General Methodology to Optimize Damping Functions to Account for Charge Penetration Effects in Electrostatic Calculations Using Multicentered Multipolar Expansions

Comparison of approximate intermolecular potentials for ab initio fragment calculations on medium sized N-heterocycles

The ground state intermolecular potential of bimolecular complexes of N-heterocycles is analyzed for the impact of individual terms in the interaction energy as provided by various, conceptually different theories. Novel combinations with several formulations of the electrostatic, Pauli repulsion, and dispersion contributions are tested at both short- and long-distance sides of the potential energy surface, for various alignments of the pyrrole dimer as well as the cytosine-uracil complex. The integration of a DFT/CCSD density embedding scheme, with dispersion terms from the effective fragment potential (EFP) method is found to provide good agreement with a reference CCSD(T) potential overall; simultaneously, a quantum mechanics/molecular mechanics approach using CHELPG atomic point charges for the electrostatic interaction, augmented by EFP dispersion and Pauli repulsion, comes also close to the reference result. Both schemes have the advantage of not relying on predefined force fields; rather, the interaction parameters can be determined for the system under study, thus being excellent candidates for ab initio modeling.

Inter-anion chalcogen bonds: Are they anti-electrostatic in nature?

Inter-anion hydrogen and halogen bonds have emerged as counterintuitive linkers and inspired us to expand the range of this unconventional bonding pattern. Here, the inter-anion chalcogen bond (IAChB) was proposed and theoretically analyzed in a series of complexes formed by negatively charged bidentate chalcogen bond donors with chloride anions. The kinetic stability of IAChB was evidenced by the minima on binding energy profiles and further supported by ab initio molecular dynamic simulations. The block-localized wave function (BLW) method and its subsequent energy decomposition (BLW-ED) approach were employed to elucidate the physical origin of IAChB. While all other energy components vary monotonically as anions get together, the electrostatic interaction behaves exceptionally as it experiences a Coulombic repulsion barrier. Before reaching the barrier, the electrostatic repulsion increases with the shortening Ch⋯Cl^- distance as expected from classical electrostatics. However, after passing the barrier, the electrostatic repulsion decreases with the Ch⋯Cl^- distance shortening and subsequently turns into the most favorable trend among all energy terms at short ranges, representing a dominating force for the kinetic stability of inter-anions. For comparison, all energy components exhibit the same trends and vary monotonically in the conventional counterparts where donors are neutral. By comparing inter-anions and their conventional counterparts, we found that only the electrostatic energy term is affected by the extra negative charge. Remarkably, the distinctive (nonmonotonic) electrostatic energy profiles were reproduced using quantum mechanical-based atomic multipoles, suggesting that the crucial electrostatic interaction in IAChB can be rationalized within the classical electrostatic theory just like conventional non-covalent interactions.

AMOEBA+ Classical Potential for Modeling Molecular Interactions

Classical potentials based on isotropic and additive atomic charges have been widely used to model molecules in computers for the past few decades. The crude approximations in the underlying physics are hindering both their accuracy and transferability across chemical and physical environments. Here we present a new classical potential, AMOEBA+, to capture essential intermolecular forces, including permanent electrostatics, repulsion, dispersion, many-body polarization, short-range charge penetration, and charge transfer, by extending the polarizable multipole-based AMOEBA (Atomic Multipole Optimized Energetics for Biomolecular Applications) model. For a set of common organic molecules, we show that AMOEBA+ with general parameters can reproduce both quantum mechanical interactions and energy decompositions according to Symmetry-Adapted Perturbation Theory (SAPT). Additionally, a new water model based on the AMOEBA+ framework captures various liquid-phase properties in molecular dynamics simulations while remaining consistent with SAPT energy decompositions, utilizing both ab initio data and experimental liquid properties. Our results demonstrate that it is possible to improve the physical basis of classical force fields to advance their accuracy and general applicability.

Scalable improvement of SPME multipolar electrostatics in anisotropic polarizable molecular mechanics using a general short-range penetration correction up to quadrupoles

We propose a general coupling of the Smooth Particle Mesh Ewald SPME approach for distributed multipoles to a short-range charge penetration correction modifying the charge-charge, charge-dipole and charge-quadrupole energies. Such an approach significantly improves electrostatics when compared to ab initio values and has been calibrated on Symmetry-Adapted Perturbation Theory reference data. Various neutral molecular dimers have been tested and results on the complexes of mono- and divalent cations with a water ligand are also provided. Transferability of the correction is adressed in the context of the implementation of the AMOEBA and SIBFA polarizable force fields in the TINKER-HP software. As the choices of the multipolar distribution are discussed, conclusions are drawn for the future penetration-corrected polarizable force fields highlighting the mandatory need of non-spurious procedures for the obtention of well balanced and physically meaningful distributed moments. Finally, scalability and parallelism of the short-range corrected SPME approach are addressed, demonstrating that the damping function is computationally affordable and accurate for molecular dynamics simulations of complex bio- or bioinorganic systems in periodic boundary conditions.

Screened Electrostatic Interactions in Molecular Mechanics

In a typical application of molecular mechanics (MM), the electrostatic interactions are calculated from parametrized partial atomic charges treated as point charges interacting by radial Coulomb potentials. This does not usually yield accurate electrostatic interactions at van der Waals distances, but this is compensated by additional parametrized terms, for example Lennard-Jones potentials. In the present work, we present a scheme involving radial screened Coulomb potentials that reproduces the accurate electrostatics much more accurately. The screening accounts for charge penetration of one subsystem's charge cloud into that of another subsystem, and it is incorporated into the interaction potential in a way similar to what we proposed in a previous article (J. Chem. Theory Comput. 2010, 6, 3330) for combined quantum mechanical and molecular mechanical (QM/MM) simulations, but the screening parameters are reoptimized for MM. The optimization is carried out with electrostatic-potential-fitted partial atomic charges, but the optimized parameters should be useful with any realistic charge model. In the model we employ, the charge density of an atom is approximated as the sum of a point charge representing the nucleus and inner electrons and a smeared charge representing the outermost electrons; in particular, for all atoms except hydrogens, the smeared charge represents the two outermost electrons in the present model. We find that the charge penetration effect can cause very significant deviations from the popular point-charge model, and by comparison to electrostatic interactions calculated by symmetry-adapted perturbation theory, we find that the present results are considerably more accurate than point-charge electrostatic interactions. The mean unsigned error in electrostatics for a large and diverse data set (192 interaction energies) decreases from 9.2 to 3.3 kcal/mol, and the error in the electrostatics for 10 water dimers decreases from 1.7 to 0.5 kcal/mol. We could have decreased the average errors further, but at the cost of sometimes significantly overestimating the screening; instead we chose a more conservative (safer) parametrization that systematically underestimates the screening (which by definition means it improves over point charges) and only occasionally overestimates it. Despite this conservative choice, we find that the screened MM method is even more accurate for the electrostatics than unscreened QM/MM calculations. This new method is easy to implement in any MM program, and it can be used to develop more physical force fields for molecular simulations.

General Model for Treating Short-Range Electrostatic Penetration in a Molecular Mechanics Force Field

Classical molecular mechanics force fields typically model interatomic electrostatic interactions with point charges or multipole expansions, which can fail for atoms in close contact due to the lack of a description of penetration effects between their electron clouds. These short-range penetration effects can be significant and are essential for accurate modeling of intermolecular interactions. In this work we report parametrization of an empirical charge-charge function previously reported (Piquemal J.-P.; J. Phys. Chem. A2003, 107, 10353) to correct for the missing penetration term in standard molecular mechanics force fields. For this purpose, we have developed a database (S101×7) of 101 unique molecular dimers, each at 7 different intermolecular distances. Electrostatic, induction/polarization, repulsion, and dispersion energies, as well as the total interaction energy for each complex in the database are calculated using the SAPT2+ method (Parker T. M.; J. Chem. Phys.2014, 140, 094106). This empirical penetration model significantly improves agreement between point multipole and quantum mechanical electrostatic energies across the set of dimers and distances, while using only a limited set of parameters for each chemical element. Given the simplicity and effectiveness of the model, we expect the electrostatic penetration correction will become a standard component of future molecular mechanics force fields.

Partial Atomic Charges and Screened Charge Models of the Electrostatic Potential

We propose a new screened charge method for calculating partial atomic charges in molecules by electrostatic potential (ESP) fitting. The model, called full density screening (FDS), is used to approximate the screening effect of full charge densities of atoms in molecules. The results are compared to the conventional ESP fitting method based on point charges and to our previously proposed outer density screening (ODS) method, in which the parameters are reoptimized for the present purpose. In ODS, the charge density of an atom is represented by the sum of a point charge and a smeared negative charge distributed in a Slater-type orbital (STO). In FDS, the charge density of an atom is taken to be the sum of the charge density of the neutral atom and a partial atomic charge (of either sign) distributed in an STO. The ζ values of the STOs used in these two models are optimized in the present study to best reproduce the electrostatic potentials. The quality of the fit to the electrostatics is improved in the screened charge methods, especially for the regions that are within one van der Waals radius of the centers of atoms. It is also found that the charges derived by fitting electrostatic potentials with screened charges are less sensitive to the positions of the fitting points than are those derived with conventional electrostatic fitting. Moreover, we found that the electrostatic-potential-fitted (ESP) charges from the screened charge methods are similar to those from the point-charge method except for molecules containing the methyl group, where we have explored the use of restraints on nonpolar H atoms. We recommend the FDS model if the only goal is ESP fitting to obtain partial atomic charges or a fit to the ESP field. However, the ODS model is more accurate for electronic embedding in combined quantum mechanical and molecular mechanical (QM/MM) modeling and is more accurate than point-charge models for ESP fitting, and it is recommended for applications involving QM/MM methods. Since the screened charges describe the electrostatic potentials more accurately than point charges, since they asymptotically act as point charges at long distances, and since the electrostatic potential in terms of the screened charges is still a sum of functions centered at the atoms, the screened-charge representation of the electrostatic potential can be used in the same way as the conventional point-charge representation to model the electrostatic interactions, but it is more realistic. For the H atom and p block elements, the error in the fit to the electrostatic potential is reduced by about a factor of 3, and the sensitivity of the derived partial atomic charges to the choice of fitting points is reduced by about a factor of 2. For s and d block elements, there are also improvements in the inner regions but not necessarily in the outer regions.