Gradients of the polarization energy in the effective fragment potential method

Abstract

The effective fragment potential (EFP) method is an ab initio based polarizable classical method in which the intermolecular interaction parameters are obtained from preparative ab initiocalculations on isolated molecules. The polarization energy in the EFP method is modeled with asymmetric anisotropic dipole polarizabilitytensors located at the centroids of localized bond and lone pair orbitals of the molecules. Analytic expressions for the translational and rotational gradients (forces and torques) of the EFP polarization energy have been derived and implemented. Periodic boundary conditions (the minimum image convention) and switching functions have also been implemented for the polarization energy, as well as for other EFP interaction terms. With these improvements, molecular dynamics simulations can be performed with the EFP method for various chemical systems. The effective fragment potential ͑EFP͒ method is an ab initio based polarizable classical method in which the intermolecular interaction parameters are obtained from preparative ab initio calculations on isolated molecules. The polarization energy in the EFP method is modeled with asymmetric anisotropic dipole polarizability tensors located at the centroids of localized bond and lone pair orbitals of the molecules. Analytic expressions for the translational and rotational gradients ͑forces and torques͒ of the EFP polarization energy have been derived and implemented. Periodic boundary conditions ͑the minimum image convention͒ and switching functions have also been implemented for the polarization energy, as well as for other EFP interaction terms. With these improvements, molecular dynamics simulations can be performed with the EFP method for various chemical systems.

Implementation of the analytic energy gradient for the combined time-dependent density functional theory/effective fragment potential method: Application to excited-state molecular dynamics simulations

“…The polarization energy of the EFP induced dipoles is given by 30 where A and B are components of the coupling matrix and X and Y are components of the transition amplitude. Note that only spin-conserving blocks, i.e., αα and ββ, of X and Y are allowed to be nonzero.…”

“…To obtain a simplified expression for the polarization potentialV pol , a matrix formulation for the EFP induced dipoles 30 is introduced. The induced dipoles at polarizable points are determined by solving the equation,…”

QM:QM electronic embedding using Mulliken atomic charges: Energies and analytic gradients in an ONIOM framework

“…For example, the effective fragment potential ͑EFP͒ method treats solvent molecules as rigid fragments represented in terms of multipoles and polarizability tensors determined from ab initio calculations, and has been used successfully in a variety of solution chemistry applications. [38][39][40][41][42][43][44][45][46][47][48][49][50][51][52][53][54][55] Carter and co-workers have developed a hybrid method that combines a high-level wave function model based on atom center basis functions, such as configuration interaction, with a planewave DFT model chemistry for studies of metallic crystals. [56][57][58][59][60][61] The frozen DFT ͑FDFT͒ and constrained DFT ͑CDFT͒ schemes of Wesolowski et al are also QM:QM models.…”

Quantum mechanical/molecular mechanical/continuum style solvation model: Linear response theory, variational treatment, and nuclear gradients

“…The energy gradients ͑forces and torques͒ for all EFP-EFP interactions, including the polarization energy, have been derived and implemented. 8,10,[12][13][14][15] When switching functions and periodic boundary conditions are applied, molecular dynamics ͑MD͒ simulations can be performed with EFP. 15 The QM/MM style EFP method was first developed for HF calculations and then extended to DFT ͓B3LYP ͑Ref.…”