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Orr L, Hernández de la Peña L, Roy PN. Formulation of state projected centroid molecular dynamics: Microcanonical ensemble and connection to the Wigner distribution. J Chem Phys. 2017;146(21):214116doi: 10.1063/1.4984229.
Orr, L., Hernández de la Peña, L., & Roy, P. N. (2017). Formulation of state projected centroid molecular dynamics: Microcanonical ensemble and connection to the Wigner distribution. The Journal of chemical physics, 146(21), 214116. https://doi.org/10.1063/1.4984229
Orr, Lindsay, et al. "Formulation of state projected centroid molecular dynamics: Microcanonical ensemble and connection to the Wigner distribution." The Journal of chemical physics vol. 146,21 (2017): 214116. doi: https://doi.org/10.1063/1.4984229
Orr L, Hernández de la Peña L, Roy PN. Formulation of state projected centroid molecular dynamics: Microcanonical ensemble and connection to the Wigner distribution. J Chem Phys. 2017 Jun 07;146(21):214116. doi: 10.1063/1.4984229. PMID: 28595402; PMCID: PMC5462618.
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J Chem Phys. 2017 Jun 07;146(21):214116. doi: 10.1063/1.4984229.

Formulation of state projected centroid molecular dynamics: Microcanonical ensemble and connection to the Wigner distribution.

The Journal of chemical physics

Lindsay Orr, Lisandro Hernández de la Peña, Pierre-Nicholas Roy

Affiliations

  1. Department of Chemistry, University of Waterloo, Waterloo, Ontario N2L 3G1, Canada.
  2. Department of Chemistry and Biochemistry, Kettering University, Flint, Michigan 48504, USA.

PMID: 28595402 PMCID: PMC5462618 DOI: 10.1063/1.4984229

Abstract

A derivation of quantum statistical mechanics based on the concept of a Feynman path centroid is presented for the case of generalized density operators using the projected density operator formalism of Blinov and Roy [J. Chem. Phys. 115, 7822-7831 (2001)]. The resulting centroid densities, centroid symbols, and centroid correlation functions are formulated and analyzed in the context of the canonical equilibrium picture of Jang and Voth [J. Chem. Phys. 111, 2357-2370 (1999)]. The case where the density operator projects onto a particular energy eigenstate of the system is discussed, and it is shown that one can extract microcanonical dynamical information from double Kubo transformed correlation functions. It is also shown that the proposed projection operator approach can be used to formally connect the centroid and Wigner phase-space distributions in the zero reciprocal temperature β limit. A Centroid Molecular Dynamics (CMD) approximation to the state-projected exact quantum dynamics is proposed and proven to be exact in the harmonic limit. The state projected CMD method is also tested numerically for a quartic oscillator and a double-well potential and found to be more accurate than canonical CMD. In the case of a ground state projection, this method can resolve tunnelling splittings of the double well problem in the higher barrier regime where canonical CMD fails. Finally, the state-projected CMD framework is cast in a path integral form.

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