Incomputational chemistry,post–Hartree–Fock[1][2](post-HF) methods are the set of methods developed to improve on theHartree–Fock(HF), or self-consistent field (SCF) method. They addelectron correlationwhich is a more accurate way of including the repulsions between electrons than in theHartree–Fock methodwhere repulsions are only averaged.
Details
editIn general, the SCF procedure makes several assumptions about the nature of the multi-bodySchrödinger equationand its set of solutions:
- For molecules, theBorn–Oppenheimer approximationis inherently assumed. The true wavefunction should also be a function of the coordinates of each of the nuclei.
- Typically,relativisticeffects are completely neglected. Themomentum operatoris assumed to be completely nonrelativistic.
- Thebasis setis composed of a finite number oforthogonalfunctions. The general wavefunction is alinear combinationof functions from acomplete(infinite) basis set.
- Theenergy eigenfunctionsare assumed to be products of one-electron wavefunctions. The effects ofelectron correlation,beyond that of exchange energy resulting from theanti-symmetrizationof 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 termpost–Hartree–Fock methodis typically used for methods of approximating the electron correlation of a system.
Usually, post–Hartree–Fock methods[3][4]give more accurate results than Hartree–Fock calculations, although the added accuracy comes with the price of added computational cost.
Post–Hartree–Fock methods
edit- Configuration interaction(CI)[5][6]
- Coupled cluster(CC)[7][8][9]
- Multi-configuration time-dependent Hartree(MCTDH,[10])
- Møller–Plesset perturbation theory(MP2,[11]MP3, MP4,[12]etc.)
- Quadratic configuration interaction(QCI)[13]
- Quantum chemistry composite methods(G2,[14]G3,[15]CBS, T1.[16]etc.)
Related methods
editMethods 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:
References
edit- ^Cramer, Christopher J. (2002).Essentials of Computational Chemistry.John Wiley & Sons.ISBN0-470-09182-7.
- ^Jensen, Frank (1999).Introduction to Computational Chemistry2nd edition.John Wiley & Sons.ISBN0-470-01187-4.
- ^"Post-Hartree–Fock Methods",Methods of Molecular Quantum Mechanics,John Wiley & Sons, Ltd, 2009, pp. 133–139,doi:10.1002/9780470684559.ch8,ISBN9780470684559
- ^DaCosta, Herbert (2011).Rate Constant Calculation for Thermal Reactions: Methods and Applications.John Wiley & Sons.ISBN9781118166123.OCLC769342424.
- ^David Maurice & 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.96(10). Taylor & Francis: 1533–1541.Bibcode:1999MolPh..96.1533M.doi:10.1080/00268979909483096.
- ^Martin Head-Gordon; Rudolph J. Rico; Manabu Oumi & Timothy J. Lee (1994)."A doubles correction to electronic excited states from configuration interaction in the space of single substitutions".Chemical Physics Letters.219(1–2). Elsevier: 21–29.Bibcode:1994CPL...219...21H.doi:10.1016/0009-2614(94)00070-0.
- ^George D. Purvis & Rodney J. Bartlett (1982). "A full coupled‐cluster singles and doubles model: The inclusion of disconnected triples".The Journal of Chemical Physics.76(4). The American Institute of Physics: 1910–1919.Bibcode:1982JChPh..76.1910P.doi:10.1063/1.443164.
- ^Krishnan Raghavachari; Gary W. Trucks; John A. Pople & Martin Head-Gordon (March 24, 1989). "A fifth-order perturbation comparison of electron correlation theories".Chemical Physics Letters.157(6). Elsevier Science: 479–483.Bibcode:1989CPL...157..479R.doi:10.1016/S0009-2614(89)87395-6.
- ^Troy Van Voorhis & Martin Head-Gordon (June 19, 2001). "Two-body coupled cluster expansions".The Journal of Chemical Physics.115(11). The American Institute of Physics: 5033–5041.Bibcode:2001JChPh.115.5033V.doi:10.1063/1.1390516.
- ^H. D. Meyer; U. Manthe & L. S. Cederbaum (1990). "The multi-configurational time-dependent Hartree approach".Chem. Phys. Lett.165(73): 73–78.Bibcode:1990CPL...165...73M.doi:10.1016/0009-2614(90)87014-I.
- ^Chr. Møller & M. S. Plesset (October 1934)."Note on an Approximation Treatment form Many-Electron Systems".Physical Review.46(7). The American Physical Society: 618–622.Bibcode:1934PhRv...46..618M.doi:10.1103/PhysRev.46.618.
- ^Krishnan Raghavachari & John A. Pople (February 22, 1978). "Approximate fourth-order perturbation theory of the electron correlation energy".International Journal of Quantum Chemistry.14(1). Wiley InterScience: 91–100.doi:10.1002/qua.560140109.
- ^John A. Pople; Martin Head‐Gordon & Krishnan Raghavachari (1987). "Quadratic configuration interaction. A general technique for determining electron correlation energies".The Journal of Chemical Physics.87(10). American Institute of Physics: 5968–35975.Bibcode:1987JChPh..87.5968P.doi:10.1063/1.453520.
- ^Larry A. Curtiss; Krishnan Raghavachari; Gary W. Trucks & John A. Pople (February 15, 1991)."Gaussian‐2 theory for molecular energies of first‐ and second‐row compounds".The Journal of Chemical Physics.94(11). The American Institute of Physics: 7221–7231.Bibcode:1991JChPh..94.7221C.doi:10.1063/1.460205.
- ^Larry A. Curtiss; Krishnan Raghavachari; Paul C. Redfern; Vitaly Rassolov & John A. Pople (July 22, 1998). "Gaussian-3 (G3) theory for molecules containing first and second-row atoms".The Journal of Chemical Physics.109(18). The American Institute of Physics: 7764–7776.Bibcode:1998JChPh.109.7764C.doi:10.1063/1.477422.
- ^William S. Ohlinger; Philip E. Klunzinger; Bernard J. Deppmeier & Warren J. Hehre (January 2009). "Efficient Calculation of Heats of Formation".The Journal of Physical Chemistry A.113(10). ACS Publications: 2165–2175.Bibcode:2009JPCA..113.2165O.doi:10.1021/jp810144q.PMID19222177.
Further reading
edit- Jensen, F. (1999).Introduction to Computational Chemistry.New York: John Wiley & Sons.ISBN0471980854.