Theoretica chimica acta

, Volume 31, Issue 3, pp 195–200 | Cite as

Integration points for the reduction of boundary conditions

  • N. C. Handy
  • S. F. Boys


An analysis of a method for the numerical evaluation of the integral \(\int\limits_a^b { f\left( x \right)} dx\) is presented. The method introduces a change of variable, x = x(q), with the property that dnx/dqnis zero at x = a, x = b for n = 0, 1, 2,... N, where N is an integer to be chosen. The Euler-Maclaurin formula shows that the resulting integral in the variable q is ideally suited for numerical integration, using equally spaced points and equal weights in q-space. Examples are given for various integrals which occur in quantum chemistry and applications to more than one dimension are discussed.

Key words

Numerical integration 


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Copyright information

© Springer-Verlag 1973

Authors and Affiliations

  • N. C. Handy
    • 1
  • S. F. Boys
    • 1
  1. 1.Theoretical Chemistry DepartmentUniversity Chemical LaboratoryCambridge

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