Classical mapping for second-order quantized Hamiltonian dynamics

Second-order quantized Hamiltonian dynamics (QHD-2) is mapped onto classical mechanics by doubling the dimensionality. The mapping establishes the classical canonical structure for QHD-2 and permits its application to problems showing zero-point energy and tunneling via a standard molecular dynamics simulation, without modifying the simulation algorithms, by introducing new potentials for the extra variables. The mapping is applied to the family of Gaussian approximations, including frozen and thawed Gaussians, which are special cases of QHD-2. The mapping simplifies numerous applications of Gaussians to simulations of spectral intensities and line shapes, nonadiabatic and other quantum phenomena. The analysis shows that frozen Gaussians conserve the total energy, while thawed Gaussians do not, unless an additional term is introduced to the equation of motion for the thawed Gaussian momentum. The classical mapping of QHD-2 is illustrated by tunneling and zero-point energy effects in the harmonic oscillator, cubic and double-well potential, and the Morse oscillator representing the O-H stretch of the SPC-F water model. (C) 2002 American Institute of Physics.