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Calculation of NMR chemical shifts. V. The gauge invariant coupled Hartree–Fock calculation for H2O, H3O+, and OH−
Magnetic shielding constants are calculated for the hydrogens and oxygens in the isolated species of H2O, H3O+, and OH− using the coupled Hartree–Fock (CHF) method with gauge invariant ato...

Generalized discrete variable approximation in quantum mechanicsa)

J. Chem. Phys. 82, 1400 (1985); doi:10.1063/1.448462

Issue Date: 1 February 1985

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J. C. Light, I. P. Hamilton, and J. V. Lill
The James Franck Institute and The Department of Chemistry, The University of Chicago, Chicago, Illinois 60637
The formal definition of the generalized discrete variable representation (DVR) for quantum mechanics and its connection to the usual variational basis representation (VBR) is given. Using the one dimensional Morse oscillator example, we compare the ``Gaussian quadrature'' DVR, more general DVR's, and other ``pointwise'' representations such as the finite difference method and a Simpson's rule quadrature. The DVR is shown to be accurate in itself, and an efficient representation for optimizing basis set parameters. Extensions to multidimensional problems are discussed. The Journal of Chemical Physics is copyrighted by The American Institute of Physics.
History: Received 8 May 1984; accepted 26 October 1984
Permalink: http://link.aip.org/link/?JCPSA6/82/1400/1
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KEYWORDS and PACS

Keywords
PACS
  • 03.65.Ge
    Classical and quantum physics: mechanics and fields Quantum theory; quantum mechanics Solutions of wave equations: bound states
  • YEAR: 1985

PUBLICATION DATA

ISSN:
0021-9606 (print)   1089-7690 (online)
Publisher:
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REFERENCES (17)
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  1. J. V. Lill, G. A. Parker, and J. C. Light, Chem. Phys. Lett. 89, 483 (1982).
  2. R. W. Heather and J. C. Light, J. Chem. Phys. 79, 147 (1983).
  3. J. V. Lill, Ph.D. thesis, University of Chicago, 1982.
  4. D. G. Truhlar, J. Comput. Phys. 10, 123 (1972).
  5. G. Strang and G. J. Fix, An Analysis of the Finite Element Method (Prentice-Hall, Englewood Cliffs, NJ, 1973).
  6. V. I. Krylov, Approximate Calculation of Integrals (Macmillan, New York, 1962).
  7. (a) D. O. Harris, G. G. Engerholm, and W. D. Gwinn, J. Chem. Phys. 43, 1515 (1965);
    8. (b) P. F. Endres, J. Chem. Phys. 47, 798 (1967).
  8. A. S. Dickinson and P. R. Certain, J. Chem. Phys. 49, 4209 (1968).
  9. An excellent description is found in P. Dennery and A. Krzywicki, Mathematics for Physicists (Harper & Row, New York, 1967).
  10. B. W. Shore, J. Chem. Phys. 59, 6450 (1973).
  11. See, e.g., G. D. Carney and R. N. Porter, J. Chem. Phys. 65, 3547 (1976).
  12. P. G. Burton, E. Von Nagy-Felsobuki, G. Doherty, and M. Hamilton, Chem. Phys. 83, 83 (1984).
  13. A. H. Stroud, Approximate Calculation of Multiple Integrals (Prentice-Hall, Englewood Cliffs, N. J., 1971).
  14. A number of other authors have subsequently used this or related techniques. Apologies are delivered here for omissions.
  15. S. Kanfer and M. Shapiro, J. Phys. Chem. 88, 3964 (1984).
  16. I. P. Hamilton and J. C. Light, Chem. Phys. Lett. (submitted).
  17. K. B. Whaley, Ph.D. thesis, University of Chicago, 1984.

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