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Explicitly Correlated Wave Functions in Chemistry and Physics pp 91–147Cite as

Explicitly Correlated Functions in Variational Calculations

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Part of the book series: Progress in Theoretical Chemistry and Physics ((PTCP,volume 13))

Abstract

In this Chapter we will describe wave functions that are variational solutions of the electronic Schrödinger equation and depend explicitly on interelectronic distance, r 12. Such functions with the correlation term r u12 have been proposed for the first time in 1929 by Hylleraas to solve the Schrödinger equation for helium atom [1]. The Hylleraas wave function can be described as composed of three factors: exponential (Slater type), power expansion of the coordinates and correlation factor. Therefore this function is not based on the one-electron approximation. The same approach has been extended to the hydrogen molecule by James and Coolidge in 1933 [2]. Explicit inclusion of an r 12 dependent term into the wave function improves significantly convergence of energy as compared with other functions not having such correlation term. Today, the methods based on explicitly correlated wave functions are able to achieve the spectroscopic accuracy in atomic and molecular energy calculations (errors of the order of one μhartree). Several methods using different expressions of r 12 dependence have been developed. They can be divided into two groups depending on the form of the correlation factor used. In the first group the correlation factor has the form of r u12 whereas in the second one, the correlation factor has the exponential form of exp(−αr 212 ) [3] or less often exp(−αr 12) [4]. From the first group functions we will consider in this Chapter: Hylleraas-type functions for atoms, James-Coolidge and Kołos-Wolniewicz functions, Hylleraas-CI functions based on the orbital approach and Hylleraas-CI functions based on the general valence bond functions. From the second group we will consider only the functions with the Gaussian correlation factor. All these methods give very accurate wave functions and energies, however, the area of application of these methods is rather limited to a few-electron atoms and molecules.

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References

  1. E. A. Hylleraas, Z. Phys. 54, 347 (1929).

    Article  CAS  Google Scholar 

  2. H. M. James and A. S. Coolidge, J. Chem. Phys. 1, 825 (1933).

    Article  CAS  Google Scholar 

  3. J. Rychlewski, Electron correlation in few-electron systems, in: Handbook on Molecular Physics and Quantum Chemistry,edited by S. Wilson (John Wiley and Sons Ltd, 2002) Vol.2.

    Google Scholar 

  4. A. J. Thakkar and V. H. Smith, Jr., Phys. Rev. A 15, 1 (1977).

    CAS  Google Scholar 

  5. E. Hylleraas, Z. Phys. 65, 209 (1930).

    Article  CAS  Google Scholar 

  6. P. Jolly, Int. J. Quantum Chem. 16, 1149 (1979).

    Article  CAS  Google Scholar 

  7. T. Koga, J. Chem. Phys. 93, 3720 (1990).

    Article  CAS  Google Scholar 

  8. T. Koga, J. Chem. Phys. 96, 1276 (1992).

    Article  CAS  Google Scholar 

  9. H. M. Schwartz, Phys. Rev. 103, 110 (1956).

    Article  CAS  Google Scholar 

  10. T. Kinoshita, Phys. Rev. 105, 1490 (1957).

    Article  CAS  Google Scholar 

  11. T. Koga, Z. Phys. D 34, 71 (1995).

    Article  CAS  Google Scholar 

  12. T. Koga, J. Chem. Phys. 104, 6308 (1996).

    Article  CAS  Google Scholar 

  13. J. H. Bartlett, Phys. Rev. 51, 661 (1937).

    Article  Google Scholar 

  14. K. Frankowski and C. L. Pekeris, Phys. Rev. 146, 46 (1966).

    Article  CAS  Google Scholar 

  15. A. S. Coolidge and H. M. James, Phys. Rev. 51, 855 (1937).

    Article  Google Scholar 

  16. C. L. Pekeris, Phys. Rev. 112, 1649 (1958).

    Article  CAS  Google Scholar 

  17. C. L. Pekeris, Phys. Rev. 115, 1216 (1959).

    Article  CAS  Google Scholar 

  18. C. L. Pekeris, Phys. Rev. 126, 1470 (1962).

    Article  CAS  Google Scholar 

  19. A. S. Coolidge and H. M. James, Phys. Rev. 49, 676 (1936).

    Article  CAS  Google Scholar 

  20. G. W. F. Drake, High-Precision Calculations for the Rydberg States of Helium, in Long-Range Casimir Forces: Theory and Recent Experiments on Atomic Systems, edited by F. S. Levine and D. A. Micha ( Plenum Press, New York, 1993 ), p. 107.

    Google Scholar 

  21. G. W. F. Drake, M. M. Cassar, and R. A. Nistor, Phys. Rev. A 65, 054501 (2002).

    Google Scholar 

  22. H. M. James and A. S. Coolidge, Phys. Rev. 49, 688 (1936).

    Article  CAS  Google Scholar 

  23. E. A. Burke, Phys. Rev. 130, 1871 (1963).

    Article  Google Scholar 

  24. A. Lüchow and H. Kleindienst, Int. J. Quantum Chem. 51, 211 (1994).

    Article  Google Scholar 

  25. F. W. King, J. Mol. Struct. (Theochem) 400, 7 (1997).

    Google Scholar 

  26. Z.-C. Yan, M. Tambasco, and G. W. F. Drake, Phys. Rev. A 57, 1652 (1998).

    CAS  Google Scholar 

  27. A. J. Thakkar, T. Koga, T. Tanabe, and H. Teruya, Chem. Phys. Lett. 366, 95 (2002).

    Article  CAS  Google Scholar 

  28. R. D. Present, J. Chem. Phys. 3, 122 (1935).

    Article  Google Scholar 

  29. A. S. Coolidge, H. M. James, and R. D. Present, J. Chem. Phys. 4, 193 (1936).

    Article  CAS  Google Scholar 

  30. A. S. Coolidge and H. M. James, J. Chem. Phys. 6, 730 (1938).

    Article  CAS  Google Scholar 

  31. W. Kotos and L. Wolniewicz, J. Chem. Phys. 43, 2429 (1965).

    Article  Google Scholar 

  32. B. Jeziorski, R. Bukowski, and K. Szalewicz, Int. J. Quantum Chem. 61, 769 (1997).

    Article  CAS  Google Scholar 

  33. L. Wolniewicz, J. Mol. Spectrosc. 174, 132 (1995).

    Article  CAS  Google Scholar 

  34. K. Ruedenberg, J. Chem. Phys. 19, 1459 (1951).

    Article  Google Scholar 

  35. L. Wolniewicz and K. Dressler, J. Chem. Phys. 88, 3861 (1988).

    Article  CAS  Google Scholar 

  36. D. C. Clary, Mol. Phys. 34, 793 (1977).

    Article  Google Scholar 

  37. D. C. Clary and N. C. Handy, Chem. Phys. Lett. 51, 483 (1977).

    Article  CAS  Google Scholar 

  38. J. S. Sims and S. A. Hagstrom, Phys. Rev. A 4, 908 (1971).

    Google Scholar 

  39. A. Preiskorn and W. Woznicki, Chem. Phys. Lett. 86, 369 (1982).

    Article  CAS  Google Scholar 

  40. E. Clementi, G. Corongiu, D. Estrin, E. Hollauer, and O. G. Stradella, Int. J. Quantum Chem. 45, 511 (1993).

    Article  CAS  Google Scholar 

  41. E. Clementi, G. Corongiu, D. Bahattacharya, B. Feuston, D. Frye, A. Preiskorn, A. Rizzo, and W. Xue, Chem. Rev. 91, 679 (1991).

    Article  CAS  Google Scholar 

  42. W. Cencek, J. Komasa, and J. Rychlewski, J. Chem. Phys. 95, 2572 (1991).

    Article  CAS  Google Scholar 

  43. K. Singer, Proc. R. Soc. London, Ser. A 258, 412 (1960).

    CAS  Google Scholar 

  44. S. F. Boys, Proc. R. Soc. London, Ser. A 258, 402 (1960).

    Google Scholar 

  45. W. Cencek and J. Rychlewski, J. Chem. Phys. 98, 1252 (1993).

    Article  CAS  Google Scholar 

  46. B. Jeziorski and K. Szalewicz, Phys. Rev. A 19, 2360 (1979).

    CAS  Google Scholar 

  47. N. C. Handy, Mol. Phys. 26, 169 (1973).

    Article  CAS  Google Scholar 

  48. J. Komasa and A. J. Thakkar, Mol. Phys. 78, 1039 (1993).

    Article  CAS  Google Scholar 

  49. J. Komasa and A. J. Thakkar, Chem. Phys. Lett. 222, 65 (1994).

    Article  CAS  Google Scholar 

  50. J. Rychlewski, W. Cencek, and J. Komasa, Chem. Phys. Lett. 229, 657 (1994).

    Article  CAS  Google Scholar 

  51. J. Komasa, J. Rychlewski, and W. T. Raynes, Chem. Phys. Lett. 236, 19 (1995).

    Article  CAS  Google Scholar 

  52. W. Cencek, J. Komasa, and J. Rychlewski, Chem. Phys. Lett. 246, 417 (1995).

    Article  CAS  Google Scholar 

  53. W. Cencek and J. Rychlewski, J. Chem. Phys. 102, 2533 (1995).

    Article  CAS  Google Scholar 

  54. W. Cencek and W. Kutzelnigg, J. Chem. Phys. 105, 5878 (1996).

    Article  Google Scholar 

  55. W. Cencek and W. Kutzelnigg, Chem. Phys. Lett. 266, 383 (1997).

    Article  CAS  Google Scholar 

  56. J. V. L. Longstaff and K. Singer, J. Chem. Phys. 42, 801 (1965).

    Article  CAS  Google Scholar 

  57. R. D. Poshusta, Int. J. Quantum Chem. 13, 27 (1978).

    Article  CAS  Google Scholar 

  58. R. D. Poshusta, Int. J. Quantum Chem. Symposium 13, 59 (1979).

    CAS  Google Scholar 

  59. J. Komasa and J. Rychlewski, Chem. Phys. Lett. 249, 253 (1996).

    Article  CAS  Google Scholar 

  60. J. Komasa and J. Rychlewski, Mol. Phys. 91, 909 (1997).

    CAS  Google Scholar 

  61. J. Komasa, J. Chem. Phys. 110, 7909 (1999).

    Article  CAS  Google Scholar 

  62. J. Komasa, J. Chem. Phys. 112, 7075 (2000).

    Article  CAS  Google Scholar 

  63. D. B. Kinghorn and R. D. Poshusta, Int. J. Quantum Chem. 62, 223 (1997).

    Article  CAS  Google Scholar 

  64. J. Komasa and J. Rychlewski, Polish J. Chem. 72, 1353 (1998).

    CAS  Google Scholar 

  65. M. J. D. Powell, Comput. J. 7, 155 (1964).

    Google Scholar 

  66. W. Kutzelnigg, Theor. Chim. Acta 68, 445 (1985).

    Article  CAS  Google Scholar 

  67. G. W. F. Drake and Z.-C. Yan, Chem. Phys. Lett. 229, 486 (1994).

    CAS  Google Scholar 

  68. F. T. Newman, Int. J. Quantum Chem. 63, 1065 (1997).

    Article  CAS  Google Scholar 

  69. S. P. Goldman, Phys. Rev. A 57, R677 (1998).

    Google Scholar 

  70. G. W. F. Drake, Phys. Scr. T83, 83 (1999).

    Google Scholar 

  71. Chuluunbaatar, I. V. Puzynin, and S. I. Vinitsky, J. Phys. B 34, L425 (2001).

    Google Scholar 

  72. V. I. Korobov, Phys. Rev. A 61, 064503 (2000).

    Google Scholar 

  73. K. Pachucki and J. Sapirstein, J. Phys. B 33, 5297 (2000).

    Article  CAS  Google Scholar 

  74. D. K. McKenzie and G. W. F. Drake, Phys. Rev. A 44, R6973 (1991).

    Article  CAS  Google Scholar 

  75. W. Cencek, unpublished.

    Google Scholar 

  76. Z.-C. Yan and G. W. F. Drake, Phys. Rev. A 52, 3711 (1995).

    CAS  Google Scholar 

  77. J. Komasa Phys. Rev. A 65, 012506 (2002).

    Google Scholar 

  78. G. Pestka and W. Woinicki, Chem. Phys. Lett. 255, 281 (1996).

    Article  CAS  Google Scholar 

  79. Jitrik and C. F. Bunge, Phys. Rev. A 43, 5804 (1991).

    Google Scholar 

  80. Z.-C. Yan and G. W. F. Drake, Phys. Rev. Lett. 81, 774 (1998).

    Article  CAS  Google Scholar 

  81. Z.-C. Yan and G. W. F. Drake, Phys. Rev. A 61 022504 (2000).

    Google Scholar 

  82. R. F. Gentner and E. A. Burke, Phys. Rev. 176, 63 (1968).

    Google Scholar 

  83. E. Schwegler, P. M. Kozlowski, and L. Adamowicz, J. Comput. Chem., 14, 566 (1993).

    Article  CAS  Google Scholar 

  84. J. Komasa Chem. Phys. Lett. 363, 307 (2002).

    CAS  Google Scholar 

  85. G. Büsse, H. Kleindienst and A. Lüchow, Int. J. Quantum Chem. 66, 241 (1998).

    Article  Google Scholar 

  86. J. Komasa, unpublished.

    Google Scholar 

  87. J. Noga, D. Tunega, W. Klopper, and W. Kutzelnigg, J. Chem. Phys. 103, 309 (1995).

    Article  CAS  Google Scholar 

  88. J. Komasa, J. Rychlewski, and K. Jankowski, Phys. Rev. A 65, 042507 (2002).

    Google Scholar 

  89. W. Heitler and F. London, Z. Phys. 44, 455 (1927).

    Article  CAS  Google Scholar 

  90. Burrau, Kgl. Danske Videnskab. Selskab. 7, 1 (1927).

    Google Scholar 

  91. Y. Sugiura, Z. Phys. 45, 484 (1927).

    Article  CAS  Google Scholar 

  92. C. A. Coulson, Trans. Faraday Soc. 33, 1479 (1937).

    Article  CAS  Google Scholar 

  93. L. J. Schaad and I. L. Thomas, Theor. Chico. Acta 21, 115 (1971).

    Article  CAS  Google Scholar 

  94. S. C. Wang, Phys. Rev. 31, 579 (1928).

    Article  Google Scholar 

  95. N. Rosen, Phys. Rev. 38, 2099 (1931).

    Article  CAS  Google Scholar 

  96. S. Weinbaum, J. Chem. Phys. 1, 593 (1933).

    Article  CAS  Google Scholar 

  97. E. U. Condon, Proc. Natl. Acad. Sci. USA 13, 466 (1927).

    Article  CAS  Google Scholar 

  98. W. Kolos, The origin, development and significance of the HeitlerLondon approach, in: Perspectives in Quantum Chemistry, edited by J. Jortner and B. Pullman (Kluwer Academic Publishers, 1989 ) p. 145–159.

    Google Scholar 

  99. A. D. McLean, A. Weiss, and M. Yoshimine, Rev. Mod. Phys. 32, 211 (1960).

    Article  CAS  Google Scholar 

  100. W. Kolos and C. C. J. Roothaan, Rev. Mod. Phys. 32, 219 (1960).

    Article  CAS  Google Scholar 

  101. W. Kolos and L. Wolniewicz, J. Chem. Phys. 41, 3663 (1964).

    Article  CAS  Google Scholar 

  102. W. Kolos and L. Wolniewicz, J. Chem. Phys. 49, 409 (1968).

    Article  Google Scholar 

  103. W. Kolos and L. Wolniewicz, J. Mol. Spectrosc. 54, 303 (1975).

    Article  CAS  Google Scholar 

  104. W. Kolos and J. Rychlewski, Acta Phys. Polonica A 53, 281 (1978).

    Google Scholar 

  105. W. Kolos, K. Szalewicz, and H. J. Monkhorst, J. Chem. Phys. 84, 3278 (1986).

    Article  CAS  Google Scholar 

  106. D. Frye, G. C. Lie, and E. Clementi, J. Chem. Phys. 91, 2369 (1989).

    Article  CAS  Google Scholar 

  107. W. Kolos and J. Rychlewski, J. Chem. Phys. 98, 3960 (1993).

    Article  CAS  Google Scholar 

  108. L. Wolniewicz, J. Chem. Phys. 99, 1851 (1993).

    Article  CAS  Google Scholar 

  109. J. Rychlewski, Int. J. Quantum Chem. 49, 477 (1994).

    Article  CAS  Google Scholar 

  110. J. Komasa, W. Cencek, and J. Rychlewski, Comput. Methods Sci. Technol. 2, 87 (1996).

    Google Scholar 

  111. D. M. Bishop and L. M. Cheung, Phys. Rev. A 18, 1846 (1978).

    Article  CAS  Google Scholar 

  112. W. Kolos, J. Chem. Phys. 101, 1330 (1994).

    Article  CAS  Google Scholar 

  113. L. Wolniewicz, J. Chem. Phys. 103, 1792 (1995).

    Article  CAS  Google Scholar 

  114. W. Cencek and J. Rychlewski, unpublished data.

    Google Scholar 

  115. W. A. Lester, Jr. and M. Krauss, J. Chem. Phys. 41, 1407 (1964) and 42, 2990 (E) (1965).

    Google Scholar 

  116. J. V. L. Longstaff and K. Singer, Proc. R. Soc. London, Ser. A 258, 421 (1960).

    Article  CAS  Google Scholar 

  117. J. V. L. Longstaff and K. Singer, Theor. Chim. Acta 2, 265 (1964).

    Article  CAS  Google Scholar 

  118. L. Salmon and R. D. Poshusta, J. Chem. Phys. 59, 3497 (1973).

    Article  CAS  Google Scholar 

  119. W. Kolos, H. J. Monkhorst and K. Szalewicz, J. Chem. Phys. 77, 1323 (1982).

    Article  CAS  Google Scholar 

  120. S. A. Alexander, H. J. Monkhorst, R. Roeland, and K. Szalewicz, J. Chem. Phys. 93, 4230 (1990).

    Article  Google Scholar 

  121. A. Müller and H. Kleindienst, J. Math. Chem. 17, 139 (1995).

    Article  Google Scholar 

  122. A. Balakrishnan, V. Smith, and B. P. Stoicheff, Phys. Rev. Lett. 68, 2149 (1992).

    Article  CAS  Google Scholar 

  123. J. Komasa, W. Cencek, and J Rychlewski, Phys. Rev. A 46, 2351 (1992).

    Article  CAS  Google Scholar 

  124. R. Röhse, W. Klopper, and W. Kutzelnigg, J. Chem. Phys. 99, 8830 (1993).

    Article  Google Scholar 

  125. J. W. Liu and S. Hagstrom, Phys. Rev. A 48, 166 (1993).

    Article  CAS  Google Scholar 

  126. W. Kolos and L. Wolniewicz, Chem. Phys. Lett. 24, 457 (1974).

    Article  CAS  Google Scholar 

  127. G. Staszewska and L. Wolniewicz, J. Mol. Spectrosc. 198, 416 (1999).

    Article  CAS  Google Scholar 

  128. W. Kotos and J. Rychlewski, J. Mol. Spectrosc. 143, 237 (1990).

    Article  Google Scholar 

  129. D. Frye, G. C. Lie, and E. Clementi, J. Chem. Phys. 91, 2366 (1989).

    Article  CAS  Google Scholar 

  130. J. W. Liu and S. Hagstrom, J. Phys. B 27, L729 (1994).

    Google Scholar 

  131. S. Rothenberg and E. R. Davidson, J. Chem. Phys. 45, 2560 (1966).

    Article  CAS  Google Scholar 

  132. F. Borondo, F. Martin, and M. Yanez, J. Chem. Phys. 86, 4982 (1987).

    Article  CAS  Google Scholar 

  133. A. Preiskorn, G. C. Lie, D. Frye, and E. Clementi, J. Chem. Phys. 92, 4941 (1990).

    Article  CAS  Google Scholar 

  134. J. Rychlewski, Chem. Phys. Lett. 151, 553 (1988).

    Article  CAS  Google Scholar 

  135. W. Kotos and J. Rychlewski, J. Mol. Spectrosc. 166, 12 (1994).

    Article  Google Scholar 

  136. T. E. Sharp, Atomic Data 2, 119 (1971).

    Google Scholar 

  137. C. B. Wakefield and E. R. Davidson, J. Chem. Phys. 43, 834 (1965).

    Article  CAS  Google Scholar 

  138. W. Kolos and L. Wolniewicz, J. Chem. Phys. 48 3672 (1968).

    Google Scholar 

  139. W. Kolos, Chem. Phys. Lett. 31, 43 (1975).

    Article  CAS  Google Scholar 

  140. W. Kolos and J. Rychlewski, Chem. Phys. Lett. 59183 (1978).

    Google Scholar 

  141. D. M. Bishop and L. M. Cheung, Chem. Phys. Lett. 79, 130 (1981).

    Article  CAS  Google Scholar 

  142. W. Kolos and J. Rychlewski, J. Mol. Spectrosc. 169, 341 (1995).

    Article  CAS  Google Scholar 

  143. W. Kolos and J. Rychlewski, J. Mol. Spectrosc. 143, 212 (1990).

    Article  CAS  Google Scholar 

  144. W. Kolos and J. Rychlewski, J. Mol. Spectrosc. 177, 146 (1996).

    Article  CAS  Google Scholar 

  145. J. Rychlewski, Phys. Rev. A 45, 5270 (1992).

    Google Scholar 

  146. T. Detmer, P. Schmelcher, and L. S. Cederbaum, J. Chem. Phys. 109, 964 (1998).

    Article  Google Scholar 

  147. E. R. Davidson J. Chem. Phys. 331577 (1960).

    Google Scholar 

  148. E. Reinhold, W. Hogervorst, W. Ubachs Phys. Rev. Lett. 78 2543 (1997).

    Google Scholar 

  149. W. Kolos and L. Wolniewicz J. Chem. Phys. 50 3228 (1969).

    Google Scholar 

  150. L. Wolniewicz and K. Dressler J. Chem. Phys. 82 3292 (1985).

    Google Scholar 

  151. L. Wolniewicz and K. Dressler J. Chem. Phys. 100444 (1994).

    Google Scholar 

  152. T. Orlikowski, G. Staszewska, and L. Wolniewicz Mol. Phys. 96 1445 (1999).

    Google Scholar 

  153. J. Komasa and J. Rychlewski, unpublished data.

    Google Scholar 

  154. L. Wolniewicz and K. Dressler J. Mol. Spectrosc. 77 286 (1979).

    Google Scholar 

  155. W. Kolos J. Mol. Spectrosc. 62429 (1976).

    Google Scholar 

  156. I. Dabrowski and G. Herzberg Can. J. Phys. 52 1110 (1974).

    Google Scholar 

  157. A. de Lange, W. Hogervorst, W. Ubachs, and L. Wolniewicz Phys. Rev. Lett. 86 2988 (2001).

    Google Scholar 

  158. H. S. Taylor, J. Chem. Phys. 39, 3375 (1963).

    Article  CAS  Google Scholar 

  159. W. Kotos and L. Wolniewicz, J. Chem. Phys. 45, 509 (1966).

    Article  Google Scholar 

  160. W. Kolos and L. Wolniewicz, Can. J. Phys. 53, 2189 (1975).

    Article  CAS  Google Scholar 

  161. K. Dressler and L. Wolniewicz, Ber. Bunsenges. Phys. Chem. 99, 246 (1995).

    CAS  Google Scholar 

  162. G. Staszewska and L. Wolniewicz, J. Mol. Spectrosc. 212, 208 (2002).

    Article  CAS  Google Scholar 

  163. E. Reinhold, W. Hogervorst, W. Ubachs, and L. Wolniewicz, Phys. Rev. A 60, 1258 (1999).

    Article  CAS  Google Scholar 

  164. J. C. Browne, J. Chem. Phys. 40, 43 (1964).

    Article  Google Scholar 

  165. S. Rothenberg and E. R. Davidson, J. Chem. Phys. 44, 730 (1966).

    Article  CAS  Google Scholar 

  166. W. Kolos and J. Rychlewski, J. Mol. Spectrosc. 62, 109 (1976).

    Article  CAS  Google Scholar 

  167. L. Wolniewicz, Chem. Phys. Lett. 253, 644 (1995).

    Article  Google Scholar 

  168. L. Wolniewicz and K. Staszewska, J. Mol. Spectrosc.,in press.

    Google Scholar 

  169. W. Kolos and J. Rychlewski, J. Mol. Spectrosc. 66, 428 (1977).

    Article  CAS  Google Scholar 

  170. L. Wolniewicz, J. Mol. Spectrosc. 169, 329 (1995).

    Article  CAS  Google Scholar 

  171. R. S. Mulliken, Phys. Rev. 138, 962 (1964).

    Google Scholar 

  172. E. Reinhold, A. de Lange, W. Hogervorst, and W. Ubachs, J. Chem. Phys. 109, 9772 (1998).

    Article  CAS  Google Scholar 

  173. W. Lichten, J. Chem. Phys. 26, 306 (1957).

    Article  CAS  Google Scholar 

  174. W. Lichten, Phys. Rev. 120, 848 (1960).

    Article  CAS  Google Scholar 

  175. W. Lichten, Phys. Rev. 126, 1020 (1962).

    Article  CAS  Google Scholar 

  176. C. E. Johnson, Phys. Rev. A 5, 1026 (1972).

    Article  Google Scholar 

  177. W. Kolos and J. Rychlewski, Comput. Methods Sci. Technol. 5, 39 (1999).

    Google Scholar 

  178. E. R. Davidson, J. Chem. Phys. 42, 4199 (1965).

    Article  CAS  Google Scholar 

  179. E. A. Coulbourn, J. Phys. B 6, 2618 (1973).

    Article  Google Scholar 

  180. W. Kolos and J. Rychlewski, unpublished results.

    Google Scholar 

  181. W. M. Wright and E. R. Davidson, J. Chem. Phys. 43, 840 (1965).

    Article  CAS  Google Scholar 

  182. G. Staszewska, J. Phys. Chem. A 105, 2308 (2001).

    Article  CAS  Google Scholar 

  183. W. Kolos and J. Rychlewski, J. Mol. Spectrosc. 91, 128 (1982).

    Article  CAS  Google Scholar 

  184. J. Rychlewski, J. Mol. Spectrosc. 104, 253 (1984).

    Article  CAS  Google Scholar 

  185. J. Rychlewski, J. Mol. Spectrosc. 149, 125 (1991).

    Article  CAS  Google Scholar 

  186. L. Pauling, J. Chem. Phys. 1, 58 (1933).

    Google Scholar 

  187. H. Yagisawa, H. Sato, and T. Watanabe, Phys. Rev. A 16, 1352 (1977).

    Article  CAS  Google Scholar 

  188. L. Wolniewicz, J. Phys. B 32, 2257 (1999).

    Article  CAS  Google Scholar 

  189. P. Valtanazanos and C. A. Nicolaides, unpublished results as quoted in [190].

    Google Scholar 

  190. N. A. Bacalis, Y. Komninos, and C. A. Nicolaides, Phys. Rev. A 45, 2701 (1992).

    Article  CAS  Google Scholar 

  191. W. Roberge and A. Dalgarno, Astrophys. J 255, 489 (1982).

    Article  CAS  Google Scholar 

  192. I. Dabrowski and G. Herzberg, Trans. N. Y. Acad. Sci. Ser. II38, 14 (1977).

    Google Scholar 

  193. E. Holzshuh, Rep. Prog. Phys. 55, 1035 (1992).

    Article  Google Scholar 

  194. J. Tennyson, J. Phys. B 31, L177 (1998).

    Article  CAS  Google Scholar 

  195. D. E. Tolliver, G. A. Kyrala, and W. H. Wing, Phys. Rev. Lett. 43, 1719 (1979).

    Article  CAS  Google Scholar 

  196. A. Carrington, J. Buttenshaw, R. A. Kennedy, and T. P. Softley, Mol. Phys. 44, 1233 (1981).

    Article  CAS  Google Scholar 

  197. W. Kolos, Int. J. Quantum Chem. 10, 217 (1976).

    Article  CAS  Google Scholar 

  198. W. Kolos, J. M. Peek, Chem. Phys. Lett. 12, 381 (1976).

    CAS  Google Scholar 

  199. D. M. Bishop and L. M. Cheung, J. Mol. Spectrosc. 79, 462 (1979).

    Article  Google Scholar 

  200. J. J. Thompson, Philos. Mag. 21, 225 (1911).

    Google Scholar 

  201. T. Oka, Phys. Rev. Lett. 45, 531 (1980).

    Article  CAS  Google Scholar 

  202. W. Meyer, P. Botschwina, and P. Burton, J. Chem. Phys. 84, 891 (1986).

    Article  Google Scholar 

  203. A. Preiskorn and W. Woznicki, Mol. Phys. 52, 1291 (1984).

    Article  CAS  Google Scholar 

  204. D. Frye, A. Preiskorn, G. C. Lie, and E. Clementi, J. Chem. Phys. 92, 4948 (1990).

    Article  CAS  Google Scholar 

  205. W. Cencek, J. Rychlewski, R. Jaquet, and W. Kutzelnigg, J. Chem. Phys. 108, 2831 (1998).

    Article  CAS  Google Scholar 

  206. R. Röhse, W. Kutzelnigg, R. Jaquet, and W. Klopper, J. Chem. Phys. 101, 2231 (1994).

    Article  Google Scholar 

  207. O. L. Polyansky, R. Prosmiti, W. Klopper, and J. Tennyson, Mol. Phys. 98, 261 (2000).

    Article  CAS  Google Scholar 

  208. J. B. Anderson, J. Chem. Phys. 96, 3702 (1992).

    Google Scholar 

  209. W. Cencek and J. Rychlewski, Chem. Phys. Lett. 320, 549 (2000).

    Article  CAS  Google Scholar 

  210. D. Bressanini, M. Mella, G. Morosi, Chem. Phys. Lett. 240, 566 (1995).

    Article  CAS  Google Scholar 

  211. A. Carrington, C. H. Pyne, and P. J. Knowles, J. Chem. Phys. 102, 5979 (1995).

    Article  CAS  Google Scholar 

  212. D. L. Diedrich and J. B. Anderson, J. Chem. Phys. 100, 8089 (1994).

    Article  CAS  Google Scholar 

  213. B. Liu, J. Chem. Phys. 80, 581 (1984).

    Article  CAS  Google Scholar 

  214. D. Frye, A. Preiskorn, E. Clementi, J. Comput. Chem. 12, 560 (1991).

    Article  CAS  Google Scholar 

  215. K. P. Peterson, D. E. Woon, and T. H. Dunning, Jr., J. Chem. Phys. 100, 7410 (1994).

    Article  CAS  Google Scholar 

  216. M J Jamieson, Chem. Phys. Lett. 310, 222 (1999).

    Article  CAS  Google Scholar 

  217. H. Partridge and C. W. Bauschlicher, Jr., Mol. Phys. 96, 705 (1999).

    Article  CAS  Google Scholar 

  218. S. M. Cybulski and R. R. Toczylowski, J. Chem. Phys. 111, 10520 (1999).

    Article  CAS  Google Scholar 

  219. J. H. van Lenthe and F. Dijkstra, Mol. Phys. 96, 555 (1999).

    Article  Google Scholar 

  220. J. van de Bovenkamp and F. B. van Duijneveldt, J. Chem. Phys. 110, 11141 (1999).

    Article  Google Scholar 

  221. T. van Mourik and T. H. Dunning, Jr., J. Chem. Phys. 111, 9248 (1999).

    Article  Google Scholar 

  222. T. van Mourik, A. K. Wilson, and T. H. Dunning, Jr., Mol. Phys. 96, 529 (1999).

    Article  Google Scholar 

  223. J. Komasa, W. Cencek, and J. Rychlewski, Chem. Phys. Lett. 304, 293 (1999).

    Article  CAS  Google Scholar 

  224. J. M. Pérez-Jorda, E. San-Fabian, and A. Pérez-Jiménez, J. Chem. Phys. 110, 1916 (1999).

    Article  Google Scholar 

  225. J. J. Hurly and M. R. Moldover, J. Phys. Chem. Ref. Data 28, 1713 (1999).

    Article  Google Scholar 

  226. L. W. Bruch and F. Weinhold, J. Chem. Phys. 113, 8667 (2000).

    Article  CAS  Google Scholar 

  227. J. S. Lee and S. Y. Park, J. Chem. Phys. 112, 10746 (2000).

    Article  CAS  Google Scholar 

  228. R. J. Gdanitz, J. Chem. Phys. 113, 5145 (2000).

    Article  Google Scholar 

  229. J. B. Anderson, J. Chem. Phys. 115, 4546 (2001).

    Article  CAS  Google Scholar 

  230. M. P. Hodges and R. J. Wheatley J. Mol. Struct. (Theochem) 591, 67 (2002).

    Article  CAS  Google Scholar 

  231. M. Jeziorska, R. Bukowski, W. Cencek, M. Jaszutiski, B. Jeziorski, and K. Szalewicz Collection of Czechoslovak Chemical Communications 68, 463 (2003).

    Article  CAS  Google Scholar 

  232. J. Komasa, J. Chem. Phys. 115, 158 (2001).

    Article  CAS  Google Scholar 

  233. B. Brutschy and H. Haberland, Phys. Rev. Lett. 38, 686 (1977).

    Article  CAS  Google Scholar 

  234. B. Chen and J. B. Anderson, J. Chem. Phys. 102, 2802 (1995).

    Article  CAS  Google Scholar 

  235. N. C. Handy, R. J. Harrison, P. J. Knowles, and H. F. Schaefer III, J. Phys. Chem. 88, 4852 (1984).

    Article  CAS  Google Scholar 

  236. K. M. Karunakaran and R. E. Christoffersen, J. Chem. Phys. 62, 1992 (1975).

    Article  CAS  Google Scholar 

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Authors and Affiliations

  1. Quantum Chemistry Group, Department of Chemistry, A. Mickiewicz University, Grunwaldzka 6, 60-780, Poznań, Poland

    Jacek Rychlewski & Jacek Komasa

  2. Institute of Bioorganic Chemistry, Polish Academy of Sciences, Noskowskiego 12/14, 61-704, Poznań, Poland

    Jacek Rychlewski

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  1. Jacek Rychlewski
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  2. Jacek Komasa
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  1. Institute of Bioorganic Chemistry PAN, Adam Mickiewicz University in Poznań, Poznań, Poland

    Jacek Rychlewski

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Rychlewski, J., Komasa, J. (2003). Explicitly Correlated Functions in Variational Calculations. In: Rychlewski, J. (eds) Explicitly Correlated Wave Functions in Chemistry and Physics. Progress in Theoretical Chemistry and Physics, vol 13. Springer, Dordrecht. https://doi.org/10.1007/978-94-017-0313-0_2

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