130. Majhi, K.; Bandyopadhyay, P.; Khatun, R.; Sinha, S. Prediction of the most preferable rotamer of meta-aminophenol in β-cyclodextrin cavity in aqueous medium by using spectroscopic and DFT computational studies. J. Incl. Phenom. Macrocycl. Chem. 2020, 97, 77–86. [Google Scholar] [CrossRef]
  131. Ismahan, L.; Leila, N.; Fatiha, M.; Abdelkrim, G.; Mouna, C.; Nada, B.; Brahim, H. Computational study of inclusion complex of l-Glutamine/beta-Cycldextrin: Electronic and intermolecular interactions investigations. J. Mol. Struct. 2020, 1206, 127740. [Google Scholar] [CrossRef]
  132. Pereva, S.; Nikolova, V.; Sarafska, T.; Angelova, S.; Spassov, T.; Dudev, T. Inclusion complexes of ibuprofen and β-cyclodextrin: Supramolecular structure and stability. J. Mol. Struct. 2020, 1205, 127575. [Google Scholar] [CrossRef]
  133. Stoicescu, C.S.; Neacşu, A.D.; Bădiceanu, C.D.; Munteanu, G. Inclusion complexes of some thiourea derivatives in cyclodextrins. J. Incl. Phenom. Macrocycl. Chem. 2019, 96, 275–283. [Google Scholar] [CrossRef]
  134. Paulino, P.H.S.; Sousaab, S.M.R.; Da Silva, H.C.; De Almeida, W.B.; Ferrari, J.L.; Guimarãesa, L.; Nascimento, C.S., Jr. A theoretical investigation on the encapsulation process of mepivacaine into β-cyclodextrin. Chem. Phys. Lett. 2020, 740, 137060. [Google Scholar] [CrossRef]
  135. Wu, J.; Ma, H.; Bu, X.; Zhu, L.; Hao, B.; Zhao, B.; Tian, Y. SERS determination of the antihypertensive drugs prazosin and losartan by using silver nanoparticles coated with β-cyclodextrin. Mikrochim. Acta 2019, 186, 801. [Google Scholar] [CrossRef]
  136. Bezzina, B.; Djemil, R.; Bensouilah, N. Quantitative and qualitative analyses of intermolecular interactions in neutral/deprotonated aspirin@β-CD inclusion complexes: QTAIM and NBO analyses. Theor. Chim. Acta 2019, 138, 43. [Google Scholar] [CrossRef]
  137. Wójcik, J.; Ejchart, A.; Nowakowski, M. Shape adaptation of quinine in cyclodextrin cavities: NMR studies. Phys. Chem. Chem. Phys. 2019, 21, 6925–6934. [Google Scholar] [CrossRef]
  138. Bakirhan, N.K.; Tok, T.T.; Ozkan, S.A. The redox mechanism investigation of non-small cell lung cancer drug: Erlotinib via theoretical and experimental techniques and its host–guest detection by β-Cyclodextrin nanoparticles modified glassy carbon electrode. Sens. Actuators B Chem. 2019, 278, 172–180. [Google Scholar] [CrossRef]
  139. Li, L.; Zhou, Y.; Wang, Z.; Wu, C.; Li, Z.; Sun, C.; Sun, T. Theoretical studies on the mechanism of sugammadex for the reversal of aminosteroid-induced neuromuscular blockade. J. Mol. Liq. 2018, 265, 450–456. [Google Scholar] [CrossRef]
  140. Khavani, M.; Kalantarinezhad, R.; Izadyar, M. A joint QM/MD study on α-, β- and γ-cyclodextrins in selective complexation with cathinone. Supramol. Chem. 2017, 30, 687–696. [Google Scholar] [CrossRef]
  141. Eftaiha, A.F.; Qaroush, A.K.; Alsoubani, F.; Pehl, T.M.; Troll, C.; Rieger, B.; Al-Maythalony, B.A.; Assaf, K.I. A green sorbent for CO2 capture: α-cyclodextrin-based carbonate in DMSO solution. RSC Adv. 2018, 8, 37757–37764. [Google Scholar] [CrossRef][Green Version]
  142. Belhocine, Y.; Bouhadiba, A.; Rahim, M.; Nouar, L.; Djilani, I.; Khatmi, D.I. Inclusion Complex Formation of β-Cyclodextrin with the Nonsteroidal Anti-inflammatory Drug Flufenamic Acid: Computational Study. Macroheterocycles 2018, 11, 203–209. [Google Scholar] [CrossRef][Green Version]
  143. Sierpe, R.; Noyong, M.; Simon, U.; Aguayo, D.; Huerta, J.; Kogan, M.J.; Yutronic, N. Construction of 6-thioguanine and 6-mercaptopurine carriers based on βcyclodextrins and gold nanoparticles. Carbohydr. Polym. 2017, 177, 22–31. [Google Scholar] [CrossRef] [PubMed]
  144. Anconi, C.P.A.; Santos, T.M.R.; Souza, A.C.; Borges, W.M.S.; Sales, A.L.R. Host–guest intermolecular hydrogen bonds and stability in aqueous media: The benzaldehyde/β-CD case study. J. Incl. Phenom. Macrocycl. Chem. 2017, 89, 137–142. [Google Scholar] [CrossRef]
  145. Cao, B.; Du, J.; Cao, Z.; Sun, X.; Sun, H.; Fu, H. DFT study on the dissolution mechanisms of α-cyclodextrin and chitobiose in ionic liquid. Carbohydr. Polym. 2017, 169, 227–235. [Google Scholar] [CrossRef]
  146. Angelova, S.; Nikolova, V.; Molla, N.; Dudev, T. Factors Governing the Host–Guest Interactions between IIA/IIB Group Metal Cations and α-Cyclodextrin: A DFT/CDM Study. Inorg. Chem. 2017, 56, 1981–1987. [Google Scholar] [CrossRef]
  147. Oliveri, V.; Pietropaolo, A.; Sgarlata, C.; Vecchio, G. Zinc Complexes of Cyclodextrin-bearing 8-Hydroxyquinoline Ligands: A Comparative Study. Chem. Asian J. 2016, 12, 110–115. [Google Scholar] [CrossRef]
  148. Cheng, Y.; Wang, X.; Chang, D.; Li, W. DFT study on the effects of catalysis by β-cyclodextrin in the reaction of p-nitrophenyl acetate. J. Mol. Model. 2017, 23, 21. [Google Scholar] [CrossRef] [PubMed]
  149. Maia, P.P.; de Sousa, S.M.R.; De Almeida, W.B.; Guimaraes, L.; Nascimento, C.S. Computational investigation on the host–guest inclusion process of norfloxacin into β-cyclodextrin. J. Mol. Model. 2016, 22, 220. [Google Scholar] [CrossRef] [PubMed]
  150. Ignaczak, A.; Orszański, Ł. In Search of the Most Stable Molecular Configuration of Heptakis(2,6-O-dimethyl)-β-cyclodextrin and Its Complex with Mianserin: A Comparison of the B3LYP-GD2 and M062X-GD3 Results. J. Phys. Chem. B 2021, 125, 13077–13087. [Google Scholar] [CrossRef] [PubMed]
  151. Aree, T. Advancing insights on β-cyclodextrin inclusion complexes with SSRIs through lens of X-ray diffraction and DFT calculation. Int. J. Pharm. 2021, 609, 121113. [Google Scholar] [CrossRef] [PubMed]
  152. Aree, T. Distinctive Supramolecular Features of β-Cyclodextrin Inclusion Complexes with Antidepressants Protriptyline and Maprotiline: A Comprehensive Structural Investigation. Pharmaceuticals 2021, 14, 812. [Google Scholar] [CrossRef]
  153. Aree, T. Supramolecular Complexes of β-Cyclodextrin with Clomipramine and Doxepin: Effect of the Ring Substituent and Component of Drugs on Their Inclusion Topologies and Structural Flexibilities. Pharmaceuticals 2020, 13, 278. [Google Scholar] [CrossRef]
  154. Aree, T. β-Cyclodextrin encapsulation of nortriptyline HCl and amitriptyline HCl: Molecular insights from single-crystal X-ray diffraction and DFT calculation. Int. J. Pharm. 2020, 575, 118899. [Google Scholar] [CrossRef]
  155. Rayene, K.; Imane, D.; Abdelaziz, B.; Leila, N.; Fatiha, M.; Abdelkrim, G.; Bouzid, G.; Ismahan, L.; Brahim, H.; Rabah, O. Molecular modeling study of structures, Hirschfield surface, NBO, AIM, RDG, IGM and 1HNMR of thymoquinone/hydroxypropyl-β-cyclodextrin inclusion complex from QM calculations. J. Mol. Struct. 2022, 1249, 131565. [Google Scholar] [CrossRef]
  156. Macernis, M.; Bockuviene, A.; Gruskiene, R.; Krivorotova, T.; Sereikaite, J. Raman study for β-ring positioning in β-Carotene complexes with Cyclodextrins and Chitooligosaccharides. J. Mol. Struct. 2021, 1226, 129362. [Google Scholar] [CrossRef]
  157. Kerdpol, K.; Daengngern, R.; Sattayanon, C.; Namuangruk, S.; Rungrotmongkol, T.; Wolschann, P.; Kungwan, N.; Hannongbua, S. Effect of Water Microsolvation on the Excited-State Proton Transfer of 3-Hydroxyflavone Enclosed in γ-Cyclodextrin. Molecules 2021, 26, 843. [Google Scholar] [CrossRef]
  158. Bouchemela, H.; Madi, F.; Nouar, L. DFT investigation of host–guest interactions between α-Terpineol and β-cyclodextrin. J. Incl. Phenom. Macrocycl. Chem. 2019, 95, 247–258. [Google Scholar] [CrossRef]
  159. Seridi, L.; Boufelfel, A. Naringenin encapsulation in β-CD and in heptakis(2,6-di-O-methyl)-β-CD:NMR, NBO and QTAIM analysis. J. Incl. Phenom. Macrocycl. Chem. 2018, 90, 287–304. [Google Scholar] [CrossRef]
  160. Nutho, B.; Nunthaboot, N.; Wolschann, P.; Kungwan, N.; Rungrotmongkol, T. Metadynamics supports molecular dynamics simulation-based binding affinities of eucalyptol and beta-cyclodextrin inclusion complexes. RSC Adv. 2017, 7, 50899–50911. [Google Scholar] [CrossRef][Green Version]
  161. Nutho, B.; Khuntawee, W.; Rungnim, C.; Pongsawasdi, P.; Wolschann, P.; Karpfen, A.; Kungwan, N.; Rungrotmongkol, T. Binding mode and free energy prediction of fisetin/β-cyclodextrin inclusion complexes. Beilstein J. Org. Chem. 2014, 10, 2789–2799. [Google Scholar] [CrossRef] [PubMed][Green Version]
  162. Guendouzi, O.; Guendouzi, A.; Ouici, H.B.; Brahim, H.; Boumediene, M.; Elkeurti, M. A quantum chemical study of encapsulation and stabilization of gallic acid in β-cyclodextrin as a drug delivery system. Can. J. Chem. 2020, 98, 204–214. [Google Scholar] [CrossRef]
  163. Yang, L.; Li, D.; Guo, B.; Wei, D. Theoretical Study on the Inclusion Interaction of β-Cyclodextrin with Gabapentin and Its Stability. J. Struct. Chem. 2019, 60, 564–574. [Google Scholar] [CrossRef]
  164. Asztemborska, M.; Ceborska, M.; Pietrzak, M. Complexation of tropane alkaloids by cyclodextrins. Carbohydr. Polym. 2020, 209, 74–81. [Google Scholar] [CrossRef]
  165. Abdel-Mottaleb, M.S.A.; Hamed, E.; Saif, M.; Hafez, H.S. Binding, and thermodynamics of β-cyclodextrin inclusion complexes with some coumarin laser dyes and coumarin-based enzyme substrates: A simulation study. J. Incl. Phenom. Macrocycl. Chem. 2018, 92, 319–327. [Google Scholar] [CrossRef]
  166. Diamantis, D.A.; Ramesova, S.; Chatzigiannis, C.M.; Degano, I.; Gerogianni, P.S.; Karadima, K.E.; Perikleous, S.; Rekkas, D.; Gerothanassis, I.P.; Galaris, D.; et al. Exploring the oxidation and iron binding profile of a cyclodextrin encapsulated quercetin complex unveiled a controlled complex dissociation through a chemical stimulus. Biochim. Biophys. Acta (BBA) Gen. Subj. 2018, 1862, 1913–1924. [Google Scholar] [CrossRef]
  167. Guendouzi, A.; Mekelleche, S.M.; Brahim, H.; Litim, K. Quantitative conformational stability host-guest complex of Carvacrol and Thymol with β-cyclodextrin: A theoretical investigation. J. Incl. Phenom. Macrocycl. Chem. 2017, 89, 143–155. [Google Scholar] [CrossRef]
  168. Abdelaali, M.; Fatiha, M.; Leila, N.; Nora, M.; Mouna, C.; Sakina, H.; Eddine, K.D. Computational approach in the study of the inclusion processes of Thymol with β-cyclodextrin. J. Mol. Liq. 2017, 242, 714–721. [Google Scholar] [CrossRef]
  169. Aree, T. β-Cyclodextrin Inclusion Complexes with Catechol-Containing Antioxidants Protocatechuic Aldehyde and Protocatechuic Acid—An Atomistic Perspective on Structural and Thermodynamic Stabilities. Molecules 2021, 26, 3574. [Google Scholar] [CrossRef] [PubMed]
  170. Aree, T.; Jongrungruangchok, S. Structure–antioxidant activity relationship of β-cyclodextrin inclusion complexes with olive tyrosol, hydroxytyrosol and oleuropein: Deep insights from X-ray analysis, DFT calculation and DPPH assay. Carbohydr. Polym. 2018, 199, 661–669. [Google Scholar] [CrossRef] [PubMed]
  171. Huang, F.; Zhuang, S.; Liu, W.; Lin, L.; Sun, L. Computational investigation on the chiral differentiation of D- and L-penicillamine by β-cyclodextrin. Spectrochim. Acta Part A Mol. Biomol. Spectrosc. 2020, 248, 119277. [Google Scholar] [CrossRef]
  172. Yang, S.; Wu, F.; Yu, F.; Gu, L.; Wang, H.; Liu, Y.; Chu, Y.; Wang, F.; Fang, X.; Ding, C.-F. Distinction of chiral penicillamine using metal-ion coupled cyclodextrin complex as chiral selector by trapped ion mobility-mass spectrometry and a structure investigation of the complexes. Anal. Chim. Acta 2021, 1184, 339017. [Google Scholar] [CrossRef]
  173. Știufiuc, G.F.; Toma, V.; Onaciu, A.; Chiș, V.; Lucaciu, C.M.; Știufiuc, R.I. Proving Nanoscale Chiral Interactions of Cyclodextrins and Propranolol Enantiomers by Means of SERS Measurements Performed on a Solid Plasmonic Substrate. Pharmaceutics 2021, 13, 1594. [Google Scholar] [CrossRef]
  174. Lee, S.-S.; Lee, J.-U.; Oh, J.H.; Park, S.; Hong, Y.; Min, B.K.; Lee, H.H.L.; Kim, H.I.; Kong, X.; Lee, S.; et al. Chiral differentiation of d- and l-isoleucine using permethylated β-cyclodextrin: Infrared multiple photon dissociation spectroscopy, ion-mobility mass spectrometry, and DFT calculations. Phys. Chem. Chem. Phys. 2018, 20, 30428–30436. [Google Scholar] [CrossRef]
  175. Lee, S.; Park, S.; Hong, Y.; Lee, J.U.; Kim, J.H.; Yoon, D.; Kong, X.; Lee, S.; Bin Oh, H. Chiral differentiation of d- and l-alanine by permethylated β-cyclodextrin: IRMPD spectroscopy and DFT methods. Phys. Chem. Chem. Phys. 2017, 19, 14729–14737. [Google Scholar] [CrossRef]
  176. Reyes-Reyes, M.L.; Roa-Morales, G.; Melgar-Fernández, R.; Reyes-Pérez, H.; Gómez-Oliván, L.M.; Gonzalez-Rivas, N.; Bautista-Renedo, J.; Balderas-Hernández, P. Chiral recognition of abacavir enantiomers by (2-hydroxy)propyl-β-cyclodextrin: UHPLC, NMR and DFT studies. J. Incl. Phenom. Macrocycl. Chem. 2015, 82, 373–382. [Google Scholar] [CrossRef]
Figure 1. Number of the search results for the ‘cyclodextrin AND DFT’ phrase in the Web of Science. Each column shows the number of articles in the given year and all years before. For example, the column entitled ‘2010’ depicts the number of articles published in the period 2000–2010, including 2010.
Figure 1. Number of the search results for the ‘cyclodextrin AND DFT’ phrase in the Web of Science. Each column shows the number of articles in the given year and all years before. For example, the column entitled ‘2010’ depicts the number of articles published in the period 2000–2010, including 2010.
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Figure 2. Changes in the number of articles published on the topic of cyclodextrin and either different semi-empirical or DFT methods over the years.
Figure 2. Changes in the number of articles published on the topic of cyclodextrin and either different semi-empirical or DFT methods over the years.
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Figure 3. Comparison between the structures of the αCD complex with benzaldehyde. Top left: the best pose from molecular docking; top right: the best pose from molecular docking after optimization using DFT; bottom left: one of the poses obtained from molecular docking; bottom right: “bottom left” structure after optimization using DFT; middle one: experimental structure (CSDC ref. code: BOHWUQ). It should be noted that while the top left structure has energy lower than the bottom left by 3.4 kcal/mol, the top right structure has energy higher than the bottom right by 4.2 kcal/mol. Source: author’s archive.
Figure 3. Comparison between the structures of the αCD complex with benzaldehyde. Top left: the best pose from molecular docking; top right: the best pose from molecular docking after optimization using DFT; bottom left: one of the poses obtained from molecular docking; bottom right: “bottom left” structure after optimization using DFT; middle one: experimental structure (CSDC ref. code: BOHWUQ). It should be noted that while the top left structure has energy lower than the bottom left by 3.4 kcal/mol, the top right structure has energy higher than the bottom right by 4.2 kcal/mol. Source: author’s archive.
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Mazurek, A.H.; Szeleszczuk, Ł. Current Status of Quantum Chemical Studies of Cyclodextrin Host–Guest Complexes. Molecules 2022, 27, 3874.

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Mazurek AH, Szeleszczuk Ł. Current Status of Quantum Chemical Studies of Cyclodextrin Host–Guest Complexes. Molecules. 2022; 27(12):3874.

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Mazurek, Anna Helena, and Łukasz Szeleszczuk. 2022. "Current Status of Quantum Chemical Studies of Cyclodextrin Host–Guest Complexes" Molecules 27, no. 12: 3874.

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