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Active-space two-electron reduced-density-matrix method: Complete active-space calculations without diagonalization of the N-electron Hamiltonian

J. Chem. Phys. 129, 134108 (2008); doi:10.1063/1.2983652

Published 3 October 2008

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Gergely Gidofalvi and David A. Mazziotti
Department of Chemistry and The James Franck Institute, The University of Chicago, Chicago, Illinois 60637, USA
Molecular systems in chemistry often have wave functions with substantial contributions from two-or-more electronic configurations. Because traditional complete-active-space self-consistent-field (CASSCF) methods scale exponentially with the number N of active electrons, their applicability is limited to small active spaces. In this paper we develop an active-space variational two-electron reduced-density-matrix (2-RDM) method in which the expensive diagonalization is replaced by a variational 2-RDM calculation where the 2-RDM is constrained by approximate N-representability conditions. Optimization of the constrained 2-RDM is accomplished by large-scale semidefinite programming [Mazziotti, Phys. Rev. Lett. 93, 213001 (2004)]. Because the computational cost of the active-space 2-RDM method scales polynomially as r<sub>a</sub><sup>6</sup> where ra is the number of active orbitals, the method can be applied to treat active spaces that are too large for conventional CASSCF. The active-space 2-RDM method performs two steps: (i) variational calculation of the 2-RDM in the active space and (ii) optimization of the active orbitals by Jacobi rotations. For large basis sets this two-step 2-RDM method is more efficient than the one-step, low-rank variational 2-RDM method [Gidofalvi and Mazziotti, J. Chem. Phys. 127, 244105 (2007)]. Applications are made to HF, H2O, and N2 as well as n-acene chains for n=2–8. When n>4, the acenes cannot be treated by conventional CASSCF methods; for example, when n=8, CASSCF requires optimization over approximately 1.47×1017 configuration state functions. The natural occupation numbers of the n-acenes show the emergence of bi- and polyradical character with increasing chain length. ©2008 American Institute of Physics
History: Received 30 July 2008; accepted 27 August 2008; published 3 October 2008
Permalink: http://link.aip.org/link/?JCPSA6/129/134108/1
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KEYWORDS and PACS

Keywords
PACS
  • 31.15.X-
    Alternative approaches (calculations/mathematical techniques in atomic and molecular physics)
  • 02.10.-v
    Logic, set theory, and algebra
  • 02.30.-f
    Function theory, analysis
  • YEAR: 2008

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ISSN:
0021-9606 (print)   1089-7690 (online)
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REFERENCES (46)
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For access to fully linked references, you need to log in. For access to fully linked references, you need to Log in.
  1. T. Helgaker, P. Jørgensen, and J. Olsen, Molecular Electronic-Structure Theory (Wiley, New York, 2000).
  2. B. O. Roos, P. R. Taylor, and P. E. M. Siegbahn, Chem. Phys. 48, 157 (1980).
  3. B. O. Roos, Adv. Chem. Phys. 69, 399 (1987).
  4. D. L. Yeager and P. Jøregensen, J. Chem. Phys. 71, 755 (1979)
    5. H. -J. Werner and W. Meyer, ibid. 73, 2342 (1980).
  5. B. H. Lengsfield III, J. Chem. Phys. 73, 382 (1980)
    6. D. R. Yarkony, Chem. Phys. Lett. 77, 634 (1981)
    G. Chaban, M. W. Schmidt, and M. S. Gordon, Theor. Chem. Acc. 97, 88 (1997).
  6. J. Ivanic and K. Ruedenberg, J. Comput. Chem. 24, 1250 (2003).
  7. P. O. Löwdin, Phys. Rev. 97, 1474 (1955)
    8. J. E. Mayer, ibid. 100, 1579 (1955).
  8. D. A. Mazziotti, Phys. Rev. Lett. 97, 143002 (2006)
    9. Phys. Rev. A 75, 022505 (2007)
    J. Chem. Phys. 126, 184101 (2007)
    Phys. Rev. A 76, 052502 (2007)
    J. Phys. Chem. A 111, 12635 (2007).
  9. C. Valdemoro, L. M. Tel, D. R. Alcoba, and E. Perez-Romero, Theor. Chem. Acc. 118, 503 (2007).
  10. H. Nakatsuji and K. Yasuda, Phys. Rev. Lett. 76, 1039 (1996)
    11. K. Yasuda and H. Nakatsuji, Phys. Rev. A 56, 2648 (1997).
  11. F. Colmenero and C. Valdemoro, Phys. Rev. A 47, 979 (1993)
    12. Int. J. Quantum Chem. 51, 369 (1994)
    C. Valdemoro, L. M. Tel, and E. Perez-Romero, Adv. Quantum Chem. 28, 33 (1997).
  12. D. A. Mazziotti, Phys. Rev. A 57, 4219 (1998)
    13. 60, 4396 (1999)
    Int. J. Quantum Chem. 70, 557 (1998)
    Chem. Phys. Lett. 289, 419 (1998)
    326, 212 (2000)
    J. Chem. Phys. 116, 1239 (2002)
    Phys. Rev. E 65, 026704 (2002).
  13. D. A. Mazziotti and R. M. Erdahl, Phys. Rev. A 63, 042113 (2001).
  14. R. M. Erdahl and B. Jin, in Many-Electron Densities and Density Matrices, edited by J. Cioslowski (Kluwer, Boston, 2000).
  15. M. Nakata, H. Nakatsuji, M. Ehara, M. Fukuda, K. Nakata, and K. Fujisawa, J. Chem. Phys. 114, 8282 (2001)
    16. M. Nakata, M. Ehara, and H. Nakatsuji, ibid. 116, 5432 (2002).
  16. D. A. Mazziotti, Phys. Rev. A 65, 062511 (2002)
    17. 66, 062503 (2002).
  17. D. A. Mazziotti, Phys. Rev. Lett. 93, 213001 (2004)
    18. J. Chem. Phys. 121, 10957 (2004)
    Math. Modell. Numer. Anal. 41, 249 (2007).
  18. D. A. Mazziotti, Phys. Rev. A 72, 032510 (2005).
  19. Reduced-Density-Matrix Mechanics with Application to Many-Electron Atoms and Molecules, Advances in Chemical Physics Vol. 134, edited by D. A. Mazziotti (Wiley, New York, 2007).
  20. E. Cancés, G. Stoltz, and M. Lewin, J. Chem. Phys. 125, 064101 (2006).
  21. G. Gidofalvi and D. A. Mazziotti, J. Chem. Phys. 122, 094107 (2005).
  22. G. Gidofalvi and D. A. Mazziotti, J. Chem. Phys. 122, 194104 (2005)
    23. J. Phys. Chem. A110, 5481 (2006)
    Phys. Rev. A 69, 042511 (2004)
    74, 012501 (2006).
  23. G. Gidofalvi and D. A. Mazziotti, Phys. Rev. A 72, 052505 (2005).
  24. T. Juhász and D. A. Mazziotti, J. Chem. Phys. 121, 1201 (2004).
  25. Z. Zhao, B. Braams, M. Fukuda, M. L. Overton, and J. K. Percus, J. Chem. Phys. 120, 2095 (2004)
    26. M. Fukuda, B. J. Braams, M. Nakata, M. L. Overton, J. K. Percus, M. Yamashita, and Z. Zhao, Math. Program. Ser. B 109, 553 (2007)
    M. Nakata, B. J. Braams, K. Fujisawa, M. Fukuda, J. K. Percus, M. Yamashita, and Z. Zhao, J. Chem. Phys. 128, 164113 (2008).
  26. J. R. Hammond and D. A. Mazziotti, Phys. Rev. A 71, 062503 (2005)
    27. 73, 062505 (2006).
  27. J. R. Hammond and D. A. Mazziotti, Phys. Rev. A 73, 012509 (2006).
  28. G. Gidofalvi and D. A. Mazziotti, J. Chem. Phys. 125, 144102 (2006).
  29. E. Kamarchik and D. A. Mazziotti, Phys. Rev. A 75, 013203 (2007).
  30. D. A. Mazziotti, Phys. Rev. A 74, 032501 (2006)
    31. G. Gidofalvi and D. A. Mazziotti, J. Chem. Phys. 126, 024105 (2007).
  31. G. Gidofalvi and D. A. Mazziotti, J. Chem. Phys. 127, 244105 (2007).
  32. R. H. Tredgold, Phys. Rev. 105, 1421 (1957)
    33. Y. Mizuno and T. Izuyama, Prog. Theor. Phys. 18, 33 (1957)
    R. U. Ayres, Phys. Rev. 111, 1453 (1958)
    F. Bopp, Z. Phys. 156, 1421 (1959).
  33. A. J. Coleman, Rev. Mod. Phys. 35, 668 (1963).
  34. A. J. Coleman and V. I. Yukalov, Reduced Density Matrices: Coulson's Challenge (Springer-Verlag, New York, 2000).
  35. C. Garrod and J. Percus, J. Math. Phys. 5, 1756 (1964).
  36. R. M. Erdahl, Int. J. Quantum Chem. 13, 697 (1978).
  37. S. Wright, Primal-Dual Interior-Point Methods (SIAM, Philadelphia, 1997).
  38. F. D. Murnaghan, The Unitary Group and Rotation Groups (Spartan, Washington, 1962).
  39. T. H. Dunning, Jr. and P. J. Hay, in Methods of Electronic Structure Theory, edited by H. F. Schaefer, III (Plenum, New York, 1977).
  40. T. H. Dunning, Jr., J. Chem. Phys. 90, 1007 (1989).
  41. M. W. Schmidt, K. K. Baldridge, J. A. Boatz, S. T. Elbert, M. S. Gordon, J. J. Jensen, S. Koseki, N. Matsunaga, K. A. Nguyen, S. Su, T. L. Windus, M. Dupuis, and J. A. Montgomery, J. Comput. Chem. 14, 1347 (1993).
  42. W. J. Hehre, R. F. Stewart, and J. A. Pople, J. Chem. Phys. 51, 2657 (1969).
  43. J. Hachmann, J. J. Dorando, M. Avilés, and G. K.-L. Chan, J. Chem. Phys. 127, 134309 (2007).
  44. D. A. Mazziotti, Phys. Rev. A 68, 052501 (2003).
  45. J. D. Farnum and D. A. Mazziotti, Chem. Phys. Lett. 400, 90 (2004).
  46. L. Greenman and D. A. Mazziotti, J. Chem. Phys. 128, 114109 (2008).

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