## Ⅲ. QUANTUM DYNAMICS CALCULATIONS

### 1. PROTON TRANSFER REACTION IN SOLUTIONS AND BIOSYSTEMS

Mixed quantum-classical molecular dynamics calculations have been done for proton transfer reaction in solutions. Tunneling and vibrational excitation mechanisms have been analyzed for a molecule in water and nonpolar solvent focusing our attention on the role of solvent molecules. In the calculations, time-dependent Schrödinger equation is solved numerically assuming surface hopping and averaged field.

Fig. Schematic picture of the proton transfer reaction in solutions. Thermal activation process (blue) starts with vibrational excitation followed by the transfer to the product state and ends with vibrational relaxation. Tunneling process (red) takes place suddenly even when the system is in the ground state of the reaction system of interest.

### 2. VIBRATIONAL RELAXATION IN SOLUTIONS

Vibrational relaxation and vibrational decoherence between states have been investigated based on path integral influence functional theory. Mixed quantum-classical molecular dynamics calculation has also been applied to analyze the vibrational relaxation. The figure shows a calculated quantum beat of phonon of metal atoms absorbed on the surface of other metal substrate, in collaboration with experiment group, Prof. Matsumoto at Kyoto University, and electronic state theory group, Prof. Yamashita at Tokyo University.

Fig. Calculated quantum beat for the decoherence of superposition state of phonon formed by metal atoms absorbed on the surface of other metal substrate.