Neha Patil (Editor)

Post Hartree–Fock

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In computational chemistry, post-Hartree–Fock methods are the set of methods developed to improve on the Hartree–Fock (HF), or self-consistent field (SCF) method. They add electron correlation which is a more accurate way of including the repulsions between electrons than in the Hartree–Fock method where repulsions are only averaged.

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In general, the SCF procedure makes several assumptions about the nature of the multi-body Schrödinger equation and its set of solutions:

  • For molecules, the Born–Oppenheimer approximation is inherently assumed. The true wavefunction should also be a function of the coordinates of each of the nuclei.
  • Typically, relativistic effects are completely neglected. The momentum operator is assumed to be completely nonrelativistic.
  • The basis set is composed of a finite number of orthogonal functions. The true wavefunction is a linear combination of functions from a complete (infinite) basis set.
  • The energy eigenfunctions are assumed to be products of one-electron wavefunctions. The effects of electron correlation, beyond that of exchange energy resulting from the anti-symmetrization of the wavefunction, are completely neglected.
  • For the great majority of systems under study, in particular for excited states and processes such as molecular dissociation reactions, the fourth item is by far the most important. As a result, the term post-Hartree–Fock method is typically used for methods of approximating the electron correlation of a system.

    Usually, post-Hartree–Fock methods give more accurate results than Hartree–Fock calculations, although the added accuracy comes with the price of added computational cost.

    Post-Hartree–Fock methods

  • Configuration interaction (CI)
  • Coupled cluster (CC)
  • Multi-configuration time-dependent Hartree (MCTDH,)
  • Møller–Plesset perturbation theory (MP2, MP3, MP4, etc.)
  • Quadratic configuration interaction (QCI)
  • Quantum chemistry composite methods (G2, G3, CBS, T1. etc.)
  • Methods that use more than one determinant are not strictly post-Hartree–Fock methods, as they use a single determinant as reference, but they often use similar perturbation, or configuration interaction methods to improve the description of electron correlation. These methods include:

  • Multi-configurational self-consistent field (MCSCF)
  • Multireference single and double configuration interaction (MRCISD)
  • N-electron valence state perturbation theory (NEVPT).
  • References

    Post-Hartree–Fock Wikipedia