Grand-canonical-ensemble representability problem for the one-electron reduced density matrix

Physical Review A - Atomic, Molecular, and Optical Physics

Volumn 75, Issue 1, 2007, Pages

  Alcoba, D R ^a   Bochicchio, R C ^a   Massacessi, G E ^a   Lain, L ^b   Torre, A ^b  

^a UNIVERSIDAD DE BUENOS AIRES   (Argentina)

^b UNIVERSITY OF THE BASQUE COUNTRY UPV EHU   (Spain)

Author keywords

[No Author keywords available]

Indexed keywords

ELECTRON DENSITY MEASUREMENT; PROBLEM SOLVING; STATISTICAL METHODS;

DENSITY MATRIX; ELECTRON REDUCED DENSITY MATRIX; ELECTRON SYSTEMS;

ELECTRONS;

EID: 33846497805     PISSN: 10502947     EISSN: 10941622     Source Type: Journal    
DOI: 10.1103/PhysRevA.75.012509     Document Type: Article

References (56)

1. P. A. M. Dirac, Proc. Cambridge Philos. Soc. PCPSA4 0068-6735 27, 240 (1931).
2. K. Husimi, Proc. Phys. Math. Soc. Jpn. PPMJAJ 0370-1239 22, 264 (1940).
3. P. O. Löwdin, Phys. Rev. PHRVAO 0031-899X 10.1103/PhysRev.97.1474 97, 1474 (1955).
4. E. R. Davidson, Reduced Density Matrices in Quantum Chemistry (Academic, New York, 1976).
5. Reduced Density Matrices with Applications to Physical and Chemical Systems, Queen’s Papers on Pure and Applied Mathematics, No. 11, edited by, A. J. Coleman, and, R. M. Erdahl, (Queen’s University, Kingston, Ontario, 1968).
6. Reduced Density Matrices with Applications to Physical and Chemical Systems II, Queen’s Papers on Pure and Applied Mathematics, No. 40, edited by, R. M. Erdahl, (Queen’s University, Kingston, Ontario, 1974).
7. Density Matrices and Density Functionals, Proceedings of the A. J. Coleman Symposium, Kingston, Ontario, 1985, edited by, R. Erdahl, and, V. Smith, (Reidel, Dordrecht, 1987).
8. R. G. Parr and W. Yang, Density-Functional Theory of Atoms and Molecules (Oxford University Press, New York, 1989).
9. A. J. Coleman and V. I. Yukalov, Reduced Density Matrices: Coulson’s Challenge (Springer-Verlag, New York, 2000).
10. Many-electron Densities and Reduced Density Matrices, edited by, J. Cioslowsky, (Kluwer, Dordrecht, 2001).
11. A. J. Coleman, Int. J. Quantum Chem. IJQCB2 0020-7608 10.1002/qua.1537 85, 196 (2001) and references therein.
12. Reduced-Density-matrix Mechanics with Applications to Many-electron Atoms and Molecules, Advances in Chemical Physics, Vol. 134, edited by, D. A. Mazziotti, (Wiley, New York, 2007).
13. A. J. Coleman, Rev. Mod. Phys. RMPHAT 0034-6861 10.1103/RevModPhys.35.668 35, 668 (1963).
14. H. Kummer, J. Math. Phys. JMAPAQ 0022-2488 10.1063/1.1705122 8, 2063 (1967).
15. R. M. Erdahl, Int. J. Quantum Chem. IJQCB2 0020-7608 10.1002/qua. 560130603 13, 697 (1978).
16. C. Garrod and J. Percus, J. Math. Phys. JMAPAQ 0022-2488 10.1063/1.1704098 5, 1756 (1964).
17. E. B. Davies, Quantum Theory of Open Systems (Academic, New York, 1976) and references therein.
18. R. G. Parr, R. A. Donnelly, M. Levy, and W. E. Palke, J. Chem. Phys. JCPSA6 0021-9606 10.1063/1.436185 68, 3801 (1978).
19. S. M. Valone, J. Chem. Phys. JCPSA6 0021-9606 10.1063/1.440249 73, 1344 (1980);
20. S. M. Valone, J. Chem. Phys. JCPSA6 0021-9606 10.1063/1.440656 73, 4653 (1980).
21. J. P. Perdew, R. G. Parr, M. Levy, and J. L. Balduz, Jr., Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.49.1691 49, 1691 (1982).
22. J. P. Perdew, in Density Functional Methods in Physics, edited by, R. M. Dreizler, (Plenum Press, New York, 1985).
23. V. Russier, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.45.8894 45, 8894 (1992).
24. A. Savin, in Recent Developments and Applications of Modern Density Functional Theory, edited by, J. M. Seminario, (Elsevier, Amsterdam, 1996).
25. J. P. Perdew and M. Levy, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.56.16021 56, 16021 (1997).
26. W. Yang, Y. Zhang, and P. W. Ayers, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.84.5172 84, 5172 (2000).
27. L. Wei and C. Sun, Physica A PHYADX 0378-4371 334, 144 (2004).
28. R. Balawender and P. Geerlings, J. Chem. Phys. JCPSA6 0021-9606 10.1063/1.2012329 123, 124102 (2005).
29. S. Jacobi and R. Baer, J. Chem. Phys. JCPSA6 0021-9606 10.1063/1.1949202 123, 44112 (2005).
30. N. Helbig, N. N. Lathiotakis, M. Albrecht, and E. K. U. Gross, e-print cond-mat/0504436.
31. C. Cardenas, E. Chamorro, M. Galvan, and P. Fuentealba, Int. J. Quantum Chem. IJQCB2 0020-7608 10.1002/qua.21202 107, 807 (2007).
32. M. Piris, L. A. Montero, and N. Cruz, J. Chem. Phys. JCPSA6 0021-9606 10.1063/1.474363 107, 180 (1997).
33. R. Daudel, R. F. W. Bader, M. E. Stephens, and D. S. Borrett. Can. J. Chem. CJCHAG 0008-4042 52, 1310 (1974);
34. R. Daudel, R. F. W. Bader, M. E. Stephens, and D. S. Borrett. Can. J. Chem. CJCHAG 0008-4042 52, 3077 (1974).
35. F. L. Hirshfeld, Theor. Chim. Acta TCHAAM 0040-5744 10.1007/BF00549096 44, 129 (1977).
36. R. F. W. Bader, Atoms in Molecules: A Quantum Theory (Oxford University Press, Oxford, 1990).
37. R. C. Bochicchio, L. Lain, and A. Torre, J. Chem. Phys. JCPSA6 0021-9606 10.1063/1.1851976 122, 84117 (2005);
38. D. R. Alcoba, L. Lain, A. Torre, and R. C. Bochicchio, J. Chem. Phys. JCPSA6 0021-9606 10.1063/1.2069927 123, 144113 (2005);
39. D. R. Alcoba, R. C. Bochicchio, A. Torre, and L. Lain, J. Phys. Chem. A JPCAFH 1089-5639 110, 9254 (2006).
40. K. Blum, Density Matrix Theory and Applications (Plenum Press, New York, 1981).
41. A. Beste, K. Runge, and R. Barlett, Chem. Phys. Lett. CHPLBC 0009-2614 10.1016/S0009-2614(02)00239-7 355, 263 (2002).
42. V. Chvátal, Linear Programming (Freeman, New York, 1983);
43. A. Barvinok, A Course in Convexity, Graduate Studies in Mathematics, Vol. 54 (American Mathematical Society, Providence, RI, 2002).
44. F. Weinhold and E. B. Wilson, J. Chem. Phys. JCPSA6 0021-9606 10.1063/1.1703311 47, 2298 (1967).
45. M. L. Yoseloff and H. W. Kuhn, J. Math. Phys. JMAPAQ 0022-2488 10.1063/1.1664896 10, 703 (1969).
46. J. E. Harriman, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.17.1249 17, 1249 (1978);
47. J. E. Harriman, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.17.1257 17, 1257 (1978).
48. E. R. Davidson, J. Math. Phys. JMAPAQ 0022-2488 10.1063/1.1664899 10, 725 (1969);
49. W. E. McRae and E. R. Davidson, J. Math. Phys. JMAPAQ 0022-2488 10.1063/1.1665874 13, 1527 (1972);
50. E. R. Davidson, Int. J. Quantum Chem. IJQCB2 0020-7608 10.1002/qua.10340 91, 1 (2003).
51. C. Valdemoro, L. M. Tel, and E. Perez-Romero, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.61.032507 61, 032507 (2000);
52. C. Valdemoro, D. R. Alcoba, L. M. Tel, and E. Perez-Romero, Int. J. Quantum Chem. IJQCB2 0020-7608 10.1002/qua.1517 85, 214 (2001);
53. C. Valdemoro, D. R. Alcoba, and L. M. Tel, Int. J. Quantum Chem. IJQCB2 0020-7608 10.1002/qua.10553 93, 212 (2003).
54. A. J. Coleman, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.66.022503 66, 022503 (2002).
55. D. A. Mazziotti, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.65.026704 65, 026704 (2002).
56. P. W. Ayers and M. Levy, J. Chem. Sci. JCSBB5 0253-4134 117, 507 (2005).