A classical model for three-body interactions in aqueous ionic systems.

We present a classical induction model to evaluate the three-body ion-water-water (I-W-W) and water-water-water (W-W-W) interactions in aqueous ionic systems. The classical description of the induction energy is based on electrostatic distributed multipoles up to hexadecapole and distributed polarizabilities up to quadrupole-quadrupole on the O and H atoms of water. The monatomic ions were described by a point charge and a dipole-dipole polarizability, while for the polyatomic ions, distributed multipoles up to hexadecapole and distributed polarizabilities up to quadrupole-quadrupole were used. The accuracy of the classical model is benchmarked against an accurate dataset of 936 (I-W-W) and 2184 (W-W-W) three-body terms for 13 different monatomic and polyatomic cation and anion systems. The classical model shows excellent agreement with the reference second order Moller-Plesset and coupled-cluster single double and perturbative triple [CCSD(T)] three-body energies. The Root-Mean-Square-Errors (RMSEs) for monatomic cations, monatomic anions, and polyatomic ions were 0.29, 0.25, and 0.12 kcal/mol, respectively. The corresponding RMSE for 1744 CCSD(T)/aVTZ three-body (W-W-W) energies, used to train MB-pol, was 0.12 kcal/mol. The accuracy of the proposed classical model demonstrates that the three-body term for aqueous ionic systems can be accurately modeled classically. This approach provides a fast, efficient, and as-accurate path toward modeling the three-body term in aqueous ionic systems that is fully transferable across systems with different ions without the need to fit to tens of thousands of ab initio calculations for each ion to extend existing many-body force fields to interactions between water and ions.

Natural Bond Orbitals and the Nature of the Hydrogen Bond.

The charge-transfer component of the energy of interaction between molecules has been a controversial issue for many years. In particular, the values reported from the use of the natural bond orbital analysis of Weinhold and his co-workers are several times larger than those obtained by other methods. I argue that these values are heavily contaminated with basis-set superposition error and are meaningless in the context of intermolecular interactions.

An OHD-RIKES and simulation study comparing a benzylmethylimidazolium ionic liquid with an equimolar mixture of dimethylimidazolium and benzene.

The principal difference between 1-benzyl-3-methyl-imidazolium triflimide [BzC1im][NTf2] and an equimolar mixture of benzene and dimethylimidazolium triflimide [C1C1im][NTf2] is that in the former the benzene moieties are tied to the imidazolium ring, while in the latter they move independently. We use femtosecond optical heterodyne-detected Raman-induced Kerr effect spectroscopy (OHD-RIKES) and molecular simulations to explore some properties of these two systems. The Kerr spectra show small differences in the spectral densities; the simulations also show very similar environments for both the imidazolium rings and the phenyl or benzene parts of the molecules. The low frequency vibrational densities of states are also similar in the model systems. In order to perform the simulations we developed a model for the [BzC1im](+) cation and found that the barriers to rotation of the two parts of the molecule are low.

Are halogen bonded structures electrostatically driven?

Halogen-bonded complexes B···XY, where B is a Lewis base and X a halogen atom, have been described as electrostatically driven, largely because of the close analogy between their structures and those of corresponding hydrogen-bonded complexes. Analysis of the components of the binding energy using symmetry-adapted perturbation theory suggests that while the main contribution to the binding is usually the electrostatic energy, the geometries are not always determined by electrostatics alone. In particular, the strong tendency to linearity of the B···XY bond is a consequence of exchange-repulsion, not electrostatics.

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.

Electrostatic damping functions and the penetration energy.

The use of damping functions to correct the multipole expansion at short-range is explored. Damping functions for the terms in the multipole expansion can be determined ab initio as a linear combination of analytic functions of the separation between sites, but there are additional short-range terms that have different angular dependence. The approach provides a detailed ab initio description of the penetration energy correction to the multipole expansion in an easily comprehensible form.

Ab Initio Atom-Atom Potentials Using CamCASP: Theory and Application to Many-Body Models for the Pyridine Dimer.

Creating accurate, analytic atom-atom potentials for small organic molecules from first principles can be a time-consuming and computationally intensive task, particularly if we also require them to include explicit polarization terms, which are essential in many systems. We describe how the CamCASP suite of programs can be used to generate such potentials using some of the most accurate electronic structure methods currently applicable. We derive the long-range terms from monomer properties and determine the short-range anisotropy parameters by a novel and robust method based on the iterated stockholder atom approach. Using these techniques, we develop distributed multipole models for the electrostatic, polarization, and dispersion interactions in the pyridine dimer and develop a series of many-body potentials for the pyridine system. Even the simplest of these potentials exhibits root mean square errors of only about 0.6 kJ mol(-1) for the low-energy pyridine dimers, significantly surpassing the best empirical potentials. Our best model is shown to support eight stable minima, four of which have not been reported before in the literature. Further, the functional form can be made systematically more elaborate so as to improve the accuracy without a significant increase in the human-time spent in their generation. We investigate the effects of anisotropy, rank of multipoles, and choice of polarizability and dispersion models.

Beyond Born-Mayer: Improved Models for Short-Range Repulsion in ab Initio Force Fields.

Short-range repulsion within intermolecular force fields is conventionally described by either Lennard-Jones (A/r(12)) or Born-Mayer (A exp(-Br)) forms. Despite their widespread use, these simple functional forms are often unable to describe the interaction energy accurately over a broad range of intermolecular distances, thus creating challenges in the development of ab initio force fields and potentially leading to decreased accuracy and transferability. Herein, we derive a novel short-range functional form based on a simple Slater-like model of overlapping atomic densities and an iterated stockholder atom (ISA) partitioning of the molecular electron density. We demonstrate that this Slater-ISA methodology yields a more accurate, transferable, and robust description of the short-range interactions at minimal additional computational cost compared to standard Lennard-Jones or Born-Mayer approaches. Finally, we show how this methodology can be adapted to yield the standard Born-Mayer functional form while still retaining many of the advantages of the Slater-ISA approach.

Distributed Multipoles from a Robust Basis-Space Implementation of the Iterated Stockholder Atoms Procedure.

The recently developed iterated stockholder atoms (ISA) approach of Lillestolen and Wheatley (Chem. Commun. 2008, 5909) offers a powerful method for defining atoms in a molecule. However, the real-space algorithm is known to converge very slowly, if at all. Here, we present a robust, basis-space algorithm of the ISA method and demonstrate its applicability on a variety of systems. We show that this algorithm exhibits rapid convergence (taking around 10-80 iterations) with the number of iterations needed being unrelated to the system size or basis set used. Further, we show that the multipole moments calculated using this basis-space ISA method are as good as, or better than, those obtained from Stone's distributed multipole analysis (J. Chem. Theory Comput. 2005, 1, 1128), exhibiting better convergence properties and resulting in better behaved penetration energies. This can have significant consequences in the development of intermolecular interaction models.

Accurate Induction Energies for Small Organic Molecules: 1. Theory.

The induction energy often plays a very important role in determining the structure and properties of clusters of organic molecules, but only in recent years has an effort been made to include this energy in such calculations, notably in the field of organic crystal structure prediction. In this paper and the following one in this issue we provide ab initio methods suitable for the accurate inclusion of the induction energy for molecules containing as many as 30 atoms or so. These techniques are based on Symmetry-Adapted Perturbation Theory using Density Functional Theory [SAPT(DFT)] and use distributed polarizabilities computed using the recently developed density-fitting algorithm with constrained refinement. With this approach we are able to obtain induction models of varying complexity and study the effects of overlap and related numerical issues. Basis set effects on the exact and asymptotic induction energies are investigated, and the roles of higher-order induction energies and many-body effects are explored.

Accurate Induction Energies for Small Organic Molecules. 2. Development and Testing of Distributed Polarizability Models against SAPT(DFT) Energies.

In part 1 of this two-part investigation we set out the theoretical basis for constructing accurate models of the induction energy of clusters of moderately sized organic molecules. In this paper we use these techniques to develop a variety of accurate distributed polarizability models for a set of representative molecules that include formamide, N-methyl propanamide, benzene, and 3-azabicyclo[3.3.1]nonane-2,4-dione. We have also explored damping, penetration, and basis set effects. In particular, we have provided a way to treat the damping of the induction expansion. Different approximations to the induction energy are evaluated against accurate SAPT(DFT) energies, and we demonstrate the accuracy of our induction models on the formamide-water dimer.

Is the Induction Energy Important for Modeling Organic Crystals?

We compare two methods for estimating the induction energy in organic molecular crystals by approximating the charge density polarization in the crystalline state. The first is a distributed atomic polarizability model combined with distributed multipole moments, derived from ab initio monomer properties. The second uses an ab initio calculation of the molecular charge density in a point-charge field. Various parameters of the models, such as the rank of polarizability model, effect of self-consistent iterations, and damping, are investigated. The methods are applied to a range of observed and predicted crystal structures of three particularly challenging molecules, namely oxalyl dihydrazide, 3-azabicyclo[3,3,1]nonane-2,4-dione, and carbamazepine, as well as demonstrating the importance of induction in the naphthalene crystal. The two models agree well considering the different approximations made, and it is shown that the induction energy can be an important discriminator in the relative lattice energies of structures with substantially different hydrogen-bonding motifs.

Distributed polarizabilities obtained using a constrained density-fitting algorithm.

A computationally efficient method for obtaining distributed polarizabilities of arbitrary rank using a constrained density-fitting algorithm is demonstrated on the hydrogen, carbon dioxide, formamide, and N-methylpropanamide molecules. A description of the molecular polarization in terms of local polarizabilities without charge-flow terms is obtained when the nonlocal components of the polarizability tensor are transformed away using the localization method of Le Sueur and Stone [Mol. Phys. 83, 293 (1994)]. The resulting local polarizabilities are shown to be stable with respect to basis set used, exhibiting none of the artifacts of earlier basis-space partitioning methods. We also investigate the transferability of the resulting local polarizability models.

Distributed Multipole Analysis: Stability for Large Basis Sets.

The distributed multipole analysis procedure, for describing a molecular charge distribution in terms of multipole moments on the individual atoms (or other sites) of the molecule, is not stable with respect to a change of basis set, and indeed, the calculated moments change substantially and unpredictably when the basis set is improved, even though the resulting electrostatic potential changes very little. A revised procedure is proposed, which uses grid-based quadrature for partitioning the contributions to the charge density from diffuse basis functions. The resulting procedure is very stable, and the calculated multipole moments converge rapidly to stable values as the size of the basis is increased.

Ice nucleation on a model hexagonal surface.

The adsorption of water on a model hexagonal surface has been studied using accurate intermolecular potentials. The structure and binding energies of single molecules, clusters, and adlayers are obtained. The limiting case of weak, nondirectional surface-water interactions presented here is compared with other cases involving water-water and water-surface interactions of a similar magnitude (partial templating) and dominating water-surface interactions (perfect templating) from the literature. None of these models is conducive to the nucleation of ice, each for different reasons. We comment on the requirements for a good ice-nucleating surface.