Explicit density functionals for the energy by means of padé approximants to local-scaling transformations

Theoretical and Computational Chemistry

Volumn 4, Issue C, 1996, Pages 25-65

  Ludeña, Eduardo V ^a   López Boada, Roberto ^a   Pino, Ramiro ^a  

^a INSTITUTO VENEZOLANO DE INVESTIGACIONES CIENTÍFICAS   (Venezuela)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 77956710155     PISSN: 13807323     EISSN: None     Source Type: Book Series    
DOI: 10.1016/S1380-7323(96)80084-7     Document Type: Chapter

References (120)

1. Kryachko E.S., and Ludeña E.V. Energy Density Functional Theory of Many-Electron Systems (1990), Kluwer Academic Publishers, Dordrecht
2. Parr R.G., and Yang W. Density Functional Theory of Atoms and Molecules (1989), Oxford University Press, Oxford
3. Dreizler R.M., and Gross E.K.U. Density Functional Theory (1990), Springer-Verlag, Berlin
4. March N.H. Electron Density Theory of Atoms and Molecules (1992), Academic Press, New York
5. Hohenberg P.C., and Kohn W. Phys. Rev. 136B (1964) 864
6. Hohenberg P.C., Kohn W., and Sham L.J. Adv. Quantum Chem. 21 (1990) 7
7. Kohn W., and Sham L.J. Phys. Rev. 140A (1965) 1133
8. Löwdin P.-O. In: Erdahl R., and Smith V.H. (Eds). Density Matrices and Density Functionals (1987), D. Reidel, Dordrecht 21
9. March N.H. Adv. in Phys. 6 (1957) 1
10. Coleman A.J. Revs. Mod. Phys. 35 (1963) 668
11. Lieb E.H. Rev. Mod. Phys. 53 (1981) 603
12. Coleman A.J. In: Erdahl R., and Smith V.H. (Eds). Density Matrices and Density Functional (1987), D. Reidel, Dordrecht 5
13. See also, Reference [1], Section 4.4
14. Kryachko E.S., and Ludeña E.V. Phys. Rev. A 43 (1991) 2179
15. See laso, Reference [1], Chapter 7 and 8.
16. Petkov I.Zh., Stoitsov M.V., and Kryachko E.S. Int. J. Quantum Chem. 29 (1986) 149
17. Kryachko E.S., Petkov I.Zh., and Stoitsov M.V. Int. J. Quantum Chem. 32 (1987) 467
18. Kryachko E.S., Petkov I.Zh., and Stoitsov M.V. Int. J. Quantum Chem. 32 (1987) 473
19. Kryachko E.S., and Ludeña E.V. Phys. Rev. A 35 (1987) 957
20. Kryachko E.S., Petkov I.Zh., and Stoitsov M.V. Int. J. Quantum Chem. 34 (1988) 305E
21. Kryachko E.S., and Ludeña E.V. Phys. Rev. A 43 (1991) 2194
22. Petkov I.Zh., and Stoitsov M.V. Nuclear Density Functional Theory (1991), Oxford University Press, New York
23. Kryachko E.S., and Ludeña E.V. In: Fraga S. (Ed). Computational Chemistry: Structure, Interactions and Reactivity (1992), Elsevier, Amsterdam 136
24. Ludeña E.V., and Kryachko E.S. Rev. Mex. Astr. y Astrofis. 23 (1992) 95
25. Kryachko E.S., and Ludeña E.V. In: Proto A.N., and Aliaga J.L. (Eds). Condensed Matter Theories Vol. 7 (1992), Plenum, New York 101
26. Kryachko E.S., and Ludeña E.V. New J. Chem. 16 (1992) 1089
27. Kryachko E.S., and Ludeña E.V. J. Chem. Phys. 95 (1991) 9054
28. Kryachko E.S., and Koga T. J. Chem. Phys. 91 (1989) 1108
29. Koga T., Yamamoto Y., and Kryachko E.S. J. Chem. Phys. 91 (1989) 4785
30. Koga T. Phys. Rev. A 41 (1990) 1274
31. Koga T. Phys. Rev. A 42 (1990) 3763
32. Koga T. J. Chem. Phys. 93 (1990) 5856
33. Koga T., and Yamamoto Y. Phys. Rev. A 42 (1990) 6336
34. Koga T., and Kryachko E.S. J. Chem. Phys. 94 (1991) 2910
35. Koga T., Yamamoto Y., and Ludeña E.V. J. Chem. Phys. 94 (1991) 3805
36. Koga T., Yamamoto Y., and Ludeña E.V. Phys. Rev. A 43 (1991) 5814
37. Koga T. J. Chem. Phys. 95 (1991) 4306
38. Kryachko E.S., and Koga T. Int. J. Quantum Chem. 42 (1992) 591
39. Koga T., and Matsuyama H. Phys. Rev. A 45 (1992) 5266
40. Kryachko E.S., Ludeña E.V., and Koga T. In: Clementi E. (Ed). Methods and Techniques in Computational Chemistry, METECC-94, Vol. B: Medium Size Systems (1993), STEF, Cagliari 23
41. Kryachko E.S., Ludeña E.V., and Koga T. J. Math. Chem. 11 (1992) 325
42. Kryachko E.S., and Ludeña E.V. Int. J. Quantum Chem. 43 (1992) 769
43. Kryachko E.S., Ludeña E.V., López-Boada R., and Maldonado J. In: Blum L., and Malik F.B. (Eds). Condensed Matter Theories Vol. 8 (1993), Plenum, New York 373
44. Ludeña E.V., López-Boada R., Maldonado J., Koga T., and Kryachko E.S. Phys. Rev. A 48 (1993) 1937
45. Kryachko E.V., López-Boada R., and Maldonado J. In: Clark J.W., Sadiq A., and Shoaib K.A. (Eds). Condensed Matter Theories Vol. 9 (1994), Nova Science Publishers, Commack, N.Y. 97
46. E.V. Ludeña, R. López-Boada and J. Maldonado, J. Mol. Struct. (Theochem) 330, 33.
47. Ludeña E.V., Maldonado J., López-Boada R., Koga T., and Kryachko E.S. J. Chem. Phys. 102 (1995) 318
48. Ludeña E.V., Kryachko E.S., Koga T., López-Boada R., Hinze J., Maldonado J., and Valderrama E. In: Seminario J.M., and Politzer P. (Eds). Density Functional Theory: A Tool for Chemistry (1995), Elsevier, Amsterdam 75
49. J. Maldonado, E.V. Ludeña, R. López-Boada, V. Karasiev, O. Bokanowski. Application of the local-scaling transformation version of density functional theory to diatomic molecules. Int. J. Quantum Chem. (to be submitted).
50. Thomas L.H. Proc. Cambridge Phil. Soc. 23 (1927) 542
51. Fermi E. Rend. Accad. Naz. Lincei 6 (1927) 602
52. Dirac P.A.M. Proc. Cambridge Phil. Soc. 26 (1930) 376
53. Wigner E. Phys. Rev. A 96 (1935) 431
54. Kirzhnitz D.A. Zh. Eksp. Teor. Fiz. 32 (1957) 115
55. Hodges C.H. Can. J. Phys. 51 (1973) 1428
56. Grammaticos B., and Voros A. Ann. Phys. 129 (1979) 153
57. Murphy D.R. Phys. Rev. A 24 (1981) 1682
58. Yang W. Phys. Rev. A 34 (1986) 4575
59. Holas A., and March N.H. Phys. Rev. A 51 (1993) 2040
60. Holas A., March N.H., Takahashi Y., and Zhang C. Phys. Rev. A 48 (1993) 2708
61. Dawson K.A., and March N.H. J. Chem. Phys. 81 (1984) 5850
62. March N.H. In: Ludeña E.V., Vashishta P., and Bishop R.F. (Eds). Condensed Matter Theories Vol. 11 (1996), Nova Science Pubkishers, Commack, N.Y. 23
63. Cohen L., and Frishberg C. Phys. Rev. A 13 (1976) 927
64. Nakatsuji H. Phys. Rev. A 14 (1976) 41
65. Hunter G. In: Erdahl R., and Smith V.H. (Eds). Density Matrices and Density Functionals (1985), Reidel, Dordrecht 583
66. Hunter G. Int. J. Quantum Chem. 29 (1986) 197
67. Hunter G. Int. J. Quantum Chem. 19 (1981) 755
68. Hunter G. Int. J. Quantum Chem. 9 (1975) 237
69. Harbola M.K., and Sahni V. Phys. Rev. Lett. 62 (1989) 489
70. Valdemoro C. Phys. Rev. A 45 (1992) 4462
71. Sule P., Gritsenko O.V., Nagy A., and Baerends E.V. J. Chem. Phys. 103 (1995) 10085
72. Nguyen-Dang T.T., Ludeña E.V., and Tal Y. J. Mol. Struct. (Theochem) 120 (1985) 247
73. Ludeña E.v., and Keller J. Adv. Quantum Chem. 21 (1990) 47
74. Pino R., Ludeña E.V., and López-Boada R. In: Navarro J., and de Llano M. (Eds). condensed Matter Theories 10 (1995), Nova Science Publishers, Commack, N.Y. 189
75. Levy M. Proc. Natl. Acad. Sci. USA 76 (1979) 6062
76. Lieb E.H. Int. J. Quantum Chem. 24 (1983) 243
77. Payne P.W. J. Chem. Phys. 71 (1979) 490
78. Percus J.K. Int. J. Quantum Chem. 13 (1978) 89
79. Cioslowski J. Adv. Quantum Chem. 21 (1990) 303
80. McWeeny R. Phil. Mag. B 69 (1994) 727
81. It may be argued, however, that this example only proves that if such universal functional exists it cannot be expressed in GGA form (we thank J.M. Seminario for bringing up this point). Gill P.M.W., and Pople J.A. Phys. Rev. A 47 (1993) 2383
82. Macke W. Phys. Rev. 100 (1955) 992
83. Macke W. Ann. Phys. (Leipzig) 17 (1955) 1
84. March N.H., and Young W.H. Proc. Roy. Soc. London 72 (1958) 182
85. Hall G.G. Proc. Roy. Soc. London 75 (1960) 575
86. Moser J. Trans. Amer. Math. Soc. 120 (1965) 286
87. Gilbert T.L. Phys. Rev. B 12 (1975) 2111
88. Harriman J.E. Phys. Rev. A 24 (1981) 680
89. Lieb E.H. In: Feshback H., and Shimony A. (Eds). Physics as Natural Philosophy: Essays in Honor of Laszlo Tisza on his 75th Birthday (1982), MIT Press, Cambridge, MA 111
90. Lieb E.H. In: Dreizler R.M., and da Providencia J. (Eds). Density Functional Methods in Physics (1985), Plenum, New York 31
91. Ludeña E.V. J. Chem. Phys. 79 (1983) 6174
92. Zumbach G., and Maschke K. Phys. Rev. A 28 (1983) 544
93. Zumbach G., and Maschke K. Phys. Rev. A 29 (1984) 1585E
94. Nyden M.R., and Parr R.G. J. Chem. Phys. 78 (1983) 4044
95. Ghosh S.K., and Parr R.G. J. Chem. Phys. 82 (1985) 3307
96. Ten Hoor M.J. Int. J. Quantum Chem. 33 (1988) 563
97. Ten Hoor M.J. J. Chem. Ed. 66 (1989) 633
98. Kozlowski P.M., and March N.H. Int. J. Quantum Chem. 36 (1989) 741
99. Ludeña E.V., López-Boada R., Maldonado J., Valderrama E., Koga T., Kryachko E.S., and Hinze J. Int. J. Quantum Chem. 56 (1995) 285
100. Cioslowski J. Phys. Rev. Lett. 60 (1988) 2141
101. Cioslowski J. J. Chem. Phys. 89 (1988) 4871
102. Cioslowski J. Int. J. Quantum Chem. S23 (1989)
103. (in press). Ludeña E.V., and López-Boada R. Top. Curr. Chem. (1996)
104. Bokanowski O., and Grébert B. Math. Models and Meth. Appl. Sci 6 (1996) 0000
105. Davidson E.R. Reduced Density Matrices in Quantum Chemistry (1976), Academic Press, New York 135
106. Bokanowski O., and Grébert B. Int. Rep. MIP No. 95-18 UFR-MIG (1995), Univ. P. Sabatier, Toulouse, France
107. (in press). Ludeña E.V., López-Boada R., and Pino R. Can. J. Chem. (1996)
108. Ludeña E.V., López-Boada R., Pino R., Vashishta P., and Bishop R.F. In: Ludeña E.V. (Ed). Condensed Matter Theories Vol. 11 (1996), Nova Science Publishers, Commack, N.Y. 51
109. Slater J.C. Quantum Theory of Atomic structure v. 1 (1960), MacGraw-Hill, New York 311
110. Calais J.L., and Löwdin P.-O. J. Mol. Spectrosc. 8 (1962) 203
111. x [π] by means of Padé approximants to local-scaling transformations. Int. J. Quantum Chem. (submitted).
112. Cuyt A., and Wuytack L. Nonlinear Methods in Numerical Analysis, North Holland Mathematical Studies 136 (1988), North Holland, Amsterdam
113. R. López-Boada and E.V. Ludeña. Hartree-Fock calculations in the context of the local-scaling transformation version of density functional theory. Applications to the lithium and beryllium atoms. Phys. Rev. A (submitted).
114. R. López-Boada, R. Pino and E.V. Ludeña. Hartree-Fock energy density functionals generated by local-scaling transformations: Applications of first-row atoms. J. Chem. Phys. (submitted).
115. Clementi E., and Roetti C. At. Data and Nucl. Data Tables 14 (1974) 177
116. Sahni V. Int. J. Quantum Chem. 53 (1995) 591
117. Sahni V., Li Y., and Harbola M.K. Phys. Rev. A 45 (1992) 1434
118. R. López-Boada, E.V. Ludeña, V. Karasiev and R. Colle. Generation of explicit electron correlation functionals by means of local-scaling transformations. J. Chem. Phys. (to be submitted).
119. Boys S.F., and Handy N.C. Proc. Roy. Soc. A 310 (1969) 43
120. Clark J.W., Mead R.L., Krotscheck E., Kürten K.E., and Ristig M.L. Nucl. Phys. A328 (1979) 45