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Title: Molecular structure calculations: A unified quantum mechanical description of electrons and nuclei using explicitly correlated Gaussian functions and the global vector representation

Abstract

We elaborate on the theory for the variational solution of the Schroedinger equation of small atomic and molecular systems without relying on the Born-Oppenheimer paradigm. The all-particle Schroedinger equation is solved in a numerical procedure using the variational principle, Cartesian coordinates, parameterized explicitly correlated Gaussian functions with polynomial prefactors, and the global vector representation. As a result, non-relativistic energy levels and wave functions of few-particle systems can be obtained for various angular momentum, parity, and spin quantum numbers. A stochastic variational optimization of the basis function parameters facilitates the calculation of accurate energies and wave functions for the ground and some excited rotational-(vibrational-)electronic states of H{sub 2}{sup +} and H{sub 2}, three bound states of the positronium molecule, Ps{sub 2}, and the ground and two excited states of the {sup 7}Li atom.

Authors:
;  [1]
  1. Laboratory of Physical Chemistry, ETH Zuerich, Wolfgang-Pauli-Str. 10, CH-8093 Zuerich (Switzerland)
Publication Date:
OSTI Identifier:
22098915
Resource Type:
Journal Article
Journal Name:
Journal of Chemical Physics
Additional Journal Information:
Journal Volume: 137; Journal Issue: 2; Other Information: (c) 2012 American Institute of Physics; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 0021-9606
Country of Publication:
United States
Language:
English
Subject:
74 ATOMIC AND MOLECULAR PHYSICS; 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; BORN-OPPENHEIMER APPROXIMATION; BOUND STATE; CARTESIAN COORDINATES; GAUSS FUNCTION; GROUND STATES; HYDROGEN; HYDROGEN IONS 2 PLUS; LITHIUM 7; MOLECULAR STRUCTURE; NUMERICAL ANALYSIS; POLYNOMIALS; POSITRONIUM; QUANTUM MECHANICS; QUANTUM NUMBERS; ROTATIONAL STATES; SCHROEDINGER EQUATION; SPIN; VIBRATIONAL STATES; WAVE FUNCTIONS

Citation Formats

Matyus, Edit, and Reiher, Markus. Molecular structure calculations: A unified quantum mechanical description of electrons and nuclei using explicitly correlated Gaussian functions and the global vector representation. United States: N. p., 2012. Web. doi:10.1063/1.4731696.
Matyus, Edit, & Reiher, Markus. Molecular structure calculations: A unified quantum mechanical description of electrons and nuclei using explicitly correlated Gaussian functions and the global vector representation. United States. doi:10.1063/1.4731696.
Matyus, Edit, and Reiher, Markus. Sat . "Molecular structure calculations: A unified quantum mechanical description of electrons and nuclei using explicitly correlated Gaussian functions and the global vector representation". United States. doi:10.1063/1.4731696.
@article{osti_22098915,
title = {Molecular structure calculations: A unified quantum mechanical description of electrons and nuclei using explicitly correlated Gaussian functions and the global vector representation},
author = {Matyus, Edit and Reiher, Markus},
abstractNote = {We elaborate on the theory for the variational solution of the Schroedinger equation of small atomic and molecular systems without relying on the Born-Oppenheimer paradigm. The all-particle Schroedinger equation is solved in a numerical procedure using the variational principle, Cartesian coordinates, parameterized explicitly correlated Gaussian functions with polynomial prefactors, and the global vector representation. As a result, non-relativistic energy levels and wave functions of few-particle systems can be obtained for various angular momentum, parity, and spin quantum numbers. A stochastic variational optimization of the basis function parameters facilitates the calculation of accurate energies and wave functions for the ground and some excited rotational-(vibrational-)electronic states of H{sub 2}{sup +} and H{sub 2}, three bound states of the positronium molecule, Ps{sub 2}, and the ground and two excited states of the {sup 7}Li atom.},
doi = {10.1063/1.4731696},
journal = {Journal of Chemical Physics},
issn = {0021-9606},
number = 2,
volume = 137,
place = {United States},
year = {2012},
month = {7}
}