An algorithm for nonrelativistic quantum-mechanical finite-nuclear-mass variational calculations of nitrogen atom in L = 0, M = 0 states using all-electrons explicitly correlated Gaussian basis functions

Keeper L. Sharkey, Ludwik Adamowicz

Research output: Contribution to journalArticle

7 Citations (Scopus)

Abstract

An algorithm for quantum-mechanical nonrelativistic variational calculations of L = 0 and M = 0 states of atoms with an arbitrary number of s electrons and with three p electrons have been implemented and tested in the calculations of the ground 4S state of the nitrogen atom. The spatial part of the wave function is expanded in terms of all-electrons explicitly correlated Gaussian functions with the appropriate pre-exponential Cartesian angular factors for states with the L = 0 andM= 0 symmetry. The algorithm includes formulas for calculating the Hamiltonian and overlap matrix elements, as well as formulas for calculating the analytic energy gradient determined with respect to the Gaussian exponential parameters. The gradient is used in the variational optimization of these parameters. The Hamiltonian used in the approach is obtained by rigorously separating the center-of-mass motion from the laboratory-frame all-particle Hamiltonian, and thus it explicitly depends on the finite mass of the nucleus. With that, the mass effect on the total ground-state energy is determined.

Original languageEnglish (US)
Article number1747112
JournalThe Journal of Chemical Physics
Volume140
Issue number17
DOIs
StatePublished - May 7 2014

Fingerprint

Hamiltonians
nitrogen atoms
Nitrogen
Atoms
Electrons
Ground state
gradients
electrons
ground state
center of mass
Wave functions
wave functions
optimization
nuclei
energy
symmetry
matrices
atoms

ASJC Scopus subject areas

  • Physics and Astronomy(all)
  • Physical and Theoretical Chemistry

Cite this

@article{45d6aff171b54bed9a5100b1af2df8b6,
title = "An algorithm for nonrelativistic quantum-mechanical finite-nuclear-mass variational calculations of nitrogen atom in L = 0, M = 0 states using all-electrons explicitly correlated Gaussian basis functions",
abstract = "An algorithm for quantum-mechanical nonrelativistic variational calculations of L = 0 and M = 0 states of atoms with an arbitrary number of s electrons and with three p electrons have been implemented and tested in the calculations of the ground 4S state of the nitrogen atom. The spatial part of the wave function is expanded in terms of all-electrons explicitly correlated Gaussian functions with the appropriate pre-exponential Cartesian angular factors for states with the L = 0 andM= 0 symmetry. The algorithm includes formulas for calculating the Hamiltonian and overlap matrix elements, as well as formulas for calculating the analytic energy gradient determined with respect to the Gaussian exponential parameters. The gradient is used in the variational optimization of these parameters. The Hamiltonian used in the approach is obtained by rigorously separating the center-of-mass motion from the laboratory-frame all-particle Hamiltonian, and thus it explicitly depends on the finite mass of the nucleus. With that, the mass effect on the total ground-state energy is determined.",
author = "Sharkey, {Keeper L.} and Ludwik Adamowicz",
year = "2014",
month = "5",
day = "7",
doi = "10.1063/1.4873916",
language = "English (US)",
volume = "140",
journal = "Journal of Chemical Physics",
issn = "0021-9606",
publisher = "American Institute of Physics Publising LLC",
number = "17",

}

TY - JOUR

T1 - An algorithm for nonrelativistic quantum-mechanical finite-nuclear-mass variational calculations of nitrogen atom in L = 0, M = 0 states using all-electrons explicitly correlated Gaussian basis functions

AU - Sharkey, Keeper L.

AU - Adamowicz, Ludwik

PY - 2014/5/7

Y1 - 2014/5/7

N2 - An algorithm for quantum-mechanical nonrelativistic variational calculations of L = 0 and M = 0 states of atoms with an arbitrary number of s electrons and with three p electrons have been implemented and tested in the calculations of the ground 4S state of the nitrogen atom. The spatial part of the wave function is expanded in terms of all-electrons explicitly correlated Gaussian functions with the appropriate pre-exponential Cartesian angular factors for states with the L = 0 andM= 0 symmetry. The algorithm includes formulas for calculating the Hamiltonian and overlap matrix elements, as well as formulas for calculating the analytic energy gradient determined with respect to the Gaussian exponential parameters. The gradient is used in the variational optimization of these parameters. The Hamiltonian used in the approach is obtained by rigorously separating the center-of-mass motion from the laboratory-frame all-particle Hamiltonian, and thus it explicitly depends on the finite mass of the nucleus. With that, the mass effect on the total ground-state energy is determined.

AB - An algorithm for quantum-mechanical nonrelativistic variational calculations of L = 0 and M = 0 states of atoms with an arbitrary number of s electrons and with three p electrons have been implemented and tested in the calculations of the ground 4S state of the nitrogen atom. The spatial part of the wave function is expanded in terms of all-electrons explicitly correlated Gaussian functions with the appropriate pre-exponential Cartesian angular factors for states with the L = 0 andM= 0 symmetry. The algorithm includes formulas for calculating the Hamiltonian and overlap matrix elements, as well as formulas for calculating the analytic energy gradient determined with respect to the Gaussian exponential parameters. The gradient is used in the variational optimization of these parameters. The Hamiltonian used in the approach is obtained by rigorously separating the center-of-mass motion from the laboratory-frame all-particle Hamiltonian, and thus it explicitly depends on the finite mass of the nucleus. With that, the mass effect on the total ground-state energy is determined.

UR - http://www.scopus.com/inward/record.url?scp=84899997707&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84899997707&partnerID=8YFLogxK

U2 - 10.1063/1.4873916

DO - 10.1063/1.4873916

M3 - Article

AN - SCOPUS:84899997707

VL - 140

JO - Journal of Chemical Physics

JF - Journal of Chemical Physics

SN - 0021-9606

IS - 17

M1 - 1747112

ER -