Molecular Dynamics with Conformationally Dependent, Distributed Charges

Abstract

Accounting for geometry-induced changes in the electronic distribution in molecular simulation is important for capturing effects such as charge flow, charge anisotropy, and polarization. Multipolar force fields have demonstrated their ability to correctly represent chemically significant features such as anisotropy and sigma holes. It has also been shown that off-center point charges offer a compact alternative with similar accuracy. Here, it is demonstrated that allowing relocation of charges within a minimally distributed charge model (MDCM) with respect to their reference atoms is a viable route to capture changes in the molecular charge distribution depending on geometry, i.e., intramolecular polarization. The approach, referred to as “flexible MDCM” (fMDCM), is validated on a number of small molecules and provides accuracies in the electrostatic potential (ESP) of 0.5 kcal/mol on average compared with reference data from electronic structure calculations, whereas MDCM and point charges have root mean squared errors of a factor of 2 to 5 higher. In addition, MD simulations in the NVE ensemble using fMDCM for a box of flexible water molecules with periodic boundary conditions show a width of 0.1 kcal/mol for the fluctuation around the mean at 300 K on the 10 ns time scale. For water, the equilibrium valence angle in the gas phase is found to increase by 2° for simulations in the condensed phase which is consistent with experiment. The accuracy in capturing the geometry dependence of the ESP together with the long-time stability in energy conserving simulations makes fMDCM a promising tool to introduce advanced electrostatics into atomistic simulations.

Systematic improvement of empirical energy functions in the era of machine learning

“…The electrostatic interaction term in empirical force fields such as CHARMM, 8,18 GROMACS, 20 or AMBER 17 has commonly been described using point charges at nuclear positions. The charges do not usually respond to changes in molecular conformation or to changes in the external electric field created by surrounding molecules (i.e., such force fields are not polarizable), although exceptions to this exist 21–23 . As such, electrostatic energies from atom‐centered charges are conceptually related to a sum of interactions between frozen monomer charge densities: …”

“…The charges do not usually respond to changes in molecular conformation or to changes in the external electric field created by surrounding molecules (i.e., such force fields are not polarizable), although exceptions to this exist. [21][22][23] As such, electrostatic energies from atom-centered charges are conceptually related to a sum of interactions between frozen monomer charge densities:…”

“…In empirical force fields a degree of averaged "prepolarization" can be introduced to better represent electrostatics in condensed phases, [24][25][26] but only at the cost of decreased accuracy in environments that do not resemble the condensed phase. 27,28 Here, gas-phase densities are employed to provide reference data for fitting atom-centered point charges and "minimally distributed charge models" (MDCMs) 23,[29][30][31][32] that-similar to multipole moments [33][34][35][36][37][38] -more accurately approximate E elec than atom-centered point charges alone as they better describe anisotropic electrostatic interactions. MDCM uses differential evolution, an energy-based global optimization machine learning technique, to determine the magnitude and position of a user-specified number of off-center point charges to best reproduce the ESP.…”

“…Numerous approaches to describe the response of a monomer electron density to both external electric fields generated from molecular environments 22,42 and due to changes in monomer conformation 21,23,[43][44][45] exist. Here, a polarization correction based on FMO electrostatic embedding is used that accounts for changes in electrostatic interaction due to distortions in the electron cloud of each monomer and also resulting destabilization of the polarized monomer energies.…”

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

“…The necessity of representing this charge flux in potentials has been previously discussed by Dinur . The TTM2.1-F revision of the TTM2-F potential, the AMOEBA+CF potential, and the flexible MDCM potential incorporate, to some extent, the redistribution of charge density with intramolecular geometry by including a geometry-dependent correction to the atomic monopoles, as has been done for geometry-dependent point charges for studies of photodissociated CO in myoglobin. , Very recently, the SCME-f model introduced a single-site multipolar description of water which has a dipole and a quadrupole moment, both dependent on the intramolecular geometry. In addition, the FFLUX model recently used Gaussian process regression (GPR) to predict geometry-dependent distributed atomic multipoles up to hexadecapole for water.…”