Theoretica chimica acta

, Volume 76, Issue 4, pp 227–245 | Cite as

A numerically stable procedure for calculating Møller-Plesset energy derivatives, derived using the theory of Lagrangians

  • Trygve Helgaker
  • Poul Jørgensen
  • Nicholas C. Handy


When Møller-Plesset energy derivatives are determined in the canonical Hartree-Fock basis, singularities or instabilities may arise due to degeneracies among the occupied or unoccupied orbitals. If a non-canonical basis is used these singularities disappear. Numerically stable expressions are presented for the molecular gradient and Hessian of the second-order Møller-Plesset energy, obtained by differentiating a fully variational Lagrangian of the energy constructed in a non-canonical representation. By using a non-canonical representation, singularities and instabilities are avoided, and the variational property of the Lagrangian ensures that Wigner's 2n + 1 rule is satisfied for the orbital derivatives and that the multipliers satisfy the stronger 2n + 2 rule. It is shown that the most expensive step in the calculation of the Hessian scales as Mn4o, where M is the number of independent Cartesian distortions, n the total number of orbitals, and o the number of occupied orbitals.

Key words

Energy derivatives Møller-Plesset Non-canonical basis Lagrangian formulation 


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Copyright information

© Springer-Verlag 1989

Authors and Affiliations

  • Trygve Helgaker
    • 1
  • Poul Jørgensen
    • 1
  • Nicholas C. Handy
    • 2
  1. 1.Department of ChemistryÅrhus UniversityAarhus CDenmark
  2. 2.University Chemical LaboratoryCambridgeUK

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