Improving numerical integration through basis set expansion

D.A. McCormack; E.J. Baerends; E. van Lenthe; N.C. Handy

doi:10.1007/s00214-004-0613-0

Improving numerical integration through basis set expansion

D.A. McCormack, E.J. Baerends, E. van Lenthe, N.C. Handy

Theoretical Chemistry

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Abstract

Calculations are presented to assess a theorem presented by S.F. Boys [(1969) Proc. R. Soc. A. 309:195], regarding the accuracy of numerical integration in quantum chemical calculations. The theorem states that the error due to numerical integration can be made proportional to the error due to basis set truncation, and thus goes to zero in the limit of a complete basis. We test this theorem on the hydrogen atom, showing that with a solution-spanning basis, the numerically exact orbital energy can indeed be calculated with a small number of integration points. Moreover, tests for H and H

Original language	English
Pages (from-to)	410-418
Journal	Theoretical Chemistry Accounts
Volume	112
Issue number	5-6
DOIs	https://doi.org/10.1007/s00214-004-0613-0
Publication status	Published - 2004

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AB - Calculations are presented to assess a theorem presented by S.F. Boys [(1969) Proc. R. Soc. A. 309:195], regarding the accuracy of numerical integration in quantum chemical calculations. The theorem states that the error due to numerical integration can be made proportional to the error due to basis set truncation, and thus goes to zero in the limit of a complete basis. We test this theorem on the hydrogen atom, showing that with a solution-spanning basis, the numerically exact orbital energy can indeed be calculated with a small number of integration points. Moreover, tests for H and H

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Improving numerical integration through basis set expansion

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