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Eclectic Electron-Correlation Methods

  • So HirataEmail author
  • Toru Shiozaki
  • Edward F. Valeev
  • Marcel Nooijen
Chapter
Part of the Challenges and Advances in Computational Chemistry and Physics book series (COCH, volume 11)

Abstract

An eclectic combination of cluster, perturbation, and linear expansions often provides the most compact mathematical descriptions of molecular electronic wave functions. A general theory is introduced to define a hierarchy of systematic electron-correlation approximations that use two or three of these expansion types. It encompasses coupled-cluster and equation-of-motion coupled-cluster methods and generates various perturbation corrections thereto, which, in some instances, reduce to the standard many-body perturbation methods. Some of these methods are also equipped with the ability to use basis functions of interelectronic distances via the so-called R12 and F12 schemes. Two computer algebraic techniques are devised to dramatically expedite implementation, verification, and validation of these complex electron-correlation methods. Numerical assessments support the unmatched utility of the proposed approximations for a range of molecular problems.

Keywords:

Coupled cluster Equation-of-motion coupled cluster Perturbation corrections Explicitly correlated Automated derivation and implementation 

Notes

Acknowledgment

S.H. thanks the financial support from the US Department of Energy (DE-FG02-04ER15621), the US National Science Foundation (CHE-0844448), and the American Chemical Society Petroleum Research Fund (48440-AC6). S.H. is a Camille Dreyfus Teacher-Scholar. T.S. thanks the Japan Society for the Promotion of Science Research Fellowship for Young Scientists. E.F.V. thanks the financial support from the American Chemical Society Petroleum Research Fund (46811-G6). E.F.V. is a Sloan Research Fellow.

References

  1. 1.
    R. J. Bartlett, M. Musiał, Rev. Mod. Phys.79, 291 (2007)CrossRefGoogle Scholar
  2. 2.
    I. Shavitt, R. J. Bartlett,Many-Body Methods in Chemistry and Physics. (Cambridge University Press, Cambridge, 2009)CrossRefGoogle Scholar
  3. 3.
    R. J. Bartlett, Ann. Rev. Phys. Chem.32, 359 (1981)CrossRefGoogle Scholar
  4. 4.
    I. Shavitt, Mol. Phys.94, 3 (1998)CrossRefGoogle Scholar
  5. 5.
    S. Hirata, K. Yagi, Chem. Phys. Lett.464, 123 (2008)CrossRefGoogle Scholar
  6. 6.
    K. Raghavachari, G. W. Trucks, J. A. Pople, M. Head-Gordon, Chem. Phys. Lett.157, 479 (1989)CrossRefGoogle Scholar
  7. 7.
    J. D. Watts, J. Gauss, R. J. Bartlett, J. Chem. Phys.98, 8718 (1993)Google Scholar
  8. 8.
    K. Andersson, P.-Å. Malmqvist, B. O. Roos, A. J. Sadlej, K. Wolinski, J. Phys. Chem.94, 5483 (1990)Google Scholar
  9. 9.
    K. Hirao, Chem. Phys. Lett.190, 374 (1992)CrossRefGoogle Scholar
  10. 10.
    J. F. Stanton, R. J. Bartlett, J. Chem. Phys.98, 7029 (1993)Google Scholar
  11. 11.
    H. Nakatsuji, K. Hirao, Int. J. Quantum Chem.20, 1301 (1981)CrossRefGoogle Scholar
  12. 12.
    H. Nakatsuji, K. Ohta, K. Hirao, J. Chem. Phys.75, 2952 (1981)Google Scholar
  13. 13.
    H. Koch, P. Jørgensen, J. Chem. Phys.93, 3333 (1990)Google Scholar
  14. 14.
    H. Koch, H. J. A. Jensen, P. Jørgensen, T. Helgaker, J. Chem. Phys.93, 3345 (1990)Google Scholar
  15. 15.
    R. J. Rico, M. Head-Gordon, Chem. Phys. Lett.213, 224 (1993)CrossRefGoogle Scholar
  16. 16.
    S. Hirata, J. Chem. Phys.121, 51 (2004)Google Scholar
  17. 17.
    M. Ká llay, J. Gauss, J. Chem. Phys.121, 9257 (2004)Google Scholar
  18. 18.
    S. Hirata, M. Nooijen, I. Grabowski, R. J. Bartlett, J. Chem. Phys.114, 3919 (2001);115, 3967 (2001) (Erratum)Google Scholar
  19. 19.
    S. Hirata, P.-D. Fan, T. Shiozaki, Y. Shigeta, inRadiation Induced Molecular Phenomena in Nucleic Acid: A Comprehensive Theoretical and Experimental Analysis, Eds. J. Leszczynski, M. Shukla (Springer, New York, 2008), p. 15Google Scholar
  20. 20.
    S. Hirata, P.-D. Fan, A. A. Auer, M. Nooijen, P. Piecuch, J. Chem. Phys.121, 12197 (2004)Google Scholar
  21. 21.
    S. Hirata, J. Chem. Phys.122, 094105 (2005)Google Scholar
  22. 22.
    T. Shiozaki, K. Hirao, S. Hirata, J. Chem. Phys.126, 244106 (2007)Google Scholar
  23. 23.
    S. Hirata, Theor. Chem. Acc.116, 2 (2006)CrossRefGoogle Scholar
  24. 24.
    S. Hirata, R. J. Bartlett, Chem. Phys. Lett.321, 216 (2000)CrossRefGoogle Scholar
  25. 25.
    M. Ká llay, P. R. Surjá n, J. Chem. Phys.113, 1359 (2000)Google Scholar
  26. 26.
    J. Olsen, J. Chem. Phys.113, 7140 (2000)Google Scholar
  27. 27.
    S. Hirata, J. Phys. Chem. A107, 9887 (2003)Google Scholar
  28. 28.
    M. Ká llay, P. R. Surjá n, J. Chem. Phys.115, 2945 (2001)Google Scholar
  29. 29.
    W. Kutzelnigg, Theor. Chim. Acta68, 445 (1985)CrossRefGoogle Scholar
  30. 30.
    W. Kutzelnigg, W. Klopper, J. Chem. Phys.94, 1985 (1991)Google Scholar
  31. 31.
    W. Klopper, F. R. Manby, S. Ten-no, E. F. Valeev, Int. Rev. Phys. Chem.25, 427 (2006)CrossRefGoogle Scholar
  32. 32.
    T. Shiozaki, E. F. Valeev, S. Hirata, Ann. Rep. Comp. Chem.5, 131 (2009)CrossRefGoogle Scholar
  33. 33.
    H. Fliegl, C. Hättig, W. Klopper, Int. J. Quantum Chem.106, 2306 (2006)CrossRefGoogle Scholar
  34. 34.
    T. B. Adler, G. Knizia, H.-J. Werner, J. Chem. Phys.127, 221106 (2007)Google Scholar
  35. 35.
    D. Bokhan, S. Ten-no, J. Noga, Phys. Chem. Chem. Phys.10, 3320 (2008)CrossRefGoogle Scholar
  36. 36.
    D. Bokhan, S. Bernadotte, S. Ten-no, Chem. Phys. Lett.469, 214 (2009)CrossRefGoogle Scholar
  37. 37.
    G. Knizia, T. B. Adler, H. J. Werner, J. Chem. Phys.130, 054104 (2009)Google Scholar
  38. 38.
    A. Kö hn, J. Chem. Phys.130, 131101 (2009)Google Scholar
  39. 39.
    T. Shiozaki, E. F. Valeev, S. Hirata, J. Chem. Phys.131, 044118 (2009)Google Scholar
  40. 40.
    J. Noga, W. Kutzelnigg, W. Klopper, Chem. Phys. Lett.199, 497 (1992)CrossRefGoogle Scholar
  41. 41.
    J. Noga, W. Kutzelnigg, J. Chem. Phys.101, 7738 (1994)Google Scholar
  42. 42.
    J. Noga, P. Valiron, Chem. Phys. Lett.324, 166 (2000)CrossRefGoogle Scholar
  43. 43.
    H. Fliegl, W. Klopper, C. Hättig, J. Chem. Phys.122, 084107 (2005)Google Scholar
  44. 44.
    D. P. Tew, W. Klopper, C. Neiss, C. Hättig, Phys. Chem. Chem. Phys.9, 1921 (2007)CrossRefGoogle Scholar
  45. 45.
    D. P. Tew, W. Klopper, C. Hättig, Chem. Phys. Lett.452, 326 (2008)CrossRefGoogle Scholar
  46. 46.
    J. Noga, S. Kedžuch, J. Šimunek, S. Ten-no, J. Chem. Phys.128, 174103 (2008)Google Scholar
  47. 47.
    E. F. Valeev, Phys. Chem. Chem. Phys.10, 106 (2008)CrossRefGoogle Scholar
  48. 48.
    T. Shiozaki, M. Kamiya, S. Hirata, E. F. Valeev, Phys. Chem. Chem. Phys.10, 3358 (2008)CrossRefGoogle Scholar
  49. 49.
    E. F. Valeev, T. D. Crawford, J. Chem. Phys.128, 244113 (2008)Google Scholar
  50. 50.
    M. Torheyden, E. F. Valeev, Phys. Chem. Chem. Phys.10, 3410 (2008)CrossRefGoogle Scholar
  51. 51.
    T. Shiozaki, M. Kamiya, S. Hirata, E. F. Valeev, J. Chem. Phys.129, 071101 (2008)Google Scholar
  52. 52.
    A. Kö hn, G. W. Richings, D. P. Tew, J. Chem. Phys.129, 201103 (2008)Google Scholar
  53. 53.
    T. Shiozaki, M. Kamiya, S. Hirata, E. F. Valeev, J. Chem. Phys.130, 054101 (2009)Google Scholar
  54. 54.
    W. Klopper, W. Kutzelnigg, Chem. Phys. Lett.134, 17 (1987)CrossRefGoogle Scholar
  55. 55.
    W. Klopper, C. C. M. Samson, J. Chem. Phys.116, 6397 (2002)Google Scholar
  56. 56.
    F. R. Manby, J. Chem. Phys.119, 4607 (2003)Google Scholar
  57. 57.
    S. Ten-no, F. R. Manby, J. Chem. Phys.119, 5358 (2003)Google Scholar
  58. 58.
    E. F. Valeev, Chem. Phys. Lett.395, 190 (2004)CrossRefGoogle Scholar
  59. 59.
    S. Ten-no, J. Chem. Phys.121, 117 (2004)Google Scholar
  60. 60.
    S. Ten-no, Chem. Phys. Lett.398, 56 (2004)CrossRefGoogle Scholar
  61. 61.
    A. J. May, E. Valeev, R. Polly, F. R. Manby, Phys. Chem. Chem. Phys.7, 2710 (2005)CrossRefGoogle Scholar
  62. 62.
    S. Kedžuch, M. Milko, J. Noga, Int. J. Quantum Chem.105, 929 (2005)CrossRefGoogle Scholar
  63. 63.
    H.-J. Werner, F. R. Manby, J. Chem. Phys.124, 054114 (2006)Google Scholar
  64. 64.
    F. R. Manby, H. J. Werner, T. B. Adler, A. J. May, J. Chem. Phys.124, 094103 (2006)Google Scholar
  65. 65.
    H. J. Werner, T. B. Adler, F. R. Manby, J. Chem. Phys.126, 164102 (2007)Google Scholar
  66. 66.
    S. Ten-no, J. Chem. Phys.126, 014108 (2007)Google Scholar
  67. 67.
    P.-D. Fan, S. Hirata, J. Chem. Phys.124, 104108 (2006)Google Scholar
  68. 68.
    M. Kamiya, S. Hirata, J. Chem. Phys.125, 074111 (2006)Google Scholar
  69. 69.
    M. Kamiya, S. Hirata, J. Chem. Phys.126, 134112 (2007)Google Scholar
  70. 70.
    P.-D. Fan, M. Kamiya, S. Hirata, J. Chem. Theo. Comp.3, 1036 (2007)CrossRefGoogle Scholar
  71. 71.
    J. D. Watts, inRadiation Induced Molecular Phenomena in Nucleic Acid: A Comprehensive Theoretical and Experimental Analysis, Eds. J. Leszczynski, M. Shukla (Springer, New York, 2008), p. 65CrossRefGoogle Scholar
  72. 72.
    J. B. Foresman, M. Head-Gordon, J. A. Pople, M. J. Frisch, J. Phys. Chem.96, 135 (1992)Google Scholar
  73. 73.
    J. F. Stanton, J. Gauss, J. Chem. Phys.101, 8938 (1994)Google Scholar
  74. 74.
    M. Nooijen, R. J. Bartlett, J. Chem. Phys.102, 3629 (1995)Google Scholar
  75. 75.
    S. A. Kucharski, R. J. Bartlett, J. Chem. Phys.108, 5243 (1998)Google Scholar
  76. 76.
    S. A. Kucharski, R. J. Bartlett, J. Chem. Phys.108, 5255 (1998)Google Scholar
  77. 77.
    S. A. Kucharski, R. J. Bartlett, J. Chem. Phys.108, 9221 (1998)Google Scholar
  78. 78.
    J. F. Stanton, J. Gauss, J. Chem. Phys.103, 1064 (1995)Google Scholar
  79. 79.
    J. F. Stanton, J. Gauss, Theor. Chim. Acc.93, 303 (1996)CrossRefGoogle Scholar
  80. 80.
    J. F. Stanton, J. Gauss, Theor. Chim. Acc.95, 97 (1997)CrossRefGoogle Scholar
  81. 81.
    T. D. Crawford, J. F. Stanton, Int. J. Quantum Chem.70, 601 (1998)CrossRefGoogle Scholar
  82. 82.
    S. R. Gwaltney, M. Head-Gordon, Chem. Phys. Lett.323, 21 (2000)CrossRefGoogle Scholar
  83. 83.
    K. Kowalski, P. Piecuch, J. Chem. Phys.113, 5644 (2000)Google Scholar
  84. 84.
    S. R. Gwaltney, M. Head-Gordon, J. Chem. Phys.115, 2014 (2001)Google Scholar
  85. 85.
    K. Kowalski, P. Piecuch, Chem. Phys. Lett.344, 165 (2001)CrossRefGoogle Scholar
  86. 86.
    M. Nooijen, K. R. Shamasundar, D. Mukherjee, Mol. Phys.103, 2277 (2005)CrossRefGoogle Scholar
  87. 87.
    M. Urban, J. Noga, S. J. Cole, R. J. Bartlett, J. Chem. Phys.83, 4041 (1985)Google Scholar
  88. 88.
    M. Head-Gordon, R. J. Rico, M. Oumi, T. J. Lee, Chem. Phys. Lett.219, 21 (1994)CrossRefGoogle Scholar
  89. 89.
    J. D. Watts, R. J. Bartlett, Chem. Phys. Lett.233, 81 (1995)CrossRefGoogle Scholar
  90. 90.
    J. D. Watts, R. J. Bartlett, Chem. Phys. Lett.258, 581 (1996)CrossRefGoogle Scholar
  91. 91.
    M. Włoch, J. R. Gour, K. Kowalski, P. Piecuch, J. Chem. Phys.122, 214107 (2005)Google Scholar
  92. 92.
    W. Klopper, Chem. Phys. Lett.186, 583 (1991)CrossRefGoogle Scholar
  93. 93.
    P. J. Knowles, N. C. Handy, Chem. Phys. Lett.111, 315 (1984)CrossRefGoogle Scholar
  94. 94.
    P. J. Knowles, K. Somasundram, N. C. Handy, K. Hirao, Chem. Phys. Lett.113, 8 (1985)CrossRefGoogle Scholar
  95. 95.
    J. Olsen, O. Christiansen, H. Koch, P. Jørgensen, J. Chem. Phys.105, 5082 (1996)Google Scholar
  96. 96.
    S. Hirata, M. Nooijen, R. J. Bartlett, Chem. Phys. Lett.326, 255 (2000)CrossRefGoogle Scholar
  97. 97.
    S. Hirata, M. Nooijen, R. J. Bartlett, Chem. Phys. Lett.328, 459 (2000)CrossRefGoogle Scholar
  98. 98.
    Y. S. Lee, S. A. Kucharski, R. J. Bartlett, J. Chem. Phys.81, 5906 (1984)CrossRefGoogle Scholar
  99. 99.
    S. Hirata, unpublished (2009)Google Scholar

Copyright information

© Springer Science+Business Media B.V. 2010

Authors and Affiliations

  • So Hirata
    • 1
    Email author
  • Toru Shiozaki
    • 1
    • 2
  • Edward F. Valeev
    • 3
  • Marcel Nooijen
    • 4
  1. 1.Quantum Theory Project, Departments of Chemistry and Physics, The Center for Macromolecular Science and EngineeringUniversity of FloridaGainesvilleUSA
  2. 2.Department of Applied Chemistry, Graduate School of EngineeringThe University of TokyoTokyoJapan
  3. 3.Department of ChemistryVirginia TechBlacksburgUSA
  4. 4.Department of ChemistryUniversity of WaterlooWaterlooCanada

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