Proton transfer reactions in nanomaterials and biomolecules: Proton transfer is the key to understanding many phenomena in nanochemistry and biology. Quantum-classical methods have been developed to solve general transport properties and applied to proton transfer reactions in nanomaterials and biomolecules. One of major findings is that the reaction rates are strongly influenced by nonadiabaticity, quantum structure descriptions, and kinetic isotope effects.

Intramolecular electron transfer reactions in polar solvents: Electron transfer reactions in a large molecule in polar solvents are fascinating but challenging problems since the electronic structure of a solute involving many solvent molecules should be accurately calculated. Large-scale quantum simulations of intramolecular electron transfer of a dye molecule in solvents have been performed. Obtaining results comparable to experimental values, multiple high-frequency quantum modes as well as low-frequency modes are proved to play a crucial role in the electron transfer as many theorists predicted.

 Evaluation of quantum effects using only classical data: Discovering relations between quantum and classical correction functions, an efficient quantum correction approach has been proposed to provide very accurate results using classical data in many quantum problems including vibrational energy relaxations, nonlinear oscillators, and nonadiabatic transitions.

Diffusion-influenced biomolecular reactions: Numerous in vivo biomolecular reactions are influenced by diffusion. I discovered exact analytical solutions of many diffusion-influenced reaction problems including a reversible pair, the reversible trapping, an excited-state pair in field, and Michaelis-Menten kinetics. The exact solutions are employed to devise Brownian dynamics simulation methods that can provide numerically exact results useful for many biomolecular and polymer problems in liquids, surfaces, and interfaces.