Theoretical Chemistry Accounts

, Volume 97, Issue 1, pp 331–340

RI-MP2: first derivatives and global consistency


  • Florian Weigend
    • Institut für Physikalische Chemie, Universität Karlsruhe (TH), D-76128 Karlsruhe, Germany
  • Marco Häser
    • Institut für Physikalische Chemie, Universität Karlsruhe (TH), D-76128 Karlsruhe, Germany

DOI: 10.1007/s002140050269

Cite this article as:
Weigend, F. & Häser, M. Theor Chem Acta (1997) 97: 331. doi:10.1007/s002140050269


The evaluation of RI-MP2 first derivatives with respect to nuclear coordinates or with respect to an external electric field is described. The prefix RI indicates the use of an approximate resolution of identity in the Hilbert space of interacting charge distributions (Coulomb metric), i.e., the use of an auxiliary basis set to approximate charge distributions. The RI technique is applied to first derivatives of the MP2 correlation energy expression while the (restricted) Hartree-Fock reference is treated in the usual way. Computational savings by a factor of 10 over conventional approaches are demonstrated in an application to porphyrin. It is shown that the RI approximation to MP2 derivatives does not entail any significant loss in accuracy. Finally, the relative energetic stabilities of a representative sample of closed-shell molecules built from first and second row elements have been investigated by the RI-MP2 approach, and thus it is tested whether such properties that refer to potential energy hypersurfaces in a more global way can be described with similar consistency to the more locally defined derivatives.

Key words: GradientsPerturbation theory of electronic structureMP2Electron correlationCoulomb interaction

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© Springer-Verlag Berlin Heidelberg 1997