Anharmonic Rovibrational Partition Functions for Fluxional Species at High Temperatures via Monte Carlo Phase Space Integrals

The vibrational and rovibrational partition functions of diatomic molecules are considered in the regime of intermediate temperatures. The low temperatures are those at which the harmonic oscillator approximation is appropriate, and the high temperatures are those at which classical partition function (with Wigner–Kirkwood correction) is applicable. The complementarity of the harmonic oscillator and classical integration over the phase space approaches is investigated for the CO and H2+ molecules showing that those two approaches are complementary in the sense that they smoothly overlap.

Download Full-text

Hamilton-Jacobi Theory

10.1093/oso/9780198822370.003.0019 ◽

2018 ◽

Author(s):

Peter Mann

Keyword(s):

Phase Space ◽

Bbgky Hierarchy ◽

Distribution Functions ◽

Symplectic Integrators ◽

Partition Functions ◽

Von Neumann ◽

Equipartition Theorem ◽

Recurrence Theorem ◽

Phase Amplitude ◽

Canonical Ensembles

This chapter focuses on Liouville’s theorem and classical statistical mechanics, deriving the classical propagator. The terms ‘phase space volume element’ and ‘Liouville operator’ are defined and an n-particle phase space probability density function is constructed to derive the Liouville equation. This is deconstructed into the BBGKY hierarchy, and radial distribution functions are used to develop n-body correlation functions. Koopman–von Neumann theory is investigated as a classical wavefunction approach. The chapter develops an operatorial mechanics based on classical Hilbert space, and discusses the de Broglie–Bohm formulation of quantum mechanics. Partition functions, ensemble averages and the virial theorem of Clausius are defined and Poincaré’s recurrence theorem, the Gibbs H-theorem and the Gibbs paradox are discussed. The chapter also discusses commuting observables, phase–amplitude decoupling, microcanonical ensembles, canonical ensembles, grand canonical ensembles, the Boltzmann factor, Mayer–Montroll cluster expansion and the equipartition theorem and investigates symplectic integrators, focusing on molecular dynamics.

Download Full-text

A phase‐space theory and Monte Carlo sampling method for studying nonadiabatic unimolecular reactions

The Journal of Chemical Physics ◽

10.1063/1.462092 ◽

1992 ◽

Vol 96 (3) ◽

pp. 1911-1918 ◽

Cited By ~ 24

Author(s):

Alison J. Marks ◽

Donald L. Thompson

Keyword(s):

Monte Carlo ◽

Phase Space ◽

Sampling Method ◽

Monte Carlo Sampling ◽

Space Theory ◽

Unimolecular Reactions ◽

Phase Space Theory

Download Full-text

TI/PIMC METHOD WITH THE TAKAHASHI–IMADA APPROXIMATION FOR THE EQUILIBRIUM CONSTANT OF THE O + HCl ⇌ OH + Cl REACTION

Journal of Theoretical and Computational Chemistry ◽

10.1142/s0219633613500260 ◽

2013 ◽

Vol 12 (04) ◽

pp. 1350026 ◽

Cited By ~ 1

Author(s):

MARCIN BUCHOWIECKI

Keyword(s):

Monte Carlo ◽

Temperature Dependence ◽

Equilibrium Constant ◽

Path Integral ◽

Thermodynamic Integration ◽

Partition Functions ◽

Integration Path ◽

Path Integral Monte Carlo

The thermodynamic integration/path integral Monte Carlo (TI/PIMC) method of calculating the temperature dependence of the equilibrium constant quantum mechanically is applied to O + HCl ⇌ OH + Cl reaction. The method is based upon PIMC simulations for energies of the reactants and the products and subsequently on thermodynamic integration for the ratios of partition functions. PIMC calculations are performed with the primitive approximation (PA) and the Takahashi–Imada approximation (TIA).

Download Full-text