Quantum Dynamics

We were the first to develop a practical quantum dynamics method satisfying the two critical fundamental criteria: conservation of the quantum Boltzmann distribution for the thermal equilibrium system and being exact for any thermal correlation functions (of even nonlinear operators, i.e., nonlinear functions of position or momentum operators) in the classical and harmonic limits. The so-called path integral Liouville dynamics (PILD) [J. Chem. Phys. 140, 224107 (2014)] was derived from the elaborate combination of the imaginary time path integral and the three new theoretical frameworks that we formulated for generating trajectory-based dynamics methods in the quantum phase space [J. Chem. Phys. 134, 104101 (2011); 134, 104102 (2011); 134, 194110 (2011). Scientia Sinica Chimica, 46, 27 (2016)].

PILD was applied to vibrational dynamics of several simple but representative realistic molecular systems (OH, water, ammonia, and methane) [J. Chem. Phys. 144, 034307 (2016)]. The dipole-derivative autocorrelation function was employed to obtain the infrared spectrum as a function of temperature and isotopic substitution. Comparison to the exact vibrational frequency shows that PILD produces a reasonably accurate peak position with a relatively small full width at half maximum. PILD offers a potentially useful trajectory-based quantum dynamics approach to compute vibrational spectra of molecular systems. We are extending the approach to study larger systems.

The relevant peer-reviewed papers are

1. “Path integral Liouville dynamics for thermal equilibrium systems”

   Jian Liu*

   Journal of Chemical Physics, 140, 224107 (2014)

   https://doi.org/10.1063/1.4881518

   Note: In the article we propose a practical quantum dynamics method satisfying the two critical fundamental criteria: conservation of the quantum Boltzmann distribution for the thermal equilibrium system and being exact for any thermal correlation functions (of even nonlinear operators, i.e., nonlinear functions of position or momentum operators) in the classical and harmonic limits.

2. "Further study of path integral Liouville dynamics"

   Jian Liu*, Dezhang Li, Xinzijian Liu

   Scientia Sinica Chimica, 46, 27 (2016)

   [Invited article for the special issue for the Festschrift for Professor Lemin Li's 80th birthday]

   http://dx.doi.org/10.1360/N032015-00143

   Note: In the article we show how to derive PILD from each of the three frameworks in the phase space formulation of quantum mechanics which we formulated in 2011.

3. "Path integral Liouville dynamics: Applications to infrared spectra of OH, water, ammonia, and methane"

   Jian Liu*, Zhijun Zhang

   Journal of Chemical Physics, 144, 034307 (2016)

   http://dx.doi.org/10.1063/1.4939953

   Note: In the article we apply PILD to study vibrational dynamics of several simple but representative realistic molecular systems, which demonstrates that PILD offers a potentially useful trajectory-based quantum dynamics approach to compute vibrational spectra of molecular systems.