Post-Hartree–Fock

In computational chemistry, post-Hartree–Fock^[1][2] 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.

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)^[3][4]
• Coupled cluster (CC)^[5][6][7]
• Møller–Plesset perturbation theory (MP2,^[8] MP3, MP4,^[9] etc.)
• Quadratic configuration interaction (QCI)^[10]
• Quantum chemistry composite methods (G2,^[11] G3,^[12] CBS, T1.^[13] etc.)

Related methods

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

1. Cramer, Christopher J. (2002). Essentials of Computational Chemistry. John Wiley & Sons. ISBN 0-470-09182-7.
2. Jensen, Frank (1999). Introduction to Computational Chemistry 2nd edition. John Wiley & Sons. ISBN 0-470-01187-4.
3. David Maurice and Martin Head-Gordon (May 10, 1999). "Analytical second derivatives for excited electronic states using the single excitation configuration interaction method: theory and application to benzo[a]pyrene and chalcone". Molecular Physics. Taylor & Francis. 96 (10): 1533–1541. Bibcode:1999MolPh..96.1533M. doi:10.1080/00268979909483096.
4. Martin Head-Gordon, Rudolph J. Rico, Manabu Oumi, and Timothy J. Lee (1994). "A doubles correction to electronic excited states from configuration interaction in the space of single substitutions". Chemical Physics Letters. Elsevier. 219 (1–2): 21–29. Bibcode:1994CPL...219...21H. doi:10.1016/0009-2614(94)00070-0.
5. George D. Purvis and Rodney J. Bartlett (1982). "A full coupled‐cluster singles and doubles model: The inclusion of disconnected triples". The Journal of Chemical Physics. The American Institute of Physics. 76 (4): 1910–1919. Bibcode:1982JChPh..76.1910P. doi:10.1063/1.443164.
6. Krishnan Raghavachari, Gary W. Trucks, John A. Pople and, Martin Head-Gordon (March 24, 1989). "A fifth-order perturbation comparison of electron correlation theories". Chemical Physics Letters. Elsevier Science. 157 (6): 479–483. Bibcode:1989CPL...157..479R. doi:10.1016/S0009-2614(89)87395-6.
7. Troy Van Voorhis and Martin Head-Gordon (June 19, 2001). "Two-body coupled cluster expansions". The Journal of Chemical Physics. The American Institute of Physics. 115 (11): 5033–5041. Bibcode:2001JChPh.115.5033V. doi:10.1063/1.1390516.
8. Chr. Møller and M. S. Plesset (October 1934). "Note on an Approximation Treatment form Many-Electron Systems". Physical Review. The American Physical Society. 46 (7): 618–622. Bibcode:1934PhRv...46..618M. doi:10.1103/PhysRev.46.618.
9. Krishnan Raghavachari and John A. Pople (February 22, 1978). "Approximate fourth-order perturbation theory of the electron correlation energy". International Journal of Quantum Chemistry. Wiley InterScience. 14 (1): 91–100. doi:10.1002/qua.560140109.
10. John A. Pople, Martin Head‐Gordon, and Krishnan Raghavachari (1987). "Quadratic configuration interaction. A general technique for determining electron correlation energies". The Journal of Chemical Physics. American Institute of Physics. 87 (10): 5968–35975. Bibcode:1987JChPh..87.5968P. doi:10.1063/1.453520.
11. Larry A. Curtiss, Krishnan Raghavachari, Gary W. Trucks, and John A. Pople (February 15, 1991). "Gaussian‐2 theory for molecular energies of first‐ and second‐row compounds". The Journal of Chemical Physics. The American Institute of Physics. 94 (11): 7221–7231. Bibcode:1991JChPh..94.7221C. doi:10.1063/1.460205.
12. Larry A. Curtiss, Krishnan Raghavachari, Paul C. Redfern, Vitaly Rassolov, and John A. Pople (July 22, 1998). "Gaussian-3 (G3) theory for molecules containing first and second-row atoms". The Journal of Chemical Physics. The American Institute of Physics. 109 (18): 7764–7776. Bibcode:1998JChPh.109.7764C. doi:10.1063/1.477422.
13. William S. Ohlinger, Philip E. Klunzinger, Bernard J. Deppmeier, and Warren J. Hehre (January 2009). "Efficient Calculation of Heats of Formation". The Journal of Physical Chemistry A. ACS Publications. 113 (10): 2165–2175. doi:10.1021/jp810144q. PMID 19222177.

Further reading

• Jensen, F. (1999). Introduction to Computational Chemistry. New York: John Wiley & Sons. ISBN 0471980854.