Journal of Chemical Physics
Feedback | Help | Exit
The Journal of Chemical Physics
   
 
 
 
Previous Article
Path ensembles and path sampling in nonequilibrium stochastic systems
Markovian models based on the stochastic master equation are often encountered in single molecule dynamics, reaction networks, and nonequilibrium problems in chemistry, physics, and biology. An effici...
Next Article
Dynamical effects in line shapes for coupled chromophores: Time-averaging approximation
For an isolated resonance of an isolated chromophore in a condensed phase, the absorption line shape is often more sharply peaked than the distribution of transition frequencies as a result of motiona...

Cumulant reconstruction of the three-electron reduced density matrix in the anti-Hermitian contracted Schrödinger equation

J. Chem. Phys. 127, 104104 (2007); doi:10.1063/1.2768354

Published 12 September 2007

You are not logged in to this journal. Log in

A. Eugene DePrince, III and David A. Mazziotti
Department of Chemistry and The James Franck Institute, The University of Chicago, Chicago, Illinois 60637, USA
Differing perspectives on the accuracy of three-electron reduced-density-matrix (3-RDM) reconstruction in nonminimal basis sets exist in the literature. This paper demonstrates the accuracy of cumulant-based reconstructions, developed by Valdemoro (V) [F. Colmenero et al., Phys. Rev. A 47, 971 (1993)], Nakatsuji and Yasuda (NY) [Phys. Rev. Lett. 76, 1039 (1996)], Mazziotti (M) [Phys. Rev. A 60, 3618 (1999)], and Valdemoro–Tel–Pérez–Romero (VTP) [Many-electron Densities and Density Matrices, edited by J. Cioslowski (Kluwer, Boston, 2000)]. Computationally, we extend previous investigations to study a variety of molecules, including LiH, HF, NH3, H2O, and N2, in Slater-type, double-zeta, and polarized double-zeta basis sets at both equilibrium and nonequilibrium geometries. The reconstructed 3-RDMs, compared with 3-RDMs from full configuration interaction, demonstrate in nonminimal basis sets the accuracy of the first-order expansion (V) as well as the important role of the second-order corrections (NY, M, and VTP). Calculations at nonequilibrium geometries further show that cumulant functionals can reconstruct the 3-RDM from a multireferenced 2-RDM with reasonable accuracy, which is relevant to recent multireferenced formulations of the anti-Hermitian contracted Schrödinger equation (ACSE) and canonical diagonalization. Theoretically, we perform a detailed perturbative analysis of the M functional to identify its second-order components. With these second-order components we connect the M, NY, and VTP reconstructions for the first time by deriving both the NY and VTP functionals from the M functional. Finally, these 3-RDM reconstructions are employed within the ACSE [D. Mazziotti, Phys. Rev. Lett. 97, 143002 (2006)] to compute ground-state energies which are compared with the energies from the contracted Schrödinger equation and several wave function methods. ©2007 American Institute of Physics
History: Received 22 February 2007; accepted 10 July 2007; published 12 September 2007
Permalink: http://link.aip.org/link/?JCPSA6/127/104104/1
BUY THIS ARTICLE   (US$28)
Download HTML Download Sectioned HTML Download PDF (585 kB) View Cart

KEYWORDS and PACS

Keywords
PACS
  • 31.10.+z
    Theory of electronic structure, electronic transitions, and chemical binding in atoms and molecules
  • 03.65.Ge
    Solutions of wave equations: bound states in quantum mechanics
  • 31.15.Md
    Perturbation theory (atoms and molecules)
  • YEAR: 2007

RELATED DATABASES


To view database links for this article,
you need to log in.
To view database links for this article,
you need to log in.

PUBLICATION DATA

ISSN:
0021-9606 (print)   1089-7690 (online)
Publisher:
AIP is a member of CrossRef AIP

REFERENCES (73)
View in Separate Window/Tab
For access to fully linked references, you need to log in. For access to fully linked references, you need to Log in.
  1. J. E. Mayer, Phys. Rev. 100, 1579 (1955);
  2. P. O. Löwdin, Phys. Rev. 97, 1474 (1955).
  3. A. J. Coleman and V. I. Yukalov, Reduced Density Matrices: Coulson's Challenge (Springer-Verlag, New York, 2000).
  4. 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).
  5. C. Garrod, V. Mihailović, and M. Rosina, J. Math. Phys. 10, 1855 (1975).
  6. R. M. Erdahl and B. Jin, in Many-electron Densities and Density Matrices, edited by J. Cioslowski (Kluwer, Boston, 2000).
  7. D. A. Mazziotti and R. M. Erdahl, Phys. Rev. A 63, 042113 (2001).
  8. M. Nakata, H. Nakatsuji, M. Ehara, M. Fukuda, K. Nakata, and K. Fujisawa, J. Chem. Phys. 114, 8282 (2001).
  9. D. A. Mazziotti, Phys. Rev. A 65, 062511 (2002).
  10. T. Juhász and D. A. Mazziotti, J. Chem. Phys. 121, 1201 (2004).
  11. Z. Zhao, B. J. Braams, H. Fukuda, M. L. Overton, and J. K. Percus, J. Chem. Phys. 120, 2095 (2004).
  12. D. A. Mazziotti, Phys. Rev. Lett. 93, 213001 (2004).
  13. D. A. Mazziotti, J. Chem. Phys. 121, 10957 (2004).
  14. G. Gidofalvi and D. A. Mazziotti, J. Chem. Phys. 122, 194104 (2005).
  15. J. R. Hammond and D. A. Mazziotti, Phys. Rev. A 73, 012509 (2006).
  16. G. Gidofalvi and D. A. Mazziotti, J. Phys. Chem. A 110, 5481 (2006).
  17. E. Cancès, G. Stoltz, and M. Lewin, J. Chem. Phys. 125, 064101 (2006).
  18. D. A. Mazziotti, Phys. Rev. A 74, 032501 (2006).
  19. G. Gidofalvi and D. A. Mazziotti, J. Chem. Phys. 125, 144102 (2006).
  20. G. Gidofalvi and D. A. Mazziotti, J. Chem. Phys. 126, 024105 (2007).
  21. D. A. Mazziotti, Acc. Chem. Res. 39, 207 (2006).
  22. F. Colmenero, C. Pérez del Valle, and C. Valdemoro, Phys. Rev. A 47, 971 (1993).
  23. F. Colmenero and C. Valdemoro, Phys. Rev. A 47, 979 (1993).
  24. F. Colmenero and C. Valdemoro, Int. J. Quantum Chem. 51, 369 (1994).
  25. C. Valdemoro, L. M. Tel, and E. Pérez-Romero, Adv. Quantum Chem. 28, 33 (1997).
  26. H. Nakatsuji and K. Yasuda, Phys. Rev. Lett. 76, 1039 (1996).
  27. K. Yasuda and H. Nakatsuji, Phys. Rev. A 56, 2648 (1997).
  28. D. A. Mazziotti, Phys. Rev. A 57, 4219 (1998).
  29. D. A. Mazziotti, Chem. Phys. Lett. 289, 419 (1998).
  30. D. A. Mazziotti, Int. J. Quantum Chem. 70, 557 (1998).
  31. K. Yasuda, Phys. Rev. A 59, 4133 (1999).
  32. D. A. Mazziotti, Phys. Rev. A 60, 3618 (1999).
  33. D. A. Mazziotti, Phys. Rev. A 60, 4396 (1999).
  34. W. Kutzelnigg and D. Mukherjee, J. Chem. Phys. 110, 2800 (1999).
  35. C. Valdemoro, M. P. de Lara-Castells, E. Pérez-Romero, and L. M. Tel, Adv. Quantum Chem. 31, 37 (1999).
  36. C. Valdemoro, L. M. Tel, and E. Pérez-Romero, in Many-electron Densities and Density Matrices, edited by J. Cioslowski (Kluwer, Boston, 2000).
  37. H. Nakatsuji, in Many-electron Densities and Density Matrices, edited by J. Cioslowski (Kluwer, Boston, 2000).
  38. D. A. Mazziotti, in Many-electron Densities and Density Matrices, edited by J. Cioslowski (Kluwer, Boston, 2000).
  39. D. A. Mazziotti, Chem. Phys. Lett. 326, 212 (2000).
  40. W. Kutzelnigg and D. Mukherjee, J. Chem. Phys. 114, 2047 (2001).
  41. D. A. Mazziotti, Chem. Phys. Lett. 338, 323 (2001).
  42. D. A. Mazziotti, Phys. Rev. E 65, 026704 (2002).
  43. D. A. Mazziotti, J. Chem. Phys. 116, 1239 (2002).
  44. J. E. Harriman, Phys. Rev. A 65, 052507 (2002).
  45. J. M. Herbert and J. E. Harriman, Phys. Rev. A 65, 022511 (2002).
  46. D. A. Mazziotti, Phys. Rev. A 66, 062503 (2002).
  47. J. M. Herbert and J. E. Harriman, J. Chem. Phys. 117, 7464 (2002).
  48. F. E. Harris, Int. J. Quantum Chem. 90, 105 (2002).
  49. M. Nooijen, M. Wladyslawski, and A. Hazra, J. Chem. Phys. 118, 4832 (2003).
  50. W. Kutzelnigg and D. Mukherjee, J. Chem. Phys. 120, 7350 (2004).
  51. D. A. Mazziotti, Phys. Rev. A 69, 012507 (2004).
  52. M. D. Benayoun, A. Y. Lu, and D. A. Mazziotti, Chem. Phys. Lett. 387, 485 (2004).
  53. D. R. Alcoba and C. Valdemoro, Int. J. Quantum Chem. 102, 629 (2005).
  54. D. R. Alcoba, F. J. Casquero, L. M. Tel, E. Pérez-Romero, and C. Valdemoro, Int. J. Quantum Chem. 102, 620 (2005).
  55. D. A. Mazziotti, Phys. Rev. Lett. 97, 143002 (2006).
  56. D. A. Mazziotti, Phys. Rev. A 75, 022505 (2007).
  57. D. A. Mazziotti, J. Chem. Phys. 126, 184101 (2007).
  58. C. Valdemoro, L. M. Tel, D. R. Alcoba, and E. Pérez-Romero (unpublished).
  59. J. M. Herbert, Int. J. Quantum Chem. 107, 703 (2007).
  60. A. J. Coleman, Rev. Mod. Phys. 35, 668 (1963).
  61. C. Garrod and J. Percus, J. Math. Phys. 5, 1756 (1964).
  62. D. A. Mazziotti (submitted).
  63. T. Yanai and G. K. Chan, J. Chem. Phys. 124, 194106 (2006).
  64. L. Cohen and C. Frishberg, Phys. Rev. A 13, 927 (1976).
  65. H. Nakatsuji, Phys. Rev. A 14, 41 (1976).
  66. W. Slebodziński, Exterior Forms and their Applications (Polish Scientific, Warsaw, 1970).
  67. L. Brillouin, J. Phys. Radium 3, 373 (1932).
  68. D. A. Mazziotti (unpublished).
  69. M. W. Schmidt, K. K. Bladridge, J. A. Boatz et al., J. Comput. Chem. 14, 1347 (1993).
  70. Handbook of Chemistry and Physics, 79th ed. (CRC, Boca Raton, 1998).
  71. W. J. Hehre, R. F. Stewart, and J. A. Pople, J. Chem. Phys. 51, 2657 (1969).
  72. T. H. Dunning, Jr. and P. J. Hay, in Methods of Electronic Structure Theory, edited by H. F. Schaeffer, III (Plenum, New York, 1977), Vol. 2.
  73. T. H. Dunning, Jr., J. Chem. Phys. 90, 1007 (1989).
  74. R. A. Kendall, E. Apra, D. E. Bernholdt et al., Comput. Phys. Commun. 128, 260 (2000).

CITING ARTICLES
For access to citing articles, you need to log in.
For access to citing articles, you need to Log in.


Copyright © American Institute of Physics