Three-body Interaction Energies Research Articles

Role of Exact Exchange and Empirical Dispersion in Density Functional Theory-Based Three-Body Noncovalent Interactions.

Total and three-body interaction energies are calculated for a benchmark set of three-body systems using a range of different types of density functional theory (DFT) methods, with the results compared to CCSD(T)/CBS results from the benchmark reference [Phys. Chem. Chem. Phys. 2023, 25, 28621-28637]. Inclusion of Hartree-Fock exchange, via either a global or range-separated hybrid approach or inclusion of empirical dispersion corrections, increases accuracy for total and three-body interactions. Basis set convergence testing shows that the aug-cc-pVTZ basis set is well converged with little to no change seen when using quadruple-ζ basis sets. The accuracy of the DFT methods is similar when calculating interaction energies for both global and local minimum structures. Overall, the CAM-B3LYP-D3BJ, B97D3, and ωB97XD functionals are recommended for calculating three-body interactions.

On the Role of Charge Transfer in Many-Body Non-Covalent Interactions.

Charge transfer is one of the mechanisms involved in non-covalent interactions. In molecular dimers, its contribution to pairwise interaction energies has been studied extensively using a variety of interaction energy decomposition schemes. In polar interactions such as hydrogen bonds, it can contribute ten or several tens of percent of the interaction energy. Less is known about its importance in higher-order interactions in many-body systems, mainly because of the lack of methods applicable to this problem. In this work, we extend our method for the quantification of the charge-transfer energy based on constrained DFT to many-body cases and apply it to model trimers extracted from molecular crystals. Our calculations show that charge transfer can account for a large fraction of the total three-body interaction energy. This also has implications for DFT calculations of many-body interactions in general as it is known that many DFT functionals struggle to describe charge-transfer effects correctly.

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 Prediction of Three-Body Intermolecular Interactions via Electron Deformation Density-Based Machine Learning.

This work extends the electron deformation density-based descriptor, originally developed in the electron deformation density-based interaction energy machine learning (EDDIE-ML) algorithm to predict dimer interaction energies, to the prediction of three-body interactions in trimers. Using a sequential learning process to select the training data, the resulting Gaussian process regression (GPR) model predicts the three-body interaction energy within 0.2 kcal mol-1 of the SRS-MP2/cc-pVTZ reference values for the 3B69 and S22-3 trimer data sets. A hybrid kernel function is introduced, which combines contributions from the average and individual atomic environments, allowing the total trimer interaction energy to be predicted in addition to the three-body contribution using the same descriptor. To extend the range and diversity of trimer interaction energies available in the literature, a new data set based on a protein-ligand crystal structure is introduced, consisting of 509 structures of a central ligand with two protein fragments. Benchmark calculations are provided for the new data set, which contains significantly larger molecular interactions than current databases in the literature in addition to charged fragments. Compared to density funtional theory (DFT)- and wavefunction-based methods for calculating the three-body interaction energy, our model makes predictions in a significantly shorter time frame by reducing the number of required SCF calculations from 7 to 4 performed at the PBE0 level of theory, showcasing the utility and efficiency of our Δ-ML method particularly when applied to larger systems.

Three-body potential and third virial coefficients for helium including relativistic and nuclear-motion effects.

The non-additive three-body interaction potential for helium was computed using the coupled-cluster theory and the full configuration interaction method. The obtained potential comprises an improved nonrelativistic Born-Oppenheimer energy and the leading relativistic and nuclear-motion corrections. The mean absolute uncertainty of our calculations due to the incompleteness of the orbital basis set was determined employing complete-basis-set extrapolation techniques and was found to be 1.2%. For three helium atoms forming an equilateral triangle with the side length of 5.6 bohr - a geometry close to the minimum of the total potential energy surface - our three-body potential amounts to -90.6 mK, with an estimated uncertainty of 0.5 mK. An analytic function, developed to accurately fit the computed three-body interaction energies, was chosen to correctly describe the asymptotic behavior of the three-body potential for trimer configurations corresponding to both the three-atomic and the atom-diatom fragmentation channels. For large triangles with sides r12, r23, and r31, the potential takes correctly into account all angular terms decaying as r-l12 r-m23 r-n21 with l + m + n ≤ 14 for the nonrelativistic Born-Oppenheimer energy and l + m + n ≤ 9 for the post-Born-Oppenheimer corrections. We also developed a short-range analytic function describing the local behavior of the total uncertainty of the computed three-body interaction energies. Using both fits we calculated the third pressure and acoustic virial coefficients for helium and their uncertainties for a wide range of temperatures. The results of these calculations were compared with available experimental data and with previous theoretical determinations. The estimated uncertainties of present calculations are 3-5 times smaller than those reported in the best previous works.

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.

A scheme for rapid evaluation of the intermolecular three-body polarization effect in water clusters.

The ability to accurately and rapidly evaluate the intermolecular many-body polarization effect of the water system is very important for computer simulations of biomolecule in aqueous. In this paper, a scheme is proposed based on the polarizable dipole-dipole interaction model and used to rapidly estimate the intermolecular many-body polarization effect in water clusters. We use a bond-dipole-based polarization function to evaluate the polarization energy. We regard two OH bonds of a water molecule as two bond-dipoles and set the permanent OH bond-dipole moment of a water molecule to be 1.51 Debye. We estimate the induced OH bond-dipole moment via a simple formula in which only one correction factor is needed. This scheme is then applied to tens of water clusters to calculate the three- and four-body interaction energies. The three-body interaction energies of 93 water clusters produced by our scheme are compared with those produced by the counterpoise-corrected CCSD(T)/aug-cc-pVDZ, MP2/aug-cc-pVDZ, M06-2X/jul-cc-pVTZ methods, by the AMOEBApro13, iAMOEBA, AMOEBA+, AMOEBA+(CF) methods, and by the MB-pol method. The four-body interaction energies of 47 water clusters yielded by our scheme are compared with those yielded by the counterpoise-corrected MP2/aug-cc-pVDZ and M06-2X/ jul-cc-pVTZ methods, by the AMOEBApro13, AMOEBA+, AMOEBA+(CF) methods, and by the MB-pol method. The comparison results show that the scheme proposed in this paper can reproduce the counterpoise-corrected CCSD(T)/aug-cc-pVDZ three-body interaction energies and reproduce the counterpoise-corrected MP2/aug-cc-pVDZ four-body interaction energies both accurately and efficiently. We anticipate the scheme proposed here can be useful for computer simulations of liquid water and aqueous solutions.

Prediction of lattice energy of benzene crystals: A robust theoretical approach.

We present an inexpensive and robust theoretical approach based on the fragment molecular orbital methodology and the spin-ratio scaled second-order Møller-Plesset perturbation theory to predict the lattice energy of benzene crystals within 2 kJ⋅mol-1 . Inspired by the Harrison method to estimate the Madelung constant, the proposed approach calculates the lattice energy as a sum of two- and three-body interaction energies between a reference molecule and the surrounding molecules arranged in a sphere. The lattice energy converges rapidly at a radius of 13 Å. Adding the corrections to account for a higher correlated level of theory and basis set superposition for the Hartree Fock (HF) level produced a lattice energy of -57.5 kJ⋅mol-1 for the benzene crystal structure at 138 K. This estimate is within 1.6 kJ⋅mol-1 off the best theoretical prediction of -55.9 kJ⋅mol-1 . We applied this approach to calculate lattice energies of the crystal structures of phase I and phase II-polymorphs of benzene-observed at a higher temperature of 295 K. The stability of these polymorphs was correctly predicted, with phase II being energetically preferred by 3.7 kJ⋅mol-1 over phase I. The proposed approach gives a tremendous potential to predict stability of other molecular crystal polymorphs.

Linearization of moment tensor potentials for multicomponent systems with a preliminary assessment for short-range interaction energy in water dimer and trimer

Moment tensor potentials have been recently proposed as a promising novel method of polynomial expansion for the systematic approximation of molecular potential energy surfaces. However, its current formulation for multicomponent systems has not been fully linearized and requires nonlinear optimization techniques for parameter estimation. We propose an alternative relaxed formulation of the original potential energy function where parameter optimization is expressed as a linear sparse approximation problem. The main difficulty arising in sparse approximation is finding a suitable subset of predictors in highly multi-collinear variable space where the number of variables largely exceeds the size of the training set. To efficiently reduce the number of descriptors to an optimal size and prevent overfitting, we present a simple heuristic that is based on importance ranking of variables and Bayesian information criterion. For the empirical assessment of our approach, we employed published data on short-range components of water two-body and three-body interaction energies that have previously been used for the comparison of various potential energy representations. Numerical experiments suggest that our proposed methodology allows achieving accuracy that is comparable to other popular interpolation and machine learning techniques and requires significantly less time for model training than nonlinearly parameterized formulation.

First-Principles Study on Crystal Configuration and Many-Body Cohesive Energy of Solid Argon

Based on the first-principles, using CCSD(T) ab initio calculation method, many-body potential energy of solid argon are accurately calculated with the atomic distance R from 2.0Å to 3.6Å at T=300K, and firstly establish and discuss the face-centered cubic (fcc) atomic crystal configurations of two-, three-, and four-body terms by geometry optimization. The results shows that the total number of (Ar)2 clusters is 903, which belongs to 12 different geometric configurations, the total number of (Ar)3 clusters is 861, which belongs to 25 different geometric configurations, and the total number of (Ar)4 clusters of is 816 which belongs to 27 different geometric configurations. We find that the CCSD(T) with the aug-cc-pVQZ basis set is most accurate and practical by comprehensive consideration. The total potential energy Un reachs saturation at R>2.0Å when the only two-and three-body interaction energy are considered. When R≤2.0Å, the total potential energy Un must consider four-and higher-body interaction energy to achieve saturation. Many-body expansion potential of fcc solid argon is an exchange convergent series.

Two- and three-body, and relaxation energy terms in water clusters: Application of the hierarchical BSSE corrected decomposition scheme

A detailed analysis of the two- and three-body interaction energy components in water clusters containing up to 30 water molecules is performed at the M05-2X/6-311G** level of theory, using the “hierarchical” basis set superposition error (BSSE)-corrected energy decomposition scheme, VMFC(3), of Valiron and Mayer. We showed that the average BSSE-corrected two- and three-body interaction energy terms are about 74 to 80 and 20 to 26%, respectively, of the total BSSE-corrected interaction energy for all investigated clusters. It was observed that the three-body interaction energy component is significantly negative/positive if there are two H-bonds and one attraction/repulsion interaction energy in the corresponding trimer, respectively. Our calculations also revealed that the deformation energy of water molecules is dependent on their H-bonded environment. To assess the accuracy of the calculations presented here, benchmark calculations were carried out at the high, LNO-CCSD(T)/CBS, level of theory.

Rapid Calculation of the Three-body Interaction Energies in Water Clusters†

Rapid Calculation of the Three-body Interaction Energies in Water Clusters†

Dispersion-Corrected DFT Struggles with Predicting Three-Body Interaction Energies.

We demonstrate that the dispersion-corrected density functional theory (DFT-D) schemes fall short of predicting reliable three-body interaction energies. This concerns also a popular variant of DFT-D called the "many-body dispersion" (MBD) method, which might seem surprising in the light of the fact that its name contains the very phrase "many-body". The main reason for the inaccuracy of the three-body interaction energies in the DFT-D schemes can be attributed to internal deficiencies of the standard DFT functionals that the existing "-D" methods are incapable of correcting since the main problems emerge from the terms not related to the dispersion component. At present, it seems that none of the a posteriori dispersion techniques are able to predict accurately the total interaction energy for a supermolecular system together with its simultaneous decomposition into the many-body components. On the other hand, if one is interested only in the three-body interaction energies, we propose an adjustment to the MBD approach that achieves good accuracy in conjunction with the supermolecular MP2.

Comparison of permutationally invariant polynomials, neural networks, and Gaussian approximation potentials in representing water interactions through many-body expansions.

The accurate representation of multidimensional potential energy surfaces is a necessary requirement for realistic computer simulations of molecular systems. The continued increase in computer power accompanied by advances in correlated electronic structure methods nowadays enables routine calculations of accurate interaction energies for small systems, which can then be used as references for the development of analytical potential energy functions (PEFs) rigorously derived from many-body (MB) expansions. Building on the accuracy of the MB-pol many-body PEF, we investigate here the performance of permutationally invariant polynomials (PIPs), neural networks, and Gaussian approximation potentials (GAPs) in representing water two-body and three-body interaction energies, denoting the resulting potentials PIP-MB-pol, Behler-Parrinello neural network-MB-pol, and GAP-MB-pol, respectively. Our analysis shows that all three analytical representations exhibit similar levels of accuracy in reproducing both two-body and three-body reference data as well as interaction energies of small water clusters obtained from calculations carried out at the coupled cluster level of theory, the current gold standard for chemical accuracy. These results demonstrate the synergy between interatomic potentials formulated in terms of a many-body expansion, such as MB-pol, that are physically sound and transferable, and machine-learning techniques that provide a flexible framework to approximate the short-range interaction energy terms.

Origins of possible synergistic effects in the interactions between metal atoms and MoS2/graphene heterostructures for battery applications.

The interactions between metals and two-dimensional materials, in particular, the adsorption energies, strongly determine the performances of rechargeable batteries. Previously, it has been demonstrated that heterostructures of two dimensional (2D) materials can lead to enhanced metal adsorptions, which were ascribed to the existence of 'synergistic' effects amongst metal atoms and two different 2D materials. However, further investigations are still required to reveal the physical mechanisms behind the contribution of these possible 'synergistic' effects for metal intercalations in 2D heterostructures. Here, we selected MoS2/graphene as a prototypical system, and we examined the adsorption and intercalation thermochemistry of monovalent atoms (Li, Na and K) and multivalent atoms (Mg, Ca and Al) using density-functional theory (DFT) calculations. The synergistic effects arising from charge polarizations in these systems were quantified using the three-body interaction energy terms. Our results show strong system dependencies whereby the interactions between the Mg or Ca atom with the MoS2/graphene heterostructures might exhibit cooperative bindings. Nevertheless, metal adsorptions on top of the graphene surface were all found to be anti-cooperative in this case. Our results suggest that enhancement of metal adsorptions using 2D heterostructures is predominantly driven by increasing dispersion interactions due to increases in the interaction surface areas.

Nonadditive three-body potential and third to eighth virial coefficients of carbon dioxide.

A new nonadditive three-body interaction potential for carbon dioxide was determined from supermolecular ab initio calculations up to the coupled cluster with single, double, and perturbative triple excitations [CCSD(T)] level of theory for 9401 configurations. A physically motivated analytical function with terms for describing nonadditive dispersion, induction, and exchange contributions was fitted to the calculated nonadditive three-body interaction energies. For the 7996 configurations with a total interaction energy of less than 3000 K, the mean absolute error of the analytical function is 0.32 K. The new nonadditive three-body potential was applied together with a previously published pair potential [R. Hellmann, Chem. Phys. Lett. 613, 133 (2014)] to calculate the third to seventh virial coefficients of CO2 at subcritical and supercritical temperatures up to 2000 K. The eighth virial coefficient was also calculated, but using only the pair potential and only at temperatures from 600 K to 2000 K because of the enormous computational costs. A simple analytical function was fitted individually to the calculated values of each virial coefficient, including previously determined values of the second virial coefficient, to obtain an analytical virial equation of state (VEOS). For densities at which the VEOS is converged, the agreement in pressure with the reference EOS of Span and Wagner [J. Phys. Chem. Ref. Data 25, 1509 (1996)] is mostly within ±0.5%. However, for temperatures above about 700 K, much larger deviations occur at higher densities, which we ascribe mainly to deficiencies of the reference EOS due to the lack of accurate data for these experimentally difficult conditions.

Tuning Intermolecular Interactions with Nanostructured Environments

It is known that interactions between molecules may change in the presence of nanostructures. However, the exact mechanisms that dictate the tuning of intermolecular interactions remain largely unexplored in computational studies. Here, we employ density-functional calculations with the recently developed many-body dispersion (MBD) method to investigate intermolecular three-body interaction energies (where bodies can be molecules or nanostructures) in a set of nanocomposites. We analyze three representative complexes that display distinct behavior in their interaction profiles, and unravel the physical reasons behind the observed differences. We demonstrate that many-body van der Waals (vdW) interactions can be repulsive, attractive, or neutral with respect to a pairwise treatment of vdW dispersion interactions. Our results indicate that vdW interactions in a given complex can be tuned by suitably choosing its environment. Such tuning may lead to either stabilization or destabilization of the complex, est...

Chalcogen- and halogen-bonds involving SX2 (X = F, Cl, and Br) with formaldehyde.

The capacity of SX2 (X = F, Cl, and Br) to engage in different kinds of noncovalent bonds was investigated by ab initio calculations. SCl2 (SBr2) has two σ-holes upon extension of Cl (Br)-S bonds, and two σ-holes upon extension of S-Cl (Br) bonds. SF2 contains only two σ-holes upon extension of the F-S bond. Consequently, SCl2 and SBr2 form chalcogen and halogen bonds with the electron donor H2CO while SF2 forms only a chalcogen bond, i.e., no F···O halogen bond was found in the SF2:H2CO complex. The S···O chalcogen bond between SF2 and H2CO is the strongest, while the strongest halogen bond is Br···O between SBr2 and H2CO. The nature of these two types of noncovalent interaction was probed by a variety of methods, including molecular electrostatic potentials, QTAIM, energy decomposition, and electron density shift maps. Termolecular complexes X2S···H2CO···SX'2 (X = F, Cl, Br, and X' = Cl, Br) were constructed to study the interplay between chalcogen bonds and halogen bonds. All these complexes contained S···O and Cl (Br)···O bonds, with longer intermolecular distances, smaller values of electron density, and more positive three-body interaction energies, indicating negative cooperativity between the chalcogen bond and the halogen bond. In addition, for all complexes studied, interactions involving chalcogen bonds were more favorable than those involving halogen bonds. Graphical Abstract Molecular electrostatic potential and contour map of the Laplacian of the electron density in Cl2S···H2CO···SCl2 complex.

Understanding Packing Patterns in Crystals by Analysis of Small Aggregates: A Case Study of CS2.

The molecular electrostatic potential (MESP) of the CS2 molecule, in conjunction with the cluster building algorithm, is utilized for generating trial geometries of medium-sized (CS2)n (n = 5-8) aggregates. MESP features suggest crossed, parallel stacked, T-shaped and L-shaped geometries for CS2 clusters. These initial geometries are subjected to geometry optimization employing second-order Møller-Plesset (MP2) theory, with correlation consistent aug-cc-pvDZ (aDZ) basis set. Single-point energies at MP2/aTZ levels are calculated for the estimation of binding energies at complete basis set (CBS) limit. The minimal nature of the reported structures is confirmed by doing vibrational frequency run at MP2/aDZ level of theory using the molecular tailoring approach (MTA). The two- and three-body interaction energies are computed for clusters with n = 5, 6, and 7 and these are suggestive of change in contact patterns with increasing n. Such an analysis is found to offer a qualitative explanation of the packing pattern found in the crystal structure.

Theoretical insight into the interplay between lithium and halogen–hydride bonds: Anab initiostudy

Quantum chemical calculations have been performed to analyze the intermolecular interactions in the ternary NCLi ⋯ NCX ⋯ HMgY complexes ( X = F , Cl , Br ; Y = H , F , Cl , Br , Li ). A cooperative effect is observed between the lithium and halogen–hydride bonds in these complexes. The cooperative energy ranges from -1.81 kJ/mol to -5.21 kJ/mol, -3.59 kJ/mol to -9.86 kJ/mol and -4.77 kJ/mol to -14.27 kJ/mol for X = F , Cl and Br , respectively (at MP2/6-311++G(d,p) level). The geometrical and interaction energies analysis reveal that the lithium bond has a greater enhancing effect on the halogen–hydride bond. The results of many-body analysis indicate that two- and three-body interaction energies have a positive contribution to the total interaction energy. The electronic characteristics of the complexes have been analyzed through molecular electrostatic potential (MEP), atoms in molecules (AIM), electron localization function (ELF) and natural bond orbital (NBO) methodologies.