Zero point energy leakage in condensed phase dynamics: An assessment of quantum simulation methods for liquid water

Abstract

The approximate quantum mechanical ring polymer molecular dynamics (RPMD) and linearized semiclassical initial value representation (LSC-IVR) methods are compared and contrasted in a study of the dynamics of the flexible q-TIP4P/F water model at room temperature. For this water model, a RPMD simulation gives a diffusion coefficient that is only a few percent larger than the classical diffusion coefficient, whereas a LSC-IVR simulation gives a diffusion coefficient that is three times larger. We attribute this discrepancy to the unphysical leakage of initially quantized zero point energy (ZPE) from the intramolecular to the intermolecular modes of the liquid as the LSC-IVR simulation progresses. In spite of this problem, which is avoided by construction in RPMD, the LSC-IVR may still provide a useful approximation to certain short-time dynamical properties which are not so strongly affected by the ZPE leakage. We illustrate this with an application to the liquid water dipole absorption spectrum, for which the RPMD approximation breaks down at frequencies in the O-H stretching region owing to contamination from the internal modes of the ring polymer. The LSC-IVR does not suffer from this difficulty and it appears to provide quite a promising way to calculate condensed phase vibrational spectra.

Nuclear Quantum Effects in Water and Aqueous Systems: Experiment, Theory, and Current Challenges

“…4.1) to construct initial configurations consistent with quantum statistics, from which approximate trajectories are then initiated to calculate the relevant time correlation function for the dynamical property of interest. Linearized semi-classical initial value representation methods use Newtonian dynamics to evolve these trajectories in time (212)(213)(214)(215), which in the case of liquid water has been shown to be seriously affected by issues arising from unphysical ZPE leakage (216). Very recently, a modified formulation of this approach, Matsubara dynamics, has been introduced that preserves detailed balance and might help formulate more rigorous approximations of quantum dynamics (217,218).…”

Accelerating the convergence of path integral dynamics with a generalized Langevin equation

“…When applying this idea to a multidimensional system one faces the problem of zero-point energy leakage. 22 Anharmonic coupling causes a flow of heat from high-frequency to low-frequency vibrations and a departure from the desired behavior in Eq. (10).…”

Deriving the exact nonadiabatic quantum propagator in the mapping variable representation

“…Although these methods have been very successful at investigating non-adiabatic systems, [19,[23][24][25][26][27][28][29][30]49] and provide ways to systematically improve the dynamics [50], truncation to finite powers in does not generally mean that the error in the overall correlation function scales as O( ). [47] In addition, the dynamics does not normally conserve the quantum Boltzmann distribution, which can lead to spurious effects in numerical simulations [51]. Nevertheless, for a single electronic surface, semiclassical methods have recently been developed whereby classical trajectories conserve the quantum Boltzmann distribution [42].…”