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31 July 2025

Unveiling the Power of Computational Tools in Chiral Liquid Chromatography

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Laboratório de Química Orgânica e Farmacêutica, Departamento de Ciências Químicas, Faculdade de Farmácia, Universidade do Porto, Rua Jorge Viterbo Ferreira, 228, 4050-313 Porto, Portugal
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Centro Interdisciplinar de Investigação Marinho e Ambiental (CIIMAR), Edifício do Terminal de Cruzeiros do Porto de Leixões, Av. General Norton de Matos, s/n, 4050-208 Matosinhos, Portugal
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LAQV, REQUIMTE, Departamento de Química e Bioquímica, Faculdade de Ciências, Universidade do Porto, Rua do Campo Alegre, s/n, 4169-007 Porto, Portugal
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LAQV, REQUIMTE, Departamento de Química, Universidade de Aveiro, 3810-193 Aveiro, Portugal
Molecules2025, 30(15), 3218;https://doi.org/10.3390/molecules30153218
This article belongs to the Special Issue Enantioselective Synthesis, Enantiomeric Separations and Chiral Recognition: 3rd Edition
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Abstract

Chiral liquid chromatography (cLC) using chiral stationary phases (CSPs) has become a crucial technique for separating enantiomers. Understanding enantiomeric discrimination is essential for improving chromatographic conditions and elucidating chiral molecular recognition; the computational methods are extremely helpful for this. To assess the relevance of the association of these two approaches and to analyze the current trends, in this review, a systematic analysis of the scientific literature was performed, covering recently published works (from 2015 to January 2025) on enantioseparation by cLC using CSPs and computational studies. CSPs based on polysaccharides and Pirkle-type were the most described (accounting for 52% and 14% of the studies, respectively). Regarding the computational methods, molecular docking and molecular dynamics (MD) were the most reported (accounting for 50% and 25% of the studies, respectively). In the articles surveyed, a significant growth in research concerning both cLC enantioseparation and computational studies is evident, emphasizing the benefit of the synergy between these two approaches.

1. Introduction

Over the last few decades, chiral liquid chromatography (cLC) has proven to be one of the most versatile and widely applied techniques for the analysis and purification of enantiomers in diverse research fields, such as food [1,2], pharmaceutical [3], biomedical [4], environmental [5,6], forensic and toxicological sciences [7,8], drug discovery and development [9,10], and cosmetics [11], among others. cLC demonstrated great potential in academic research and industrial fields, being responsible for a considerable economic impact in the industry [12]. Several advantages of this technique may justify this trend, such as remarkable selectivity, robustness, speed, sensitivity, reproducibility, rigorous quantification, and the possibility of combination with diverse detectors and/or analytical instruments [13]. In addition, diverse types of chiral stationary phases (CSPs) have been developed over the years for analytical and preparative applications [14,15]. More than a hundred CSPs are currently commercially available [16]. The CSPs include polysaccharide derivatives, macrocyclic antibiotics, cyclodextrins (CD), proteins, crown-ethers, cyclofructans, synthetic polymers, molecularly-imprinted, Pirkle-type, and ion-exchange chiral selectors [17].
To follow the challenges in different research areas as well as the progress in instrumentation and technical advancement [18,19], the development of new CSPs continues to be a field of great interest among the scientific community [20,21,22].
In recent years, the computational study of chromatographic enantioseparation has become an important tool in understanding the chiral recognition mechanisms for diverse CSPs [23,24]. With the advances in computational studies, its successful application in the chromatographic field has progressively increased over time, allowing researchers to understand and anticipate experimental results. Computational studies can be very helpful in estimating the magnitude of the enantioselectivity, anticipating the elution order, predicting other classes of chiral analytes that can be separated, and establishing the more suitable chromatographic conditions, including the choice of the CSP, solvent system as mobile phase, chemical additives or modifiers, pH conditions, and column temperature. In addition, even when experimental results are available, computational studies can elucidate molecular mechanisms of enantioselectivity and provide solutions, proposing innovative procedures for specific challenges [25,26,27]. The elucidation of chiral recognition mechanisms is essential to clarify the enantioselective binding properties and the kind of noncovalent interactions between the chiral selector and enantiomers [28,29].
Chiral molecular recognition and enantioseparation involve the formation of transient diastereomeric complexes with different stability, through a sum of diverse types of interactions, including hydrogen-bond, ionic, π–π, ion–dipole, dipole–dipole, and Van der Waals interactions [30,31]. In addition to attractive interactions involved in forming enantiomer-selector complexes, steric repulsion, repulsive charges, and entry into chiral cavities within the selector also play key roles in some types of CSPs [32]. The presence of bulky moieties can prevent an enantiomer from accessing the chiral selector, giving rise to high enantioselectivity [33,34]. Many CSPs are known to incorporate bulky rigid elements to induce such high levels of enantioselectivity [35,36].
Figure 1 summarizes the main intermolecular interactions between the chiral selector and the enantiomers to be separated for each type of CSP [32,37,38,39,40].
Figure 1. Intermolecular interactions associated with each type of chiral stationary phase (CSP).
Nevertheless, despite numerous reported studies, the specific nature of the interaction between the selector for all types of CSPs and the enantiomers remains a challenge [28,41]. It is established that the forces acting on one enantiomer during the interaction with the selector may differ from those acting on the other enantiomer. Thus, the goal is to develop an approach that allows for the identification and quantification of the forces present [42]. Hence, a comprehensive understanding of chiral separation is pivotal because it allows the development of better chromatographic systems and elucidates fundamental concepts in chiral recognition [23]. The elucidation of chiral recognition mechanisms is also useful to guide structural modifications of the selectors to achieve a higher enantiomeric selectivity for a specific class or a wider range of enantiomers.
Chiral recognition is a type of molecular recognition involving the selective formation of transient complexes formed in a mixture of enantiomers [43]. The groundwork for understanding chiral recognition at a molecular level was laid by Bentley [44], who introduced rigid geometric models based on a biochemical and pharmacological perspective. From this concept, Easson and Stedman [45] developed a structural model to elucidate the differences in the biological activity of enantiomers. According to this model, enantioselectivity arises from the distinct interactions of a pair of enantiomers with biotargets, requiring at least three attractive contact points for chiral discrimination [28,45,46].
The “three-point model” was put aside for a period of time until Ogston [47] decided to reclaim it to explain the enzymatic decarboxylation of L-serine to glycine. Later, Topiol and Sabio [48] introduced the “four-contact point model”, which states that chiral recognition is associated with attractive or repulsive interactions between eight centers. Then, Mesecar and Koshland [49] introduced a “four-location model” where a minimum of four designed locations, such as four attachment sites or three attachment sites and a direction, is needed.
In the chromatography field, Dalgliesh [50] resorted to the “three-point model” to explain the chiral separation of aromatic amino acids using a CSP based on cellulose. This model of chiral recognition was later restated by Pirkle and coworkers [51,52,53], as follows: “Chiral recognition requires a minimum of three simultaneous interactions between the CSP and at least one of the enantiomers, with at least one of these interactions being stereochemically dependent.”
For some authors, the “three-point model” is considered simplistic, so it turns out not to be suitable for all selectors [54,55,56]. Actually, for macromolecules as chiral selectors, the mechanism can be much more complex [32,57]. Moreover, it can only be considered when selector-enantiomer interactions occur on only one side [58]. Additionally, it must always be taken into account that chiral recognition is a dynamic process and not a static process as it is often considered [59]. Nevertheless, this model has been widely used to design CSPs and for the rational study of the mechanisms associated with chiral discrimination [60,61,62].
A wide variety of tools has been described to shed light on the mechanisms involved in chiral molecular recognition and enantioseparation as well as elucidate the type of interactions that occur between a chiral selector and the enantiomers [63,64]. Nuclear magnetic resonance (NMR) spectroscopy, particularly nuclear Overhauser effect spectroscopy (NOESY) and rotating-frame Overhauser enhancement spectroscopy (ROESY), has proven to be a very valuable technique for determining the spatial proximity of functional groups of the selectors and enantiomers [65,66,67]. Additionally, ultraviolet (UV) spectroscopy, fluorimetry, Fourier transform, attenuated total reflectance infrared (IR) spectroscopy, and circular dichroism spectroscopy can be applied only for soluble selectors [64]. It is important to note that interactions will change with solvents, emphasizing the need for careful consideration when different solvents are used in certain studies and chromatographic separations [68,69]. X-ray crystallography provides the structures of the complexes between chiral selectors and enantiomers in a solid state; however, these differ from the structures in a solution [57,70,71]. Furthermore, immobilized chiral selectors adopt distinct conformations compared to their crystalline or solution states due to chemical modifications during immobilization and steric hindrance [72,73]. These constraints force structural adaptations to achieve optimal stability, directly impacting their chiral recognition properties [69,74].
The first example of molecular modeling regarding enantioseparation was the study developed by Armstrong et al. [75], where the formation of the inclusion complexes of β-CD was analyzed. Next, Weinstein et al. [76] introduced a molecular model to elucidate the intricacies of stereoselective interaction within a series of chiral secondary amines. Nevertheless, it was Lipkowitz et al. [77] who have notably led the computational studies in this field using quantum mechanics (QM), molecular mechanics (MM), molecular dynamics (MD), and Monte Carlo methods. Their extensive investigations have mainly focused on unravelling the enantioselectivity of various chiral selectors through the prediction/confirmation of the enantiomeric elution order [77] and, with a special focus, on understanding the chiral recognition mechanisms associated with chromatographic separations by CSPs developed by Pirkle’s group [78,79].
It is also important to highlight Scriba et al., who used MD and molecular modeling to examine binding thermodynamics and to visualize selector-analyte complex structures, contributing significantly to the understanding and development of computational studies in chiral molecular recognition [63,80]. This collective effort underscores the pivotal role of computational methods in advancing the understanding of chiral chromatography, offering invaluable insights into its underlying principles and applications.
In recent years, a number of fundamental reviews and book chapters on chiral recognition mechanisms in separation science have been published [23,25,32,57,63,64,69,80,81,82,83], focusing mainly on relevant examples across different types of CSPs. This review systematically compiles enantioseparation studies by cLC that incorporate both CSPs and computational analysis. The main aim of this review is to unfold the synergy between computational studies and cLC, to assess the relevance of the association of these two approaches, and to analyze current trends in the field. Special emphasis is placed on how computational advancements are reshaping the landscape of cLC, providing deeper insights and supporting the development of more efficient and selective separation strategies.
The key novelty of this review, in comparison with the existing literature, lies in the exhaustive compilation of studies integrating these two methodologies. This comprehensive survey offers a clear perspective on emerging trends over recent years, including year-by-year developments. It not only traces the evolution of computational applications but also examines various aspects of cLC, such as the types of CSPs employed, the composition of mobile phases, and the range of analytes investigated.

2. Molecular Modeling in Chiral Liquid Chromatography

In this review, a literature survey covering the reports on enantioseparation by cLC using CSPs and computational studies was conducted, covering recently published works (from 2015 to January 2025). The scientific compilation took place in January 2025 and was based on the PRISMA guidelines [84]. The identification of papers was conducted through a search on the SCOPUS database considering the following keywords or expressions: “chiral stationary phase AND computational OR docking OR molecular dynamics OR molecular modeling,” “enantioseparation AND computational OR molecular modeling AND liquid chromatography.”
Inclusion criteria for paper selection were works published as original articles, in English, that addressed the topics of this research. Studies describing other types of chromatography, not related to the separation of enantiomers, as well as studies not relevant to the topic, were excluded. All data collected were interpreted in a critical and impartial manner. The methodological path that led to the selection of the scientific articles included in this review was outlined according to the flowchart shown in Figure 2.
Figure 2. Flow diagram of literature search (n = number of scientific articles time frame: 2015–January 2025; database: SCOPUS).
Through the comprehensive literature survey, 94 articles that included computational studies and enantioseparation by LC were found. Table 1 summarizes relevant information about the articles.
Table 1. Compilation of studies comprising both LC enantioseparation using chiral stationary phases (CSPs) and computational approaches.
A significant growth in research concerning both enantioseparation by cLC and computational studies is evident from 2015 to 2023, as illustrated in Figure 3A. Particularly, between 2019 and 2023, there is a notable spike in interest in this field, leading to an increase in article publications. Moreover, during 2024, 11 articles were published. These data emphasize the fact that the relationship between cLC and computational studies tends to grow over time. It was found that a diverse range of computational methods were employed.
Figure 3. (A) Distribution of the selected computational studies between 2015 and 2024. (B) Distribution of the reported works considering the computational methods used. (C) Main aims of reported methods. DFT: Density functional theory; MMFF: Merck Molecular Force Field; QM/MM: Quantum mechanics/Molecular mechanics; QSPR: Quantitative structure-activity relationship; QM/MM: Quantum mechanics/Molecular mechanics.
As emphasized in Figure 3B, molecular docking emerges as the predominant computational method, accounting for 50% of the reported studies. The reasons that can justify this number are its user-friendly interface and light computational cost [177]. Following closely behind is MD (25% of the studies), also widely employed due to its ability to dynamically simulate the chiral separation process, including the solvent effect [178]. It is noteworthy that most of the studies include multiple computational approaches simultaneously to mitigate the limitations inherent to each technique.
Computational studies have been used to achieve various purposes, being extremely valuable in the enantioseparation field. As summarized in Figure 3C, the most common goal is the understanding of the chiral recognition mechanisms, accounting for 80% of the reported studies, followed by the prediction of the enantiomeric elution order, accounting for 14% of the studies.
The success of an efficient enantioseparation is mostly determined by the chiral discriminative capability of the CSP [16]. Figure 4A summarizes the different types of CSPs reported from 2015 until the end of December 2024. In general, the most used CSPs, over the years, are polysaccharide-based and Pirkle-type. It is important to point out a notable increase in the number of studies describing both enantioseparation using polysaccharide-based CSPs and computational studies from 2018.
Figure 4. (A) Distribution of the reported studies considering the type of chiral stationary phases (CSPs) from 2015 to 2024; (B) Distribution regarding the types of CSPs. (C) Tested analytes in the studies reported in Table 1; (D) Modes of elution for each type of CSP. CD: Cyclodextrin; MP: Mobile phase; NP: Normal phase; PI: Polar ionic; PO: Polar organic; RP: Reversed-phase.
Polysaccharide-based CSPs are recognized as being the most successful and widely applied for both analytical and preparative enantioseparations [179]. The high recognition ability of polysaccharide derivatives, their abundance in nature, and their compatibility with various solvents are some of the reasons that can justify this trend [180]. The chiral recognition ability of polysaccharides is dependent on diverse structural features, including sugar units, stereogenic centers, type of linkage and its position, as well as the adjacent polymer chains [181]. The helical twist of the polymer backbone also has a key role in enantioselectivity [182]. Although polysaccharide-based selectors are complex polymeric structures and, consequently, computational studies are more demanding when compared with selectors based on small molecules, in the last years, there has been an increased interest in computational approaches for this type of CSPs. As shown in Figure 4B, CSPs based on polysaccharides are the most employed, accounting for 52% of the reported studies. The second most used and investigated CSPs are Pirkle-type (14% of the reported studies). Since the 1980s and for many years, Pirkle-type CSPs have been the most widely investigated concerning the knowledge of chiral recognition mechanisms [62]. The reasons are because they comprise small molecules as chiral selectors covalently bound to chromatographic support via a spacer, being apparently easier to study [15,183]. The distribution of the chiral molecules on the surface of the inert matrix allows easy access to the analytes, enabling numerous interactions between the chiral selector and the enantiomers [15].
The next analysis concerns the type of analytes tested in each of the studies (Figure 4C). A great variety of analytes can be enantioseparated using different CSPs, including synthetic products, drugs, natural products, standard analytes typically used to evaluate the performance of CSPs, among others. It is evident that certain compounds are more frequently tested for enantioseparation than others, especially synthetic products and drugs, accounting for 44% and 27% of the reported studies, respectively.
Another important aspect of the enantioseparation process is the mobile phase, which greatly influences the retention of the enantiomers, enantioselectivity, and resolution [184]. As shown in Figure 4D, different types of CSPs, including Pirkle-type, polysaccharide-based, and macrocyclic antibiotics, can be used in diverse elution modes (normal-phase (NP), reversed-phase (RP), polar organic (PO), polar-ionic (PI)), being compatible with a wide range of solvents as mobile phases. Although they can be used in different elution modes, it was found that Pirkle-type and polysaccharide-based CSPs were most used in NP and PO conditions. PI conditions were preferred for zwitterionic-ion exchange CSPs and, as expected, RP mode for protein-based, macrocyclic antibiotic-based, CD-based, and crown ether-based CSPs.
As examples, representative studies reported in Table 1 covering the computational approaches used in cLC will be explored in more detail to emphasize the benefit of the association of these two approaches. To select examples involving the most commonly used computational techniques, our primary criterion was to include studies encompassing different types of CSPs. This approach was intended to highlight the distinct molecular recognition mechanisms associated with each CSP type, which we consider a key factor in understanding the interplay between chromatographic performance and computational analysis.

2.1. Molecular Docking

Molecular docking is a computational technique used to predict the interaction geometry (pose) of two molecules, in this specific field, a chiral selector and enantiomers, based on their molecular structures [185]. It helps predict binding geometries and rank binding affinities of enantiomers with CSPs [23,25]. The main goal is to identify the most stable diastereomeric complex and assess enantiomer elution order based on interaction energy [23]. The docking process involves two stages: search phase and scoring phase [186]. The search phase predicts the conformation of enantiomers at the binding site [186,187]. This can be conducted with a rigid selector (lock and key model) or a flexible selector (induced-fit model) [188,189]. Grid points are used to map the selector’s binding sites, and an algorithm explores different enantiomer conformers to find the best binding site [23,25,190]. After obtaining several poses, the second phase is reached, the scoring phase, where poses are scored and ranked according to their interaction with the receptor using simple scoring functions [191]. The main types of scoring functions are force field-based, which calculate energies based on physics-based potentials, empirical ones, which use linear combinations of terms with adjustable coefficients optimized from experimental data, and knowledge-based, which use statistical descriptors based on crystallography data [192,193,194]. Although molecular docking has been the preferred computational approach to address the interaction between chiral selectors and enantiomeric pairs, these calculations are generally insufficient to provide thermodynamic and kinetic detail on the separation process since they rely on a static representation of the interaction between selector and enantiomeric pairs and often struggle to accurately describe the nature of the interaction between these, in particular when non-polar interactions are determinant for the interaction. Nevertheless, these simple calculations have consistently provided atomistic detail on selector:enantiomer interactions and helped explain experimental data.
Recently, Adhikari et al. [153] performed a molecular docking study of three naphthaldimine derivatives of leucinol on tris(3,5-dimethylphenylcarbamate) cellulose-based CSP Chiralcel OD-H® to estimate the binding energies and conformations of the CSP-analyte complexes. The study included 100 docking runs, 25 × 105 energy evaluations, and 27.00 iterations using the Lamarckian genetic algorithm. Furthermore, the poses obtained were ranked using different scoring functions. The (S)-enantiomers of naphthaldimine derivatives exhibited stronger retention and binding affinity for the selector due to additional hydrogen-bonds, π–π and dipole–dipole interactions compared to the (R)-enantiomers. These differences in non-covalent interactions significantly enhanced enantioselectivity. The results obtained agreed with the experimental data of enantioseparation and elution order, where the (R)-enantiomer elutes before. In Figure 5, the docking poses of the enantiomers of each naphthaldimine derivative of leucinol are represented, alongside the main interactions responsible for chiral recognition (hydrogen-bond and π–π interactions) [153].
Figure 5. Docking poses of the enantiomers of 1-naphthaldimines (A,B), 2-naphthaldimines (C,D), and 2-hydroxynaphthaldimines (E,F) with tris(3,5-dimethylphenylcarbamate) cellulose-based CSP, respectively. The hydrogen-bond interactions are represented as yellow dotted lines, the analytes and the CSP are represented as light pink and cyan sticks, respectively. (Reprint with permission from [153], Copyright (2022) John Wiley and Sons).
Another example of a molecular docking study was conducted by Dombi et al. [157], which focused on examining how apremilast (APR) enantiomers interact with human serum albumin (HSA) in a stereoselective manner. The docking data shed light on the interactions between APR enantiomers and HSA-based CSP, providing insights into the molecular mechanisms underlying their binding. The calculations were carried out using the Schrodinger suite, the system minimization was conducted by the OPLS3e force field, and the potential binding sites on HSA were identified using SiteMap. Flexible molecular docking was performed using the extra precision mode of Glide.
The results showed that (S)-APR bound more strongly to the HSA, mainly due to an extra π-stacking interaction between this enantiomer and a Phe residue of HSA (Figure 6) [157].
Figure 6. S-enantiomer and R-enantiomer of apremilast (APR) docked to binding sites of human serum albumin (HSA) (top, left corner). I, II, and III are HSA domains. The structures are highlighted in red, blue, lime, yellow, and cyan. The best binding pose for APR regarding the sites was chosen, along with the corresponding enantiomer (top, right corner). Amino acid residues within 2 Å of the ligands are highlighted (bottom) [157]. R and S enantiomers are colored orange.
Phyo et al. [195] conducted a molecular docking study to understand the chromatographic results and to identify the chiral recognition mechanisms responsible for the enantioseparation of xanthones and benzophenones using (S,S)-Whelk-O1® CSP. Additionally, the analysis of the interactions between the tested enantiomers and the chiral selector illustrated the role of the structural characteristics of the compounds for enantiodiscrimination. Docking data showed that the π–π stacking interactions established by the phenyl ring bonded to the stereogenic centers and the aromatic moiety of the selector were crucial for enantiorecognition. In Figure 7, it is possible to verify the interactions between the analytes (in this case, four of them as examples) and the selector responsible for enantioseparation [195].
Figure 7. The most stable conformations of four analytes (A–D) docked onto (S,S)-Whelk-O1® (grey). (R) and (S) enantiomers are represented as cyan and yellow sticks, respectively. Hydrogen-bond and π–π stacking interactions are represented as a red broken line and a yellow double arrow, respectively. (Reprint with permission from [195], Copyright (2021) John Wiley and Sons).

2.2. Molecular Dynamics

MD simulations offer an effective way to study the dynamic interactions between enantiomers and CSPs in chromatographic separations, providing a more realistic representation than static calculations, such as in docking [39,59,141]. MD simulates molecular movement and interactions over time by solving Newton’s equations of motion for all atoms in a system, which often includes the CSP, solvent, and analytes [25,39,196]. The CSP is typically modeled in one of four ways: a dynamic amorphous silica plate, a fixed layer of silicon atoms, a polymer with limited mobility, and a loose selector molecule [86,197,198,199]. Solvent modeling can be conducted using explicit solvent (thousands of molecules), implicit solvent (dielectric solvent), or no solvent (vacuum) [96,129,200].
Both the analyte and selector can be treated as flexible or rigid molecules depending on the system’s requirements [201,202]. Those changes in the components of the system allow for conformational changes and exploration of different binding poses. MD simulations can reveal binding locations, intermolecular interactions responsible for diastereomeric complex formation, and the key forces driving enantioselectivity [141,178,203], and are thus powerful approaches to study dynamical and thermodynamic properties of complex systems. However, they are often time-consuming and computationally demanding, especially for large and heterogeneous systems, such as is the case for chromatographic ones. Aside from the complexity of the chemical composition of chromatographic systems, chromatographic separations generally take minutes to hours to occur, timescales that are unfeasible for atomistic simulations even with available computational power nowadays. Most common examples in the literature resort to the modeling of simple mixtures of the chiral separator and enantiomeric pairs in solution, but a few examples can be found where the modeling of materials functionalized with chiral separators and the mobile phase is attempted, allowing for a dynamic study of the interaction between chiral selectors and enantiomeric pairs [127]. Hence, despite the obvious challenges posed to the field, we can find several examples in literature where MD simulations provided valuable insights into the molecular basis of chiral separations [196,204].
For example, in a study developed by Saleh et al. [163], the enantioseparation, quantification, and chiral recognition mechanisms of five β-adrenergic blockers, namely bisoprolol, carvedilol, atenolol, metoprolol, and nebivolol, on a cellulose tris(3-chloro-4-methylphenyl carbamate column (Lux-Cellulose-2®), were investigated by molecular docking and MD. Docking studies identified the most stable complex for each enantiomer and the key interactions driving separation, while MD simulations were used to evaluate the stability of the enantiomer-CSP complex and confirmed the main interactions involved. Through a series of short MD simulations on simple systems solvated with ethanol, the authors could confirm the column’s separation capability for the analytes and their enantiomeric elution order: (S)-metoprolol > (R)-metoprolol; (R)-bisoprolol > (S)-bisoprolol; (S,R,R,R)-nebivolol > (R,S,S,S)-nebivolol; (R)-carvedilol > (S)-carvedilol; (S)-atenolol > (R)-atenolol, in line with experimental results. Furthermore, chiral recognition mechanisms were also identified, the main interactions being hydrogen-bond and π–π interactions. The (R)-atenolol showed stronger retention due to π–π stacking and two hydrogen-bonds, while the (S)-atenolol established one hydrogen-bond and one halogen bond. For carvedilol, the (S)-enantiomer was more retained due to two additional hydrogen bonds. For nebivolol, the (S,R,R,R)-enantiomer formed one hydrogen-bond and one π–π interaction, while the (R,S,S,S)-enantiomer established an extra hydrogen-bond, leading to stronger retention. Lastly, both bisoprolol enantiomers had π-alkyl interactions, but the (S)-enantiomer established two hydrogen bonds compared to one for the (R)-enantiomer. For example, in Figure 8 are represented the binding interactions of carvedilol, nebivolol, and bisoprolol with the CSP [163].
Figure 8. Binding interactions obtained from molecular dynamics (MD) simulations between cellulose-based chiral stationary phase (CSP) and three analytes, at 600 ps, adapted from [163]. Cellulose-based CSP is colored gray, R and S enantiomeric pairs are colored orange and cyan respectively.
Varfaj et al. [140] used ab initio time-dependent density functional theory (DFT) simulations coupled with electronic circular dichroism to obtain the enantiomeric elution order under optimized mobile phase conditions. Additionally, MD simulations were carried out to determine the chiral recognition mechanisms associated with the enantioseparation of aromatic α-hydroxy acids with cinchona alkaloid-based zwitterionic CSP (ChiralPack® ZWIX (-)) (Figure 9). The time-dependent DFT simulations were performed using the ωB7X-D3 density functional and the 6-311++G** basis set, and the 50 lowest energy electronic transitions of each optimized conformer were then used to calculate their theoretical electronic circular dichroism spectra. The MD simulations were performed in the canonical ensemble at 298 K, using the Desmond Molecular Dynamics System for 300 ns [140].
Figure 9. Examples of frames of hydrogen-bond interactions (yellow dashed lines) promoted by Chiralpack® ZWIX (-) (cyan sticks) and the (S)-enantiomer (green sticks) (A) and (R)-enantiomer (magenta sticks) (B) of 3-(4-hydroxyphenyl) lactic acid. Adapted from [140]. (Reprint with permission from [140], Copyright (2021) Elsevier).
By benchmarking different theoretical electronic circular dichroism spectra obtained against an experimentally obtained one, the authors developed a computational strategy to determine the enantiomeric elution order: (S)-enantiomer first, followed by (R)-enantiomer. Subsequent MD simulations showed that the hydrogen bond interaction of the p-hydroxy group of 3-(4-hydroxyphenyl) lactic acid with the sulfonic acid moiety of the chiral selector (Figure 9) was essential for the retention and supported the experimental enantiomeric elution order [140].
Another example was described by Wang et al. [98], which modeled the enantioseparation of a flavanone with β-CD-based CSPs with different orientations (normal and reversed) by MD simulations, using a 1:1 methanol/water mixture as mobile phase (Figure 10). The system was described with the CHARMM36 force field, β-CD were described by the CHARMM carbohydrate force field and parameters for the flavanones were derived from the CGenFF force field, and simulations were performed with the NAMD software. The simulations were carried out at 298 K and 1 atm conditions, controlled by Langevin Dynamics and Langevin Piston methods, respectively, and the dynamic simulation process was performed with a time step of 2.0 fs [98].
Figure 10. Snapshots from molecular dynamics (MD) simulation of the inclusion complexes of flavanone with β-CD-based chiral stationary phases (CSPs) with different orientations, reversed (CSP1) and normal (CSP2), adapted from [98]. (Reprint with permission from [98], Copyright (2017) Elsevier).
The results showed that the CD selector with the normal orientation (CSP2) allowed a better enantioseparation for almost 30 racemates, and the CD selector with the reversed orientation (CSP1) had a better resolution for analytes with polar functional groups in cyclic moieties. The MD simulations revealed inclusion complexes of the CSPs with different orientations (Figure 10); the main interactions responsible for enantioseparation, namely hydrophobic and hydrogen-bond interactions, were able to predict enantiomeric elution order and racemate resolution [98].

2.3. Other Computational Approaches

Although scarcer in the literature, QM calculations have also been reported to study chromatographic systems. QM is used to describe the properties of electrons and nuclei on a subatomic scale, allowing the study of molecular phenomena with electronic resolution [205,206]. The calculation of molecular properties with electronic resolution requires the resolution of the Schrodinger equation [206], in particular of the wavefunction of the system from which observable quantities of the system can be drawn [207]. DFT is the most common QM method for studying chromatographic systems [208]. The main disadvantage of these methods is that the systems under study cannot generally scale beyond a few hundred atoms, nor can their dynamic properties be simulated for periods longer than a few picoseconds. In particular, solvation must generally be addressed with simplistic implicit solvation models to reduce the number of atoms in the system and render QM calculations feasible. As such, they are generally employed to characterize interactions between selectors and enantiomeric pairs, complementing molecular docking studies. QM calculations have also been used to compute the spectroscopic properties, namely by using TD-DFT to calculate the circular dichroism spectra of enantiomeric pairs [140]. More recent developments in the calculation of UV circular dichroism spectra of biological molecules combining TD-DFT and range-separated density functionals, explicitly including solvent representation or accounting for the conformational molecular diversity, are also expanding the use of these techniques to more complex molecules [209,210,211]. These advancements should also enhance the application of QM methods for the characterization of enantiomeric mixtures, namely enantiomeric pairs of biological relevance.
For example, Núñez-Rico et al. [161] investigated the effectiveness of a homochiral metal-organic framework-based CSP, TAMOF-1, to separate a wide range of racemic mixtures of organic compounds. Using the semiempirical GFN2-xTB method and implicit solvation models, the study made use of the Conformer–Rotamer Ensemble Sampling Tool (CREST) program and enhanced sampling MD simulations in water to predict and rationalize the separation and capabilities of TAMOF-1. Additionally, DFT was employed to predict activation energy barriers for chiral inversion where low resolution occurred or where theoretical predictions differed from experimental results. The study accurately predicted the enantiomers elution order within the TAMOF-1′s channels, with computational predictions aligning with experimental results in over 90% of cases, highlighting TAMOF-1’s potential as an effective tool for chiral separations [161].
In a study developed by Protti et al. [162], time-dependent (TD)-DFT calculations were employed to investigate the absolute stereochemistry of the synthetic cathinones mephedone, methylone, and butylone and to infer about the enantiomeric elution order on a crown ether-based CSP. The molecules were submitted to geometry optimization and frequency calculations at the DFT level, using the B97-D3 functional, the def2-TZVP basis set, the density fitting approximation, and the IEFPCM solvation model for methanol. Then, TD-DFT calculations, using PBE0- 1 3 functional combined with the def2-TZVPD basis set and IEFPCM solvation model for methanol, were performed to calculate UV and circular dichroism spectra, from which the results showed a (R) < (S)-enantiomeric elution order for mephedrone, methylone, and butylone [162].
Another example was described by Peluso et al. [103], which investigated the enantioseparation of atropisomeric fluorinated 3-arylthio-4,4’-bipyridines on cellulose-based CSPs, focusing on identifying additional interactions, particularly those involving electronic charge depletion regions as recognition sites at both chiral and achiral levels. The study aimed to assess the influence of pentafluorophenyl-centered π-hole on enantioseparation. Geometry optimization and calculation of electrostatic potential surfaces, as well as related parameters at the B3LYP/6-311G* level of theory, were performed. The computational data identified additional interactions, specifically stereoselective chalcogen and π-hole bonds. The evaluation of molecular properties also aided the design of analytes as probes and provided insights into the experimental chromatographic behaviors [103].

3. Conclusions

In chiral liquid chromatography (cLC), understanding enantiomeric discrimination mechanisms is of pivotal relevance. The key concept behind enantioseparation involves the formation of labile diastereomeric complexes, driven by various intermolecular interactions such as hydrogen-bond, ionic, π–π, ion–dipole, dipole–dipole, induced dipole–dipole, and Van der Waals interactions between the chiral selector and enantiomers. The Gibbs energy difference between these diastereomeric complexes is responsible for chiral recognition.
Computational methods, such as molecular docking and molecular dynamics (MD), offer valuable insights into these interactions, helping to investigate chiral recognition mechanisms, rationalize experimental enantiomeric elution orders, and optimize chromatographic and solvation systems. However, computational methods face challenges, including reliance on approximations that may not fully capture system complexities, high computational resource demands, and difficulties in accurately representing solvent effects. Other drawbacks include rigid or semi-flexible models, as they can overlook conformational changes during enantioseparation, and often computational data require validation, normally through experimental studies, as simplified in silico models may not fully align with the experimental outcomes.
Nevertheless, even with the associated disadvantages, integrating computational methods in cLC is essential as it allows a better understanding of the recognition mechanisms of chiral selectors and establishes a connection between theoretical insights and experimental data, thus serving as a complementary approach to LC experiments.
This systematic review, although grounded in a well-defined and robust methodological framework, as outlined in the flowchart presented in Figure 2, has certain limitations. It does not include a formal assessment of bias and may be subject to publication bias, which could influence the overall findings. Additionally, heterogeneity in study designs, sample types, and experimental conditions makes direct comparisons across studies difficult. Moreover, the rapid emergence of new cLC enantioseparation studies, including both CSPs and computational analysis, means that the conclusions drawn may quickly become outdated.
The data compiled in this review highlights the current trend of combining cLC enantioseparation and computational studies within the same work, due to the synergistic benefits of these two approaches.

Author Contributions

Conceptualization: C.F.; Data collection and analysis: R.L.; Writing—original draft preparation: R.L.; Writing—reviewing and editing: R.P.P.N., P.A.F., A.M.S.S., and C.F. All authors have read and agreed to the published version of the manuscript.

Funding

This research was supported by national funds through FCT (Foundation for Science and Technology) within the scope of Base Funding UIDB/04423/2020 and UIDP/04423/2020 (Group of Marine Products and Medicinal Chemistry—CIIMAR) and the project PTDC/CTA-AMB/0853/2021.

Institutional Review Board Statement

Not applicable.

Data Availability Statement

No new data were created or analyzed in this study. Data sharing is not applicable to this article.

Acknowledgments

R.L. acknowledges her PhD grant provided by FCT 2022.11168. A.M.S.S., P.A.F., and R.P.P.N. acknowledge the support from FCT/MCTES: LA/P/0008/2020 DOI: https://doi.org/10.54499/LA/P/0008/2020, UIDP/50006/2020 DOI: https://doi.org/10.54499/UIDP/50006/2020, and UIDB/50006/2020 DOI: https://doi.org/10.54499/UIDB/50006/2020. R. P. P. N. further thanks FCT for funding through the Individual Call to Scientific Employment Stimulus (Ref. 2021.00391.CEECIND/CPI662/CT003 DOI: https://doi.org/10.54499/2021.00391.CEECIND/CP1662/CT0003).

Conflicts of Interest

The authors declare no conflicts of interest.

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