Conical intersections of free energy surfaces in solution: Effect of electron correlation on a protonated Schiff base in methanol solution

The minimum energy conical intersection (MECI) optimization method with taking account of the dynamic electron correlation effect [T. Mori and S. Kato, Chem. Phys. Lett. 476, 97 (2009)] is extended to locate the MECI of nonequilibrium free energy surfaces in solution. A multistate electronic perturbation theory is introduced into the nonequilibrium free energy formula, which is defined as a function of solute and solvation coordinates. The analytical free energy gradient and interstate coupling vectors are derived, and are applied to locate MECIs in solution. The present method is applied to study the cis-trans photoisomerization reaction of a protonated Schiff base molecule (PSB3) in methanol (MeOH) solution. It is found that the effect of dynamic electron correlation largely lowers the energy of S1 state. We also show that the solvation effect strongly stabilizes the MECI obtained by twisting the terminal C=N bond to become accessible in MeOH solution, whereas the conical intersection is found to be unstable in gas phase. The present study indicates that both electron correlation and solvation effects are important in the photoisomerization reaction of PSB3. The effect of counterion is also examined, and seems to be rather small in solution. The structures of free energy surfaces around MECIs are also discussed.