後哈特里-福克方法

在計算化學中，後哈特里－福克方法（英語：post-Hartree–Fock）^[1]^[2]是對哈特里－福克方法（HF）或自洽場方法（SCF）加以改進而發展的一系列方法。在哈特里－福克方法中，電子排斥力的計算使用了平均場論的方法，只考慮平均電子密度下的排斥力。這些方法增加了電子耦合項，更準確地考慮了電子間的排斥；

細節

HF-SCF程序對多體薛定諤方程的性質及其解集做出了幾點假設：

在考慮分子時使用了玻恩–奧本海默近似。真正的波函數應當也和每個原子核坐標有關。
通常情況下，完全了忽略狹義相對論效應，動量算符被假定為完全非相對論情況下的。
基組由有限數量的正交函數組成。真正的波函數是完備基組中函數的線性組合，包含無限個正交函數。
能量本徵函數被假定為多個單電子波函數的乘積或者是單個斯萊特行列式；除了因波函數的反對稱性而產生的交換能量外，組態相互作用(electron correlation)的影響被完全忽略。

對於絕大多數系統而言，特別是激發態及化學反應（例如分子解離反應），上述假設中的第四條的影響是最大的。因此，術語「後哈特里－福克方法」常被用於表示計算電子校正的近似方法。

通常情況下，後哈特里－福克方法比哈特里－福克方法更加準確，但是也需要消耗更多的計算資源。

方法

組態相互作用方法（CI）^[3]^[4]
耦合簇方法（CC）^[5]^[6]^[7]
多配置含時哈特里方法（Multi-configuration time-dependent Hartree，MCTDH^[8]）
多體微擾理論（MP2^[9]、MP3、MP4^[10]等）
二次組態相互作用（QCI）^[11]
量子化學複合方法（G2^[12]、G3^[13]、CBS、T1^[14]等）

參考文獻

^ Cramer, Christopher J. Essentials of Computational Chemistry. John Wiley & Sons. 2002. ISBN 0-470-09182-7.
^ Jensen, Frank. Introduction to Computational Chemistry 2nd edition. John Wiley & Sons. 1999. ISBN 0-470-01187-4.
^ David Maurice & Martin Head-Gordon. 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). May 10, 1999, 96 (10): 1533–1541. Bibcode:1999MolPh..96.1533M. doi:10.1080/00268979909483096.
^ Martin Head-Gordon; Rudolph J. Rico; Manabu Oumi & Timothy J. Lee. A doubles correction to electronic excited states from configuration interaction in the space of single substitutions. Chemical Physics Letters (Elsevier). 1994, 219 (1–2): 21–29. Bibcode:1994CPL...219...21H. doi:10.1016/0009-2614(94)00070-0.
^ George D. Purvis & Rodney J. Bartlett. A full coupled‐cluster singles and doubles model: The inclusion of disconnected triples. The Journal of Chemical Physics (The American Institute of Physics). 1982, 76 (4): 1910–1919. Bibcode:1982JChPh..76.1910P. doi:10.1063/1.443164.
^ Krishnan Raghavachari; Gary W. Trucks; John A. Pople & Martin Head-Gordon. A fifth-order perturbation comparison of electron correlation theories. Chemical Physics Letters (Elsevier Science). March 24, 1989, 157 (6): 479–483. Bibcode:1989CPL...157..479R. doi:10.1016/S0009-2614(89)87395-6.
^ Troy Van Voorhis & Martin Head-Gordon. Two-body coupled cluster expansions. The Journal of Chemical Physics (The American Institute of Physics). June 19, 2001, 115 (11): 5033–5041. Bibcode:2001JChPh.115.5033V. doi:10.1063/1.1390516.
^ H. D. Meyer; U. Manthe & L. S. Cederbaum. The multi-configurational time-dependent Hartree approach. Chem. Phys. Lett. 1990, 165 (73). doi:10.1016/0009-2614(90)87014-I.
^ Chr. Møller & M. S. Plesset. Note on an Approximation Treatment form Many-Electron Systems. Physical Review (The American Physical Society). October 1934, 46 (7): 618–622. Bibcode:1934PhRv...46..618M. doi:10.1103/PhysRev.46.618.
^ Krishnan Raghavachari & John A. Pople. Approximate fourth-order perturbation theory of the electron correlation energy. International Journal of Quantum Chemistry (Wiley InterScience). February 22, 1978, 14 (1): 91–100. doi:10.1002/qua.560140109.
^ John A. Pople; Martin Head‐Gordon & Krishnan Raghavachari. Quadratic configuration interaction. A general technique for determining electron correlation energies. The Journal of Chemical Physics (American Institute of Physics). 1987, 87 (10): 5968–35975. Bibcode:1987JChPh..87.5968P. doi:10.1063/1.453520.
^ Larry A. Curtiss; Krishnan Raghavachari; Gary W. Trucks & John A. Pople. Gaussian‐2 theory for molecular energies of first‐ and second‐row compounds. The Journal of Chemical Physics (The American Institute of Physics). February 15, 1991, 94 (11): 7221–7231. Bibcode:1991JChPh..94.7221C. doi:10.1063/1.460205.
^ Larry A. Curtiss; Krishnan Raghavachari; Paul C. Redfern; Vitaly Rassolov & John A. Pople. Gaussian-3 (G3) theory for molecules containing first and second-row atoms. The Journal of Chemical Physics (The American Institute of Physics). July 22, 1998, 109 (18): 7764–7776. Bibcode:1998JChPh.109.7764C. doi:10.1063/1.477422.
^ William S. Ohlinger; Philip E. Klunzinger; Bernard J. Deppmeier & Warren J. Hehre. Efficient Calculation of Heats of Formation. The Journal of Physical Chemistry A (ACS Publications). January 2009, 113 (10): 2165–2175. PMID 19222177. doi:10.1021/jp810144q.

進一步閱讀

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

[1] Cramer, Christopher J. Essentials of Computational Chemistry. John Wiley & Sons. 2002. ISBN 0-470-09182-7.

[2] Jensen, Frank. Introduction to Computational Chemistry 2nd edition. John Wiley & Sons. 1999. ISBN 0-470-01187-4.

[3] David Maurice & Martin Head-Gordon. 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). May 10, 1999, 96 (10): 1533–1541. Bibcode:1999MolPh..96.1533M. doi:10.1080/00268979909483096.

[4] Martin Head-Gordon; Rudolph J. Rico; Manabu Oumi & Timothy J. Lee. A doubles correction to electronic excited states from configuration interaction in the space of single substitutions. Chemical Physics Letters (Elsevier). 1994, 219 (1–2): 21–29. Bibcode:1994CPL...219...21H. doi:10.1016/0009-2614(94)00070-0.

[5] George D. Purvis & Rodney J. Bartlett. A full coupled‐cluster singles and doubles model: The inclusion of disconnected triples. The Journal of Chemical Physics (The American Institute of Physics). 1982, 76 (4): 1910–1919. Bibcode:1982JChPh..76.1910P. doi:10.1063/1.443164.

[6] Krishnan Raghavachari; Gary W. Trucks; John A. Pople & Martin Head-Gordon. A fifth-order perturbation comparison of electron correlation theories. Chemical Physics Letters (Elsevier Science). March 24, 1989, 157 (6): 479–483. Bibcode:1989CPL...157..479R. doi:10.1016/S0009-2614(89)87395-6.

[7] Troy Van Voorhis & Martin Head-Gordon. Two-body coupled cluster expansions. The Journal of Chemical Physics (The American Institute of Physics). June 19, 2001, 115 (11): 5033–5041. Bibcode:2001JChPh.115.5033V. doi:10.1063/1.1390516.

[8] H. D. Meyer; U. Manthe & L. S. Cederbaum. The multi-configurational time-dependent Hartree approach. Chem. Phys. Lett. 1990, 165 (73). doi:10.1016/0009-2614(90)87014-I.

[9] Chr. Møller & M. S. Plesset. Note on an Approximation Treatment form Many-Electron Systems. Physical Review (The American Physical Society). October 1934, 46 (7): 618–622. Bibcode:1934PhRv...46..618M. doi:10.1103/PhysRev.46.618.

[10] Krishnan Raghavachari & John A. Pople. Approximate fourth-order perturbation theory of the electron correlation energy. International Journal of Quantum Chemistry (Wiley InterScience). February 22, 1978, 14 (1): 91–100. doi:10.1002/qua.560140109.

[QCI-11] John A. Pople; Martin Head‐Gordon & Krishnan Raghavachari. Quadratic configuration interaction. A general technique for determining electron correlation energies. The Journal of Chemical Physics (American Institute of Physics). 1987, 87 (10): 5968–35975. Bibcode:1987JChPh..87.5968P. doi:10.1063/1.453520.

[12] Larry A. Curtiss; Krishnan Raghavachari; Gary W. Trucks & John A. Pople. Gaussian‐2 theory for molecular energies of first‐ and second‐row compounds. The Journal of Chemical Physics (The American Institute of Physics). February 15, 1991, 94 (11): 7221–7231. Bibcode:1991JChPh..94.7221C. doi:10.1063/1.460205.

[13] Larry A. Curtiss; Krishnan Raghavachari; Paul C. Redfern; Vitaly Rassolov & John A. Pople. Gaussian-3 (G3) theory for molecules containing first and second-row atoms. The Journal of Chemical Physics (The American Institute of Physics). July 22, 1998, 109 (18): 7764–7776. Bibcode:1998JChPh.109.7764C. doi:10.1063/1.477422.

[14] William S. Ohlinger; Philip E. Klunzinger; Bernard J. Deppmeier & Warren J. Hehre. Efficient Calculation of Heats of Formation. The Journal of Physical Chemistry A (ACS Publications). January 2009, 113 (10): 2165–2175. PMID 19222177. doi:10.1021/jp810144q.

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後哈特里-福克方法

目次

細節

方法

相關方法

參考文獻

進一步閱讀