Investigation of binding features: Effects on the interaction between CYP2A6 and inhibitors

A computational investigation has been carried out on CYP2A6 and its naphthalene inhibitors to explore the crucial molecular features contributing to binding specificity. The molecular bioactive orientations were obtained by docking (FlexX) these compounds into the active site of the enzyme. And the density functional theory method was further used to optimize the molecular structures with the subsequent analysis of molecular lipophilic potential (MLP) and molecular electrostatic potential (MEP). The minimal MLPs, minimal MEPs, and the band gap energies (the energy difference between the highest occupied molecular orbital and lowest unoccupied molecular orbital) showed high correlations with the inhibition activities (pIC₅₀s), illustrating their significant roles in driving the inhibitor to adopt an appropriate bioactive conformation oriented in the active site of CYP2A6 enzyme. The differences in MLPs, MEPs, and the orbital energies have been identified as key features in determining the binding specificity of this series of compounds to CYP2A6 and the consequent inhibitory effects. In addition, the combinational use of the docking, MLP and MEP analysis is also demonstrated as a good attempt to gain an insight into the interaction between CYP2A6 and its inhibitors. © 2010 Wiley Periodicals, Inc. J Comput Chem, 2010     

Using a homology model of cytochrome P450 2D6 to predict substrate site of metabolism

CYP2D6 is an important enzyme that is involved in first pass metabolism and is responsible for metabolizing ~25% of currently marketed drugs. A homology model of CYP2D6 was built using X-ray structures of ligand-bound CYP2C5 complexes as templates. This homology model was used in docking studies to rationalize and predict the site of metabolism of known CYP2D6 substrates. While the homology model was generally found to be in good agreement with the recently solved apo (ligand-free) X-ray structure of CYP2D6, significant differences between the structures were observed in the B′ and F–G helical region. These structural differences are similar to those observed between ligand-free and ligand-bound structures of other CYPs and suggest that these conformational changes result from induced-fit adaptations upon ligand binding. By docking to the homology model using Glide, it was possible to identify the correct site of metabolism for a set of 16 CYP2D6 substrates 85% of the time when the 5 top scoring poses were examined. On the other hand, docking to the apo CYP2D6 X-ray structure led to a loss in accuracy in predicting the sites of metabolism for many of the CYP2D6 substrates considered in this study. These results demonstrate the importance of describing substrate-induced conformational changes that occur upon binding. The best results were obtained using Glide SP with van der Waals scaling set to 0.8 for both the receptor and ligand atoms. A discussion of putative binding modes that explain the distribution of metabolic sites for substrates, as well as a relationship between the number of metabolic sites and substrate size, are also presented. In addition, analysis of these binding modes enabled us to rationalize the typical hydroxylation and O-demethylation reactions catalyzed by CYP2D6 as well as the less common N-dealkylation.     

Site of metabolism prediction on cytochrome P450 2C9: a knowledge-based docking approach

A novel structure-based approach for site of metabolism prediction has been developed. This knowledge-based method consists of three steps: (1) generation of possible metabolites, (2) docking the predicted metabolites to the CYP binding site and (3) selection of the most probable metabolites based on their complementarity to the binding site. As a proof of concept we evaluated our method by using MetabolExpert for metabolite generation and Glide for docking into the binding site of the CYP2C9 crystal structure. Our method could identify the correct metabolite among the three best-ranked compounds in 69% of the cases. The predictive power of our knowledge-based method was compared to that achieved by substrate docking and two alternative literature approaches.     

Comparative analysis of binding energy of chymostatin with human cathepsin A and its homologous proteins by molecular orbital calculation

Cathepsin A is a mammalian lysosomal enzyme that catalyzes the hydrolysis of the carboxy-terminal amino acids of polypeptides and also regulates beta-galactosidase and neuraminidase-1 activities through the formation of a multienzymic complex in lysosomes. Human cathepsin A (hCathA), yeast carboxypeptidase (CPY), and wheat carboxypeptidase II (CPW) belong to the alpha/beta-hydrolase fold family. They have structurally similar active-site clefts, but there are small differences in the amino acid residues comprising their active sites that might determine the substrate specificity and sensitivity to microbial inhibitors including chymostatin. To examine the selectivity and binding mechanism of chymostatin as to hCathA, CPY, and CPW at the atomic level, we analyzed the interaction energy between chymostatin and each protein quantitatively by semiempirical molecular orbital calculation AM1 with the continuum solvent model. We predicted the electrostatic repulsion between the P3 cyclic arginine residue of the inhibitor and the Arg344 in the S3 active subsite of hCathA. Genetic conversion of Arg344 of the wild-type hCathA to Ile also caused an increase in its sensitivity to chymostatin, which was correlated with the decrease in the interaction energy calculated with the molecular orbital method. The present results suggest that such molecular calculation should be useful for evaluating the interactions between ligands, including inhibitors and homologous enzymes, in their docking models.     

Prediction of activation energies for aromatic oxidation by cytochrome P450

We have estimated the activation energy for aromatic oxidation by compound I in cytochrome P450 for a diverse set of 17 substrates using state-of-the-art density functional theory (B3LYP) with large basis sets. The activation energies vary from 60 to 87 kJ/mol. We then test if these results can be reproduced by computationally less demanding methods. The best methods (a B3LYP calculation of the activation energy of a methoxy-radical model or a partial least-squares model of the semiempirical AM1 bond dissociation energies and spin densities of the tetrahedral intermediate for both a hydroxyl-cation and a hydroxyl-radical model) give correlations with r(2) of 0.8 and mean absolute deviations of 3 kJ/mol. Finally, we apply these simpler methods on several sets of reactions for which experimental data are available and show that we can predict the reactive sites by combining calculations of the activation energies with the solvent-accessible surface area of each site.     

Characterization of the CYP3A4 active site by homology modeling

Human microsomal cytochrome P450s participate in drug metabolism and detoxification. Among them, CYP3A4 is the most important isoform for drug-drug interactions. To gain a better understanding of the active site, a homology model of CYP3A4 was constructed based on the crystallographic coordinates of mammalian CYP2C5. The putative active site is much larger than that of CYP2C5 and is divided into three parts (i.e. a proximal and two distal sites from the heme). Most residues reported to be important for ligand-binding are located in the active site of the model. Moreover, some inhibitors (paclitaxel etc.) docked into the model have complementary shapes to the pocket. Pharmacophore docking of 14 substrates was also performed using Ph4Dock of MOE. Calculated interaction energies showed a moderate correlation with the logarithm of apparent K(m) values. These results suggest that this model is reliable enough to be used in the design of compounds for removing undesirable CYP3A4 inhibition.     

QM/QM docking method based on the variational finite localized molecular orbital approximation

We present a derivation of the semiempirical variational finite localized molecular orbital (VFL) approximation, which was introduced by Anikin et al. (J Chem Phys 2004, 121, 1266). On the basis of VFL approximation, we developed the novel semiempirical (quantum mechanical) QM/QM method in which a part of the system, including the ligand and protein active site, are treated self-consistently, while the protein bulk is considered as carrying a frozen electronic density matrix. The developed method is applied toward the QM docking study for the p56 LCK SH2 domain. The virtual search has predicted 10 most potent inhibitors by searching through the database of 200,000 empirically docked poses of 20,000 drug-like molecules. Energy score calculation of each complex roughly consisting of 1700 atoms took 14.54 s of single-CPU time at the NDDO AM1 level. The entire computation performed on a 32-CPU cluster would be accomplished in 1 day. Flexible ligand QM docking studies, performed on a subset of 10,000 poses, required 153.03 s of single-CPU time per complex. The entire calculation performed on the 32-CPU cluster would be finished in half-day.     

Exploration of enzyme-ligand interactions in CYP2D6 & 3A4 homology models and crystal structures using a novel computational approach

New crystal structures of human CYP2D6 and CYP3A4 have recently been reported, and in this study, we wanted to compare them with previously used homology models with respect to predictions of site of metabolism and ligand-enzyme interactions. The data set consisted of a family of synthetic opioid analgesics with the aim to cover both CYP2D6 and CYP3A4, as most of these compounds are metabolized by both isoforms. The program MetaSite was used for the site of metabolism predictions, and the results were validated by experimental assessment of the major metabolites formed with recombinant CYP450s. This was made on a selection of 14 compounds in the data set. The prediction rates for MetaSite were 79-100% except for the CYP3A4 homology model, which picked the correct site in half of the cases. Despite differences in orientation of some important amino acids in the active sites, the MetaSite-predicted sites were the same for the different structures, with the exception of the CYP3A4 homology model. Further exploration of interactions with ligands was done by docking substrates/inhibitors in the different structures with the docking program GLUE. To address the challenge in interpreting patterns of enzyme-ligand interactions for the large number of different docking poses, a new computational tool to handle the results from the dockings was developed, in which the output highlights the relative importance of amino acids in CYP450-substrate/inhibitor interactions. The method is based on calculations of the interaction energies for each pose with the surrounding amino acids. For the CYP3A4 structures, this method was compared with consensus principal component analysis (CPCA), a commonly used method for structural comparison to evaluate the usefulness of the new method. The results from the two methods were comparable with each other, and the highlighted amino acids resemble those that were identified to have a different orientation in the compared structures. The new method has clear advantages over CPCA in that it is far simpler to interpret and there is no need for protein alignment. The methodology enables structural comparison but also gives insights on important amino acid substrate/inhibitor interactions and can therefore be very useful when suggesting modifications of new chemical entities to improve their metabolic profiles.     

2D SMARTCyp reactivity-based site of metabolism prediction for major drug-metabolizing cytochrome P450 enzymes

Cytochrome P450 (CYP) 3A4, 2D6, 2C9, 2C19, and 1A2 are the most important drug-metabolizing enzymes in the human liver. Knowledge of which parts of a drug molecule are subject to metabolic reactions catalyzed by these enzymes is crucial for rational drug design to mitigate ADME/toxicity issues. SMARTCyp, a recently developed 2D ligand structure-based method, is able to predict site-specific metabolic reactivity of CYP3A4 and CYP2D6 substrates with an accuracy that rivals the best and more computationally demanding 3D structure-based methods. In this article, the SMARTCyp approach was extended to predict the metabolic hotspots for CYP2C9, CYP2C19, and CYP1A2 substrates. This was accomplished by taking into account the impact of a key substrate-receptor recognition feature of each enzyme as a correction term to the SMARTCyp reactivity. The corrected reactivity was then used to rank order the likely sites of CYP-mediated metabolic reactions. For 60 CYP1A2 substrates, the observed major sites of CYP1A2 catalyzed metabolic reactions were among the top-ranked 1, 2, and 3 positions in 67%, 80%, and 83% of the cases, respectively. The results were similar to those obtained by MetaSite and the reactivity + docking approach. For 70 CYP2C9 substrates, the observed sites of CYP2C9 metabolism were among the top-ranked 1, 2, and 3 positions in 66%, 86%, and 87% of the cases, respectively. These results were better than the corresponding results of StarDrop version 5.0, which were 61%, 73%, and 77%, respectively. For 36 compounds metabolized by CYP2C19, the observed sites of metabolism were found to be among the top-ranked 1, 2, and 3 sites in 78%, 89%, and 94% of the cases, respectively. The computational procedure was implemented as an extension to the program SMARTCyp 2.0. With the extension, the program can now predict the site of metabolism for all five major drug-metabolizing enzymes with an accuracy similar to or better than that achieved by the best 3D structure-based methods. Both the Java source code and the binary executable of the program are freely available to interested users.     

Ligand- and protein-based modeling studies of the inhibitors of human cytochrome P450 2D6 and a virtual screening for potential inhibitors from the Chinese herbal medicine, Scutellaria baicalensis (Huangqin,Baikal Skullcap)

We have previously examined the binding patterns of various substrates to human cytochrome P450 2D6 (CYP2D6) using a series of molecular modeling methods. In this study, we further explored the binding modes of various types of inhibitors to CYP2D6 using a combination of ligand- and protein-based modeling approaches. Firstly, we developed and validated a pharmacophore model for CYP2D6 inhibitors, which consisted of two hydrophobic features and one hydrogen bond acceptor feature. Secondly, we constructed and validated a quantitative structure-activity relationship (QSAR) model for CYP2D6 inhibitors which gave a poor to moderate prediction accuracy. Thirdly, a panel of CYP2D6 inhibitors were subject to molecular docking into the active site of wild-type and mutated CYP2D6 enzyme. We demonstrated that 8 residues in the active site (Leu213, Glu216, Ser217, Gln244, Asp301, Ser304, Ala305, and Phe483) played an important role in the binding to the inhibitors via hydrogen bond formation and/or π-π stacking interaction. Apparent changes in the binding modes of the inhibitors have been observed with Phe120Ile, Glu216Asp, Asp301Glu mutations in CYP2D6. Finally, we screened for potential binders/inhibitors from the Chinese herbal medicine Scutellaria baicalensis (Huangqin, Baikal Skullcap) using the established pharmacophore model for CYP2D6 inhibitors and molecular docking approach. Overall, 18 out of 40 compounds from S. baicalensis were mapped to the pharmacophore model of CYP2D6 inhibitors and most herbal compounds from S. baicalensis could be docked into the active site of CYP2D6. Our study has provided insights into the molecular mechanisms of interaction of synthetic and herbal compounds with human CYP2D6 and further benchmarking studies are needed to validate our modeling and virtual screening results.     

On the relationship between the preferred site of hydrogen bonding and protonation

Ab initio molecular orbital calculations have been employed to investigate the interactions between a set of basic substrates (B) with H+ and HF, and the interaction between acids of varying strength (AH+) with two bases, vinylamine and furan. The preferred site for protonation of the substrates appears to be determined primarily by the ability of the protonated species (BH+) to delocalize the acquired positive charge. On the other hand, localization of a pair of electrons at a proton-acceptor site of B tends to be more important in determining the preferred site for hydrogen bonding with HF. The behavior of acids stronger than HF lies between these extremes. Consistent with a previously proposed Hammond postulate for complexes, when a substrate (B) interacts with a range of acids (AH+), proton transfer is generally found to occur when the proton affinity of A is significantly less than that of B. When the proton affinity of A is greater than that of B, a hydrogen-bonded complex is generally formed without proton transfer. Strongest binding (relative to the lowest energy components) occurs when the proton affinities of A and B are comparable. Proton transfer from AH+ is found to take place in some cases when this would not be predicted on the basis of protonation energies alone, because of specific interactions in the resulting complexes.     

Computational Analysis of Triazole-Based Kojic Acid Analogs as Tyrosinase Inhibitors by Molecular Dynamics and Free Energy Calculations

Molecular docking, molecular dynamics (MD) simulations and the linear interaction energy (LIE) method were used here to predict binding modes and free energy for a set of 1,2,3-triazole-based KA analogs as potent inhibitors of Tyrosinase (TYR), a key metalloenzyme of the melanogenesis process. Initially, molecular docking calculations satisfactorily predicted the binding mode of evaluated KA analogs, where the KA part overlays the crystal conformation of the KA inhibitor into the catalytic site of TYR. The MD simulations were followed by the LIE method, which reproduced the experimental binding free energies for KA analogs with an r² equal to 0.97, suggesting the robustness of our theoretical model. Moreover, the van der Waals contributions performed by some residues such as Phe197, Pro201, Arg209, Met215 and Val218 are responsible for the binding recognition of 1,2,3-triazole-based KA analogs in TYR catalytic site. Finally, our calculations provide suitable validation of the combination of molecular docking, MD, and LIE approaches as a powerful tool in the structure-based drug design of new and potent TYR inhibitors.     

Comparison of metabolic soft spot predictions of CYP3A4, CYP2C9 and CYP2D6 substrates using MetaSite and StarDrop

Metabolite identification study plays an important role in determining the sites of metabolic liability of new chemical entities (NCEs) in drug discovery for lead optimization. Here we compare the two predictive software, MetaSite and StarDrop, available for this purpose. They work very differently but are used to predict the site of oxidation by major human cytochrome P450 (CYP) isoforms. Neither software can predict non-CYP catalyzed metabolism nor the rates of metabolism. For the purpose of comparing the two software packages, we tested known probe substrate for these enzymes, which included 12 substrates of CYP3A4 and 18 substrates of CYP2C9 and CYP2D6 were analyzed by each software and the results were compared. It is possible that these known substrates were part of the training set but we are not aware of it. To assess the performance of each software we assigned a point system for each correct prediction. The total points assigned for each CYP isoform experimentally were compared as a percentage of the total points assigned theoretically for the first choice prediction for all substrates for each isoform. Our results show that MetaSite and StarDrop are similar in predicting the correct site of metabolism by CYP3A4 (78% vs 83%, respectively). StarDrop appears to do slightly better in predicting the correct site of metabolism by CYP2C9 and CYP2D6 metabolism (89% and 93%, respectively) compared to MetaSite (63% and 70%, respectively). The sites of metabolism (SOM) from 34 in-house NCEs incubated in human liver microsomes or human hepatocytes were also evaluated using two prediction software packages and the results showed comparable SOM predictions. What makes this comparison challenging is that the contribution of each isoform to the intrinsic clearance (Clint) is not known. Overall the software were comparable except for MetaSite performing better for CYP2D6 and that MetaSite has a liver model that is absent in StarDrop that predicted with 82% accuracy.     

A semiempirical free energy force field with charge-based desolvation

The authors describe the development and testing of a semiempirical free energy force field for use in AutoDock4 and similar grid-based docking methods. The force field is based on a comprehensive thermodynamic model that allows incorporation of intramolecular energies into the predicted free energy of binding. It also incorporates a charge-based method for evaluation of desolvation designed to use a typical set of atom types. The method has been calibrated on a set of 188 diverse protein-ligand complexes of known structure and binding energy, and tested on a set of 100 complexes of ligands with retroviral proteases. The force field shows improvement in redocking simulations over the previous AutoDock3 force field.     

Molecular docking,PKPD, and assessment of toxicity of few chalcone analogues as EGFR inhibitor in search of anticancer agents

In the present work, molecular docking of the chalcone analogues with receptor EGFR carried out using erlotinib as reference drug is reported. About 15 chalcone analogues were analyzed CHL(1–15). Molecules CHL2, CHL3, CHL9, CHL11, and CHL15 found strong affinity for receptor EGFR exhibiting binding energies ??7.7 kcal/mol, ??7.5 kcal/mol, ??7.6 kcal/mol, ??7.9 kcal/mol, and ??8.1 kcal/mol, respectively, when erlotinib a reference drug exhibits binding energy ??7.6 kcal/mol. Toxicity for molecules was assessed against the cytochromes P450 (CYP) and P-gp using Swiss ADMET. Molecule CHL9 could be a suitable lead compound inhibitor to CYP1A2 followed by CHL2 inhibitor of CYP1A2 and CYP2C9 and CHL15 with a most stable binding affinity of ??8.1 kcal/mol, inhibiting CYP1A2, CYP2C19, and CYP2D6. CHL3 has a binding affinity of ??7.5 kcal/mol, inhibiting all the 05 CYP enzymes (CYP1A2, CYP2C19, CYP2C9, CYP2D6, and CYP3A4). CHL11 has a binding affinity of ??7.9 kcal/mol, inhibiting CYP1A2, CYP2C19, and CYP2C9. Considering inhibition of CYP family enzymes by molecules, further here we have perform the enrichment analysis to these CYP family enzymes and reported the metabolic pathways which were probably affected by inhibition of these enzymes using EnrichR online enrichment analysis server. The current predictions over these 15 chalcone derivatives will be needed to further investigate in vivo and in vitro conditions to identify the optimum therapeutic efficacy and least toxicity.

     

Molecular Docking of 3-Methylindole-containing Drugs Binding into CYP3A4

Drugs SPD-304(6,7-dimethyl-3-{[methyl-(2-{methyl-[1-(3-trifluoromethyl-phenyl)-1H-indol-3-ylmethyl]- amino}-ethyl)-amino]-methyl}-chromen-4-one) and zafirlukast contain a common structural element of 3-substituted indole moiety which closely relates to a dehydrogenated reaction catalyzed by cytochrome P450s(CYPs). It was reported that the dehydrogenation can produce a reactive electrophilic intermediate which cause toxicities and inactivate CYPs. Drug L-745,870(3-{[4-(4-chlorophenyl)piperazin-1-yl]-methyl}-1H-pyrrolo- 2,3-β-pyridine) might have similar effect since it contains the same structural element. We used molecular docking approach combined with molecular dynamics(MD) simulation to model three-dimensional(3D) complex structures of SPD-304, zafirlukast and L-745,870 into CYP3A4, respectively. The results show that these three drugs can stably bind into the active site and the 3-methylene carbons of the drugs keep a reasonable reactive distance from the heme iron. The complex structure of SPD-304-CYP3A4 is in agreement with experimental data. For zafirlukast, the calculation results indicate that 3-methylene carbon might be the dehydrogenation reaction site. Docking model of L-745,870-CYP3A4 shows a potential possibility of L-745,870 dehydrogenated by CYP3A4 at 3-methylene carbon which is in agreement with experiment in vivo. In addition, residues in the phenylalanine cluster as well as S119 and R212 play a critical role in the ligands binding based on our calculations. The docking models could provide some clues to understand the metabolic mechanism of the drugs by CYP3A4.     

Structural and Dynamic Basis of Human Cytochrome P450 7B1: A Survey of Substrate Selectivity and Major Active Site Access Channels

Cytochrome P450 (CYP) 7B1 is a steroid cytochrome P450 7α‐hydroxylase that has been linked directly with bile salt synthesis and hereditary spastic paraplegia type 5 (SPG5). The enzyme provides the primary metabolic route for neurosteroids dehydroepiandrosterone (DHEA), cholesterol derivatives 25‐hydroxycholesterol (25‐HOChol), and other steroids such as 5α‐androstane‐3β,17β‐diol (anediol), and 5α‐androstene‐3β,17β‐diol (enediol). A series of investigations including homology modeling, molecular dynamics (MD), and automatic docking, combined with the results of previous experimental site‐directed mutagenesis studies and access channels analysis, have identified the structural features relevant to the substrate selectivity of CYP7B1. The results clearly identify the dominant access channels and critical residues responsible for ligand binding. Both binding free energy analysis and total interaction energy analysis are consistent with the experimental conclusion that 25‐HOChol is the best substrate. According to 20 ns MD simulations, the Phe cluster residues that lie above the active site, particularly Phe489, are proposed to merge the active site with the adjacent channel to the surface and accommodate substrate binding in a reasonable orientation. The investigation of CYP7B1–substrate binding modes provides detailed insights into the poorly understood structural features of human CYP7B1 at the atomic level, and will be valuable information for drug development and protein engineering.     

ZINDO calculations of the ground state and electronic transitions in the tetracyanonickelate Ion,Ni(CN)(4)(2-)

ZINDO semiempirical calculations on the Ni(CN)(4)(2-) ion were performed, and ground-state energies for all 41 valence-orbital-based MOs and orbital transition components of the two lowest energy fully allowed electronic transitions are reported. Gaussian 94 was used to calculate ground-state energies as a comparison. The ground-state energies using ZINDO compare much more favorably with those found through ab initio techniques than with those from a reported INDO calculation. The found electronic transitions agree substantially with earlier assignments with the exception that several orbital transitions are required to adequately model the lowest energy allowed x,y-polarized experimental transition. Calculation parameters were optimized to give excellent agreement with experiment and may serve well for more complex arrangements of this ion.     

In silico study of porphyrin-anthraquinone hybrids as CDK2 inhibitor

Cyclin-Dependent Kinases (CDKs) are known to play crucial roles in controlling cell cycle progression of eukaryotic cell and inhibition of their activity has long been considered as potential strategy in anti-cancer drug research. In the present work, a series of porphyrin-anthraquinone hybrids bearing meso-substituents, i.e. either pyridine or pyrazole rings were designed and computationally evaluated for their Cyclin Dependent Kinase-2 (CDK2) inhibitory activity using molecular docking, molecular dynamics simulation, and binding free energy calculation. The molecular docking simulation revealed that all six porphyrin hybrids were able to bind to ATP-binding site of CDK2 and interacted with key residues constituted the active cavity of CDK2, while molecular dynamics simulation indicated that all porphyrins bound to CDK2 were stable for 6 ns. The binding free energies predicted by MM-PBSA method showed that most compounds exhibited higher affinity than that of native ligand (4-anilinoquinazoline, DTQ) and the affinity of mono-H₂PyP-AQ was about three times better than that of DTQ, indicating its potential to be advanced as a new CDK2 inhibitor.     

Interaction energy calculation scheme employing one-electron hamiltonian approximation for the evaluation of short-range interactions

A semiempirical scheme for the calculation of intermolecular energy is presented. A distinctive feature of the scheme is the employment of the one-electron Hamiltonian approximation in EHT parametrization for the calculation of exchange repulsion and charge transfer energies. Electrostatic, induction and dispersion components are calculated according to known approximate formulas containing point multipole moments and bond polarizabilities. The proposed scheme is applied to the calculation of binding energies and equilibrium geometries of various molecular dimers.