High-rank quantum topological electrostatic potential: Molecular dynamics simulation of liquid hydrogen fluoride

Hidden Halogen-Bonding Ability of Fluorine Manifesting in the Hydrogen-Bond Configurations of Hydrogen Fluoride

Elucidating how the intermolecular interactions of a covalently bonded fluorine atom are similar to and different from those of the other halogen atoms will be helpful for a better unified understanding of them. In the present study, the case of hydrogen fluoride is theoretically studied from this viewpoint by using the techniques of electron density analysis, molecular dynamics of liquid, and others. It is shown that the extra-point model, which locates an additional charge site on the line extended from (not within) the covalent bond and has been adopted for halogen-bonding systems as a key to the generation of proper stability and directionality, works well also in this case. A significantly bent hydrogen-bond configuration, which is characteristic of the intermolecular interactions of hydrogen fluoride, is reasonably well reproduced, meaning that it is a manifestation of the latent halogen-bonding ability, which is hidden by the strongly electronegative nature.

A FFLUX Water Model: Flexible, Polarizable and with a Multipolar Description of Electrostatics

Key to progress in molecular simulation is the development of advanced models that go beyond the limitations of traditional force fields that employ a fixed, point charge-based description of electrostatics. Taking water as an example system, the FFLUX framework is shown capable of producing models that are flexible, polarizable and have a multipolar description of the electrostatics. The kriging machine-learning methods used in FFLUX are able to reproduce the intramolecular potential energy surface and multipole moments of a single water molecule with chemical accuracy using as few as 50 training configurations. Molecular dynamics simulations of water clusters (25-216 molecules) using the new FFLUX model reveal that incorporating charge-quadrupole, dipole-dipole, and quadrupole-charge interactions into the description of the electrostatics results in significant changes to the intermolecular structuring of the water molecules. © 2019 The Authors. Journal of Computational Chemistry published by Wiley Periodicals, Inc.

Assessing Force Field Potential Energy Function Accuracy via a Multipolar Description of Atomic Electrostatic Interactions in RNA

Computational investigations of RNA properties often rely on a molecular mechanical approach to define molecular potential energy. Force fields for RNA typically employ a point charge model of electrostatics, which does not provide a realistic quantum-mechanical picture. In reality, electron distributions around nuclei are not spherically symmetric and are geometry dependent. A multipole expansion method which allows for incorporation of polarizability and anisotropy in a force field is described, and its applicability to modeling the behavior of RNA molecules is investigated. Transferability of the model, critical for force field development, is also investigated.

Minimal distributed charges: Multipolar quality at the cost of point charge electrostatics

Most empirical force fields use atom-centered point charges (PCs) to represent the electrostatic potential (ESP) around molecules. While such PC models are computationally efficient, they are unable to capture anisotropic electronic features, such as σ holes or lone pairs. These features are better described using atomic multipole (MTP) moments, which significantly improve the quality of the resulting ESP. However, the improvement comes at the expense of a considerably increased computational complexity and cost for calculating the interaction energies and forces. In the present work, a novel minimal distributed charge model (MDCM) based on off-centered point charges is presented and the quality of the resulting ESP is compared to the performance of MTPs and atom-centered PC models for several test molecules. All three models are fitted using the same algorithm based on differential evolution, which is available as a Fortran90 program from the authors upon request. We show that the MDCM is capable of approximating the reference ab initio ESP with an accuracy as good as, or better than, MTPs without the need for computationally expensive higher order multipoles. Further it is demonstrated that the MDCM is numerically stable in molecular dynamics simulations and is able to reproduce electrostatic interaction energies and thermodynamic quantities with the same accuracy as MTPs at reduced computational cost.

Accurate prediction of polarised high order electrostatic interactions for hydrogen bonded complexes using the machine learning method kriging

As intermolecular interactions such as the hydrogen bond are electrostatic in origin, rigorous treatment of this term within force field methodologies should be mandatory. We present a method able of accurately reproducing such interactions for seven van der Waals complexes. It uses atomic multipole moments up to hexadecupole moment mapped to the positions of the nuclear coordinates by the machine learning method kriging. Models were built at three levels of theory: HF/6-31G(**), B3LYP/aug-cc-pVDZ and M06-2X/aug-cc-pVDZ. The quality of the kriging models was measured by their ability to predict the electrostatic interaction energy between atoms in external test examples for which the true energies are known. At all levels of theory, >90% of test cases for small van der Waals complexes were predicted within 1 kJ mol(-1), decreasing to 60-70% of test cases for larger base pair complexes. Models built on moments obtained at B3LYP and M06-2X level generally outperformed those at HF level. For all systems the individual interactions were predicted with a mean unsigned error of less than 1 kJ mol(-1).

A Novel, Computationally Efficient Multipolar Model Employing Distributed Charges for Molecular Dynamics Simulations

A truncated multipole expansion can be re-expressed exactly using an appropriate arrangement of point charges. This means that groups of point charges that are shifted away from nuclear coordinates can be used to achieve accurate electrostatics for molecular systems. We introduce a multipolar electrostatic model formulated in this way for use in computationally efficient multipolar molecular dynamics simulations with well-defined forces and energy conservation in NVE (constant number-volume-energy) simulations. A framework is introduced to distribute torques arising from multipole moments throughout a molecule, and a refined fitting approach is suggested to obtain atomic multipole moments that are optimized for accuracy and numerical stability in a force field context. The formulation of the charge model is outlined as it has been implemented into CHARMM, with application to test systems involving H2O and chlorobenzene. As well as ease of implementation and computational efficiency, the approach can be used to provide snapshots for multipolar QM/MM calculations in QM/MM-MD studies and easily combined with a standard point-charge force field to allow mixed multipolar/point charge simulations of large systems.

Accuracy and tractability of a kriging model of intramolecular polarizable multipolar electrostatics and its application to histidine

We propose a generic method to model polarization in the context of high-rank multipolar electrostatics. This method involves the machine learning technique kriging, here used to capture the response of an atomic multipole moment of a given atom to a change in the positions of the atoms surrounding this atom. The atoms are malleable boxes with sharp boundaries, they do not overlap and exhaust space. The method is applied to histidine where it is able to predict atomic multipole moments (up to hexadecapole) for unseen configurations, after training on 600 geometries distorted using normal modes of each of its 24 local energy minima at B3LYP/apc-1 level. The quality of the predictions is assessed by calculating the Coulomb energy between an atom for which the moments have been predicted and the surrounding atoms (having exact moments). Only interactions between atoms separated by three or more bonds ("1, 4 and higher" interactions) are included in this energy error. This energy is compared with that of a central atom with exact multipole moments interacting with the same environment. The resulting energy discrepancies are summed for 328 atom-atom interactions, for each of the 29 atoms of histidine being a central atom in turn. For 80% of the 539 test configurations (outside the training set), this summed energy deviates by less than 1 kcal mol(-1).

Application of multipolar charge models and molecular dynamics simulations to study stark shifts in inhomogeneous electric fields

Atomic multipole moments are used to investigate vibrational frequency shifts of CO and H(2) in uniform and inhomogeneous electric fields using ab initio calculations and Molecular Dynamics (MD) simulations. The importance of using atomic multipole moments that can accurately represent both molecular electrostatics and the vibrational response of the molecule to changes in the local electric field is highlighted. The vibrational response of CO to applied uniform and inhomogeneous electric fields is examined using Density Functional Theory calculations for a range of test fields, and the results are used to assess the performance of different atomic multipole models. In uniform fields, the calculated Stark tuning rates of Deltamu = 0.52 cm(-1)/(MV/cm) (DFT), Deltamu = 0.55 cm(-1)/(MV/cm) (fluctuating three-point charge model), and Deltamu = 0.64 cm(-1)/(MV/cm) (Multipole model up to octupole), compare favorably with the experimentally measured value of 0.67 cm(-1)/(MV/cm). For H(2), which has no permanent dipole moment, CCSD(T) calculations demonstrate the importance of bond-weakening effects in force fields in response to the applied inhomogeneous electric field. Finally, CO in hexagonal ice is considered as a test system to highlight the performance of selected multipolar models in MD simulations. The approach discussed here can be applied to calibrate a range of multipolar charge models for diatomic probes, with applications to interpret Stark spectroscopy measurements in protein active sites.

The DL_POLY molecular dynamics package

The DL_POLY package provides a set of classical molecular dynamics programs that have application over a wide range of atomic and molecular systems. Written for parallel computers they offer capabilities stretching from small systems consisting of a few hundred atoms running on a single processor, up to systems of several million atoms running on massively parallel computers with thousands of processors. In this article we describe the structure of the programs and some applications.

Advancing beyond charge analysis using the electronic localization function: Chemically intuitive distribution of electrostatic moments

We propose here an evaluation of chemically intuitive distributed electrostatic moments using the topological analysis of the electron localization function (ELF). As this partition of the total charge density provides an accurate representation of the molecular dipole, the distributed electrostatic moments based on the ELF partition (DEMEP) allows computing of local moments located at non atomic centers such as lone pairs, sigma bonds and pi systems. As the local dipole contribution can be decomposed in polarization and charge transfer components, our results indicate that local dipolar polarization of the lone pairs and chemical reactivity are closely related whereas the charge transfer contribution is the key factor driving the local bond dipole. Results on relevant molecules show that local dipole contributions can be used to rationalize inductive polarization effects in alcohols derivatives and typical hydrogen bond interactions. Moreover, bond quadrupole polarization moments being related to a pi character enable to discuss bond multiplicities, and to sort families of molecules according to their bond order. That way, the nature of the C-O bond has been revisited for several typical systems by means of the DEMEP analysis which appears also helpful to discuss aromaticity. Special attention has been given to the carbon monoxide molecule, to the CuCO complex and to a weak intramolecular N|-CO interaction involved in several biological systems. In this latter case, it is confirmed that the bond formation is mainly linked to the CO bond polarization. Transferability tests show that the approach is suitable for the design of advanced force fields.

Simple Formulas for Improved Point-Charge Electrostatics in Classical Force Fields and Hybrid Quantum Mechanical/Molecular Mechanical Embedding

We present a simple damping scheme for point-charge electrostatics that could be used directly in classical force fields. The approach acts at the charge (or monopole) level only and allows the inclusion of short-range electrostatic penetration effects at a very low cost. Results are compared with density functional theory Coulomb intermolecular interaction energies and with several other methods such as distributed multipoles, damped distributed multipoles, and transferable Hermite-Gaussian densities. Realistic trends in the interactions are observed for atom-centered Mertz-Kollman corrected point-charge distributions. The approach allows increasing the selectivity of parameters in the case of metal complexes. In addition, two QM/MM calculations are presented where the damping function is employed to include the MM atoms located at the QM/MM boundary. The first calculation corresponds to the gas-phase proton transfer of aspartic acid through water and the second is the first step of the reaction catalyzed by the 4-oxalocrotonate tautomerase (4OT) enzyme. First, improved agreement is observed when using the damping approach compared with the conventional excluded charge method or when including all charges in the calculation. Second, in the case of 4OT, the damped charge approach is in agreement with previous calculations, whereas including all charges gives a significantly higher energy barrier. In both cases, no reparameterization of the van der Waals part of the force field was performed.

Effective force field for liquid hydrogen fluoride from ab initio molecular dynamics simulation using the force-matching method

A recently developed force-matching method for obtaining effective force fields for condensed matter systems from ab initio molecular dynamics (MD) simulations has been applied to fit a simple nonpolarizable two-site pairwise force field for liquid hydrogen fluoride. The ab initio MD in this case was a Car-Parrinello (CP) MD simulation of 64 HF molecules at nearly ambient conditions within the Becke-Lee-Yang-Parr approximation to the electronic density functional theory. The force-matching procedure included a fit of short-ranged nonbonded forces, bonded forces, and atomic partial charges. The performance of the force-match potential was examined for the gas-phase dimer and for the liquid phase at various temperatures. The model was able to reproduce correctly the bent structure and energetics of the gas-phase dimer, while the results for the structural properties, self-diffusion, vibrational spectra, density, and thermodynamic properties of liquid HF were compared to both experiment and the CP MD simulation. The force-matching model performs well in reproducing nearly all of the liquid properties as well as the aggregation behavior at different temperatures. The model is computationally cheap and compares favorably to many more computationally expensive potential energy functions for liquid HF.

On the variation of the structure of liquid deuterium fluoride with temperature

The structure of liquid deuterium fluoride has been measured using pulsed neutron diffraction and high energy x-ray diffraction techniques as a function of temperature. The neutron experiments were performed at T=296+/-2 K, 246+/-2 K, and 193+/-2 K and the x-ray measurements carried out at 296+/-2 K and 195+/-2 K. The x-ray pair correlation functions, which are dominated by fluorine-fluorine interactions, show the first peak at approximately 2.53+/-0.05 A remains very nearly invariant with decreasing temperature. Peaks around 4.5 and 5.0 A also appear at both temperatures in the x-ray data. In contrast, the intermolecular peaks in the total neutron pair correlation function show that significant systematic local structural changes occur as the temperature is lowered. The first intermolecular peak position shortens from 1.64+/-0.05 A at 296 K to 1.56+/-0.05 A at 195 K. Although there are overlapping contributions from the intermolecular hydrogen-fluorine and hydrogen-hydrogen correlations, it is clear that the temperature dependent structural changes are largely due to a rearrangement of the deuterium atom positions in the fluid. By comparison with partial structure factor data the hydrogen bonds appear to become more linear at lower temperatures.

Long range behavior of high-rank topological multipole moments

The construction of a high-rank multipolar force field (for peptides) is a complex task, leading to several intermediate questions in need of a clear answer. Here we focus on the convergence of the (electrostatic) multipolar expansion at medium and long range. Using molecular electron densities, quantum chemical topology (QCT) defines the atoms as finite volumes, each endowed with multipole moments. The terms in the multipole expansion are grouped according to powers of the internuclear distance, R(-L). Given two atom types at a given distance, we determine which rank (L) is necessary for the electrostatic energy to converge to the exact interaction energy within a certain error. With this information, the rank of the expansion for each interaction can be adapted to the required accuracy and the available computing power.