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Practical Ab Initio Methods for Molecular Electronic Structure Studies. II. Finite Basis Sets and the Algebraic Approximation

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Part of the book series: NATO ASI Series ((ASIC,volume 500))

Abstract

The use of finite analytic basis sets in molecular electronic structure calculations is ubiquitous. In this article, a review of the fundamentals of the algebraic aprroximation is given together with a survey of some of the more promising recent developments in the systematic approximation of molecular electronic structure by means of finite basis set expansions.

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References

  1. D.R. Hartree, W. Hartree and B. Swirles, Phil. Trans. Roy. Soc. (London) A238, 229 (1939)

    CAS  Google Scholar 

  2. L. Laaksonen, P. Pyykkö and D. Sundholm, Intern. J. Quantum Chem. 23 309, 319 (1983)

    CAS  Google Scholar 

  3. D. Heinemann, D. Kolb and B. Fricke, Chem. Phys. Lett. 137, 180 (1987).

    Google Scholar 

  4. D. Heinemann, D. Kolb and B. Fricke, Chem. Phys. Lett. 145, 125 (1988).

    CAS  Google Scholar 

  5. Phys. Rev. A 38, 4994 (1988)

    CAS  Google Scholar 

  6. K.G. Wilson, Nucl. Phys. B (Proc. Suppl.) 17, 82 (1990)

    Google Scholar 

  7. G.G. Hall, Proc. Roy. Soc. A205, 541 (1951)

    Google Scholar 

  8. C.C.J. Roothaan, Rev. Mod. Phys. 23, 69 (1951)

    CAS  Google Scholar 

  9. S. Wilson, in Methods in Computational Molecular Physics, NATO ASI Series 113, p. 71, edited by G.H.F. Diercksen and S. Wilson, Reidel, Dordrecht (1983)

    Google Scholar 

  10. E.R. Davidson and D. Feller, Chem. Rev. 86, 681 (1986)

    CAS  Google Scholar 

  11. S. Huzinaga, Comput. Phys. Rept. 2, 279 (1985)

    CAS  Google Scholar 

  12. E. Clementi, S. Chakravorty, G. Corongiu and V. Sonnad, in Modern Techniques in Computational Chemistry, edited by E. Clementi, ESCOM, Leiden (1990)

    Google Scholar 

  13. P.R. Taylor, in European Summer School in Quantum Chemistry, Lecture Notes in Chemistry 58, p. 399, edited by B.O. Roos, Springer-Verlag, Berlin (1992)

    Google Scholar 

  14. I.P. Grant, in Relativistic effects in atoms and molecules, Methods in Computational Chemistry 2, edited by S. Wilson, Plenum Press, New York (1988)

    Google Scholar 

  15. H.P. Kelly, Phys. Rev. 131, 684 (1963).

    Google Scholar 

  16. H.P. Kelly, ibid. A 134, 1450 (1964).

    Google Scholar 

  17. H.P. Kelly, ibid. B 136, 896 (1964).

    Google Scholar 

  18. Adv. Theoret. Phys. 2, 75 (1968).

    Google Scholar 

  19. Adv. Chem. Phys. 14, 129 (1969)

    CAS  Google Scholar 

  20. P.J. Rossky and M. Karplus, J. Chem. Phys. 67, 5419 (1977)

    CAS  Google Scholar 

  21. H.M. Quiney, I.P. Grant and S. Wilson, J. Phys. B: At. Mol. Phys. 18, 577 (1985)

    CAS  Google Scholar 

  22. S. Wilson, Adv. Chem. Phys. 67, 439 (1987)

    CAS  Google Scholar 

  23. L. Laaksonen, P. Pyykkö and D. Sundholm, Comput. Phys. Rept. 4, 313 (1986)

    CAS  Google Scholar 

  24. P. Pyykkö, in Numerical Determination of the Electronic Structure of Atoms, Diatomic and Polyatomic Molecules, edited by M. Defranceschi and J. Delhalle, Kluwer, Dordrecht (1989)

    Google Scholar 

  25. J. Kobus, Chem. Phys. Lett. 202, 7 (1993)

    CAS  Google Scholar 

  26. D. Heinemann, A. Rosen and B. Fricke, Phys. Scripta 42, 692 (1990)

    CAS  Google Scholar 

  27. J. Kobus, Comput. Phys. Commun. 78, 247 (1994)

    Google Scholar 

  28. J. Kobus, L. Laaksonen and D. Sundholm, Comput. Phys. Commun. 98, 346 (1996)

    CAS  Google Scholar 

  29. J. Kobus, D. Moncrieff and S. Wilson, J. Phys. B: At. Mol. Opt. Phys. 27, 5139 (1994)

    CAS  Google Scholar 

  30. J. Kobus, D. Moncrieff and S. Wilson, J. Phys. B: At. Mol. Opt. Phys. 27, 2867 (1994)

    CAS  Google Scholar 

  31. D. Moncrieff, J. Kobus and S. Wilson, J. Phys. B: At. Mol. Opt. Phys. 28, 4555 (1995)

    CAS  Google Scholar 

  32. J. Kobus, D. Moncrieff and S. Wilson, Mol. Phys. 86, 1315 (1995)

    CAS  Google Scholar 

  33. I.G. Kaplan, Symmetry of Many-Electron Systems, p. 269, Academic Press, London (1975)

    Google Scholar 

  34. S. Wilson and D.M. Silver, Phys. Rev. A 14, 1949 (1976)

    CAS  Google Scholar 

  35. S. Wilson, Electron correlation in molecules, Clarendon Press, Oxford (1984)

    Google Scholar 

  36. M.F. Guest and S. Wilson, in Supercomputers in Chemistry, edited by P. Lykos and I. Shavitt, ACS Symposium Series 173, American Chemical Society, Washington D.C. (1981)

    Google Scholar 

  37. V.R. Saunders and M.F. Guest, Comput. Phys. Commun. 26, 389 (1982)

    CAS  Google Scholar 

  38. S. Wilson and V.R. Saunders, Comput. Phys. Commun. 19, 293 (1980)

    CAS  Google Scholar 

  39. D. Moncrieff, V.R. Saunders and S. Wilson, in Proceedings Supercomputing Symposium ’92 “Grand Challenges in Supercomputing”, edited by C. Krupat, Environment Canada, Canadian Meteorological Centre, Dorval, Quebec (1992)

    Google Scholar 

  40. A. Bohr and V.F. Weisskopf, Phys. Rev. 77, 94 (1950)

    CAS  Google Scholar 

  41. Y. Ishikawa, R. Barretty and R.C. Binning, Chem. Phys. Letts. 121, 130 (1985)

    CAS  Google Scholar 

  42. Y. Ishikawa and H.M. Quiney, Intern. J. Quantum Chem. Symp. 21, 523 (1987)

    CAS  Google Scholar 

  43. L. Laaksonen, I.P. Grant and S. Wilson, J. Phys. B: At. Mol. Phys. 21, 1969 (1988)

    CAS  Google Scholar 

  44. B. Klahn and J.D. Morgan III, J. Chem. Phys. 81, 410 (1984)

    CAS  Google Scholar 

  45. R.N. Hill, J. Chem. Phys. 83, 1173 (1985)

    CAS  Google Scholar 

  46. J. Morgan III, in Numerical Determination of the Electronic Structure of Atoms, Diatomic and Polyatomic Molecules, edited by M. Defranceschi and J. Delhalle, NATO-ASI Series C 271, Kluwer, Dordrecht (1989)

    Google Scholar 

  47. H.M. Quiney, LP. Grant and S. Wilson, J. Phys. B: At. Mol. Phys. 20, 1413 (1987)

    CAS  Google Scholar 

  48. H.M. Quiney, I.P. Grant and S. Wilson, in Numerical Determination of the Electronic Structure of Atoms, Diatomic and Polyatomic Molecules, edited by M. Defranceschi and J. Delhalle, NATO-ASI Series C 271, Kluwer, Dordrecht (1989)

    Google Scholar 

  49. H.M. Quiney, I.P. Grant and S. Wilson, in Many-Body Methods in Quantum Chemistry, Lecture Notes in Chemistry 52, edited by U. Kaldor, Springer, Berlin (1989)

    Google Scholar 

  50. H.M. Quiney, I.P. Grant and S. Wilson, J. Phys. B: At. Mol. Opt. Phys. 22, L15 (1989)

    CAS  Google Scholar 

  51. H.M. Quiney, I.P. Grant and S. Wilson, Physica Scripta 36, 460 (1987)

    CAS  Google Scholar 

  52. M.W. Schmidt and K. Ruedenberg, J. Chem. Phys. 71, 3951 (1979)

    CAS  Google Scholar 

  53. J. Kobus, D. Moncrieff and S. Wilson, Molec. Phys. 86, 1315 (1995)

    CAS  Google Scholar 

  54. Part IV.

    Google Scholar 

  55. M.J. Frisch, G.W. Trucks, H.B. Schlegel, P.M.W. Gill, B.G. Johnson, M.A. Robb, J.R. Cheeseman, T. Keith, G.A. Petersson, J.A. Montgomery, K. Raghavachari, M.A. Al-Laham, V.G. Zakrzewski, J.V. Ortiz, J.B. Foresman, J. Cioslowski, B.B. Stefanov, A. Nanayakkara, M. Challacombe, C.Y. Peng, P.Y. Ayala, W. Chen, M.W. Wong, J.L. Andres, E.S. Replogle, R. Gomperts, R.L. Martin, D.J. Fox, J.S. Binkley, D.J. Defrees, J. Baker, J.R Stewart, M. Head-Gordon, C. Gonzalaz and J.A. Pople, GAUSSIAN94, Gaussian Inc., Pittsburgh PA, 1995

    Google Scholar 

  56. UNICHEM was originally developed by Cray Research Inc. Details can be obtained from Oxford Molecular Ltd., The Medawar Centre, Oxford Science Park, Oxford OX4 4GA, England.

    Google Scholar 

  57. D. Moncrieff and S. Wilson, J. Phys. B: At. Mol. Opt. Phys. 28, 4007 (1995)

    CAS  Google Scholar 

  58. W.J. Hehre, R.F. Stewart and J.A. Pople, J. Chem. Phys. 51, 2657 (1969)

    CAS  Google Scholar 

  59. J.B. Collins, P. v. R. Schleyer, J.S. Binkley and J.A. Pople, J. Chem. Phys. 64, 5142 (1976)

    CAS  Google Scholar 

  60. J.S. Binkley, J.A. Pople and W.J. Hehre, J. Amer. Chem. Soc. 102, 939 (1980)

    CAS  Google Scholar 

  61. M.S. Gordon, J.S, Binkley, J.A. Pople, W.J. Pietro and W.J. Hehre, J. Amer. Chem. Soc. 104, 2797 (1982)

    CAS  Google Scholar 

  62. W.J. Pietro, M.M. Francl, W.J. Hehre, D.J. Defrees, J.A. Pople and J.S. Binkley, J. Amer. Chem. Soc. 104, 5039 (1982)

    CAS  Google Scholar 

  63. R. Ditchfìeld, W. Hehre and J.A. Pople, J. Chem. Phys. 54, 724 (1971)

    Google Scholar 

  64. W. Hehre, R. Ditchfìeld and J.A. Pople, J. Chem. Phys. 56, 2257 (1972)

    CAS  Google Scholar 

  65. P.C. Hariharan and J.A. Pople, Molec. Phys. 27, 209 (1974)

    CAS  Google Scholar 

  66. M.S. Gordon Chem. Phys. Lett. 76, 163 (1980)

    CAS  Google Scholar 

  67. P.C. Hariharan and J.A. Pople, Theo. Chim. Acta. 28, 213 (1973)

    CAS  Google Scholar 

  68. T.H. Dunning, Jr., and P.J. Hay, in Modern Theoretical Chemistry, edited by H.F. Schaefer III, Plenum, New York, 1976

    Google Scholar 

  69. T.H. Dunning, Jr., J. Chem. Phys. 90, 1007 (1989)

    CAS  Google Scholar 

  70. R.A. Kendall, T.H. Dunning, Jr. and R.J. Harrison, J. Chem. Phys. 96, 6796 (1992)

    CAS  Google Scholar 

  71. D.E. Woon and T.H. Dunning, Jr., J. Chem. Phys. 98, 1358 (1993)

    CAS  Google Scholar 

  72. D.E. Woon and T.H. Dunning, Jr., J. Chem. Phys. 100, 2975 (1994)

    CAS  Google Scholar 

  73. D.E. Woon and T.H. Dunning, Jr., J. Chem. Phys. 103, 4572 (1995)

    CAS  Google Scholar 

  74. R.C. Raffenetti, J. Chem. Phys. 58, 4452 (1973)

    CAS  Google Scholar 

  75. Partridge H 1989 J. Chem. Phys. 90 1043

    CAS  Google Scholar 

  76. Widmark PO, Malmqvist PA and Roos BO 1990 Theoret. chim. Acta. 77 291

    CAS  Google Scholar 

  77. Widmark PO, Persson BJ and Roos BO 1991 Theoret. chim. Acta. 79 419

    CAS  Google Scholar 

  78. Almlöf J and Taylor PR 1987 J. Chem. Phys. 86 4070

    Google Scholar 

  79. N.H. March, W.H. Young and S. Sampanthar, The many-body problem in quantum mechanics, Cambridge University Press (1967)

    Google Scholar 

  80. I. Lindgren and J. Morrison, Atomic many-body theory, (Springer-Verlag, Berlin, 1982)

    Google Scholar 

  81. F.E. Harris, H.J. Monkhorst and D.L. Freeman, Algebraic and diagrammatic methods in many-fermion theory, (Oxford, University Press, New York, 1992)

    Google Scholar 

  82. S. Wilson, Comput. Phys. Repts. 2, 389 (1985)

    CAS  Google Scholar 

  83. D. Moncrieff, D.J. Baker and S. Wilson 1989 Comput. Phys. Commun. 55 31

    CAS  Google Scholar 

  84. Márquez AM and Dupuis M 1995 J. Comput. Chem. 16 395

    Google Scholar 

  85. Feenberg E 1956 Phys. Rev. 103 1116

    Google Scholar 

  86. Wilson S, Silver DM and Farrell RA 1977 Proc. Roy. Soc. (London) A 356 363

    Google Scholar 

  87. Wilson S 1979 J. Phys. B: At. Mol. Phys. 12 L135

    CAS  Google Scholar 

  88. Wilson S 1981 J. Phys. B: At. Mol. Phys. 14 L31

    CAS  Google Scholar 

  89. Wilson S 1981 Theoret. chim. Acta 59 71

    CAS  Google Scholar 

  90. Sadlej AJ and Wilson S 1981 Molec. Phys. 44 229

    Google Scholar 

  91. Silver DM and Wilson S 1982 Proc. Roy. Soc. (London) A 383 477

    Google Scholar 

  92. Wilson S, Kellö V, Noga J and Urban M 1983 Molec. Phys. 50 1323

    CAS  Google Scholar 

  93. Dietz K, Schmidt C, Warken M and Hess BA 1993 J. Phys. B: At. Mol. Opt. Phys. 26 1885

    CAS  Google Scholar 

  94. Dietz K, Schmidt C, Warken M and Hess BA 1993 J. Phys. B: At. Mol. Opt. Phys. 26 1897

    CAS  Google Scholar 

  95. Dietz K, Schmidt C, Warken M and Hess BA 1993 Chem. Phys. Letts. 207 281

    CAS  Google Scholar 

  96. Schmidt C, Warken M and Handy NC 1993 Chem. Phys. Lett. 211 272

    CAS  Google Scholar 

  97. Dietz K, Schmidt C, Warken M and Hess BA 1994 Chem. Phys. Lett. 220 397

    CAS  Google Scholar 

  98. Dietz K, Schmidt C, Warken M and Hess BA 1994 J. Chem. Phys. 100 7421

    CAS  Google Scholar 

  99. T.E. Sorensen, W.B. England, D.M. Silver and E.O. Steinborn, Theoret. chim. Acta. 84, 1 (1992)

    CAS  Google Scholar 

  100. T.E. Sorensen, W.B. England and D.M. Silver, J. Phys. B: At. Mol. Opt. Phys. 22, L539

    Google Scholar 

  101. Wilson S 1988 Meth. Comput. Chem. 2 73

    Google Scholar 

  102. Quiney HM, Grant IP and Wilson S 1989 in Many body methods in Quantum Chemistry, edited by U. Kaldor, Lecture Notes in Chemistry 52, 331 (Springer-Verlag, Berlin)

    Google Scholar 

  103. Wilson S, Grant IP and Gyorffy BL 1991 editors, The Effects of Relativity in Atoms, Molecules and the Solid State, (Plenum, New York)

    Google Scholar 

  104. Wilson S 1992 in Methods in Computational Molecular Physics, edited by S. Wilson and G.H.F. Diercksen, NATO ASI Series B293, p. 253 (Plenum, New York)

    Google Scholar 

  105. D. Moncrieff and S. Wilson, J. Phys. B: At. Mol. Opt. Phys. 29, 2425 (1996)

    CAS  Google Scholar 

  106. D. Moncrieff & S. Wilson, J.Phys.B: At. Mol. & Opt. Phys. 26, 1605 (1993).

    CAS  Google Scholar 

  107. Chem. Phys. Lett. 209, 423 (1993)

    CAS  Google Scholar 

  108. S. Wilson, in Methods in Computational Molecular Physics, ed. G.H.F. Diercksen and S. Wilson, Reidel, Dordrecht (1983)

    Google Scholar 

  109. C. Schwartz, Meth. Comput. Phys. 2, 241 (1962)

    Google Scholar 

  110. K. Ruedenberg, R.C. Raffenetti and R. Bardo, in Energy structure and reactivity, Proc. 2nd. Boulder Research Confer. in Theoret. Chem., Wiley, New York (1973)

    Google Scholar 

  111. R.C. Raffenetti, J. Chem. Phys. 58, 4452 (1973)

    CAS  Google Scholar 

  112. R.C. Raffenetti, J. Chem. Phys. 59, 5936 (1973)

    CAS  Google Scholar 

  113. R.C. Raffenetti and K. Ruedenberg, J. Chem. Phys. 59, 5978 (1973)

    CAS  Google Scholar 

  114. R. Bardo and K. Ruedenberg, J. Chem. Phys. 59, 5956, 5966 (1973)

    CAS  Google Scholar 

  115. R. Bardo and K. Ruedenberg, J. Chem. Phys. 60, 918 (1974)

    CAS  Google Scholar 

  116. D.F. Feller and K. Ruedenberg, Theoret. chim. Acta. 52, 231 (1979)

    CAS  Google Scholar 

  117. S. Wilson, Theoret. chim. Acta 57, 53 (1980)

    CAS  Google Scholar 

  118. S. Wilson, Theoret. chim. Acta 58, 31 (1980)

    CAS  Google Scholar 

  119. D.M. Silver, S. Wilson and W.C. Nieuwpoort, Intern. J. Quantum Chem. 14, 635 (1978).

    CAS  Google Scholar 

  120. D.M. Silver and W.C. Nieuwpoort, Chem. Phys. Lett. 57, 421 (1978).

    CAS  Google Scholar 

  121. D.M. Silver and S. Wilson, J. Chem. Phys. 69, 3787 (1978).

    CAS  Google Scholar 

  122. S. Wilson and D.M. Silver, Chem. Phys. Lett. 63, 367 (1979).

    CAS  Google Scholar 

  123. S. Wilson and D.M. Silver, J. Chem. Phys. 72, 2159 (1980).

    CAS  Google Scholar 

  124. S. Wilson, in Specialist Periodical Report: Theoretical Chemistry 4, 1 (Royal Society of Chemistry, London, 1981).

    Google Scholar 

  125. S. Wilson and D.M. Silver, J. Chem. Phys. 77, 3674 (1982).

    CAS  Google Scholar 

  126. S. Wilson, Molec. Phys. 43, 1489 (1983).

    Google Scholar 

  127. D. Moncrieff and S. Wilson, J. Phys. B: At. Mol. Opt. Phys. 27, 1 (1994)

    CAS  Google Scholar 

  128. E. Clementi and G. Corongiu, Chem. Phys. Lett. 90, 359 (1982)

    Google Scholar 

  129. Geometric Basis Sets for Molecular Computations, IBM Tech. Rept. POK-11 (1982).

    Google Scholar 

  130. E. Clementi, S.J. Chakravorty, G. Corongiu and V. Sonnad, in Modern Techniques in Computational Chemistry, ed. E. Clementi, ESCOM, Leiden (1990)

    Google Scholar 

  131. S. Huzinaga, Comput. Phys. Repts. 2 (1985) 281

    Google Scholar 

  132. H. Muntz, Festschrift, edited by H.A. Schwartz, p.303, Springer-Verlag, Berlin (1914)

    Google Scholar 

  133. O. Szász, Math. Ann. 77 (1926)

    Google Scholar 

  134. R. Courant and D. Hilbert, Methoden der Mathamatischen Physik, Vol. 1, p.86 (Springer, 1931)

    Google Scholar 

  135. R.E.A. Paley and N. Wiener, American Mathematical Society Colloquium Publications, Vol. XIX, pp. 32-36 (New York, 1934)

    Google Scholar 

  136. A. Schönhage, Approximationstheorie, pp. 49-52, (de Gruyter, Berlin, 1971)

    Google Scholar 

  137. J.R. Higgins, Completeness and Basis Properties of Sets of Special Functions, pp. 95-97, (Cambridge University Press, Cambridge, 1977)

    Google Scholar 

  138. B. Klahn, J. Chem. Phys. 83, 5748 (1985)

    Google Scholar 

  139. A.S. Shalabi and S. Wilson, J. Molec. Struct. (THEOCHEM) 341, 165 (1995)

    CAS  Google Scholar 

  140. R.K. Nesbet, Rev. Mod. Phys. 32, 272 (1960)

    CAS  Google Scholar 

  141. C.M. Reeves, J. Chem. Phys. 39, 1 (1963)

    CAS  Google Scholar 

  142. C.M. Reeves and M.C. Harrison, J. Chem. Phys. 39, 11 (1963)

    CAS  Google Scholar 

  143. R. Fletcher and C.M. Reeves, Comput. J. 6, 287 (1963)

    Google Scholar 

  144. I. Shavitt, Israel J. Chem. 33, 357 (1993)

    CAS  Google Scholar 

  145. J. Almlof, K. Faegri and K. Korsell, J. Comput. Chem. 3, 385 (1982)

    Google Scholar 

  146. S. Wilson and D. Moncrieff, Molec. Phys. 80, 461 (1993)

    CAS  Google Scholar 

  147. D. Moncrieff and S. Wilson, Molec. Phys. 82, 523 (1994)

    CAS  Google Scholar 

  148. H. Preuss, Z. Naturforsch. 11a, 823 (1956).

    CAS  Google Scholar 

  149. H. Preuss, Z. Naturforsch. 19a, 1335 (1964).

    CAS  Google Scholar 

  150. H. Preuss, ibid. 20a, 17, 21 (1965).

    CAS  Google Scholar 

  151. J.L. Whitten, J. Chem. Phys. 39, 349 (1963).

    CAS  Google Scholar 

  152. F. Driessler and R. Ahlrichs, Chem. Phys. Lett. 23, 571 (1973).

    CAS  Google Scholar 

  153. V.R. Saunders, in Methods in Computational Molecular Physics, edited by G.H.F. Diercksen and S. Wilson, Reidel, Dordrecht

    Google Scholar 

  154. A.A. Frost, J. Chem. Phys. 47, 3707 (1967)

    CAS  Google Scholar 

  155. A.A. Frost, J. Chem. Phys. 47, 3714 (1967)

    CAS  Google Scholar 

  156. B. Ford, G.G. Hall and J.C. Packer, Intern. J. Quantum Chem. 4, 533 (1970)

    CAS  Google Scholar 

  157. L.M. Haines, J.N. Murrell, B.J. Ralston, and D.J. Woodnutt, J. Chem. Soc. Faraday Transactions II 70, 1794 (1974)

    CAS  Google Scholar 

  158. B.J. Ralston, D. Phil. Dissertation, University of Sussex, 1974

    Google Scholar 

  159. B.J. Ralston and S. Wilson, J. Molec. Struct. THEOCHEM 341, 115 (1995)

    CAS  Google Scholar 

  160. S. Wilson, J. Molec. Struct. THEOCHEM 357, 37 (1995)

    CAS  Google Scholar 

  161. S. Wilson, Intern. J. Quant. Chem. 60, 47 (1996)

    CAS  Google Scholar 

  162. S. Hackel, D. Heinemann, D. Kolb and B. Fricke, Chem. Phys. Lett. 206 (1993) 91

    CAS  Google Scholar 

  163. S. Wilson, J. Phys. B: At. Mol. Opt. Phys. 28, L495 (1995)

    CAS  Google Scholar 

  164. F.E. Harris, J. Chem. Phys. 32 (1960) 3

    CAS  Google Scholar 

  165. D.D. Ebbing, J. Chem. Phys. 36 (1962) 1361

    CAS  Google Scholar 

  166. F.E. Harris and H.S. Taylor, J. Chem. Phys. 38 (1963) 2591

    Google Scholar 

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

    CAS  Google Scholar 

  168. H.S. Taylor and F.E. Harris, Molec. Phys. 6 (1963) 183

    CAS  Google Scholar 

  169. S. Wilson, J. Phys. B: At. Mol. Phys. 16 (1983) L429

    CAS  Google Scholar 

  170. D.M. Bishop and L.M. Cheung, J. Chem. Phys. 78 (1982) 1396

    Google Scholar 

  171. B.H. Wells and S. Wilson, J. Phys. B: At. Mol. Phys. 19 (1985) 17

    Google Scholar 

  172. J.W. Thompson and S. Wilson, J. Phys. B: At. Mol.Opt. Phys. 23 (1990) 2205

    CAS  Google Scholar 

  173. J.W. Thompson and S. Wilson, J. Phys. B: At. Mol.Opt. Phys. 25 (1992) 621

    CAS  Google Scholar 

  174. D.M. Silver, Molec. Phys. 22 (1971) 1069

    CAS  Google Scholar 

  175. W. Kutzelnigg, Intern. J. Quantum Chem. 51 (1994) 447

    CAS  Google Scholar 

  176. I. Shavitt, in Methods in Computational Physics 2 (1963) 1

    Google Scholar 

  177. H. Preuss, Z. Naturforsch 19a, 1335 (1964).

    CAS  Google Scholar 

  178. H. Preuss, ibid 20a, 17, 21 (1965)

    CAS  Google Scholar 

  179. S. Rothenberg and H.F. Schaefer III, J. Chem. Phys. 54, 2765 (1971)

    Google Scholar 

  180. W. Butscher, S. Shih, R.J. Buenker and S.D. Peyerimhoff, Chem. Phys. Lett. 52, 457 (1977)

    CAS  Google Scholar 

  181. D. Neisius and G. Verhaegen, Chem. Phys. Lett. 66, 358 (1979)

    CAS  Google Scholar 

  182. L. Lawlor, K. Vasudevan and F. Grein, Chem. Phys. Lett. 75, 79 (1980)

    CAS  Google Scholar 

  183. P. Mach and O. Kysel, J. Comput. Chem. 6, 312 (1985)

    CAS  Google Scholar 

  184. J.M.L. Martin, J.P. Francois and R. Gijbels, J. Comput. Chem. 10, 152 (1989)

    CAS  Google Scholar 

  185. J.M.L. Martin, J.P. Francois and R. Gijbels, J. Comput. Chem. 10, 875 (1989)

    CAS  Google Scholar 

  186. J.M.L. Martin, J.P. Francois and R. Gijbels, Theoret. chim. Acta 76, 195 (1989)

    CAS  Google Scholar 

  187. F.M. Tao and Y.K. Pan, J. Chem. Phys. 97, 4989 (1992)

    CAS  Google Scholar 

  188. F.M. Tao and Y.K. Pan, Molec. Phys. 81, 507 (1994)

    CAS  Google Scholar 

  189. P. Cársky and M. Urban, Ab initio Calculations. Methods and Applications in Chemistry, Lecture Notes in Chemistry 16 (Springer-Verlag, Berlin)

    Google Scholar 

  190. D. Moncrieff and S. Wilson, J. Phys. B: At. Mol. Phys. 29 (1996) 6009

    CAS  Google Scholar 

  191. J. Olsen, P. Jorgensen, H. Koch, A. Balkova and R.J. Bartlett, 1996 J. Chem. Phys. 104 8007

    CAS  Google Scholar 

  192. D. Feller 1992 J. Chem. Phys. 96 6104

    CAS  Google Scholar 

  193. S.J. Chakravorty and E.R. Davidson, 1993 J. Phys. Chem. 97 6374

    Google Scholar 

  194. E. Clementi, G. Corongiu and O.G. Stradella, 1990 Modern Techniques in Computational Chemistry, MOTECC-90, ESCOM Science Publishers, Leiden, pp. 343

    Google Scholar 

  195. R. Bukowski, B. Jeriorski, S. Rybak, and K. Szalewicz, 1995 J. Chem. Phys. 102 888

    CAS  Google Scholar 

  196. W. Klopper 1995 J. Chem. Phys. 102 6168

    CAS  Google Scholar 

  197. A.J. Sadlej 1977 Chem. Phys. Lett. 47, 50

    CAS  Google Scholar 

  198. S. Wilson and A.J. Sadlej 1981 Theo. chim. Acta. 60, 19

    CAS  Google Scholar 

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Wilson, S. (1997). Practical Ab Initio Methods for Molecular Electronic Structure Studies. II. Finite Basis Sets and the Algebraic Approximation. In: Wilson, S., Diercksen, G.H.F. (eds) Problem Solving in Computational Molecular Science. NATO ASI Series, vol 500. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-0039-4_4

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  • DOI: https://doi.org/10.1007/978-94-009-0039-4_4

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