Spherical tensor theory of long-range interactions in a system ofNarbitrary molecules including quantum-mechanical many-body effects

Many-Body Dispersion

A broad range of approaches to many-body dispersion are discussed, including empirical approaches with multiple fitted parameters, augmented density functional-based approaches, symmetry adapted perturbation theory, and a supermolecule approach based on coupled cluster theory. Differing definitions of "body" are considered, specifically atom-based vs molecule-based approaches.

Many-Body Dispersion in Molecular Clusters

Many-body dispersion has gained considerable attention over the past decade, particularly for condensed phase systems. However, quantitatively accurate studies of many-body dispersion have only recently become feasible due to challenges in reliability and accuracy. Currently available methodologies for calculating many-body dispersion have been challenged, with recent evidence suggesting, for example, that dispersion-corrected density functional theory (DFT) schemes cannot consistently predict many-body dispersion accurately. This study evaluates many-body dispersion energies using a composite approach that employs singles and doubles coupled cluster theory with perturbative/noniterative triples, CCSD(T), combined with an extrapolation to the complete basis set (CBS) limit. The combined CCSD(T)/CBS approach is applied to Ar_n and (H₂O)_n, n = 3-10, clusters, and a new data set called S22(3), which includes trimers generated based on the S22 data set. In these systems, the many-body dispersion provides a very small contribution to the total interaction energy of all of the systems studied, generally 3% or less of the total interaction energy. Two-body dispersion is the dominant dispersion contribution and many-body dispersion contributes no more than 5.7% of the total dispersion energy, generally staying below 2%.

Dispersion Interactions in QM/EFP

The dispersion energy term between quantum-mechanical (QM) and classical (represented by effective fragment potentials, EFP) subsystems is developed and implemented. A new formulation is based on long-range perturbation theory and uses dynamic polarizability tensors of the effective fragments and electric field integrals and orbital energies of the quantum-mechanical subsystem. No parametrization is involved. The accuracy of the QM-EFP dispersion energy is tested on a number of model systems; the average mean unsigned error is 0.8 kcal/mol or 13% with respect to the symmetry adapted perturbation theory on the S22 data set of noncovalent interactions. The computational cost of the dispersion energy computation is low compared to the self-consistent field calculation of the QM subsystem. The dispersion energy is sensitive to the level of theory employed for the QM part and to the electrostatic interactions in the system. The latter means that the dispersion interactions in the QM/EFP method are not purely two-body but have more complex many-body behavior.

Systematic fragmentation method and the effective fragment potential: an efficient method for capturing molecular energies

The systematic fragmentation method fragments a large molecular system into smaller pieces, in such a way as to greatly reduce the computational cost while retaining nearly the accuracy of the parent ab initio electronic structure method. In order to attain the desired (sub-kcal/mol) accuracy, one must properly account for the nonbonded interactions between the separated fragments. Since, for a large molecular species, there can be a great many fragments and therefore a great many nonbonded interactions, computations of the nonbonded interactions can be very time-consuming. The present work explores the efficacy of employing the effective fragment potential (EFP) method to obtain the nonbonded interactions since the EFP method has been shown previously to capture nonbonded interactions with an accuracy that is often comparable to that of second-order perturbation theory. It is demonstrated that for nonbonded interactions that are not high on the repulsive wall (generally >2.7 A), the EFP method appears to be a viable approach for evaluating the nonbonded interactions. The efficacy of the EFP method for this purpose is illustrated by comparing the method to ab initio methods for small water clusters, the ZOVGAS molecule, retinal, and the alpha-helix. Using SFM with EFP for nonbonded interactions yields an error of 0.2 kcal/mol for the retinal cis-trans isomerization and a mean error of 1.0 kcal/mol for the isomerization energies of five small (120-170 atoms) alpha-helices.

A single molecule as a dielectric medium

For three molecules with weak or negligible charge overlap, we prove that the three-body interaction energy obtained from quantum perturbation theory (to leading order) fits a dielectric model with a nonlocal electronic screening function. The electronic charge cloud of each molecule acts as a dielectric medium for the interaction of the remaining two with the nonlocal dielectric function epsilon(r,r') obtained by O. S. Jenkins and K. L. C. Hunt [J. Chem. Phys. 119, 8250 (2003)], by considering the charge redistribution induced in a single molecule by an external perturbation. The dielectric function depends parametrically on the coordinates of the nuclei, within the Born-Oppenheimer approximation. We also prove that the force on each nucleus in molecule A depends on intramolecular dielectric screening within A. The potential from the charge distribution of B, screened by C acting as a dielectric medium, is further screened linearly within A; and similarly, with the roles of B and C reversed. In addition, the potential due to the unperturbed charge distribution of B and the potential due to the unperturbed charge distribution of C, acting simultaneously, are screened nonlinearly within A. The results show that nonlocal dielectric theory holds on the molecular level, provided that the overlap of the electronic charge distributions is weak.

Three-body symmetry-adapted perturbation theory based on Kohn-Sham description of the monomers

An implementation of three-body symmetry-adapted perturbation theory (SAPT) of intermolecular interactions based on Kohn-Sham (KS) description of monomers with dispersion and induction nonadditive energies obtained from KS frequency-dependent density susceptibilities [SAPT(DFT)] is presented. Using the density-fitting approach, the nonadditive dispersion energy can be obtained with O(N(5)) scaling with respect to the system size, the best scaling among all available methods of evaluating this quantity. Numerical results are reported for the helium, argon, water, and benzene trimers. The nonadditive energy computed for these systems is in a good agreement with benchmarks. Some hybrid perturbational-supermolecular approaches are proposed that can provide--with only O(N(5)) scaling--nonadditive energies with accuracy comparable to more expensive supermolecular methods, such as the third-order Moller-Plesset perturbation theory. Such approaches can be used for studying nonadditive effects in systems larger than it is currently possible with supermolecular methods at a level high enough to capture all essential components of the three-body interaction energy.

Third-order interactions in symmetry-adapted perturbation theory

We present an extension of many-body symmetry-adapted perturbation theory (SAPT) by including all third-order polarization and exchange contributions obtained with the neglect of intramonomer correlation effects. The third-order polarization energy, which naturally decomposes into the induction, dispersion, and mixed, induction-dispersion components, is significantly quenched at short range by electron exchange effects. We propose a decomposition of the total third-order exchange energy into the exchange-induction, exchange-dispersion, and exchange-induction-dispersion contributions which provide the quenching for the corresponding individual polarization contributions. All components of the third-order energy have been expressed in terms of molecular integrals and orbital energies. The obtained formulas, valid for both dimer- and monomer-centered basis sets, have been implemented within the general closed-shell many-electron SAPT program. Test calculations for several small dimers have been performed and their results are presented. For dispersion-bound dimers, the inclusion of the third-order effects eliminates the need for a hybrid SAPT approach, involving supermolecular Hartree-Fock calculations. For dimers consisting of strongly polar monomers, the hybrid approach remains more accurate. It is shown that, due to the extent of the quenching, the third-order polarization effects should be included only together with their exchange counterparts. Furthermore, the latter have to be calculated exactly, rather than estimated by scaling the second-order values.