Normal-ordered second-quantized Hamiltonian for molecular vibrations

Journal Article · Fri Nov 14 04:00:00 EST 2014 · Journal of Chemical Physics

DOI:https://doi.org/10.1063/1.4901061· OSTI ID:22415343

Hirata, So ^[1]; Hermes, Matthew R. ^[1]

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1. Department of Chemistry, University of Illinois at Urbana-Champaign, 600 South Mathews Avenue, Urbana, Illinois 61801 (United States)

A normal-ordered second-quantized form of the Hamiltonian is derived for quantum dynamics in a bound potential energy surface expressed as a Taylor series in an arbitrary set of orthogonal, delocalized coordinates centered at an arbitrary geometry. The constant, first-, and second-order excitation amplitudes of this Hamiltonian are identified as the ground-state energy, gradients, and frequencies, respectively, of the size-extensive vibrational self-consistent field (XVSCF) method or the self-consistent phonon method. They display the well-defined size dependence of V{sup 1−n/2}, where V is the volume and n is the number of coordinates associated with the amplitudes. It is used to rapidly derive the equations of XVSCF and vibrational many-body perturbation methods with the Møller–Plesset partitioning of the Hamiltonian.

• OSTI ID: 22415343
• Journal Information: Journal of Chemical Physics, Journal Name: Journal of Chemical Physics Journal Issue: 18 Vol. 141; ISSN JCPSA6; ISSN 0021-9606
• Country of Publication: United States
• Language: English

Related Subjects

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CHEMISTRY
97 MATHEMATICS AND COMPUTING
DISTURBANCES
EXCITATION
GROUND STATES
HAMILTONIANS
PERTURBATION THEORY
PHONONS
SELF-CONSISTENT FIELD