  An approximate approach to quantum vibrational dynamics, "Brownian Chain
Molecular Dynamics (BCMD)", is proposed to alleviate the chain resonance and
curvature problems in the imaginary time-based path integral (PI) simulation.
Here the non-centroid velocity is randomized at each step when solving the
equation of motion of path integral molecular dynamics. This leads to a
combination of the Newton equation and the overdamped Langevin equation for the
centroid and non-centroid variables, respectively. BCMD shares the basic
properties of other PI approaches such as centroid and ring polymer molecular
dynamics: It gives the correct Kubo-transformed correlation function at short
times, conserves the time symmetry, has the correct high-temperature/classical
limits, gives exactly the position and velocity autocorrelations of harmonic
oscillator systems, and does not have the zero-point leakage problem. Numerical
tests were done on simple molecular models and liquid water. On-the-fly ab
initio BCMD simulations were performed for the protonated water cluster,
H$_5$O$_2^+$, and its isotopologue, D$_5^{}$O$_2^+$.
