Dispersion Interactions in Water Clusters

Accurate Calculation of Many-Body Energies in Water Clusters Using a Classical Geometry-Dependent Induction Model

We incorporate geometry-dependent distributed multipole and polarizability surfaces into an induction model that is used to describe the 3- and 4-body terms of the interaction between water molecules. The moment expansion is carried out up to the hexadecapole with the multipoles distributed on the atom sites. Dipole-dipole, dipole-quadrupole, and quadrupole-quadrupole distributed polarizabilities are used to represent the response of the multipoles to an electric field. We compare the model against two large databases consisting of 43,844 3-body terms and 3,603 4-body terms obtained from high level ab initio calculations previously used to fit the MB-pol and q-AQUA classical interaction potentials for water. The classical induction model with no adjustable parameters reproduces the ab initio 3-/4-body terms contained in these two databases with a root-mean-square error (RMSE) of 0.104/0.058 and a mean-absolute error (MAE) of 0.054/0.026 kcal/mol, respectively. These results are on par with the ones obtained by fitting the same data using over 14,000 (for the 3-body) and 200 (for the 4-body) parameters via Permutationally Invariant Polynomials (PIPs). This demonstrates the accuracy of this physically motivated model in describing the 3- and 4-body terms in the interactions between water molecules with no adjustable parameters. The triple-dipole-dispersion energy, included in the calculation of the 3-body energy, was found to be small but not quite negligible. The model represents a practical, efficient, and transferable approach for obtaining accurate nonadditive interactions for multicomponent systems without the need to perform tens of thousands of high level electronic structure calculations and fitting them with PIPs.

An extensive assessment of the performance of pairwise and many-body interaction potentials in reproducing ab initio benchmark binding energies for water clusters n = 2-25

We assess the performance of 7 pairwise additive (TIP3P, TIP4P, TIP4P-ice, TIP5P, OPC, SPC, SPC/E) and 8 families of many-body potentials (q-AQUA, HIPPO, AMOEBA, EFP, TTM, WHBB, MB-pol, MB-UCB) in reproducing high-level ab initio benchmark values, CCSD(T) or MP2 at the complete basis set (CBS) limit for the binding energy and the many-body expansion (MBE) of water clusters n = 2-11, 16-17, 20, 25. By including a large range of cluster sizes having dissimilar hydrogen bonding networks, we obtain an understanding of how these potentials perform for different hydrogen bonding arrangements that are mostly outside of their parameterization range. While it is appropriate to compare the results of ab initio based many-body potentials directly to the electronic binding energies (D_e's), the pairwise additive ones are compared to the enthalpies at T = 298 K, ΔH(298 K), as the latter class of force fields are parametrized to reproduce enthalpies (implicitly accounting for zero-point energy corrections) rather than binding energies. We find that all pairwise additive potentials considered overestimate the reference ΔH values for the n = 2-25 clusters by >13%. For the water dimer (n = 2) in particular, the errors are in the range 83-119% for the pairwise additive potentials studied since these are based on an effective rather than the true 2-body interaction specifically designed as a means of partially accounting for the missing many-body terms. This stronger 2-body interaction is achieved by an enhanced monomer dipole moment that mimics its increase from the gas phase monomer to the condensed phase value. Indeed, for cluster sizes n ≥ 4 the percent deviations become slightly smaller (albeit all exceeding 13%). In contrast, we find that the many-body potentials perform more accurately in reproducing the electronic binding energies (D_e's) throughout the entire cluster range (n = 2-25), all reproducing the ab initio benchmark binding energies within ±7% of the respective CBS values. We further assess the ability of a subset of the many-body potentials (MB-UCB, q-AQUA, MB-pol, and TTM2.1-F) to also reproduce the magnitude of the ab initio many-body energy terms for water cluster sizes n = 7, 10, 16 and 17. The potentials show an overall good agreement with the available benchmark values. However, we identify characteristic differences upon comparing the many-body terms at both the ab initio-optimized geometries and the respective potential-optimized geometries to the reference ab initio values. Additionally, by applying this analysis to a wide range of cluster sizes, trends in the MBE of the potentials with increasing cluster size can be identified. Finally, in an attempt to draw a parallel between the pairwise additive and many-body potentials, we report the analysis of the individual molecular dipole moments for water clusters with 1 to ∼4 solvation shells with the TTM2.1-F potential. We find that the internally solvated water molecules have in general a larger molecular dipole moment ranging from 2.6-3.0 D. This justifies the use of an enhanced, with respect to the gas-phase value, molecular dipole moment for the pairwise additive potentials, which is intended to fold in the many body terms into an effective (enhanced) pairwise interaction through the choice of the charges. These results have important implications for the development of future generations of efficient, transferable, and highly accurate classical interaction potentials in both the pairwise additive and many-body categories.

Recent developments in the general atomic and molecular electronic structure system

A discussion of many of the recently implemented features of GAMESS (General Atomic and Molecular Electronic Structure System) and LibCChem (the C++ CPU/GPU library associated with GAMESS) is presented. These features include fragmentation methods such as the fragment molecular orbital, effective fragment potential and effective fragment molecular orbital methods, hybrid MPI/OpenMP approaches to Hartree-Fock, and resolution of the identity second order perturbation theory. Many new coupled cluster theory methods have been implemented in GAMESS, as have multiple levels of density functional/tight binding theory. The role of accelerators, especially graphical processing units, is discussed in the context of the new features of LibCChem, as it is the associated problem of power consumption as the power of computers increases dramatically. The process by which a complex program suite such as GAMESS is maintained and developed is considered. Future developments are briefly summarized.

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.

An Accurate Quantum-Based Approach to Explicit Solvent Effects: Interfacing the General Effective Fragment Potential Method with Ab Initio Electronic Structure Theory

An interface between ab initio quantum mechanics (QM) methods and the general effective fragment potential (EFP2) method, QM-EFP2, is implemented in which the intermolecular interactions between a QM molecule and EFP fragments consist of Coulomb, polarization, exchange repulsion (exrep), and dispersion components. In order to ensure accuracy in the QM-EFP2 exrep interaction energy, the EFP2-EFP2 spherical Gaussian overlap (SGO) approximation is abandoned and replaced with the exact electron repulsion integrals (ERI) that are evaluated with a direct method to reduce disk usage. A Gaussian damping function for the QM-EFP2 Coulomb component damps both the EFP nuclear and electronic charges. A new overlap damping function has been implemented for the QM-EFP2 dispersion component. The current QM-EFP2 implementation has been benchmarked with the S22 and S66 data sets and demonstrates excellent agreement with symmetry-adapted perturbation theory (SAPT) for component energies and with coupled cluster theory [CCSD(T)] for the total interaction energies. Water clusters of various sizes (up to 256 water molecules) have been tested; it is shown that the QM-EFP2 method has an accuracy that is comparable to that of EFP2-EFP2. It has been shown previously that the accuracy of EFP2-EFP2 intermolecular interactions is comparable to that of second-order perturbation theory (MP2) or better. The implementation of the distributed data interface (DDI) parallelization scheme significantly improves the efficiency of QM-EFP2 calculations. The time to form the QM-EFP2 Fock operator per SCF iteration for water clusters scales linearly with the number EFP basis functions.

Correlation effects and many-body interactions in water clusters

Background: The quantum-chemical description of the interactions in water clusters is an essential basis for deriving accurate and physically sound models of the interaction potential for water to be used in molecular simulations. In particular, the role of many-body interactions beyond the two-body interactions, which are often not explicitly taken into account by empirical force fields, can be accurately described by quantum chemistry methods on an adequate level, e.g., random-phase approximation electron correlation methods. The relative magnitudes of the different interaction energy contributions obtained by accurate ab initio calculations can therefore provide useful insights that can be exploited to develop enhanced force field methods. Results: In line with earlier theoretical studies of the interactions in water clusters, it has been found that the main contribution to the many-body interactions in clusters with a size of up to N = 13 molecules are higher-order polarisation interaction terms. Compared to this, many-body dispersion interactions are practically negligible for all studied sytems. The two-body dispersion interaction, however, plays a significant role in the formation of the structures of the water clusters and their stability, since it leads to a distinct compression of the cluster sizes compared to the structures optimized on an uncorrelated level. Overall, the many-body interactions amount to about 13% of the total interaction energy, irrespective of the cluster size. The electron correlation contribution to these, however, amounts to only about 30% to the total many-body interactions for the largest clusters studied and is repulsive for all structures considered in this work. Conclusion: While this shows that three- and higher-body interactions can not be neglected in the description of water complexes, the electron correlation contributions to these are much smaller in comparison to the two-body electron correlation effects. Efficient quantum chemistry approaches for describing intermolecular interactions between water molecules may therefore describe higher-body interactions on an uncorrelated Hartree-Fock level without a serious loss in accuracy.

A General Route to Include Pauli Repulsion and Quantum Dispersion Effects in QM/MM Approaches

A methodology to account for nonelectrostatic interactions in Quantum Mechanical (QM)/Molecular Mechanics (MM) approaches is developed. Formulations for Pauli repulsion and dispersion energy, explicitly depending on the QM density, are derived. Such expressions are based on the definition of an auxiliary density on the MM portion and the Tkatchenko-Scheffler (TS) approach, respectively. The developed method is general enough to be applied to any QM/MM method and partition, provided an accurate tuning of a small number of parameters is obtained. The coupling of the method with both nonpolarizable and fully polarizable QM/fluctuating charge (FQ) approaches is reported and applied. A suitable parametrization for the aqueous solution, so that its most representative features are well reproduced, is outlined. Then, the obtained parametrization and method are applied to calculate the nonelectrostatic (repulsion and dispersion) interaction energy of nicotine in aqueous solution.