Gas-phase Interaction Energies Research Articles

Efficient Computation of the Interaction Energies of Very Large Non-covalently Bound Complexes

AbstractWe present a new benchmark set consisting of 16 large non-covalently bound systems (LNCI16) ranging from 380 up to 1988 atoms and featuring diverse interaction motives. Gas-phase interaction energies are calculated with various composite DFT, semi-empirical quantum mechanical (SQM), and force field (FF) methods and are evaluated using accurate DFT reference values. Of the employed QM methods, PBEh-3c proves to be the most robust for large systems with a relative mean absolute deviation (relMAD) of 8.5% with respect to the reference interaction energies. r2SCAN-3c yields an even smaller relMAD, at least for the subset of complexes for which the calculation could be converged, but is less robust for systems with smaller HOMO–LUMO gaps. The inclusion of Fock-exchange is therefore important for the description of very large non-covalent interaction (NCI) complexes in the gas phase. GFN2-xTB was found to be the best performer of the SQM methods with an excellent result of only 11.1% deviation. From the assessed force fields, GFN-FF and GAFF achieve the best accuracy. Considering their low computational costs, both can be recommended for routine calculations of very large NCI complexes, with GFN-FF being clearly superior in terms of general applicability. Hence, GFN-FF may be routinely applied in supramolecular synthesis planning.1 Introduction2 The LNCI16 Benchmark Set3 Computational Details4 Generation of Reference Values5 Results and Discussion6 Conclusions

Hydration of amino acids: An investigation using density functional theory

Herein, we have investigated the effect of hydration of seven amino acids (AAs) such as alanine, aspartic acid,cysteine, glutamine, lysine, methionine, and phenylalanine with different number of water molecules using density functional theory. Among the hydrophobic AAs, cysteine has the highest interaction with water whereas in hydrophilic AAs, aspartic acid has the highest interaction with water. With the increase in number of water molecules, it is noted that alanine forms the most stable complex with water and methionine+water complex has least stability.In addition, we have calculated the chemical descriptors like chemical potential, electronegativity, hardness, softness, electrophilicity index of AAs to validate their interaction with water molecules. Interestingly, the gas phase interaction energy results match with the trend of electrophilicity index valuesof AAs.

Hydration of Aromatic Heterocycles as an Adversary of π-Stacking.

Hydration is one of the key players in the protein–ligand binding process. It not only influences the binding process per se, but also the drug’s absorption, distribution, metabolism, and excretion properties. To gain insights into the hydration of aromatic cores, the solvation thermodynamics of 40 aromatic mono- and bicyclic systems, frequently occurring in medicinal chemistry, are investigated. Thermodynamics is analyzed with two different methods: grid inhomogeneous solvation theory (GIST) and thermodynamic integration (TI). Our results agree well with previously published experimental and computational solvation free energies. The influence of adding heteroatoms to aromatic systems and how the position of these heteroatoms impacts the compound’s interactions with water is studied. The solvation free energies of these heteroaromatics are highly correlated to their gas phase interaction energies with benzene: compounds showing a high interaction energy also have a high solvation free energy value. Therefore, replacing a compound with one having a higher gas phase interaction energy might not result in the expected improvement in affinity. The desolvation costs counteract the higher stacking interactions, hence weakening or even inverting the expected gain in binding free energy.

Cyclohexane-Based Scaffold Molecules Acting as Anion Transport, Anionophores, via Noncovalent Interactions.

A theoretical study of a variety of cyclohexane-based anion transporters interacting with the chloride anion has been conducted using density functional theory. The calculations have been performed in the gas phase but also, in order to describe the solvation effects on the interaction, two different solvents-chloroform and dimethylsulfoxide-have been taken into account. Gas-phase interaction energies within the complexes are found to be up to 400 kJ/mol, while, when solvent effects are considered, the interaction energy values decreased drastically concomitantly with an elongation in the interatomic distances. Atoms in molecules and natural bond analysis corroborate the trends found for the intermolecular energies and Cl···H distances, suggesting strong donations from the Cl- anion into the σ*H-N antibonding orbitals, as well as with noncovalent interaction plots showing large areas of electron density overlap within the chloride anion surroundings.

Theoretical Study of Protein-Ligand Interactions Using the Molecules-in-Molecules Fragmentation-Based Method.

We have recently significantly expanded the applicability of our Molecules-in-Molecules (MIM) fragmentation method to large proteins by developing a three-layer model (MIM3) in which an accurate quantum-mechanical method is used in conjunction with a cost-effective, dispersion-corrected semiempirical model to overcome previous computational bottlenecks. In this work, we develop MIM3 as a structure-based drug design tool by application of the methodology for the accurate calculation of protein-ligand interaction energies. A systematic protocol is derived for the determination of the geometries of the protein-ligand complexes and to calculate their accurate interaction energies in the gas phase using MIM3. We also derive a simple and affordable procedure based on implicit solvation models and the ligand solvent-accessible surface area to approximate the ligand desolvation penalty in gas-phase interaction energy calculations. We have carefully assessed how closely such interaction energies, which are based on a single protein-ligand conformation, display correlations with the experimentally determined binding affinities. The performance of MIM3 was evaluated on a total of seven data sets comprising 89 protein-ligand complexes, all with experimentally known binding affinities, using a binding pocket involving a quantum region ranging in size from 250 to 600 atoms. The dispersion-corrected B97-D3BJ density functional, previously known to perform accurately for calculations involving non-covalent interactions, was used as the target level of theory for this work, with dispersion-corrected PM6-D3 as the semiempirical low level to incorporate the long-range interactions. Comparing directly to the experimental binding potencies, we obtain impressive correlations over all seven test sets, with an R2 range of 0.74-0.93 and a Spearman rank correlation coefficient (ρ) range of 0.83-0.93. Our results suggest that protein-ligand interaction energies are useful in predicting binding potency trends and validate the potential of MIM3 as a quantum-chemical structure-based drug design tool.

The intramolecular hydrogen bonded-halogen bond: a new strategy for preorganization and enhanced binding.

Natural and synthetic molecules use weak noncovalent forces to preorganize structure and enable remarkable function. Herein, we introduce the intramolecular hydrogen bonded-halogen bond (HB-XB) as a novel method to preorganize halogen bonding (XBing) molecules, while generating a polarization-enhanced XB. Positioning a fluoroaniline between two iodopyridinium XB donors engendered intramolecular hydrogen bonding (HBing) to the electron-rich belt of both XB donors. NMR solution studies established the efficacy of the HB-XB. The receptor with HB-XBs (G2XB) displayed a nearly 9-fold increase in halide binding over control receptors. Gas-phase density functional theory conformational analysis indicated that the amine stabilizes the bidentate conformation. Furthermore, gas-phase interaction energies showed that the bidentate HB-XBs of G2XBme2+ are more than 3.2 kcal mol-1 stronger than the XBs in a control without the intramolecular HB. Additionally, crystal structures confirm that HB-XBs form tighter contacts with I- and Br- and produce receptors that are more planar. Collectively the results establish the intramolecular HB-XB as a tractable strategy to preorganize XB molecules and regulate XB strength.

ChemInform Abstract: Using Dispersion‐Corrected Density Functional Theory to Understand Supramolecular Binding Thermodynamics

AbstractReview: 121 refs.

The Association of Two “Frustrated” Lewis Pairs by State‐of‐the‐Art Quantum Chemical Methods

AbstractState‐of‐the‐art quantum chemical methods have been applied to describe the association of two frustrated Lewis pairs (FLPs), B(C6F5)3/PR3 (1: R=2,4,6‐Me3C6H2; 2: R=CMe3), with different steric demands of the base component. Interaction energies are calculated at the dispersion‐corrected DFT, MP2 (second‐order Møller‐Plesset), and DLPNO‐CCSD(T) (domain‐based local pair natural orbital‐coupled cluster, including single, double and perturbative triple excitations) levels of theory, combined with extended triple‐ or quadruple‐ζ AO (atom‐centered orbital) basis sets. Thermostatistical contributions to the free binding energy are calculated from harmonic frequencies at the efficient HF‐3c (minimal basis Hartree‐Fock with three corrections) level, while solvation effects in benzene are accounted for by the COSMO‐RS (conductor‐like screening model for realistic solvents) continuum model. Comparison with the recently measured experimental value for the free association energy of the FLP 1 reveals agreement between theory and experiment within the estimated error bars. The computed gas phase interaction energies for both FLPs are similar (about −13 kcal mol−1), with only small variations (about ±3 kcal mol−1) for various quantum chemical methods, when London dispersion interactions are accounted for properly. The association of the more “frustrated” FLP 1 is mainly driven by nondirectional dispersion forces, resulting in non‐preferential orientations, which is in agreement with experimental results. On the other hand, in FLP 2 with the “smaller” base, the boron and phosphorous atoms face each other in the favored complex structure, indicating a weak PB donor‐acceptor interaction. This conformation of 2 seems to be more suitable for small molecule (e.g., H2) activations.

Design and screening of suitable ligand/diluents systems for removal of Sr2+ ion from nuclear waste: Density functional theoretical modelling

Density functional theoretical (DFT) calculation has been used for the design and screening of ligand/solvent systems for the selective and efficient extraction of Sr2+ ion from aqueous solution using free energy analysis. Present DFT study has shown that the metal ion selectivity cannot be predicted using intrinsic gas phase interaction energy alone. Even implicit solvation employing conductor like screening model (COSMO) approach unable to predict the correct trend of experimental selectivity. The COSMO solvation model when used explicitly by considering first solvation sphere around the metal ion it captures the correct trend of experimental selectivity. Organic solvent of high dielectric constant was found to be suitable for the extraction of the metal ion. Further, COSMO for real solvent (COSMO-RS) was successfully used to predict the solubility and partition coefficients of the ligands for screening. Presence of nitrate anion in the complexation reaction was shown to increase the gas as well as solvent phase complexion energy. The calculated theoretical extraction energy was found to be well correlated to the experimentally observed distribution constant of Sr2+ ion in the biphasic systems. The preferential selectivity of Sr2+ ion over other competing ions towards macrocyclic ligands was demonstrated by calculating free energy of extraction in the biphasic systems. Natural bond order (NBO) analysis was also performed to investigate the nature of bonding in Sr2+ ion-crown ether interaction.

Supramolecular Binding Thermodynamics by Dispersion‐Corrected Density Functional Theory

The equilibrium association free enthalpies ΔG(a) for typical supramolecular complexes in solution are calculated by ab initio quantum chemical methods. Ten neutral and three positively charged complexes with experimental ΔG(a) values in the range 0 to -21 kcal mol(-1) (on average -6 kcal mol(-1)) are investigated. The theoretical approach employs a (nondynamic) single-structure model, but computes the various energy terms accurately without any special empirical adjustments. Dispersion corrected density functional theory (DFT-D3) with extended basis sets (triple-ζ and quadruple-ζ quality) is used to determine structures and gas-phase interaction energies (ΔE), the COSMO-RS continuum solvation model (based on DFT data) provides solvation free enthalpies and the remaining ro-vibrational enthalpic/entropic contributions are obtained from harmonic frequency calculations. Low-lying vibrational modes are treated by a free-rotor approximation. The accurate account of London dispersion interactions is mandatory with contributions in the range -5 to -60 kcal mol(-1) (up to 200% of ΔE). Inclusion of three-body dispersion effects improves the results considerably. A semilocal (TPSS) and a hybrid density functional (PW6B95) have been tested. Although the ΔG(a) values result as a sum of individually large terms with opposite sign (ΔE vs. solvation and entropy change), the approach provides unprecedented accuracy for ΔG(a) values with errors of only 2 kcal mol(-1) on average. Relative affinities for different guests inside the same host are always obtained correctly. The procedure is suggested as a predictive tool in supramolecular chemistry and can be applied routinely to semirigid systems with 300-400 atoms. The various contributions to binding and enthalpy-entropy compensations are discussed.

Prediction of SAMPL3 host-guest binding affinities: evaluating the accuracy of generalized force-fields.

We used the second-generation mining minima method (M2) to compute the binding affinities of the novel host-guest complexes in the SAMPL3 blind prediction challenge. The predictions were in poor agreement with experiment, and we conjectured that much of the error might derive from the force field, CHARMm with Vcharge charges. Repeating the calculations with other generalized force-fields led to no significant improvement, and we observed that the predicted affinities were highly sensitive to the choice of force-field. We therefore embarked on a systematic evaluation of a set of generalized force fields, based upon comparisons with PM6-DH2, a fast yet accurate semi-empirical quantum mechanics method. In particular, we compared gas-phase interaction energies and entropies for the host-guest complexes themselves, as well as for smaller chemical fragments derived from the same molecules. The mean deviations of the force field interaction energies from the quantum results were greater than 3 kcal/mol and 9 kcal/mol, for the fragments and host-guest systems respectively. We further evaluated the accuracy of force-fields for computing the vibrational entropies and found the mean errors to be greater than 4 kcal/mol. Given these errors in energy and entropy, it is not surprising in retrospect that the predicted binding affinities deviated from the experiment by several kcal/mol. These results emphasize the need for improvements in generalized force-fields and also highlight the importance of systematic evaluation of force-field parameters prior to evaluating different free-energy methods.

Protonation of Base Pairs in RNA: Context Analysis and Quantum Chemical Investigations of Their Geometries and Stabilities

Base pairs involving protonated nucleobases play important roles in mediating global macromolecular conformational changes and in facilitation of catalysis in a variety of functional RNA molecules. Here we present our attempts at understanding the role of such base pairs by detecting possible protonated base pairs in the available RNA crystal structures using BPFind software, in their specific structural contexts, and by the characterization of their geometries, interaction energies, and stabilities using advanced quantum chemical computations. We report occurrences of 18 distinct protonated base pair combinations from a representative data set of RNA crystal structures and propose a theoretical model for one putative base pair combination. Optimization of base pair geometries was carried out at the B3LYP/cc-pVTZ level, and the BSSE corrected interaction energies were calculated at the MP2/aug-cc-pVDZ level of theory. The geometries for each of the base pairs were characterized in terms of H-bonding patterns observed, rmsd values observed on optimization, and base pair geometrical parameters. In addition, the intermolecular interaction in these complexes was also analyzed using Morokuma energy decomposition. The gas phase interaction energies of the base pairs range from -24 to -49 kcal/mol and reveal the dominance of Hartree-Fock component of interaction energy constituting 73% to 98% of the total interaction energy values. On the basis of our combined bioinformatics and quantum chemical analysis of different protonated base pairs, we suggest resolution of structural ambiguities and correlate their geometric and energetic features with their structural and functional roles. In addition, we also examine the suitability of specific base pairs as key elements in molecular switches and as nucleators for higher order structures such as base triplets and quartets.

GAS PHASE STRUCTURE AND STABILITY OF COMPLEX FORMED BY H2O, NH3, H2S AND THEIR METHYL DERIVATIVES WITH THE CATION CO2+

Ab initio molecular orbital calculations at the Hartree-Fock-Self Consistent Field (HF-SCF) have been performed in order to determine the structure and gas phase energies of complex formed by the Lewis bases of H2O, NH3, H2S and their methyl derivatives with the cation Co2+. The relative basicities of the base studied depend on both the substituent. The gas-phase interaction energies computed by the SCF method including electron correlation Møller-Plesset 2 (MP2) dan Configuration Iteration (CI) were comparable in accuracy. The binding energies computed by these two methods reach the targeted chemical accuracy. Keywords: ab initio calculation, cobalt complex, structure stability

On the Role of the cis Hoogsteen:Sugar-Edge Family of Base Pairs in Platforms and Triplets—Quantum Chemical Insights into RNA Structural Biology

Base pairs belonging to the cis Hoogsteen:sugar-edge (H:S) family play important structural roles in folded RNA molecules. Several of these are present in internal loops, where they are involved in interactions leading to planar dinucleotide platforms which stabilize higher order structures such as base triplets and quartets. We report results of analysis of 30 representative examples spanning 16 possible base pair combinations, with several of them showing multimodality of base pairing geometry. The geometries of 23 of these base pairs were modeled directly from coordinates extracted from RNA crystal structures. The other seven were predicted structures which were modeled on the basis of observed isosteric analogues. After appropriate satisfaction of residual valencies, these structures were relaxed using the B3LYP/6-31G(d,p) method and interaction energies were derived at the RIMP2/aug-cc-pVDZ level of theory. The geometries for each of the studied base pairs have been characterized in terms of the number and nature of H-bonds, rmsd values observed on optimization, base pair geometrical parameters, and sugar pucker analysis. In addition to its evaluation, the nature of intermolecular interaction in these complexes was also analyzed using Morokuma decomposition. The gas phase interaction energies range between -5.2 and -20.6 kcal/mol and, in contrast to the H:S trans base pairs, show enhanced relative importance of the electron correlation component, indicative of the greater role of dispersion energy in stabilization of these base pairs. The rich variety of hydrogen bonding pattern, involving the flexible sugar edge, appears to hold the key to several features of structural motifs, such as planarity and propensity to participate in triplets, observed in this family of base pairs. This work explores these aspects by integrating database analysis, and detailed base pairing geometry analysis at the atomistic level, with ab initio computation of interaction energies. The study, involving alternative classification of base pairs and triplets, provides insights into intrinsic properties of these base pairs and their possible structural and functional roles.

Noncovalent Interactions of a Benzo[a]pyrene Diol Epoxide with DNA Base Pairs: Insight into the Formation of Adducts of (+)-BaP DE-2 with DNA

Noncovalent complexes of a tumorigenic benzo[a]pyrene diol epoxide with the guanine-cytosine (GC) and adenine-thymine (AT) base pairs have been examined computationally. (+)-BaP DE-2 forms covalent adducts with DNA via nucleophilic attack on the (+)-BaP DE-2 epoxide. Computational results predict five thermodynamically accessible complexes of AT with (+)-BaP DE-2 that are compatible with intact DNA. Among these, two are expected to lead to adenine adducts. In the lowest energy AT...(+)-BaP DE-2 complex, which has a gas-phase interaction energy of -20.9 kcal mol(-1), the exocyclic NH(2) of adenine is positioned for backside epoxide attack and formation of a trans adduct. The most energetically favorable complex leading to formation of a cis ring-opened adduct lies only 0.6 kcal mol(-1) higher in energy. For GC...(+)-BaP DE-2, there are only two thermodynamically accessible complexes. The higher-lying complex, bound in the gas phase by 24.4 kcal mol(-1) relative to separated GC and (+)-BaP DE-2, would lead to a trans ring-opened N(2)-guanine adduct. In the global minimum energy GC...(+)-BaP DE-2 complex, bound by 27.3 kcal mol(-1), the exocyclic NH(2) group of cytosine is positioned for cis epoxide addition. However, adducts of (+)-BaP DE-2 with cytosine are rarely observed experimentally. The paucity of cytosine adducts, despite the predicted thermodynamic stability of this GC...(+)-BaP DE-2 complex, is attributed to the electrostatic destabilization of the benzylic cation intermediate thought to precede cis addition.

Trans Hoogsteen/Sugar Edge Base Pairing in RNA. Structures, Energies, and Stabilities from Quantum Chemical Calculations

Trans Hoogsteen/sugar edge (H/SE) RNA base pairs form one of the six families of RNA base pairs that utilize the 2'-hydroxyl group of ribose for base pairing and play key roles in stabilizing folded RNA molecules. Here, we provide a detailed quantum chemical characterization of intrinsic structures and interaction energies of this base pair family, along with the evaluation of solvent screening effects by a continuum solvent approach. We report DFT-optimized geometries and MP2 interaction energies for all 10 crystallographically identified members of the family, for a representative set of them, using complete basis set extrapolation. For 6 of the 10 base pairs, we had to apply geometric constraints to keep the geometries relevant to RNA. We confirm that the remaining, hitherto undetected, possible members of this family do not have appropriate steric features required to establish stable base pairing in the trans H/SE fashion. The interaction patterns in the trans H/SE family are highly diverse, with gas-phase interaction energies in the range from -1 to -17 kcal/mol. Except for the C/rC and G/rG trans H/SE base pairs, the interaction energy is roughly evenly distributed between the HF and correlation components. Thus, in the trans H/SE base pairs, the relative importance of electron correlation is noticeably smaller than in the cis WC/SE or cis and trans SE/SE base pairs, but still larger than in canonical base pairs. The trans H/SE A/rG base pair is the intrinsically most stable member of this family. This base pair is also known as the sheared AG base pair and belongs to the most prominent set of RNA base pairs utilized in molecular building blocks of functional RNAs. For all trans H/SE base pairs that we identified, in addition to conventional base pairing, viable alternative structures were stabilized by amino-acceptor interactions. In the QM calculations, these amino-acceptor complexes appear to be equally as stable as those with common H-bonds, and more importantly, the switch to amino-acceptor interaction does not require any significant geometrical rearrangement of the base pairs. Such interactions are worthy of further investigations, as X-ray crystallography cannot unambiguously distinguish between conventional and amino-acceptor interactions involving the 2'-hydroxyl group, formation of such interactions is usually not considered, and molecular modeling force fields do not include such interactions properly as a result of neglect of aminogroup pyramidalization.

Thermodynamic and structural properties of methanol–water solutions using nonadditive interaction models

We study bulk structural and thermodynamic properties of methanol-water solutions via molecular dynamics simulations using novel interaction potentials based on the charge equilibration (fluctuating charge) formalism to explicitly account for molecular polarization at the atomic level. The study uses the TIP4P-FQ potential for water-water interactions, and the CHARMM-based (Chemistry at HARvard Molecular Mechanics) fluctuating charge potential for methanol-methanol and methanol-water interactions. In terms of bulk solution properties, we discuss liquid densities, enthalpies of mixing, dielectric constants, self-diffusion constants, as well as structural properties related to local hydrogen bonding structure as manifested in radial distribution functions and cluster analysis. We further explore the electronic response of water and methanol in the differing local environments established by the interaction of each species predominantly with molecules of the other species. The current force field for the alcohol-water interaction performs reasonably well for most properties, with the greatest deviation from experiment observed for the excess mixing enthalpies, which are predicted to be too favorable. This is qualitatively consistent with the overestimation of the methanol-water gas-phase interaction energy for the lowest-energy conformer (methanol as proton donor). Hydration free energies for methanol in TIP4P-FQ water are predicted to be -5.6 +/- 0.2 kcal/mol, in respectable agreement with the experimental value of -5.1 kcal/mol. With respect to solution microstructure, the present cluster analysis suggests that the microscale environment for concentrations where select thermodynamic quantities reach extremal values is described by a bipercolating network structure.

Stabilization of a K + -( bis -Cage-Annulated 20-Crown-6) Complex by Bidentate Picrate

Bis-cage-annulated 18-crown-6 and 20-crown-6 macrocyclic ethers (i.e., 1 and 2, respectively) have been synthesized, and their alkali metal picrate extraction profiles have been determined. Host system 1 proved to be a significantly more avid alkali metal cation complexant than 2 and somewhat more avid than 18-crown-6. Both 1 and 18-crown-6 display modest selectivity toward K+ and Rb+. A stable host–guest complex was prepared by slow evaporation of a CH2Cl2–hexane solution of an equimolar mixture of 2 and potassium picrate. The X-ray crystal structure of this complex reveals that picrate anion functions as a bidentate ligand therein. The gas-phase interaction energy between the 2 ⋅ K+ complex and picrate anion was calculated to be ca. −64.9 kcal mol−1, thereby indicating that participation of picrate anion as an additional bidentate ligand results in significant stabilization of complex 10.

Liquid tin tetrachloride: a Monte Carlo simulation study

A simple five-site intermolecular potential function has been derived to reproduce the results from high-level ab initio calculations of the gas-phase interaction energy for SnCl 4. This adjusted intermolecular potential was used in a Monte Carlo statistical mechanical simulation of the liquid at a temperature of 25°C and a pressure of 1 atm. The structural results, presented as a radial distribution function, reveal that in the first solvation shell each SnCl 4 molecule is surrounded by twelve nearest neighbours. These results, as well as thermodynamical properties, are in good agreement with experimental findings.

Structure and gas phase stability of complexes L...M, where M=Li +, Na + and Mg 2+, and L=H 2O, H 2S, SiH 2, NH 3 and their methyl derivatives

Ab initio molecular orbital calculations at the G2 level of theory have been performed in order to determine the structure and gas phase energies of complexes formed by the Lewis bases NH 3, H 2O, H 2S, SiH 2 and their methyl derivatives with the cations Li +, Na + and Mg 2+. Calculated interaction energies vary as Mg 2+>>Li +>Na +. The relative basicities of the bases studied depend on both the substituent and the character of cation. The gas-phase interaction energies computed by the G2, G2(MP2) and G1 methods were comparable in accuracy. The binding energies computed by these three methods reach the targeted “chemical” accuracy.