Analytical energy gradient for the second-order Møller–Plesset perturbation theory coupled with the reference interaction site model self-consistent field explicitly including spatial electron density distribution

Abstract

Solvatochromic shifts of the activation free energies are important aspects to consider for reaction control. To predict the energies, the stationary points in a solution must be accurately determined along the reaction pathway. In this study, the second-order Møller–Plesset perturbation (MP2) theory combined with the reference interaction site model was applied using our fitting approach, and the MP2 analytical energy gradient was determined. The coupled-cluster energy and thermal correction were calculated using the MP2 optimized geometry with solvent effect, and the activation free energies of the Diels–Alder reaction between cyclopentadiene and methyl vinyl ketone are within an error of 2 kcal/mol compared with the experimental data.

Accurate Absorption Energy Calculations in Solution Using the Reference Interaction Site Model Self-Consistent Field Including the Constrained Spatial Electron Density Distribution

“…[G] with various quantum chemical approaches [5,13,15,25,27,28]. When the density functional theory (DFT) is employed, (2) is given by…”

“…where H core and F are the core Hamiltonian and the Fock matrix defined in the gas phase. The solvated Kohn-Sham equation can be obtained by taking the derivative of (3) with respect to the molecular orbital coefficients C. The free energy gradient was also derived [12,15,28] by taking the derivative of (3) with respect to the atomic coordinates. When calculating the excited state in solution, the dynamics of the solvent molecules in excitation must be considered.…”

“…The geometries of molecules in a solution were optimized using the second order Møller-Plesset perturbation theory (MP2) coupled with RISM-SCF-cSED [28]. Figure 1 presents the atomic labels of DAPDA.…”

Description of Solvatochromism of Peak Broadening in Absorption Spectra in Solution Using the Reference Interaction Site Model Self-Consistent Fields Spatial Electron Density Distribution

“…The may-cc-pv­(t+d)­z − basis sets were employed for all atoms. The optimized geometries and seminumerical Hessian matrices for the electronically ground state used in the RISM calculations were computed using the Møller–Plesset second-order perturbation theory at 298.15 K in the respective solutions using the GAMESS program package. , To calculate the seminumerical Hessian, we input the difference between the Cartesian coordinate as 0.01 Bohr. GAMESS was also employed to calculate the absorption energies using 8 States MS-XMCQDPT2­(9,12), where the reference states were optimized using the 8 State-Averaged CASSCF method coupled with RISM .…”

Vibrational Self-Consistent Field (VSCF) and Post-VSCF Method Calculations Combined with the Reference Interaction Site Model Self-Consistent Field Method Coupled with the Constrained Spatial Electron Density Distribution: Applications to NaHCOO in Aqueous Phase

“…To address these challenges, we have developed quantum chemical computations using the reference interaction site model self-consistent field method in conjunction with the constrained spatial electron density distribution (RISM–SCF–cSED). , This method combines principles from both quantum and statistical mechanics and has demonstrated versatility across various solvent systems, encompassing protic and aprotic solvents and supercritical water (SCW) systems. − In a previous investigation, we successfully expounded upon the minor nonlinear Raman shift (∼10 cm –1 ) observed in the CN stretching vibration of p -aminobenzonitrile ( p -ABN) relative to the reduced density of SCW . Additionally, we elucidated the changes in Raman intensity exhibited by p -nitroaniline ( p NA) under different solvent environments, including SCW …”