Analytical energy gradient for the reference interaction site model multiconfigurational self-consistent-field method: Application to 1,2-difluoroethylene in aqueous solution

Abstract

We have reformulated the reference interaction site model self-consistent-field (RISM-SCF) method to calculate the molecular properties of solute in solutions. The key feature is to introduce the Helmholtz free energy given as a sum of the solute electronic energy estimated by ab initio molecular orbital (MO) methods and the hypernetted-chain (HNC) excess chemical potential of solvation for the extended reference interaction site model (XRISM) method. The variational conditions for the multiconfigurational self-consistent-field (MCSCF) wave functions were derived. It was also shown that, in the case of the Hartree–Fock (HF) method, the present expression gives the same Fock matrix defined previously. Moreover the expression for first derivatives of the free energy with respect to the solute nuclear coordinates were obtained. Sample calculations for the chemical equilibrium of cis- and trans-isomers of 1,2-difluoroethylene are presented. With the use of analytical energy gradients for the MCSCF and HF methods, the solute molecular geometries were determined in an aqueous solution.

Solvent Effects on Electronic Structures of Coumarin 153: Parallel Studies by Means of Spectroscopy and RISM-SCF Calculations

“…The framework of RISM-SCF theory is detailed elsewhere. 10,11) In the present study, the RISM-SCF method was implemented into the GAMESS package for the electronic structure calculations. 12,13) In the RISM-SCF calculations, we need not to have solute charges as parameters because the electrostatic potential will be derived based on the electron densities of the solute.…”

Analytical free energy gradient for the molecular Ornstein-Zernike self-consistent-field method

“…In order to perform the geometry optimization for solvated molecule, the analytical energy gradient is introduced by a similar procedure described in reference [12]. The first derivative of the free energy with respect to the nuclear coordinate of the solute molecule R a is written as (12)+η (12) ∂η (12) ∂R a ω1ω2…”

“…The derivatives of u core (12) and u elec,a ij (12) are easily calculated in the same way as the other derivatives. In this study, since the polarizability tensor and the ionization energies of solute molecule are assumed to be constants, the derivatives of the dispersion energy are zero.…”

“…An analytical expression of the free energy gradients in the RISM-SCF formalism was proposed by Sato et al [12,13]. They have reformulated the RISM-SCF equations with the use of the free-energy expression introduced by Singer and Chandler [14].…”

Overview of Japanese science Grid project NAREGI

“…5 illustrates one example of coupled simulation. In this case, two application programs, the fragment molecular orbital method (FMO) and the reference interaction site model (RISM) [11] are coupled, where the quantum behavior of a molecule under the influence of a solvent is simulated by using the Grid middleware called Mediator.…”