Recent developments in the contracted Schrödinger equation method: Controlling the N-representability of the second-order reduced density matrix

International Journal of Quantum Chemistry

Volumn 93, Issue 3, 2003, Pages 212-222

  Valdemoro, C ^a   Alcoba, D R ^a   Tel, L M ^b  

^a INSTITUTO DE MATEMÁTICAS Y FÍSICA FUNDAMENTAL   (Spain)

^b UNIVERSITY OF SALAMANCA   (Spain)

Author keywords

Contracted Schr dinger equation; N representability; Reduced density matrices; Spin orbitals

Indexed keywords

ALGORITHMS; APPROXIMATION THEORY; CALCULATIONS; CONVERGENCE OF NUMERICAL METHODS; EIGENVALUES AND EIGENFUNCTIONS; GROUND STATE; HAMILTONIANS; ITERATIVE METHODS; MATHEMATICAL MODELS; MATRIX ALGEBRA; MOLECULES;

CONTRACTED SCHRODINGER EQUATION; N-REPRESENTABILITY; REDUCED DENSITY MATRICES; SPIN ORBITALS;

QUANTUM THEORY;

EID: 0038731121     PISSN: 00207608     EISSN: None     Source Type: Journal    
DOI: 10.1002/qua.10553     Document Type: Article

References (61)

1. Coleman, A. J.; Yukalov, V. I. Reduced Density Matrices-Coulson's Challenge, Lecture Notes in Chemistry, Vol. 72; Springer: New York, 2000.
2. Coleman, A. J. Rev Mod Phys 1963, 35, 668.
3. Davidson, E. R. Reduced Density Matrices in Quantum Chemistry; Academic Press: New York, 1976; and references therein.
4. Reduced Density Matrices with Applications to Physical and Chemical Systems, Queen's Papers on Pure and Applied Mathematics, No. 11; Queen's University: Kingston, Ontario, 1968.
5. Erdahl, R. M., ed. Reduced Density Matrices with Applications to Physical and Chemical Systems II, Queen's Papers on Pure and Applied Mathematics, No. 40; Queen's University: Kingston, Ontario, 1974.
6. Erdahl, R; Smith, V., eds. Density Matrices and Density Functionals, Proceedings of the A. J. Coleman Symposium; Reidel: Dordrecht, The Netherlands, 1987.
7. Cioslowsky, J., ed. Many-Electron Densities and Reduced Density Matrices; Kluwer: Berlin, 2000.
8. Valdemoro, C. In: Erdahl, R.; Smith, V., eds. Density Matrices and Density Functionals, Proceedings of the A. J. Coleman Symposium; Reidel: Dordrecht, The Netherlands, 1987; p 275.
9. Cho, S. Sci Rep Gumma Univ 1962, 11, 1.
10. Cohen, L.; Frishberg, C. Phys Rev A 1976, 13, 927.
11. Cohen, L.; Frishberg, C. J Chem Phys 1976, 65, 4234.
12. Nakatsuji, H. Phys Rev A 1976, 14, 41.
13. Mazziotti, D. Phys Rev E 2002, 65, 026704.
14. Coleman, A. J. In: Erdahl, R. M., ed. Reduced Density Matrices with Applications to Physical and Chemical Systems II, Queen's Papers on Pure and Applied Mathematics, No. 40; Queen's University: Kingston, Ontario, 1974.
15. Coleman, A. J.; Absar, I. Chem Phys Lett 1976, 39, 609.
16. Coleman, A. J.; Absar, I. Int J Quantum Chem 1980, 18, 1279.
17. Tang, A.-C.; Guo, H. Int J Quantum Chem 1983, 23, 217.
18. Sun, C.-C.; Li, X.-Q.; Tang, A.-C. Int J Quantum Chem 1984, 25, 653.
19. Sun, C.-C.; Li, X.-Q.; Tang, A.-C. Int J Quantum Chem 1984, 25, 1045.
20. Casida, M. E.; Harriman, J. E. Int J Quantum Chem 1986, 30, 161.
21. de Lara-Castells, M. P. Thesis; Universita Autonoma de Madrid: Madrid, 1999; Chapter VII.
22. Valdemoro, C. Phys Rev A 1992, 45, 4462.
23. Colmenero, F.; Valdemoro, C. Int J Quantum Chem 1994, 51, 369.
24. Valdemoro, C.; Tel, L. M.; Pérez-Romero, E. Adv Quantum Chem 1997, 28, 33.
25. Garrod, C.; Rosina, M. J Math Phys 1969, 10, 1855.
26. Mihailovic, M. V.; Rosina, M. Nucl Phys A 1969, 130, 386.
27. Valdemoro, C.; de Lara-Castells, M. P.; Pérez-Romero, E.; Tel, L. M. Adv Quantum Chem 1999, 31, 37.
28. Mazziotti, D. A. J Chem Phys 2002, 116, 1239.
29. Garrod, C.; Percus, J. K. J Math Phys 1964, 5, 1756.
30. Erdahl, R. In: Erdahl, R.; Smith, V., eds. Density Matrices and Density Functionals, Proceedings of the A. J. Coleman Symposium; Reidel: Dordrecht, The Netherlands, 1987; p 51.
31. Coleman, A. J. Int J Quantum Chem 1977, 11, 907.
32. Kummer, H. J Math Phys 1967, 8, 2063.
33. Grudzinski, H. In: Erdahl, R.; Smith, V., eds. Density Matrices and Density Functionals, Proceedings of the A. J. Coleman Symposium; Reidel: Dordrecht, The Netherlands, 1987; p 89.
34. Beste, A.; Runge, K.; Barlett, R. Chem Phys Lett 2002, 355, 263.
35. Erdahl, R. M. Int J Quantum Chem 1978, 13, 697.
36. Percus, J. K. Int J Quantum Chem 1978, 13, 89.
37. Rosina, M.; Golli, B.; Erdahl, R. M. In: Erdahl, R.; Smith, V., eds. Density Matrices and Density Functionals, Proceedings of the A. J. Coleman Symposium; Reidel: Dordrecht, The Netherlands, 1987; p 231.
38. Valdemoro, C.; Tel, L. M.; Pérez-Romero, E. Phys Rev A 2000, 61, 32507.
39. Valdemoro, C.; Tel, L. M.; Pérez-Romero, E. In: Hernández-Laguna, A.; Maruani, J.; McWeeny, R.; Wilson, S., eds. Quantum Systems in Chemistry and Physics, I; Kluwer: Dordrecht, The Netherlands, 2000.
40. Valdemoro, C.; Alcoba, D. R.; Tel, L. M.; Pérez-Romero, E. Int J Quantum Chem 2001, 85, 214.
41. Davidson, E. R. Int J Quantum Chem (published online).
42. Valdemoro, C.; Tel, L. M.; Pérez-Romero, E. In: Cioslowsky, J., ed. Many-Electron Densities and Reduced Density Matrices; Kluwer: Dordrecht, The Netherlands, 2000.
43. Tel, L. M.; Pérez-Romero, E.; Valdemoro, C.; Casquero, F. J. Phys Rev A 2001, 82, 131.
44. Alcoba, D. R. Phys Rev A 2002, 65, 032519.
45. Mazziotti, D. A. Phys Rev A 1998, 57, 4219.
46. Mazziotti, D. A. Chem Phys Lett 1998, 289, 419.
47. Mazziotti, D. A. Int J Quantum Chem 1998, 70, 557.
48. Mazziotti, D. A. Phys Rev A 1999, 60, 3618.
49. Mazziotti, D. A. Chem Phys Lett 2000, 326, 212.
50. Kutzelnigg, W.; Mukherjee, D. J Chem Phys 1999, 110, 2800.
51. Harriman, J. E. Phys Rev A 2002, 65, 052507.
52. Valdemoro, C.; Tel, L. M.; Alcoba, D. R.; Pérez-Romero, E.; Casquero, F. J. Int J Quantum Chem (published online).
53. Valdemoro, C.; Tel, L. M.; Pérez-Romero, E. J Mol Struct Theochem 2001, 537, 1.
54. Nakatsuji, H.; Yasuda, K. Phys Rev Lett 1996, 76, 1039.
55. Yasuda, K.; Nakatsuji, H. Phys Rev A 1997, 56, 2648.
56. Valdemoro, C. In: Surjan, P., ed. Topics in Current Chemistry, Correlation and Localization; Springer-Verlag, New York, 1999.
57. Herbert, J. M.; Harriman, J. E. Phys Rev A 2002, 65, 022511.
58. McWeeny, R.; Mizuno, Y. Proc Roy Soc Lond 1961, A259, 554.
59. Valdemoro, C. Phys Rev A 1985, 31, 2114.
60. Valdemoro, C. In: Fraga, S., ed. Computational Chemistry Structure, Interactions and Reactivity, Part A; Elsevier: New York, 1992; p 114 and references therein.
61. Karwowski, J.; Duch, W.; Valdemoro, C. Phys Rev A 1986, 33, 2254.