Quantum effects in dynamics of nuclei
Quantum-mechanical effects in molecular dynamics are essential for accurate description and understanding of many chemical processes, such as those in surface reactions, photochemistry, in interactions of molecules with electric field, in chemistry of polymers, clusters and liquids. QM effects are the most pronounced in processes involving atomic and molecular hydrogen. For example, the isotope effects in water are manifested in such basic properties as melting point, which is 3.82C for the deuterated water, and the temperature of maximum density in liquid state, which is 4C for water and 11.2C for the deuterated water. Our theoretical work is guided by the ultimate goal -- to study dynamics of complex molecular systems using an accurate and efficient method which incorporates the nuclear  quantum effects and is compatible with classical molecular dynamics. Applications include the  proton transfer processes in enzymes and other bio- and nano-environments, the electron transport in open quantum systems, and properties of hybrid materials.  
The trajectory-based quantum dynamics
The time-dependent Schrodinger equation can be recast in terms of the wavefunction amplitude and phase associated with the trajectories evolving in time according to Hamilton's equations of motion. All quantum effects are expressed through the action of quantum potential dependent on the amplitude and its derivatives, acting on a trajectory in addition to the external "classical'' potential. For general problems, the exact determination of the quantum potential is at least as difficult as the solution of the standard Schrodinger equation. We develop global approximations to the quantum potential which capture the nuclear quantum effects (the zero-point energy, tunneling) in a computationally efficient manner. Our high-dimensional quantum trajectory code with on-the-fly force calculations has been applied to study the proton transfer in material (Fig. 1) and biological environments.   We are also developing  exact quantum methods such as the Quantum-Trajectory guided Adaptable Gaussian (QTAG) bases  (Fig. 2), and the Factorized electron-nuclear dynamics (FENDy). 
The Nuclear Quantum Effect in chemical systems
Recent experiments show that small effects in the changes in the zero-point energy of OH and OD affects properties of large molecular systems such as crystallization properties of P3HT this films (Fig. 3), photovoltaic properties of P3HT/CPBM blend developed for the solar cell applications, the proton conductance through atomically thin films of graphene, hexagonal boron nitride and others.  We are working closely with experimental groups, i.e. the  Shustova, L. Shimizu and C. Tang   groups at USC, and the Makris group at NC State University, investigating the properties of complex molecular systems  (Fig. 4) and mechanisms of the charge, energy, hydrogen (Fig. 5) and hydroxide transfer in complex molecular environments using chemical theory, computations and machine learning.