Intermolecular Perturbation Theory Research Articles

Improved Description of Intra- and Intermolecular Interactions through Dispersion-Corrected Second-Order Møller-Plesset Perturbation Theory.

ConspectusThe quantum chemical modeling of organic crystals and other molecular condensed-phase problems requires computationally affordable electronic structure methods which can simultaneously describe intramolecular conformational energies and intermolecular interactions accurately. To achieve this, we have developed a spin-component-scaled, dispersion-corrected second-order Møller-Plesset perturbation theory (SCS-MP2D) model. SCS-MP2D augments canonical MP2 with a dispersion correction which removes the uncoupled Hartree-Fock dispersion energy present in canonical MP2 and replaces it with a more reliable coupled Kohn-Sham treatment, all evaluated within the framework of Grimme's D3 dispersion model. The spin-component scaling is then used to improve the description of the residual (nondispersion) portion of the correlation energy.The SCS-MP2D model improves upon earlier corrected MP2 models in a few ways. Compared to the highly successful dispersion-corrected MP2C model, which is based solely on intermolecular perturbation theory, the SCS-MP2D dispersion correction improves the description of both inter- and intramolecular interactions. The dispersion correction can also be evaluated with trivial computational cost, and nuclear analytic gradients are computed readily to enable geometry optimizations. In contrast to earlier spin-component scaling MP2 models, the optimal spin-component scaling coefficients are only mildly sensitive to the choice of training data, and a single global parametrization of the model can describe both thermochemistry and noncovalent interactions.The resulting dispersion-corrected, spin-component-scaled MP2 (SCS-MP2D) model predicts conformational energies and intermolecular interactions with accuracy comparable to or better than those of many range-separated and double-hybrid density functionals, as is demonstrated on a variety of benchmark tests. Among the functionals considered here, only the revDSD-PBEP86-D3(BJ) functional gives consistently smaller errors in benchmark tests. The results presented also hint that further improvements of SCS-MP2D may be possible through a more robust fitting procedure for the seven empirical parameters.To demonstrate the performance of SCS-MP2D further, several applications to molecular crystal problems are presented. The three chosen examples all represent cases where density-driven delocalization error causes GGA or hybrid density functionals to artificially stabilize crystals exhibiting more extended π-conjugation. Our pragmatic strategy addresses the delocalization error by combining a periodic density functional theory (DFT) treatment of the infinite lattice with intramolecular/conformational energy corrections computed with SCS-MP2D. For the anticancer drug axitinib, applying the SCS-MP2D conformational energy correction produces crystal polymorph stabilities that are consistent with experiment, in contrast to earlier studies. For the crystal structure prediction of the ROY molecule, so named for its colorful red, orange, and yellow crystals, this approach leads to the first plausible crystal energy landscape, and it reveals that the lowest-energy polymorphs have already been found experimentally. Finally, in the context of photomechanical crystals, which transform light into mechanical work, these techniques are used to predict the structural transformations and extract design principles for maximizing the work performed.

Noncovalent Intra‐ and Intermolecular Interactions in Peri‐Substituted Pnicta Naphthalene and Acenaphthalene Complexes

AbstractFive peri‐substituted naphthalene and acenaphthalene complexes (Ph2Pn)2Naph (E=Sb 1, Bi 3), (Ph2Sb)2Acenaph (2), (Ph2Bi)(Me3Sn)Naph (4) and (PhBiNaph)2 (5) were synthesized and characterized in solution (1H, 13C NMR, IR) and in the solid‐state (sc‐XRD). 1–5 show different types of noncovalent intermolecular interactions in the solid‐state including Naph−H⋅⋅⋅π, π⋅⋅⋅π and Bi⋅⋅⋅π (5) contacts, which were exemplarily (5) quantified by use of density functional theory and local coupled cluster electronic structure theory calculations, demonstrating that the Bi⋅⋅⋅π contact provides the main stabilizing contribution. Symmetry‐adapted intermolecular perturbation theory calculations showed that this and other contacts are dominated by London dispersion interactions.

Ab initio effective one‐electron potential operators: Applications for charge‐transfer energy in effective fragment potentials

The concept of effective one-electron potentials (EOPs) has proven to be extremely useful in efficient description of electronic structure of chemical systems, especially extended molecular aggregates such as interacting molecules in condensed phases. Here, a general method for EOP-based elimination of electron repulsion integrals is presented, that is tuned toward the fragment-based calculation methodologies such as the second generation of the effective fragment potentials (EFP2) method. Two general types of the EOP operator matrix elements are distinguished and treated either via the distributed multipole expansion or the extended density fitting (DF) schemes developed in this work. The EOP technique is then applied to reduce the high computational costs of the effective fragment charge-transfer (CT) terms being the bottleneck of EFP2 potentials. The alternative EOP-based CT energy model is proposed, derived within the framework of intermolecular perturbation theory with Hartree-Fock noninteracting reference wavefunctions, compatible with the original EFP2 formulation. It is found that the computational cost of the EFP2 total interaction energy calculation can be reduced by up to 38 times when using the EOP-based formulation of CT energy, as compared to the original EFP2 scheme, without compromising the accuracy for a wide range of weakly interacting neutral and ionic molecular fragments. The proposed model can thus be used routinely within the EFP2 framework.

First-Principles Many-Body Nonadditive Polarization Energies from Monomer and Dimer Calculations Only: A Case Study on Water.

The many-body polarization energy is the major source of nonadditivity in strongly polar systems such as water. This nonadditivity is often considerable and must be included, if only in an average manner, to correctly describe the physical properties of the system. Models for the polarization energy are usually parametrized using experimental data, or theoretical estimates of the many-body effects. Here we show how many-body polarization models can be developed for water complexes using data for the monomer and dimer only using ideas recently developed in the field of intermolecular perturbation theory and state-of-the-art approaches for calculating distributed molecular properties based on the iterated stockholder atoms (ISA) algorithm. We show how these models can be calculated, and we validate their accuracy in describing the many-body nonadditive energies of a range of water clusters. We further investigate their sensitivity to the details of the polarization damping models used. We show how our very best polarization models yield many-body energies that agree with those computed with coupled-cluster methods, but at a fraction of the computational cost.

Perspective: Ab initio force field methods derived from quantum mechanics

It is often desirable to accurately and efficiently model the behavior of large molecular systems in the condensed phase (thousands to tens of thousands of atoms) over long time scales (from nanoseconds to milliseconds). In these cases, ab initio methods are difficult due to the increasing computational cost with the number of electrons. A more computationally attractive alternative is to perform the simulations at the atomic level using a parameterized function to model the electronic energy. Many empirical force fields have been developed for this purpose. However, the functions that are used to model interatomic and intermolecular interactions contain many fitted parameters obtained from selected model systems, and such classical force fields cannot properly simulate important electronic effects. Furthermore, while such force fields are computationally affordable, they are not reliable when applied to systems that differ significantly from those used in their parameterization. They also cannot provide the information necessary to analyze the interactions that occur in the system, making the systematic improvement of the functional forms that are used difficult. Ab initio force field methods aim to combine the merits of both types of methods. The ideal ab initio force fields are built on first principles and require no fitted parameters. Ab initio force field methods surveyed in this perspective are based on fragmentation approaches and intermolecular perturbation theory. This perspective summarizes their theoretical foundation, key components in their formulation, and discusses key aspects of these methods such as accuracy and formal computational cost. The ab initio force fields considered here were developed for different targets, and this perspective also aims to provide a balanced presentation of their strengths and shortcomings. Finally, this perspective suggests some future directions for this actively developing area.

Challenging Dogmas: Hydrogen Bond Revisited.

Hydrogen bond directionality in the water dimer is explained on the basis of symmetry-adapted intermolecular perturbation theory which directly separates the intermolecular interaction energy into four physically interpretable components: electrostatics, exchange-repulsion, dispersion, and induction. Analysis of these four main contributions to the binding energy allows a deeper understanding of the dominant factors ruling the mutual arrangement of the two monomers. A preference for the linear configuration is shown to be due to a subtle interplay of all four energy components. While the first-order terms, electrostatic and exchange-repulsion, almost perfectly cancel each other near the equilibrium geometry of the dimer, the importance of the second- and higher-order terms, induction and dispersion, becomes evident.

Toward a Physically Motivated Force Field: Hydrogen Bond Directionality from a Symmetry-Adapted Perturbation Theory Perspective.

It is argued here that the functional forms adopted in almost all popular force fields are too restrictive to allow for accurate and physics-based parametrization. Some important modifications are suggested based on symmetry-adapted intermolecular perturbation theory, which directly separates the intermolecular interaction energy into four physically interpretable components: electrostatics, exchange-repulsion, dispersion, and induction. The exact electrostatic energy is approximated as a sum of the short-range contribution (due to charge density penetration effects), included explicitly, and the long-range part (via distributed atomic multipoles), whereas the induction energy is evaluated by means of the distributed induced damped point dipole model. The dispersion energy is fitted to a simple analytical function and the exchange-repulsion contribution is approximated by the overlap of the valence-only electron charge densities of monomers. The water dimer is used to illustrate the approach and to discuss its potential and possible improvements. Analysis of the four main contributions to the binding energy allows for a deeper understanding of the hydrogen bond directionality. It is found that a notorious geometrical preference in the water dimer results mainly from large polarization contributions, including induction and dispersion.

ChemInform Abstract: A Brief Review of Badger‐Bauer Rule and Its Validation from a First‐Principles Approach

AbstractReview: 55 refs.

Similarity-transformed perturbation theory on top of truncated local coupled cluster solutions: Theory and applications to intermolecular interactions.

Your correspondents develop and apply fully nonorthogonal, local-reference perturbation theories describing non-covalent interactions. Our formulations are based on a Löwdin partitioning of the similarity-transformed Hamiltonian into a zeroth-order intramonomer piece (taking local CCSD solutions as its zeroth-order eigenfunction) plus a first-order piece coupling the fragments. If considerations are limited to a single molecule, the proposed intermolecular similarity-transformed perturbation theory represents a frozen-orbital variant of the "(2)"-type theories shown to be competitive with CCSD(T) and of similar cost if all terms are retained. Different restrictions on the zeroth- and first-order amplitudes are explored in the context of large-computation tractability and elucidation of non-local effects in the space of singles and doubles. To accurately approximate CCSD intermolecular interaction energies, a quadratically growing number of variables must be included at zeroth-order.

Transferable next-generation force fields from simple liquids to complex materials.

Molecular simulations have had a transformative impact on chemists' understanding of the structure and dynamics of molecular systems. Simulations can both explain and predict chemical phenomena, and they provide a unique bridge between the microscopic and macroscopic regimes. The input for such simulations is the intermolecular interactions, which then determine the forces on the constituent atoms and therefore the time evolution and equilibrium properties of the system. However, in practice, accuracy and reliability are often limited by the fidelity of the description of those very same interactions, most typically embodied approximately in mathematical form in what are known as force fields. Force fields most often utilize conceptually simple functional forms that have been parametrized to reproduce existing experimental gas phase or bulk data. Yet, reliance on empirical parametrization can sometimes introduce limitations with respect to novel chemical systems or uncontrolled errors when moving to temperatures, pressures, or environments that differ from those for which they were developed. Alternatively, it is possible to develop force fields entirely from first principles, using accurate electronic structure calculations to determine the intermolecular interactions. This introduces a new set of challenges, including the transferability of the resulting force field to related chemical systems. In response, we recently developed an alternative approach to develop force fields entirely from first-principles electronic structure calculations based on intermolecular perturbation theory. Making use of an energy decomposition analysis ensures, by construction, that the resulting force fields contain the correct balance of the various components of intermolecular interaction (exchange repulsion, electrostatics, induction, and dispersion), each treated by a functional form that reflects the underlying physics. We therefore refer to the resulting force fields as physically motivated. We find that these physically motivated force fields exhibit both high accuracy and transferability, with the latter deriving from the universality of the fundamental physical laws governing intermolecular interactions. This basic methodology has been applied to a diverse set of systems, ranging from simple liquids to nanoporous metal-organic framework materials. A key conclusion is that, in many cases, it is feasible to account for nearly all of the relevant physics of intermolecular interactions within the context of the force field. In such cases, the structural, thermodynamic, and dynamic properties of the system become naturally emergent, even in the absence of explicit parameterization to bulk properties. We also find that, quite generally, the three-body contributions to the dispersion and exchange energies in bulk liquids are crucial for quantitative accuracy in a first-principles force field, although these contributions are almost universally neglected in existing empirical force fields.

A brief review of Badger–Bauer rule and its validation from a first-principles approach

Understanding the acid-base interactions is important in chemistry, biology and material science as it helps to rationalize materials properties such as interfacial properties, wetting, adhesion and adsorption. Quantitative relation between changes in enthalpy (ΔH) and frequency shift (Δν) during the acid-base complexation is particularly important. We investigate ΔH and Δν of twenty-five complexes of acids (methanol, ethanol, propanol, butanol and phenol) with bases (benzene, pyridine, DMSO, Et 2 O and THF) in CCl 4 using intermolecular perturbation theory calculations. ΔH and Δν of complexes of all alcohols with bases except benzene fall in the range from -14 kJ mol-1 to -30 kJ mol-1 and 215 cm-1 to 523 cm-1, respectively. Smaller values of ΔH (-2 kJ mol-1 to -6 kJ mol-1) and Δν (23 cm-1 to 70 cm-1) are estimated for benzene. Linear correlations are found between theoretical and experimental values of ΔH as well as Δν. For all the studied complexes, ΔH varies linearly (R2 ≥ 0.97) with Δν concurrent with the Badger–Bauer rule yielding the average slope and intercept of 0.053(± 0.002) kJ mol-1 cm and 2.15(± 0.56) kJ mol-1, respectively.

Intermolecular symmetry-adapted perturbation theory study of large organic complexes.

Binding energies for the complexes of the S12L database by Grimme [Chem. Eur. J. 18, 9955 (2012)] were calculated using intermolecular symmetry-adapted perturbation theory combined with a density-functional theory description of the interacting molecules. The individual interaction energy decompositions revealed no particular change in the stabilisation pattern as compared to smaller dimer systems at equilibrium structures. This demonstrates that, to some extent, the qualitative description of the interaction of small dimer systems may be extrapolated to larger systems, a method that is widely used in force-fields in which the total interaction energy is decomposed into atom-atom contributions. A comparison of the binding energies with accurate experimental reference values from Grimme, the latter including thermodynamic corrections from semiempirical calculations, has shown a fairly good agreement to within the error range of the reference binding energies.

Solubility of nonelectrolytes: a first-principles computational approach.

Using a combination of classical molecular dynamics and symmetry adapted intermolecular perturbation theory, we develop a high-accuracy computational method for examining the solubility energetics of nonelectrolytes. This approach is used to accurately compute the cohesive energy density and Hildebrand solubility parameters of 26 molecular liquids. The energy decomposition of symmetry adapted perturbation theory is then utilized to develop multicomponent Hansen-like solubility parameters. These parameters are shown to reproduce the solvent categorizations (nonpolar, polar aprotic, or polar protic) of all molecular liquids studied while lending quantitative rigor to these qualitative categorizations via the introduction of simple, easily computable parameters. Notably, we find that by monitoring the first-order exchange energy contribution to the total interaction energy, one can rigorously determine the hydrogen bonding character of a molecular liquid. Finally, this method is applied to compute explicitly the Flory interaction parameter and the free energy of mixing for two different small molecule mixtures, reproducing the known miscibilities. This methodology represents an important step toward the prediction of molecular solubility from first principles.

Achieving High-Accuracy Intermolecular Interactions by Combining Coulomb-Attenuated Second-Order Møller–Plesset Perturbation Theory with Coupled Kohn–Sham Dispersion

The dispersion-corrected second-order Møller-Plesset perturbation theory (MP2C) approach accurately describes intermolecular interactions in many systems. MP2C, however, expends much computational effort to compute the long-range correlation with MP2, only to discard and replace those contributions with a simpler long-range dispersion correction based on intermolecular perturbation theory. Here, we demonstrate that one can avoid calculating the long-range MP2 correlation by attenuating the Coulomb operator, allowing the dispersion correction to handle the long-range interactions inexpensively. With relatively modest Coulomb attenuation, one obtains results that are very similar to those from conventional MP2C. With more aggressive attenuation, one can remove just enough short-range repulsive exchange-dispersion interactions to compensate for finite basis set errors. Doing so makes it possible to approach complete basis set limit quality results with only an aug-cc-pVTZ basis, resulting in substantial computational savings. Further computational savings could be achieved by reformulating the MP2C algorithm to exploit the increased sparsity of the two-electron integrals.

Single-determinant-based symmetry-adapted perturbation theory without single-exchange approximation

It is shown that the exchange-dispersion energy contribution of symmetry-adapted intermolecular perturbation theory (SAPT) can be evaluated without invoking the single-exchange approximation in the case of single-determinant ground-state references. A succinct expression is derived which allows for efficient implementation. Making use of the corresponding exchange-induction contribution, obtained recently, this enables DFT-SAPT calculations, i.e., SAPT based on a density-functional theory description of the monomers, without an expansion in orders of the intermonomer overlap S. The approach is used to test the quality of the S 2 or single-exchange approximation for the systems He2, Ar2, N2–Ne, H2O–Ar, (H2O)2 and LiF, i.e., van der Waals and hydrogen-bridged complexes as well as an ionic molecule. While employing the S 2 approximation for the exchange-dispersion contribution is found to have minor impact on total SAPT interaction energies, its use to evaluate the exchange-induction contribution significantly affects the quality of the repulsive branches of the potential energy curves for the interacting partners. Adding appropriate Hartree–Fock level estimates of higher-order induction plus exchange-induction energies, however, restores good agreement with complete basis set limit coupled-cluster results.

Intermolecular Interactions in Weak Donor–Acceptor Complexes from Symmetry‐Adapted Perturbation and Coupled‐Cluster Theory: Tetracyanoethylene–Benzene and Tetracyanoethylene–p‐Xylene

The interactions in the complexes of tetracyanothylene (TCNE) with benzene and p-xylene, often classified as weak electron donor-acceptor (EDA) complexes, are investigated by a range of quantum chemical methods including intermolecular perturbation theory at the DFT-SAPT (symmetry-adapted perturbation theory combined with density functional theory) level and explicitly correlated coupled-cluster theory at the CCSD(T)-F12 level. The DFT-SAPT interaction energies for TCNE-benzene and TCNE-p-xylene are estimated to be -35.7 and -44.9 kJ mol(-1), respectively, at the complete basis set limit. The best estimates for the CCSD(T) interaction energy are -37.5 and -46.0 kJ mol(-1), respectively. It is shown that the second-order dispersion term provides the most important attractive contribution to the interaction energy, followed by the first-order electrostatic term. The sum of second- and higher-order induction and exchange-induction energies is found to provide nearly 40 % of the total interaction energy. After addition of vibrational, rigid-rotor, and translational contributions, the computed internal energy changes on complex formation approach results from gas-phase spectrophotometry at elevated temperatures within experimental uncertainties, while the corresponding entropy changes differ substantially.

Intermolecular exchange-induction energies without overlap expansion

An approach to evaluate the second-order exchange-induction energies of symmetry-adapted intermolecular perturbation theory (SAPT) for single-determinant ground-state monomer wavefunctions has been derived. This approach is correct to all orders of the intermonomer overlap, that is, it takes multiple electron exchange between the monomers into account. The resulting formulae can be written in a compact way and implemented efficiently. Here, the method is employed to investigate the performance of the S2- or single-exchange approximation at the Hartree-Fock-SAPT level. The list of test systems comprises the prototypical van der Waals- and hydrogen-bridge complexes Ne2, Ar–HF, and (H2O)2, but also the systems HeCl−, NeNa+ and Li+F− involving closed-shell ions. It was found that the errors introduced by the S2-approximation are more pronounced for the second-order exchange-induction energy than for the first-order exchange energy. While these errors tend to be negligible throughout the well region of complexes such as the neon dimer, they start to be significant in the repulsive part of the well regions of systems such as the water dimer, and in particular for the ionic lithium fluoride molecule. The consequences of these findings for the Hartree-Fock level estimate of higher-order induction plus exchange-induction energies, which is frequently employed in SAPT are also discussed.

Rapid computation of intermolecular interactions in molecular and ionic clusters: self-consistent polarization plus symmetry-adapted perturbation theory

A method that we have recently introduced for rapid computation of intermolecular interaction energies is reformulated and subjected to further tests. The method employs monomer-based self-consistent field calculations with an electrostatic embedding designed to capture many-body polarization (the "XPol" procedure), augmented by pairwise symmetry-adapted perturbation theory (SAPT) to capture dispersion and exchange interactions along with any remaining induction effects. A rigorous derivation of the XPol+SAPT methodology is presented here, which demonstrates that the method is systematically improvable, and moreover introduces some additional intermolecular interactions as compared to the more heuristic derivation that was presented previously. Applications to various non-covalent complexes and clusters are presented, including geometry optimizations and one-dimensional potential energy scans. The performance of the XPol+SAPT methodology in its present form (based on second-order intermolecular perturbation theory and neglecting intramolecular electron correlation) is qualitatively acceptable across a wide variety of systems-and quantitatively quite good in certain cases-but the quality of the results is rather sensitive to the choice of one-particle basis set. Basis sets that work well for dispersion-bound systems offer less-than-optimal performance for clusters dominated by induction and electrostatic interactions, and vice versa. A compromise basis set is identified that affords good results for both induction and dispersion interactions, although this favorable performance ultimately relies on error cancellation, as in traditional low-order SAPT. Suggestions for future improvements to the methodology are discussed.

On the interaction in the water–carbon dioxide complex

The interaction in the water–carbon dioxide complex was investigated. The interaction energies for the water–carbon dioxide complex in the regions close to the global and local minima were evaluated using MP2, CCSD and CCSD (T) methods. The SIMPER-P method was then applied to the MP2 interaction energies for characteristic orientations and the extrapolation of the interaction energy was carried out. The total interaction energies estimated using MP2 and SIMPER-P methods were analyzed component-wise using intermolecular perturbation theory and in terms of monomer properties.

Development of additive isotropic site potential for exchange-repulsion energy, based on intermolecular perturbation theory

We have developed an additive spherical site potential for exchange-repulsion energy by applying the local density approximation in Hilbert space, the local-site approximation, and the s-type auxiliary basis set to the equation derived from intermolecular perturbation theory. The method efficiently addresses the decomposition of molecular interactions derived from quantum chemistry into additive spherical site potentials, required as force field input in a statistical-mechanical, reference interaction site model (RISM and 3D-RISM), molecular theory of solvation. The present method reproduces the exchange-repulsion energy between simple molecules obtained from quantum chemical calculations.