A noniterative mean‐field QM/MM‐type approach with a linear response approximation toward an efficient free‐energy evaluation

Abstract

Mean‐field treatment of solvent provides an efficient technique to investigate chemical processes in solution in quantum mechanics/molecular mechanics (QM/MM) framework. In the algorithm, an iterative calculation is required to obtain the self‐consistency between QM and MM regions, which is a time‐consuming step. In the present study, we have proposed a noniterative approach by introducing a linear response approximation (LRA) into the solvation term in the one‐electron part of Fock matrix in a hybrid approach between molecular‐orbital calculations and a three‐dimensional (3D) integral equation theory for molecular liquids (multicenter molecular Ornstein–Zernike self‐consistent field [MC‐MOZ‐SCF]; Kido et al., J. Chem. Phys. 2015, 143, 014103). To save the computational time, we have also developed a fast method to generate electrostatic potential map near solute and the solvation term in Fock matrix, using Fourier transformation (FT) and real spherical harmonics expansion (RSHE). To numerically validate the LRA and FT‐RSHE method, we applied the present approach to water, carbonic acid, and their ionic species in aqueous solution. Molecular properties of the solutes were evaluated by the present approach with four different types of initial wave functions and compared with those by the original (MC‐MOZ‐SCF). We found that an initial wave function considering solvation effects is needed to appropriately reproduce the properties by MC‐MOZ‐SCF. Furthermore, a benchmark test for 32 solute molecules was performed to evaluate the accuracy of the present approach for solvation free energy (SFE) and measure the speedup ratio for MC‐MOZ‐SCF. The error of SFE for MC‐MOZ‐SCF does not correlate with the SFE but increases in proportion to the electronic reorganization energy. Similar to water and carbonic acid, an initial wave function with solvation effects is also important to make the error small. From the averaged speed up ratio, the present approach is 13.5 times faster than MC‐MOZ‐SCF. © 2019 Wiley Periodicals, Inc.

Conformation, hydration, and ligand exchange process of ruthenium nitrosyl complexes in aqueous solution: Free‐energy calculations by a combination of molecular‐orbital theories and different solvent models

“…To overcome it, we employ multicenter molecular Ornstein-Zernike self-consistent field (MC-MOZ-SCF) 52,53 method, which is a combination between MO theories (solute) and MC-MOZ [54][55][56] (solvent). MC-MOZ is an explicit solvent model based on the integral equation theory for molecular liquids [57][58][59][60] and describes the solvent as a density distribution function.…”

“…Furthermore, a free energy of solute is readily evaluated by the analytical expression of the distribution function obtained by solving the MC-MOZ equation. 52,53,61,62 Thanks to it, compared with a free-energy calculation by conventional QM/MM using molecular simulation techniques, we can perform the procedure with a very low computational cost. Hence, we can choose a sophisticated method such as MP2 and CCSD(T) in the QM region.…”

“…Previous studies show that the method provides an accurate solvation free energy (SFE) for small molecules and ions in several solvents. 53,63 In this study, we select a noniterative version of MC-MOZ-SCF method. 53 It provides a similar result to the original within an acceptable error in shorter computational time.…”

“…53,63 In this study, we select a noniterative version of MC-MOZ-SCF method. 53 It provides a similar result to the original within an acceptable error in shorter computational time. For a comparison, PCM is also used for the solvation energy evaluation.…”

“…As shown later, the method also provides the three‐dimensional (3D) solvation structure near solute. Furthermore, a free energy of solute is readily evaluated by the analytical expression of the distribution function obtained by solving the MC‐MOZ equation 52,53,61,62 . Thanks to it, compared with a free‐energy calculation by conventional QM/MM using molecular simulation techniques, we can perform the procedure with a very low computational cost.…”