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Local-scaling transformation version of density functional theory: Generation of density functionals

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Density Functional Theory I

Part of the book series: Topics in Current Chemistry ((TOPCURRCHEM,volume 180))

Abstract

We review in the present work the local-scaling transformation version of density functional theory both for ground and excited states. The historical development of the concept of space-coordinate density-transformation and of its effect on the formulation of several versions of density functional theory is discussed. We then present the various steps in the elaboration of the local-transformation version and indicate some of its accomplishments with respect to the N-representability problem for the energy functionals. Examples are given showing how the application of these methods to atomic sample systems lead to Hartree-Fock energies that are undistinguishable from the SCF values. In addition, the explicit construction of analytic density functionals for the energy, via local-scaling transformations, is discussed and is exemplified for the particular case of the Hartree-Fock approximation for atoms. Finally, applications of local-scaling transformations to the direct solution of the Kohn-Sham equations are reviewed.

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References

  1. Kryachko ES, Ludeña EV (1990) Energy density functional theory of many-electron systems. Kluwer Academic Publishers, Dordrecht.

    Google Scholar 

  2. Parr RG, Yang W (1989) Density functional theory of atoms and molecules. Oxford University Press, Oxford.

    Google Scholar 

  3. Dreizler RM, Gross EKU (1990) Density functional theory. Springer-Verlag, Berlin.

    Google Scholar 

  4. March NH (1992) Electron density theory of atoms and molecules. Academic Press, New York.

    Google Scholar 

  5. Thomas LH (1927) Proc Cambridge Phil Soc 23: 542

    CAS  Google Scholar 

  6. Fermi E (1927) Rend Accad Naz Lincei 6: 602

    CAS  Google Scholar 

  7. March NH (1957) Adv in Phys 6: 1

    Google Scholar 

  8. Lieb EH (1981) Rev Mod Phys 53: 603

    Article  CAS  Google Scholar 

  9. Dirac PAM (1930) Proc Cambridge Phil Soc 26: 376

    Article  CAS  Google Scholar 

  10. Weizsäcker von CF (1935) Z Phys 96: 431

    Article  Google Scholar 

  11. Kirzhnitz DA (1957) Zh Eksp Teor Fiz 32: 115

    Google Scholar 

  12. Hodges CH (1973) Can J Phys 51: 1428

    Google Scholar 

  13. Grammaticos B, Voros A (1979) Ann Phys 129: 153

    Google Scholar 

  14. Murphy DR (1981) Phys Rev A24: 1682

    Google Scholar 

  15. Yang W (1986) Phys Rev A34: 4575

    Google Scholar 

  16. Borman S (1990) Chem Eng News 68: 22

    Google Scholar 

  17. Hohenberg PC, Kohn W (1964) Phys Rev 136B: 864

    Article  Google Scholar 

  18. Hohenberg PC, Kohn W, Sham LJ (1990) Adv Quantum Chem 21: 7

    CAS  Google Scholar 

  19. Löwdin P-O (1987) In: Erdahl R, Smith VH (eds) Density matrices and density functionals, Reidel D, Dordrecht, p 21

    Google Scholar 

  20. Kryachko ES, Ludeña EV (1991) Phys Rev A43: 2179

    Google Scholar 

  21. Kryachko ES, Ludeña EV (1992) In: Proto AN, Aliaga JL (eds) Condensed matter theories, Vol 7. Plenum, New York, p 101

    Google Scholar 

  22. Coleman AJ (1963) Revs Mod Phys 35: 668

    Article  Google Scholar 

  23. Coleman AJ (1987) In: Erdahl R, Smith VH (eds) Density matrices and density functionals. Reidel R, Dordrecht, p 5

    Google Scholar 

  24. See also, Reference [1],, Section 4.4

    Google Scholar 

  25. , Chapters 7 and 8.

    Google Scholar 

  26. Gilbert TL (1975) Phys Rev B12: 2111

    Google Scholar 

  27. Harriman JE (1981) Phys Rev A24: 680

    Google Scholar 

  28. Petkov IZh, Stoitsov MV, Kryachko ES (1986) Int J Quantum Chem 29: 149

    Article  CAS  Google Scholar 

  29. Kryachko ES, Petkov IZh, Stoitsov MV (1987) Int J Quantum Chem 32: 467

    Article  CAS  Google Scholar 

  30. Kryachko ES, Petkov IZh, Stoitsov MV (1987) Int J Quantum Chem 32: 473

    Article  CAS  Google Scholar 

  31. Kryachko ES, Ludeña EV (1987) Phys Rev A35: 957

    Google Scholar 

  32. Kryachko ES, Petkov IZh, Stoitsov MV (1988) Int J Quantum Chem 34: 305E

    Google Scholar 

  33. Kryachko ES, Ludeña EV (1991) Phys Rev A43: 2194

    Google Scholar 

  34. Petkov IZh, Stoitsov MV (1991) Nuclear density functional theory. Oxford University Press, New York

    Google Scholar 

  35. Kryachko ES, Ludeña EV (1992) In: Fraga S (ed) Computational chemistry: Structure, interactions and reactivity Elsevier, Amsterdam, 1992, p 136.

    Google Scholar 

  36. Ludeña EV, Kryachko ES, (1992) Rev Mex Astr y Astrofis 23: 95

    Google Scholar 

  37. Kryachko ES, Ludeña EV (1992) New J Chem 16: 1089

    CAS  Google Scholar 

  38. Kryachko ES, Ludeña EV (1991) J Chem Phys 95: 9054

    Article  CAS  Google Scholar 

  39. Kryachko ES, Koga T (1989) J Chem Phys 91: 1108

    Article  Google Scholar 

  40. Koga T, Yamamoto Y, Kryachko ES (1989) J Chem Phys 91: 4785

    Article  Google Scholar 

  41. Koga T (1990) Phys Rev A41: 1274

    Google Scholar 

  42. Koga T (1990) Phys Rev A42: 3763

    Google Scholar 

  43. Koga T (1990) J Chem Phys 93: 5856

    Article  CAS  Google Scholar 

  44. Koga T, Yamamoto Y (1990) Phys Rev A42: 6336

    Google Scholar 

  45. Koga T, Kryachko ES (1991) J Chem Phys 94: 2910

    Article  CAS  Google Scholar 

  46. Kryachko ES, Koga T (1992) Int J Quantum Chem 42: 591

    Article  CAS  Google Scholar 

  47. Koga T, Matsuyama H (1992) Phys Rev A45: 5266

    Google Scholar 

  48. Kryachko ES, Ludeña EV, Koga T (1993) In: Clementi E (ed) Methods and techniques in computational chemistry, Vol B: Medium size systems. METECC-94, STEF, Cagliari, p 23

    Google Scholar 

  49. Koga T, Yamamoto Y, Ludeña EV (1991) J Chem Phys 94: 3805

    Article  CAS  Google Scholar 

  50. Koga T, Yamamoto Y, Ludeña EV (1991) Phys Rev A43: 5814

    Google Scholar 

  51. Koga T (1991) J Chem Phys 95: 4306

    Article  CAS  Google Scholar 

  52. Kryachko ES, Ludeña EV, Koga T (1992) J Math Chem 11: 325

    Article  CAS  Google Scholar 

  53. Macke W (1955) Phys Rev 100: 992

    Article  Google Scholar 

  54. Macke W (1955) Ann Phys (Leipzig) 17: 1

    Article  Google Scholar 

  55. March NH, Young WH (1958) Proc Roy Soc London 72: 182

    Article  Google Scholar 

  56. Hall GG (1960) Proc Roy Soc London 75: 575

    Article  Google Scholar 

  57. Ten Hoor MJ (1988) Int J Quantum Chem 33: 563; (1989) J Chem Ed 66: 633

    Article  Google Scholar 

  58. Moser J (1965) Trans Amer Math Soc 120: 286

    Article  Google Scholar 

  59. Percus JK (1978) Int J Quantum Chem 13: 89

    Article  CAS  Google Scholar 

  60. Ludeña EV (1983) J Chem Phys 79: 6174

    Article  Google Scholar 

  61. Zumbach G, Maschke K (1983) Phys Rev A28: 544; (1984) Ibid A29: 1585E

    Google Scholar 

  62. Nyden MR, Parr RG (1983) J Chem Phys 78: 4044

    Article  CAS  Google Scholar 

  63. Ghosh SK, Parr RG (1985) J Chem Phys 82: 3307

    Article  CAS  Google Scholar 

  64. Ludeña EV (1986) In: Malik FB (ed) Condensed matter theories, Vol 1. Plenum, New York, p 183

    Google Scholar 

  65. Bokanowski O, Grébert B (1996) Math Models and Meth Appl Sci 6

    Google Scholar 

  66. Bokanowski O, Grébert B (1995) Int Rep MIP No 95-18 UFR-MIG, Univ P Sabatier, Toulouse, France

    Google Scholar 

  67. Davidson ER (1976) Reduced density matrices in quantum chemistry. Academic Press, New York, p 135

    Google Scholar 

  68. Benesch R (1971) J Phys B, Atom Mol Phys 4: 1403

    Article  CAS  Google Scholar 

  69. Clementi E, Roetti C (1974) At Data and Nucl Data Tables 14: 177

    CAS  Google Scholar 

  70. Bunge CF, Barrientos JA, Bunge AV (1993) At Data and Nucl Data Tables 53: 113

    Article  CAS  Google Scholar 

  71. Raffenetti CR (1973) J Chem Phys 59: 5936

    Article  CAS  Google Scholar 

  72. Boyd RJ (1977) Can J Phys 55: 452

    CAS  Google Scholar 

  73. Esquivel RO, Bunge AV (1987) Int J Quantum Chem 32: 295

    Article  CAS  Google Scholar 

  74. Cioslowski J (1988) Phys Rev Lett 60: 2141

    Article  CAS  Google Scholar 

  75. Cioslowski J (1988) J Chem Phys 89: 4871

    Article  CAS  Google Scholar 

  76. Cioslowski J (1989) Int J Quantum Chem S23

    Google Scholar 

  77. Cioslowski J (1990) Adv Quantum Chem 21: 303

    Article  CAS  Google Scholar 

  78. Payne PW (1979) J Chem Phys 71: 490

    Article  CAS  Google Scholar 

  79. Hunter G (1975) Int J Quantum Chem 9: 237

    Article  CAS  Google Scholar 

  80. Hunter G (1981) Int J Quantum Chem 19: 755

    Article  CAS  Google Scholar 

  81. Hunter G (1986) Int J Quantum Chem 29: 197

    Article  CAS  Google Scholar 

  82. March NH (1985) Phys Lett 113A: 66

    CAS  Google Scholar 

  83. Dawson KA, March NH (1984) J Chem Phys 81: 5850

    Article  Google Scholar 

  84. Levy M (1979) Proc Natl Acad Sci USA 76: 6062

    Article  CAS  Google Scholar 

  85. Lieb EH (1982) In: Feshbach H, Shimony A (eds) Physics as natural philosophy: Essays in honor of Laszlo Tisza on his 75th Birthday, MIT Press, Cambridge, MA, p 111

    Google Scholar 

  86. Lieb EH (1983) Int J Quantum Chem 24: 243

    Article  CAS  Google Scholar 

  87. Lieb EH (1985) In: Dreizler RM, da Providencia J (eds) Density functional methods in physics, Plenum, New York, p 31

    Google Scholar 

  88. Bader RFW, Nguyen-Dang TT, Tal Y (1981) Rep Progr Phys 44: 893

    Article  Google Scholar 

  89. Bader RFW, Tal Y, Anderson SE, Nguyen-Dang TT (1980) Isr J Chem 19: 8

    CAS  Google Scholar 

  90. Hunter G (1985) In: Erdahl R, Smith VH (eds) Density matrices and density functionals. Reidel, Dordrecht, p 583

    Google Scholar 

  91. Reference 4, Section 8.11.

    Google Scholar 

  92. Levy M, Perdew JP, Sahni V (1984) Phys Rev A30: 2745

    Google Scholar 

  93. Lassettre EN (1985) J Chem Phys 83: 1709

    Article  CAS  Google Scholar 

  94. Kryachko ES, Ludeña EV (1992) Int J Quantum Chem 43: 769

    Article  CAS  Google Scholar 

  95. Kohn W, Sham LJ (1965) Phys Rev 140A: 1133

    Article  Google Scholar 

  96. Caffarel M (1989) In: Defranceschi M, Delhalle J (eds) Numerical determination of the electronic structure of atoms, diatomic and polyatomic molecules. Kluwer Academic Publishers, Dordrecht, p 85

    Google Scholar 

  97. Morgan III JD (1989) In: Defranceschi M, Delhalle J (eds) Numerical determination of the electronic structure of atoms, diatomic and polyatomic molecules. Kluwer Academic Publishers, Dordrecht, p 49

    Google Scholar 

  98. For a recent review, see the Naturforsch Z (1993) Proceedings of the Sagamore X Conference on Charge, Spin and Momentum Densities, 48a (1/2)

    Google Scholar 

  99. Kryachko ES, Ludeña EV, López-Boada R, Maldonado J (1993) In: Blum L, Malik FB (eds) Condensed Matter Theories, Vol 8. Plenum, New York, p 373

    Google Scholar 

  100. Levy M, Perdew JP (1985) In: Dreizler RM, da Providencia J (eds) Density functional methods in Physics. Plenum, New York, p 11

    Google Scholar 

  101. Talman JD, Shadwick WF (1976) Phys Rev A14: 36

    Google Scholar 

  102. Werden SH, Davidson ER (1984) In: Dahl JP, Avery J (eds) Local density approximations in quantum chemistry and solid state physics. Plenum, New York, p 33

    Google Scholar 

  103. Almbladh CO, Pedroza AC (1984) Phys Rev A29: 804

    Google Scholar 

  104. Aryasetiawan F, Stott MJ (1988) Phys Rev B38: 2974

    Google Scholar 

  105. Zhao Q, Parr RG (1992) Phys Rev A46: 2337

    Google Scholar 

  106. Zhao Q, Parr RG (1993) J Chem Phys 98: 543

    Article  CAS  Google Scholar 

  107. Wang Y, Parr RG (1993) Phys Rev A47: R1591

    Google Scholar 

  108. Ludeña EV, López-Boada R, Maldonado J, Koga T, Kryachko ES (1993) Phys Rev A48: 1937

    Google Scholar 

  109. Ludeña EV, López-Boada R, Maldonado J (1994) In: Clark JW, Sadiq A, Shoaib KA (eds) Condensed matter theories, Vol. 9. Nova Science Publishers, Commack, NY, p 97

    Google Scholar 

  110. Ludeña EV, López-Boada R, Maldonado J (1995) J Mol Struct (Theochem) 330: 33

    Article  Google Scholar 

  111. Ludeña EV, Maldonado J, López-Boada R, Koga T, Kryachko ES (1995) J Chem Phys 102: 318

    Article  Google Scholar 

  112. Ludeña EV, Kryachko ES, Koga T, López-Boada R, Hinze J, Maldonado J, Valderrama E (1995) In: Seminario JM, Politzer P (eds) Theoretical and computational chemistry: density functional calculations. Elsevier, Amsterdam, p 75

    Google Scholar 

  113. Ludeña EV, López-Boada R, Pino R (1996) In: Ludeña EV, Vashishta P, Bishop RF (eds) Condensed matter theories, Vol 11. Nova Science Publishers, Commack, NY, p 51

    Google Scholar 

  114. Holas A, March NH, Takahashi Y, Zhang C (1993) Phys Rev A48: 2708

    Google Scholar 

  115. Ludeña EV, López-Boada R, Maldonado J, Valderrama E, Koga T, Kryachko ES, Hinze J (1995) Int J Quantum Chem 56: 285

    Article  Google Scholar 

  116. Pino R, Ludeña EV, López-Boada R (1995) In: Navarro J, de Llano M (eds) Condensed matter theories, Vol 10. Nova Science Publishers, Commack, NY, p 189

    Google Scholar 

  117. Froese-Fischer C (1977) The Hartree-Fock method for atoms. J Wiley, New York

    Google Scholar 

  118. Koga T, Tatewaki H, Thakkar AJ (1993) Phys Rev A47: 4510

    Google Scholar 

  119. This transformation was found by O. Bokanowski and E.V. Ludeña. The important fact is that the nuclei remain invariant.

    Google Scholar 

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Authors and Affiliations

  1. Centro de Química, Instituto Venezolano de Investigaciones Científicas, IVIC, Apartado 21827, 1020-A, Caracas, Venezuela

    Eduardo V. Ludeña & Roberto López-Boada

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  1. Eduardo V. Ludeña
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  2. Roberto López-Boada
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R. F. Nalewajski

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© 1996 Springer-Verlag

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Ludeña, E.V., López-Boada, R. (1996). Local-scaling transformation version of density functional theory: Generation of density functionals. In: Nalewajski, R.F. (eds) Density Functional Theory I. Topics in Current Chemistry, vol 180. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-61091-X_5

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  • DOI: https://doi.org/10.1007/3-540-61091-X_5

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