Advertisement

Quantum Chemistry

  • Takao Tsuneda
Chapter

Abstract

This chapter first presents an overview of the history of quantum chemistry in order to show how density functional theory (DFT) fits into the field as a whole. In Sect. 1.1, the history of quantum chemistry after the appearance of the Schrödinger equation is briefly reviewed. After surveying the history of theoretical chemistry before the advent of quantum chemistry in Sect. 1.2, the analytical mechanics forming the foundation of the Schrödinger equation is presented in Sect. 1.3. This chapter then introduces the Schrödinger equation and its applications to molecular motions. From a historical standpoint, the derivation of the Schrödinger equation is explained in Sect. 1.4, and the interpretation of the wavefunction, which is controversial even today, is reviewed in Sect. 1.5. To discuss the concept of quantization, the Schrödinger equation is applied to the three basic motions of molecules: translational motion in Sect. 1.6, vibrational motion in Sect. 1.7, and rotational motion in Sect. 1.8. Finally, the quantization of the electronic motion in the hydrogen atom is presented as the simplest electronic state in Sect. 1.9.

Keywords

Density Functional Theory Quantum Chemistry Generalize Gradient Approximation Local Density Approximation Energy Eigenvalue 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

References

  1. Alder, B.J., Wainwright, T.E.: J. Chem. Phys. 31, 459–466 (1959)CrossRefGoogle Scholar
  2. Andersson, K., Malmqvist, P.A., Roos, B.O., Sadlej, A.J., Wolinski, K.: J. Phys. Chem. 94, 5483–5488 (1990)CrossRefGoogle Scholar
  3. Asimov, I.: A Short History of Chemistry. Greenwood Press Reprint, Westport (1979)Google Scholar
  4. Aspect, A., Grangier, P., Roger, G.: Phys. Rev. Lett. 49, 91–94 (1982)CrossRefGoogle Scholar
  5. Becke, A.D.: Phys. Rev. A, 38, 3098–3100 (1988)CrossRefGoogle Scholar
  6. Becke, A.D.: J. Chem. Phys. 98, 5648–5652 (1993)CrossRefGoogle Scholar
  7. Becke, A.D.: J. Chem. Phys. 107, 8554–8560 (1997)CrossRefGoogle Scholar
  8. Bell, J.: Physics 1, 195–200 (1964)Google Scholar
  9. Bell, R.P.: Proc. R. Soc. Lond. A 154, 414–429 (1936)CrossRefGoogle Scholar
  10. Bohm, D.: Phys. Rev. 85, 166–179 (1952)CrossRefGoogle Scholar
  11. Bohr, N.: Philos. Mag. 21, 1–25 (1913)CrossRefGoogle Scholar
  12. Born, M., Heisenberg, W., Jordan, P.: Z. Phys. 35, 557–615 (1926)CrossRefGoogle Scholar
  13. Boys, S.F.: Proc. R. Soc. Lond. A. 200, 542–554 (1950)CrossRefGoogle Scholar
  14. Car, R., Parrinello, M.: Phys. Rev. Lett. 55, 2471–2474 (1985)CrossRefGoogle Scholar
  15. Casida, M.E.: In: Seminario, J.J. (ed.) Recent Developments and Applications of Modern Density Functional Theory. Elsevier, Amsterdam (1996)Google Scholar
  16. C̆íz̆ek, J.: J. Chem. Phys. 45, 4256–4266 (1966)Google Scholar
  17. Compton, A.: Phys. Rev. 21, 483–502 (1923)CrossRefGoogle Scholar
  18. Condon, E.U.: Phys. Rev. 36, 1121–1133 (1930)CrossRefGoogle Scholar
  19. Coulson, C.A.: Proc. Camb. Philos. Soc. 34, 204–212 (1938)CrossRefGoogle Scholar
  20. Davidson, E.R.: J. Comput. Phys. 17, 87–94 (1975)CrossRefGoogle Scholar
  21. Davisson, C., Germer, L.H.: Phys. Rev. 30, 705–740 (1927)CrossRefGoogle Scholar
  22. Dirac, P.A.M.: Proc. R. Soc. A 117, 610–624 (1928)CrossRefGoogle Scholar
  23. Dirac, P.A.M.: Camb. Philos. Soc. 26, 376–385 (1930)CrossRefGoogle Scholar
  24. Einstein, A.: Ann. Phys. 17, 132–148 (1905)CrossRefGoogle Scholar
  25. Einstein, A., Podolsky, B., Rosen, N.: Phys. Rev. 47, 777–780 (1935)CrossRefGoogle Scholar
  26. Ekeland, I.: Le Meilleur des Mondes Possibles (Japanese). Editions du Seuil (2009)Google Scholar
  27. Evans, M.G., Polanyi, M.: Trans. Faraday Soc. 34, 11–29 (1938)CrossRefGoogle Scholar
  28. Everett, H.: Rev. Mod. Phys. 29, 454–462 (1957)CrossRefGoogle Scholar
  29. Eyring, H.: J. Chem. Phys. 3, 107–115 (1935)CrossRefGoogle Scholar
  30. Fermi, E.: Z. Phys. 48, 73–79 (1928)CrossRefGoogle Scholar
  31. Feynman, R.P.: Rev. Mod. Phys. 20, 367–387 (1948)CrossRefGoogle Scholar
  32. Fock, V.: Z. Phys. 61, 126–148 (1930)CrossRefGoogle Scholar
  33. Foster, J.M., and Boys, S.F.: Rev. Mod. Phys. 32, 300–302 (1960)CrossRefGoogle Scholar
  34. Frenkel, J.: Wave Mechanics: Advanced General Theory. Clarendon Press, Oxford (1934)Google Scholar
  35. Fukui, K., Yonezawa, T., Shingu, H.: J. Chem. Phys. 20, 722–725 (1952)CrossRefGoogle Scholar
  36. Gasiorowicz, S.: Quantum Physics 2nd edn. Wiley, New York (1996)Google Scholar
  37. Hall, G.G.: Proc. R. Soc. Lond. A 205, 541–552 (1951)CrossRefGoogle Scholar
  38. Hartree, D.R.: Math. Proc. Camb. Philos. Soc. 24, 89–132; 426–437 (1928)Google Scholar
  39. Heine, V.: Solid State Phys. 24, 1–36 (1970)Google Scholar
  40. Heisenberg, W.: Z. Phys. 33, 879–893 (1925)CrossRefGoogle Scholar
  41. Heisenberg, W.: Z. Phys. 38, 411–426 (1926)CrossRefGoogle Scholar
  42. Heisenberg, W.: Z. Phys. 43, 172–198 (1927)CrossRefGoogle Scholar
  43. Hirao, K.: Chem. Phys. Lett. 190, 374–380 (1992)CrossRefGoogle Scholar
  44. Hoffmann, R.: J. Chem. Phys. 39, 1397–1412 (1963)CrossRefGoogle Scholar
  45. Hohenberg, P., Kohn, W.: Phys. Rev. B 136, 864–871 (1964)CrossRefGoogle Scholar
  46. Hückel, E.: Z. Phys. 60, 423–456 (1930)CrossRefGoogle Scholar
  47. Hund, F.: Z. Phys. 36, 657–674 (1926)CrossRefGoogle Scholar
  48. Iikura, H., Tsuneda, T., Yanai, T., Hirao, K.: J. Chem. Phys. 115(8), 3540–3544 (2001)CrossRefGoogle Scholar
  49. Jammer, M.: The Philosophy of Quantum Mechanics: The Interpretations of Quantum Mechanics in Historical Perspective. Wiley, Chichester (1974)Google Scholar
  50. Janak, J.F.: Phys. Rev. B 103, 7165–7168 (1978)CrossRefGoogle Scholar
  51. Jönsson, C.: Z. Phys. 161, 454–474 (1961)CrossRefGoogle Scholar
  52. Kahn, L.R., Goddard, W.A.: J. Chem. Phys. 56, 2685–2701 (1972)CrossRefGoogle Scholar
  53. Kochen, S., Specker, E.P.: J. Math. Mech. 17, 59–87 (1967)Google Scholar
  54. Kohn, W., Sham, L.J.: Phys. Rev. A 140, 1133–1138 (1965)CrossRefGoogle Scholar
  55. Koopmans, T.: Physica 1, 104–113 (1934)CrossRefGoogle Scholar
  56. Lee, C., Yang, W., Parr, R.G.: Phys. Rev. B 37, 785–789 (1988)CrossRefGoogle Scholar
  57. Lennard-Jones, J.E.: Trans. Faraday Soc. 25, 668–676 (1929)CrossRefGoogle Scholar
  58. Levy, M.: Proc. Natl. Acad. Sci. USA 76, 6062–6065 (1979)CrossRefGoogle Scholar
  59. Löwdin, P.-O.: Phys. Rev. 97, 1509–1520 (1955)CrossRefGoogle Scholar
  60. Marcus, R.A.: J. Chem. Phys. 24, 979–989 (1956)CrossRefGoogle Scholar
  61. Møller, C., Plesset, M.S.: Phys. Rev. 46, 618–622 (1934)CrossRefGoogle Scholar
  62. Mulliken, R.S.: Phys. Rev. 29, 637–649 (1927)CrossRefGoogle Scholar
  63. Mulliken, R.S.: J. Chem. Phys. 23, 1833–1840 (1955)CrossRefGoogle Scholar
  64. Nakano, H.: J. Chem. Phys. 99, 7983–7992 (1993)CrossRefGoogle Scholar
  65. Nakatsuji, H., Hirao, K.: J. Chem. Phys. 68, 2053–2065 (1978)CrossRefGoogle Scholar
  66. Noether, E.A.: Nach. Ges. Wiss. Göttingen Math. Phys. 2, 235–257 (1918)Google Scholar
  67. Pariser, R., Parr, R.: J. Chem. Phys. 21, 767–776 (1953)CrossRefGoogle Scholar
  68. Pauling, L.: Proc. Natl. Acad. Sci. USA 14, 359–362 (1928)CrossRefGoogle Scholar
  69. Perdew, J.P., Zunger, A.: Phys. Rev. B 23, 5048–5079 (1981)CrossRefGoogle Scholar
  70. Pople, J.A.: Trans. Faraday Soc. 49, 1375–1385 (1953)CrossRefGoogle Scholar
  71. Pople, J.A., Nesbet, R.K.: J. Chem. Phys. 22, 571–572 (1954)CrossRefGoogle Scholar
  72. Roothaan, C.C.J.: Rev. Mod. Phys. 23, 69–89 (1951)CrossRefGoogle Scholar
  73. Rowe, D.J.: Rev. Mod. Phys. 40, 153–166 (1968)CrossRefGoogle Scholar
  74. Runge, E., Gross, E.K.U.: Phys. Rev. Lett. 52, 997–1000 (1984)CrossRefGoogle Scholar
  75. Schrödinger, E.: Phys. Rev. 28, 1049–1070 (1926)CrossRefGoogle Scholar
  76. Schrödinger, E.: Naturwissenschaften 23, 807–849 (1935)CrossRefGoogle Scholar
  77. Sinanoğlu, O.: Adv. Chem. Phys. 6, 315–412 (1964)Google Scholar
  78. Slater, J.C.: Phys. Rev. 32, 339–348 (1928)CrossRefGoogle Scholar
  79. Slater, J.C.: Phys. Rev. 34, 1293–1322 (1929)CrossRefGoogle Scholar
  80. Slater, J.C.: Phys. Rev. 35, 210–211 (1930)CrossRefGoogle Scholar
  81. Thomas, L.H.: Proc. Camb. Philos. Soc. 23, 542–548 (1927)CrossRefGoogle Scholar
  82. Vignale, G., Kohn, W.: Phys. Rev. Lett. 77, 2037–2040 (1996)CrossRefGoogle Scholar
  83. von Neumann, J.L.: Mathematische Grundlagen der Quantenmechanik. Springer, Berlin (1957)Google Scholar
  84. von Weizsäcker, C.F.: Z. Phys. 96, 431–458 (1935)CrossRefGoogle Scholar
  85. Vosko, S.H., Wilk, L., Nusair, M.: Can. J. Phys. 58, 1200–1211 (1980)CrossRefGoogle Scholar
  86. Warshell, A., Levitt, M.: J. Mol. Biol. 103, 227–249 (1976)CrossRefGoogle Scholar
  87. Whitten, J.L., Hackmeyer, M.: J. Chem. Phys. 51, 5584–5596 (1969)CrossRefGoogle Scholar
  88. Woodward, R.B., Hoffmann, R.: J. Am. Chem. Soc. 87, 395–397 (1965)CrossRefGoogle Scholar
  89. Yang, W.: Phys. Rev. Lett. 66, 1438–1441 (1991)CrossRefGoogle Scholar

Copyright information

© Springer Japan 2014

Authors and Affiliations

  • Takao Tsuneda
    • 1
  1. 1.University of YamanashiKofuJapan

Personalised recommendations