Chin SA. Analytical evaluations of the path integral Monte Carlo thermodynamic and Hamiltonian energies for the harmonic oscillator.
J Chem Phys 2023;
159:244104. [PMID:
38131478 DOI:
10.1063/5.0181447]
[Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/16/2023] [Accepted: 12/04/2023] [Indexed: 12/23/2023] Open
Abstract
By using the recently derived universal discrete imaginary-time propagator of the harmonic oscillator, both thermodynamic and Hamiltonian energies can be given analytically and evaluated numerically at each imaginary time step for any short-time propagator. This work shows that, using only currently known short-time propagators, the Hamiltonian energy can be optimized to the twelfth-order, converging to the ground state energy of the harmonic oscillator in as few as three beads. This study makes it absolutely clear that the widely used second-order primitive approximation propagator, when used in computing thermodynamic energy, converges extremely slowly with an increasing number of beads.
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