Clarification of nonadiabatic chemical dynamics by the Zhu-Nakamura theory of nonadiabatic transition: from tri-atomic systems to reactions in solutions

It is now confirmed that the Zhu-Nakamura (ZN) theory of nonadiabatic transition is useful to investigate various nonadiabatic chemical dynamics. The theory, being one-dimensional, presents a whole set of analytical formulas that enables us to treat the dynamics efficiently. It is also quite significant that classically forbidden transitions can be dealt with analytically. The theory can be combined with the trajectory surface hopping (TSH) method (ZN-TSH) and is demonstrated to be useful to clarify the dynamics of not only simple tri-atomic reactions but also large chemical systems. The whole set of analytical formulas directly applicable to practical systems is summarised and the applications to polyatomic systems are illustrated. Examples of polyatomic molecules are H2SO4, NH3, indolylmaleimide, cyclohexadiene (CHD), and retinal. The Fortran code for the whole set of ZN formulas is provided in Appendix for the convenience of a reader who is interested in using them. The ZN-TSH method can be combined with the QM/MM method to clarify reaction dynamics in the surrounding environment. This is named as ZN-QM/MM-TSH. The particle-mesh Ewald (PME) method can also be combined with ZN-TSH to clarify reaction dynamics in solutions. This is named as ZN-PME-TSH. Formulations of these methods are presented together with practical applications. Examples treated by ZN-QM/MMTSH are photoisomerization dynamics of retinal chromophore embedded in the protein environment. The differences in the isomerization mechanisms between rhodopsin and isorhodopsin are made clear. The faster and more efficient isomerization of rhodopsin compared to isorhodopsin is nicely reproduced. Examples of reactions in solutions are photoisomerizations of retinal and CHD. The experimentally observed long life time of the excited state of retinal is reproduced and is found to be due to the long-range solvation effect. The solvent dependent branching ratios of CHD: hexatriene (HT) are clarified for the ethanol and hexane solvents by the ZN-PME-TSH method. Both ZN-QM/MM-TSH and ZN-PME-TSH are thus demonstrated to be promising methods to deal with a wide range of nonadiabatic dynamics in large chemical and biological systems.