Quantum-classical molecular dynamics and its computer implementation

Quantum-classical and quantum-stochastic molecular dynamics (QCMD/QSMD) models are formulated and applied for quantum proton transfer processes. The protein dynamics are described by the time-dependent Schroedinger equation and the motion of classical atoms by the Newtonian or Langevin equations of motion. Instantaneous positions of the classical atoms determine the potential energy surface for the proton dynamics. In turn, the proton wavefunction influences the classical atoms through nonstationary Hellmann-Feynman forces (Bala et al., 1994c). The QCMD/QSMD algorithm is described and numerical results for a proton-bound ammonia-ammonia dimer and an enzyme, phospholipase A₂, are presented. In the case of the enzyme molecule a valence-bond orbital method is used to compute the potential energy function for the proton transfer. The methods are found to be promising tools in studies of molecular and enzymatic reactions in which quantum-dynamical effects cannot be neglected.