  To take into account nuclear quantum effects on the dynamics of atoms, the
path integral molecular dynamics (PIMD) method used since 1980s is based on the
formalism developed by R. P. Feynman. However, the huge computation time
required for the PIMD reduces its range of applicability. Another drawback is
the requirement of additional techniques to access time correlation functions
(ring polymer MD or centroid MD). We developed an alternative technique based
on a quantum thermal bath (QTB) which reduces the computation time by a factor
of ~20. The QTB approach consists in a classical Langevin dynamics in which the
white noise random force is replaced by a Gaussian random force having the
power spectral density given by the quantum fluctuation-dissipation theorem.
The method has yielded satisfactory results for weakly anharmonic systems: the
quantum harmonic oscillator, the heat capacity of a MgO crystal, and isotope
effects in 7 LiH and 7 LiD. Unfortunately, the QTB is subject to the problem of
zero-point energy leakage (ZPEL) in highly anharmonic systems, which is
inherent in the use of classical mechanics. Indeed, a part of the energy of the
high-frequency modes is transferred to the low-frequency modes leading to a
wrong energy distribution. We have shown that in order to reduce or even
eliminate ZPEL, it is sufficient to increase the value of the frictional
coefficient. Another way to solve the ZPEL problem is to combine the QTB and
PIMD techniques. It requires the modification of the power spectral density of
the random force within the QTB. This combination can also be seen as a way to
speed up the PIMD.
