The Monomer Electron Density Force Field (MEDFF): A Physically Inspired Model for Noncovalent Interactions

Abstract

We propose a methodology to derive pairwise-additive non-covalent force fields from monomer electron densities without any empirical input. Energy expressions are based on the Symmetry-Adapted Perturbation Theory (SAPT) decomposition of interaction energies. This ensures a physically motivated force field featuring an electrostatic, exchange-repulsion, dispersion and induction contribution, which contain two types of parameters. First, each contribution depends on several fixed atomic parameters, resulting from a partitioning of the monomer electron density. Second, each of the last three contributions (exchange-repulsion, dispersion and induction) contains exactly one linear fitting parameter. These three so-called interaction parameters in the model, are initially estimated separately using SAPT reference calculations for the S66x8 database of non-covalent dimers. In a second step, the three interaction parameters are further refined simultaneously to reproduce CCSD(T)/CBS interaction energies for the same database. The limited number of parameters that are fitted to 1 dimer interaction energies (only three), avoids ill-conditioned fits that plague conventional parameter optimizations.For the exchange-repulsion and dispersion component, good results are obtained for all dimers in the S66x8 database using one single value for the associated interaction parameters. The values of those parameters can be considered universal and can also be used for dimers not present in the original database used for fitting. For the induction component such an approach is only viable for the dispersion-dominated dimers in the S66x8 database. For other dimers (such as hydrogen-bonded complexes), we show that our methodology remains applicable. However the interaction parameter needs to be determined on a case-specific basis.As an external validation, the force field predicts interaction energies in good agreement with CCSD(T)/CBS values for dispersion-dominated dimers extracted from an HIV-II protease crystal structure with a bound ligand (indinavir). Furthermore, experimental second virial coefficients of small alkanes and alkenes are well reproduced.

Hydration Free Energies in the FreeSolv Database Calculated with Polarized Iterative Hirshfeld Charges

“…Note that the electrostatic term in the GAFF force field uses simple point charges and does not account for short-range screening due to the finite extent of the atomic electron densities, also known as the penetration effect 25 , 27 , 55 – 58 . While the inclusion of such screening makes the electrostatic term more physically sound, it is not recommended in our case.…”

“…The main drawbacks of these models are their increased complexity (more parameters) and increased computational cost. In addition, it was recently shown that polarization energy of atomic dipole polarizable force fields can deviate severely from the induction energy of Symmetry-Adapted Perturbation Theory (SAPT) calculations on the molecular dimers in the S66 set 25 . Because a polarizable force field and the SAPT induction term try to describe the same physics, this discrepancy discourages the use more expensive polarizable force fields.…”

Non-covalent interactions across organic and biological subsets of chemical space: Physics-based potentials parametrized from machine learning

“…[40][41][42][43] An extension has later been proposed by Vandenbrande et al to efficiently estimate the correction without any free parameter. 5 This is achieved by including the atomic-density population N i of atom i-the normalization term in Eq. (3).…”

“…5 The parameter q c corresponds to a core charge that is not subject to penetration effects, i.e., q = q c N, where q is determined from the multipole expansion.…”

“…5 They report root-mean squared errors of 0.36 kcal/mol for the dispersion-dominated complexes of the S66 dataset at equilibrium distances. Given that hydrogen-bonded complexes are typically more challenging, 1,5 our model likely compares favorably, keeping in mind that the dataset and error measurement are different.…”