Theoretica chimica acta

, Volume 64, Issue 1, pp 21–26 | Cite as

Some unexpected relationships between first, second and third derivative electron repulsion integrals for diatomic and triatomic molecules

  • Mark A. Vincent
  • Henry F. SchaeferIII
Original Investigations


It is demonstrated that for diatomic molecules, second and third derivative electron repulsion integrals need not be explicitly evaluated. Similarly for triatomic molecules an analogous simplification applies to all second derivative and 94% of all third derivative integrals. Such higher integral derivatives may be determined from intermediate quantities required in the evaluation of integral first derivatives, in conjunction with translational and rotational invariance properties. This result also has implications for theoretical studies of tetra-atomic and larger molecules. Specifically, the evaluation of most two- and three-center integral derivatives becomes very efficient.

Key words

Electron repulsion integrals 


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Copyright information

© Springer-Verlag 1983

Authors and Affiliations

  • Mark A. Vincent
    • 1
  • Henry F. SchaeferIII
    • 1
  1. 1.Department of ChemistryUniversity of CaliforniaBerkeleyUSA

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