Accurate Interaction Energies Research Articles

Relative cooperativity in neutral and charged molecular clusters using QM/MM calculations.

QM/MM methods have been used to study electronic structure properties and chemical reactivity in complex molecular systems where direct electronic structure calculations are not feasible. In our previous work, we showed that non-polarizable force fields, by design, describe intermolecular interactions through pairwise interactions, overlooking many-body interactions involving three or more particles. In contrast, polarizable force fields account partially for many-body effects through polarization, but still handle van der Waals and permanent electrostatic interactions pairwise. We showed that despite those limitations, polarizable and non-polarizable force fields can reproduce relative cooperativity achieved using density functional theory due to error compensation mechanisms. In this contribution, we assess the performance of QM/MM methods in reproducing these phenomena. Our study highlights the significance of the QM region size and force field choice in QM/MM calculations, emphasizing the importance of parameter validation to obtain accurate interaction energy predictions.

Exploring HCl-HCl interactions: QZVPP calculations, improved Lennard-Jones potential, and second virial coefficient analysis for thermodynamics and industrial applications.

In this paper, we present a comprehensive analysis of HCl-HCl interactions, including QZVPP calculations, energy fitting, conformation validation, and the determination of the second virial coefficient B using improved Lennard-Jones (ILJ) potential parameters. To acquire accurate interaction energies, initial QZVPP calculations are performed on approximately 1851 randomly generated HCl-HCl conformations. Then, these energies are used to fit an improved Lennard-Jones potential energy surface, allowing for a robust description of HCl-HCl interactions. The ILJ potential parameters are then used to validate particular HCl dimer conformations, ensuring their stability and consistency with experimental observations. The correlation between calculated and experimental conformations strengthens the validity of the ILJ potential parameters. In addition, the second viral coefficient B is calculated at various temperatures using the ILJ potential. The obtained B values are compared to experimental data, demonstrating close agreement, and validating the ILJ potential's ability to accurately capture the intermolecular interactions and gas-phase behavior of the HCl-HCl system. The results of this study demonstrate the effective implementation of QZVPP calculations, energy fitting, and ILJ potential parameters in validating HCl-HCl conformations and accurately determining the second virial coefficient B. The high degree of concordance between calculated B values and experimental data demonstrates the validity of the ILJ potential and its suitability for modeling HCl-HCl interactions. This research contributes to a greater comprehension of HCl-HCl interactions and their implications for numerous chemical and atmospheric processes. The validated conformations, energy fitting method, and calculated second virial coefficients provide valuable instruments for future research and pave the way for more accurate modeling and simulations of HCl-HCl systems.

Basis set customization for modeling noncovalent interactions

AbstractIn this article, a simple approach is proposed to reduce the basis set requirement for computing accurate interaction energies for bimolecular noncovalent complexes. A distributed multipole expansion is used to estimate the importance of basis functions in a given atom. Moderate truncation of basis sets results in reduced computational cost without compromising the accuracy. The approach was found fruitful for wavefunction‐based methods and density functional theory approximation using the Dunning, Karlsruhe, and Jensen basis sets.

Accurate Interaction Energies of CO2 with the 20 Naturally Occurring Amino Acids.

We have performed a series of highly accurate calculations between CO2 and the 20 naturally occurring amino acids for the investigation of the attractive noncovalent interactions. Different nucleophilic groups present in the amino acid structures are considered (α-NH2, COOH, side groups), and the stronger binding sites were identified. A database of accurate reference interactions energies was compiled as computed by explicitly-correlated coupled-cluster singles-and-doubles, together with perturbative triples extrapolated to the complete-basis-set limit. The CCSD(F12)(T)/CBS reference values were used for comparing a variety of popular density functionals with different basis sets. Our results show that most density functionals with the triple-zeta basis set def2-TZVPP align with the CCSD(F12)(T)/CBS reference values, but errors range from 0.1 kcal/mol up to 1.0 kcal/mol.

High-Order Quantum-Mechanical Analysis of Hydrogen Bonding in Hachimoji and Natural DNA Base Pairs.

High-order quantum chemistry is applied to hydrogen-bonded natural DNA nucleobase pairs [adenine:thymine (A:T) and guanine:cytosine (G:C)] and non-natural Hachimoji nucleobase pairs [isoguanine:1-methylcytosine (B:S) and 2-aminoimidazo[1,2a][1,3,5]triazin-4(1H)-one:6-amino-5-nitropyridin-2-one (P:Z)] to see how the intermolecular interaction energies and their energetic components (electrostatics, exchange-repulsion, induction/polarization, and London dispersion interactions) vary among the base pairs. We examined the Hoogsteen (HG) geometries in addition to the traditional Watson-Crick (WC) geometries. Coupled-cluster theory through perturbative triples [CCSD(T)] extrapolated to the complete basis set (CBS) limit and high-order symmetry-adapted perturbation theory (SAPT) at the SAPT2+(3)(CCD)δMP2/aug-cc-pVTZ level are used to estimate highly accurate noncovalent interaction energies. Electrostatic interactions are the most attractive component of the interaction energies, but the sum of induction/polarization and London dispersion is nearly as large, for all base pairs and geometries considered. Interestingly, the non-natural Hachimoji base pairs interact more strongly than the corresponding natural base pairs, by -21.8 (B:S) and -0.3 (P:Z) kcal mol-1 in the WC geometries, according to CCSD(T)/CBS. This is consistent with the H-bond distances being generally shorter in the non-natural base pairs. The natural base pairs are energetically more stabilized in their Hoogsteen geometries than in their WC geometries. The Hoogsteen geometry makes the A:T base pair slightly more stable, by -0.8 kcal mol-1, and it greatly stabilizes the G:C+ base pair, by -15.3 kcal mol-1. The G:C+ stabilization is mainly due to the fact that C has typically added a proton when found in Hoogsteen geometries. By contrast, Hoogsteen geometries are substantially less favorable than WC geometries for non-natural Hachimoji base pairs, by 17.3 (B:S) and 13.8 (P:Z) kcal mol-1.

A Peptide Potential Based on a Bond Dipole Representation of Electrostatics

A potential based on a bond dipole representation of electrostatics is reported for peptides. Different from those popular force fields using atom-centered point-charge or point-multipole to express the electrostatics, our peptide potential uses the chemical bond dipole–dipole interactions to express the electrostatic interactions. The parameters for permanent and induced bond dipoles are derived from fitting to the MP2 three-body interaction energy curves. The parameters for van der Waals are taken from AMBER99sb and further refined from fitting to the MP2 stacking interaction energy curve. The parameters for bonded terms are taken from AMBER99sb without any modification. The scale factors for intramolecular dipole–dipole interactions are determined from reproducing the highly qualified ab initio conformational energies of dipeptides and tetrapeptides. The resulting potential is validated by use to evaluate the conformational energies of polypeptides containing up to 15 amino acid residues. The calculation results show that our peptide potential produces the conformational energies much closer to the famous density functional theory M06-2X/cc-pVTZ results than the famous AMBER99sb and AMOEBAbio18 force fields. Our potential also produces accurate intermolecular interaction energies for hydrogen-bonded and stacked dimers. We anticipate the peptide potential proposed here could be helpful in computer simulations of polypeptides and proteins.

Accurate non-covalent interaction energies on noisy intermediate-scale quantum computers via second-order symmetry-adapted perturbation theory.

The calculation of non-covalent interaction energies on noisy intermediate-scale quantum (NISQ) computers appears to be challenging with straightforward application of existing quantum algorithms. For example, the use of the standard supermolecular method with the variational quantum eigensolver (VQE) would require extremely precise resolution of the total energies of the fragments to provide for accurate subtraction to the interaction energy. Here we present a symmetry-adapted perturbation theory (SAPT) method that may provide interaction energies with high quantum resource efficiency. Of particular note, we present a quantum extended random-phase approximation (ERPA) treatment of the SAPT second-order induction and dispersion terms, including exchange counterparts. Together with previous work on first-order terms (Chem. Sci., 2022, 13, 3094), this provides a recipe for complete SAPT(VQE) interaction energies up to second order, which is a well established truncation. The SAPT interaction energy terms are computed as first-level observables with no subtraction of monomer energies invoked, and the only quantum observations needed are the VQE one- and two-particle density matrices. We find empirically that SAPT(VQE) can provide accurate interaction energies even with coarsely optimized, low circuit depth wavefunctions from a quantum computer, simulated through ideal statevectors. The errors of the total interaction energy are orders of magnitude lower than the corresponding VQE total energy errors of the monomer wavefunctions. In addition, we present heme-nitrosyl model complexes as a system class for near term quantum computing simulations. They are strongly correlated, biologically relevant and difficult to simulate with classical quantum chemical methods. This is illustrated with density functional theory (DFT) as the predicted interaction energies exhibit a strong sensitivity with respect to the choice of functional. Thus, this work paves the way to obtain accurate interaction energies on a NISQ-era quantum computer with few quantum resources. It is the first step in alleviating one of the major challenges in quantum chemistry, where in-depth knowledge of both the method and system is required a priori to reliably generate accurate interaction energies.

Accurate three-body noncovalent interactions: the insights from energy decomposition.

An impressive collection of accurate two-body interaction energies for small complexes has been assembled into benchmark databases and used to improve the performance of multiple density functional, semiempirical, and machine learning methods. Similar benchmark data on nonadditive three-body energies in molecular trimers are comparatively scarce, and the existing ones are practically limited to homotrimers. In this work, we present a benchmark dataset of 20 equilibrium noncovalent interaction energies for a small but diverse selection of 10 heteromolecular trimers. The new 3BHET dataset presents complexes that combine different interactions including π-π, anion-π, cation-π, and various motifs of hydrogen and halogen bonding in each trimer. A detailed symmetry-adapted perturbation theory (SAPT)-based energy decomposition of the two- and three-body interaction energies shows that 3BHET consists of electrostatics- and dispersion-dominated complexes. The nonadditive three-body contribution is dominated by induction, but its influence on the overall bonding type in the complex (as exemplified by its position on the ternary diagram) is quite small. We also tested the extended SAPT (XSAPT) approach which is capable of including some nonadditive interactions in clusters of any size. The resulting three-body dispersion term (obtained from the many-body dispersion formalism) is mostly in good agreement with the supermolecular CCSD(T)-MP2 values and the nonadditive induction term is similar to the three-body SAPT(DFT) data, but the overall three-body XSAPT energies are not very accurate as they are missing the first-order exchange terms.

The effect of alkylation on the micro-solvation of ethers revealed by highly localized water librational motion.

The specific far-infrared spectral signatures associated with highly localized large-amplitude out-of-plane librational motion of water molecules have recently been demonstrated to provide sensitive spectroscopic probes for the micro-solvation of organic molecules [Mihrin et al., Phys. Chem. Chem. Phys. 21(4), 1717 (2019)]. The present work employs this direct far-infrared spectroscopic approach to investigate the non-covalent intermolecular forces involved in the micro-solvation of a selection of seven ether molecules with systematically varied alkyl substituents: dimethyl ether, diethyl ether, diisopropyl ether, ethyl methyl ether, t-butyl methyl ether, and t-butyl ethyl ether. The ranking of the observed out-of-plane water librational band signatures for this selected series of ether-water complexes embedded in inert neon matrices at 4K reveals information about the interplay of directional intermolecular hydrogen bond motifs and non-directional and long-range dispersion interactions for the micro-solvated structures. These far-infrared observables differentiate minor subtle effects introduced by specific alkyl substituents and serve as rigorous experimental benchmarks for modern quantum chemical methodologies of various levels of scalability, which often fail to accurately predict the structural variations and corresponding vibrational signatures of the closely related systems. The accurate interaction energies of the series of ether-water complexes have been predicted by the domain based local pair natural orbital coupled cluster theory with single-, double-, and perturbative triple excitations, followed by a local energy decomposition analysis of the energy components. In some cases, the secondary dispersion forces are in direct competition with the primary intermolecular hydrogen bonds as witnessed by the specific out-of-plane librational signatures.

JunChS and junChS-F12 Models: Parameter-free Efficient yet Accurate Composite Schemes for Energies and Structures of Noncovalent Complexes.

A recently developed model chemistry (denoted as junChS [Alessandrini, S.; et al. J. Chem. Theory Comput. 2020, 16, 988-1006]) has been extended to the employment of explicitly correlated (F12) methods. This led us to propose a family of effective, reliable, and parameter-free schemes for the computation of accurate interaction energies of molecular complexes ruled by noncovalent interactions. A thorough benchmark based on a wide range of interactions showed that the so-called junChS-F12 model, which employs cost-effective revDSD-PBEP86-D3(BJ) reference geometries, has an improved performance with respect to its conventional counterpart and outperforms well-known model chemistries. Without employing any empirical parameter and at an affordable computational cost, junChS-F12 reaches subchemical accuracy. Accurate characterizations of molecular complexes are usually limited to energetics. To take a step forward, the conventional and F12 composite schemes developed for interaction energies have been extended to structural determinations. A benchmark study demonstrated that the most effective option is to add MP2-F12 core-valence correlation corrections to fc-CCSD(T)-F12/jun-cc-pVTZ geometries without the need of recovering the basis set superposition error and the extrapolation to the complete basis set.

A rush to explore protein-ligand electrostatic interaction energy with Charger.

The mutual penetration of electron densities between two interacting molecules complicates the computation of an accurate electrostatic interaction energy based on a pseudo-atom representation of electron densities. The numerical exact potential and multipole moment (nEP/MM) method is time-consuming since it performs a 3D integration to obtain the electrostatic energy at short interaction distances. Nguyen et al. [(2018), Acta Cryst. A74, 524-536] recently reported a fully analytical computation of the electrostatic interaction energy (aEP/MM). This method performs much faster than nEP/MM (up to two orders of magnitude) and remains highly accurate. A new program library, Charger, contains an implementation of the aEP/MM method. Charger has been incorporated into the MoProViewer software. Benchmark tests on a series of small molecules containing only C, H, N and O atoms show the efficiency of Charger in terms of execution time and accuracy. Charger is also powerful in a study of electrostatic symbiosis between a protein and a ligand. It determines reliable protein-ligand interaction energies even when both contain S atoms. It easily estimates the individual contribution of every residue to the total protein-ligand electrostatic binding energy. Glutathione transferase (GST) in complex with a benzophenone ligand was studied due to the availability of both structural and thermodynamic data. The resulting analysis highlights not only the residues that stabilize the ligand but also those that hinder ligand binding from an electrostatic point of view. This offers new perspectives in the search for mutations to improve the interaction between the two partners. A proposed mutation would improve ligand binding to GST by removing an electrostatic obstacle, rather than by the traditional increase in the number of favourable contacts.

σ-Donation and π-Backdonation Effects in Dative Bonds of Main-Group Elements.

The nature of donor-acceptor interactions is important for the understanding of dative bonding and can provide vital insights into many chemical processes. Here, we have performed a computational study to elucidate substantial differences between different types of dative interactions. For this purpose, a data set of 20 molecular complexes stabilized by dative bonds was developed (DAT20). A benchmark study that considers many popular density functionals with respect to accurate quantum chemical interaction energies and geometries revealed two different trends between the complexes of DAT20. This behavior was further explored by means of frontier molecular orbitals, extended-transition-state natural orbitals for chemical valence (ETS-NOCV), and natural energy decomposition analysis (NEDA). These methods revealed the extent of the forward and backdonation between the donor and acceptor molecules and how they influence the total interaction energies and molecular geometries. A new classification of dative bonds is suggested.

Assessment of Computational Methods for Calculating Accurate Non-covalent Interaction Energies in 1,2,3,5-Dithiadiazolyl Radicals

Assessment of Computational Methods for Calculating Accurate Non-covalent Interaction Energies in 1,2,3,5-Dithiadiazolyl Radicals

A DFT-D guided surface engineering of 2-D functionalized graphyne analogue covalent triazine frameworks as a high-capacity anode material of Mg-ion battery

In the present study, we have explored the potential application of pure and functionalized 2-D graphyne-like covalent triazine framework (GYCTF) as an anode material for Mg-ion batteries, using dispersion-corrected DFT. The accurate interaction energies are crucial for energy storage and battery applications as they are directly related to the key properties in electrochemistry, such as storage capacities, in general, and open-circuit voltages (OCVs), in particular. We have found that Mg preferably adsorbs above the center of all carbon six-membered rings of GYCTF with adsorption energy of about 83.4 kcal mol−1. After functionalization, -SH increases the maximum coverage of Mg on surface from 4 to 9 Mg. Also, –CH3 strongly reduces the specific capacity of GYCTF in MIB application. After functionalization, -SH increases the maximum coverage of Mg on the surface from 4 to 9 Mg. Also, –CH3 strongly reduces the specific capacity of GYCTF in MIB application. The single-layer GYCTF-SH can be magnesiated on both sides yielding Mg9C13N3S4H4 with a storage capacity as high as 1462.4 mAh g−1 with an average OCV of 0.68 V. Our findings show better results in terms of storage capacity, negligible volume expansion, low OCV, and low diffusion energies comparing with commonly studied 2-D materials, making thiol-functionalized GYCTF a promising candidate as an anode material for Mg- ion batteries.

Interactions between large molecules pose a puzzle for reference quantum mechanical methods

Quantum-mechanical methods are used for understanding molecular interactions throughout the natural sciences. Quantum diffusion Monte Carlo (DMC) and coupled cluster with single, double, and perturbative triple excitations [CCSD(T)] are state-of-the-art trusted wavefunction methods that have been shown to yield accurate interaction energies for small organic molecules. These methods provide valuable reference information for widely-used semi-empirical and machine learning potentials, especially where experimental information is scarce. However, agreement for systems beyond small molecules is a crucial remaining milestone for cementing the benchmark accuracy of these methods. We show that CCSD(T) and DMC interaction energies are not consistent for a set of polarizable supramolecules. Whilst there is agreement for some of the complexes, in a few key systems disagreements of up to 8 kcal mol−1 remain. These findings thus indicate that more caution is required when aiming at reproducible non-covalent interactions between extended molecules.

How Accurate Are Approximate Density Functionals for Noncovalent Interaction of Very Large Molecular Systems?

Noncovalent intermolecular interactions are very important in many research areas. Therefore, it is vital to understand the extent to which approximate density functionals give a proper description of noncovalent interactions. Previous research has demonstrated that some approximate density functionals can predict usefully accurate interaction energies for many noncovalent systems; however, most of that work is limited to small and moderate-sized molecules. Very recently though, accurate benchmarks have become available for some very large molecules. The present work applies 21 approximate density functionals to compute the binding energies of seven large molecular systems that have a number of atoms ranging from 200 to 910. The results are judged by comparison to the recently published CIM-DLPNO-CCSD(T) results, which are assumed to provide a reliable benchmark. The five most accurate methods among those tested are found to be PW6B95-D4, PW6B95-D3(BJ), revM11, M06-L, and MN15.

AP-Net: An atomic-pairwise neural network for smooth and transferable interaction potentials.

Intermolecular interactions are critical to many chemical phenomena, but their accurate computation using ab initio methods is often limited by computational cost. The recent emergence of machine learning (ML) potentials may be a promising alternative. Useful ML models should not only estimate accurate interaction energies but also predict smooth and asymptotically correct potential energy surfaces. However, existing ML models are not guaranteed to obey these constraints. Indeed, systemic deficiencies are apparent in the predictions of our previous hydrogen-bond model as well as the popular ANI-1X model, which we attribute to the use of an atomic energy partition. As a solution, we propose an alternative atomic-pairwise framework specifically for intermolecular ML potentials, and we introduce AP-Net-a neural network model for interaction energies. The AP-Net model is developed using this physically motivated atomic-pairwise paradigm and also exploits the interpretability of symmetry adapted perturbation theory (SAPT). We show that in contrast to other models, AP-Net produces smooth, physically meaningful intermolecular potentials exhibiting correct asymptotic behavior. Initially trained on only a limited number of mostly hydrogen-bonded dimers, AP-Net makes accurate predictions across the chemically diverse S66x8 dataset, demonstrating significant transferability. On a test set including experimental hydrogen-bonded dimers, AP-Net predicts total interaction energies with a mean absolute error of 0.37 kcal mol-1, reducing errors by a factor of 2-5 across SAPT components from previous neural network potentials. The pairwise interaction energies of the model are physically interpretable, and an investigation of predicted electrostatic energies suggests that the model "learns" the physics of hydrogen-bonded interactions.

Nature of Alkali Ion-Water Interactions: Insights from Many-Body Representations and Density Functional Theory. II.

Interaction energies of alkali ion-water dimers, M+(H2O), and trimers, M+(H2O)2, with M = Li, Na, K, Rb, and Cs, are investigated using various many-body potential energy functions and exchange-correlation functionals selected across the hierarchy of density functional theory approximations. Analysis of interaction energy decompositions indicates that close-range interactions such as Pauli repulsion, charge transfer, and charge penetration must be captured in order to reproduce accurate interaction energies. In particular, it is found that simple classical polarizable models must be supplemented with dedicated terms which account for these close-range interactions in order to achieve chemical accuracy. It is also found that the exchange-correlation functionals mostly differ from each other in their Pauli repulsion + dispersion energies and, hence, benefit from the inclusion of nonlocal terms such as Hartree-Fock exchange and dependence on the electronic kinetic energy density in order to reproduce the interactions that contribute to this term, namely, Pauli repulsion and intermediate-range dispersion. As a continuation of the analysis performed in J. Chem. Theory Comput. 2019, 15, 2983, 10.1021/acs.jctc.9b00064, we make comparisons between findings for alkali ion-water interactions with those for halide-water interactions.

Quantum Mechanical Modeling of the Interactions between Noble Metal (Ag and Au) Nanoclusters and Water with the Effective Fragment Potential Method.

Explicit solvent interactions can significantly alter the physical and chemical properties of noble metal (e.g., gold and silver) nanoclusters. In order to compute these solvent interactions at a reasonable computational cost, a quantum mechanical (QM)/molecular mechanics (MM) approach, where the metal nanocluster is treated with full QM and the water molecules are treated with a MM force field, can be used. However, classical MM force fields were typically parameterized using molecules containing main group elements as the reference. The accuracy of noble metal–solvent interactions obtained with these force fields therefore remains unpredictable. The effective fragment potential (EFP) force field, designed to model explicitly solvated systems, represents an attractive method to simulate solvated noble metal nanoclusters because it is derived from first principles and contains few or no fitted parameters, depending on implementation. At the density functional theory-optimized geometries, good correlation is obtained between the nanocluster–water interaction energies computed with EFP and those computed with the reference coupled cluster singles, doubles, and perturbative triples method. It is shown that the EFP method gives qualitatively accurate interaction energies at medium–large intermolecular distances for various molecular configurations. In order to achieve higher quantitative accuracy, the first solvation shell should be treated with full QM, if possible. EFP is therefore a promising method for the QM modeling of explicitly solvated silver and gold nanoclusters.

Importance of model size in quantum mechanical studies of DNA intercalation.

The convergence of DFT-computed interaction energies with increasing binding site model size was assessed. The data show that while accurate intercalator interaction energies can be derived from binding site models featuring only the flanking nucleotides for uncharged intercalators that bind parallel to the DNA base pairs, errors remain significant even when including distant nucleotides for intercalators that are charged, exhibit groove-binding tails that engage in noncovalent interactions with distant nucleotides, or that bind perpendicular to the DNA base pairs. Consequently, binding site models that include at least three adjacent nucleotides are required to consistently predict converged binding energies. The computationally inexpensive HF-3c method is shown to provide reliable interaction energies and can be routinely applied to such large models.