We present a new method for numerical integration of the radial electronic Schrödinger equation with these characteristics: (i) it uses a quantity directly related to the logarithmic derivative of the wave function, thereby facilitating the matching of solutions obtained for different radial regions; (ii) it avoids difficulty from the singularity of the logarithmic derivative at the nodes of the wave function; and (iii) it takes appropriate cognizance of the asymptotic form of the wave function at infinite radius. Examples are presented showing that eigenvalues can be obtained by the new method by outward integration alone, but that a combination of inward and outward integration leads to efficiencies which compare favorably with those achievable by the most popular previously existent method, that of Numerov.
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15 December 1988
Research Article|
December 15 1988
New method for numerical integration of the radial electronic Schrödinger equation
Antonios G. Koures;
Antonios G. Koures
Department of Chemistry, University of Utah, Salt Lake City, Utah 84112
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Frank E. Harris
Frank E. Harris
Department of Chemistry, University of Utah, Salt Lake City, Utah 84112
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J. Chem. Phys. 89, 7344–7348 (1988)
Article history
Received:
February 05 1988
Accepted:
March 21 1988
Citation
Antonios G. Koures, Frank E. Harris; New method for numerical integration of the radial electronic Schrödinger equation. J. Chem. Phys. 15 December 1988; 89 (12): 7344–7348. https://doi.org/10.1063/1.455265
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