CONFIGURATION INTERACTION METHODS
Karwowski Jacek 1, Pestka Grzegorz 2
Institute of Physics, M. Kopernik University
Grudziądzka 5, 87-100 Toruń, Poland
e-mail: 1 jka@phys.uni.torun.pl, 2gp@phys.uni.torun.pl
DOI: 10.12921/cmst.1998.04.01.57-69
OAI: oai:lib.psnc.pl:492
Abstract:
In this article configuration interaction methods of solving the Schrödinger eigenvalue problem are reviewed. In particular computational aspects of the “traditional” and of the direct approach are briefly discussed. A special attention is given to the group-theory based formulations known as the unitary group approach and the symmetric group approach. Recent developments and implementations to relativistic theory of many-electron systems are also described.
References:
[1] E. A. Hylleraas, Z. Phys., 48, 469 (1928).
[2] S. F. Boys, Proc. Roy. Soc. (London), A217 136, 235 (1953).
[3] R. G. Parr, D. P. Craig, I. G. Roos, J. Chem. Phys., 18, 1561 (1950).
[4] A. Meckler, J. Chem. Phys., 21, 1750 (1953).
[5] P. -O. Löwdin, Phys. Rev., 97, 1509 (1955).
[6] I. Shavitt, in Methods of Electronic Structure Theory, ed. H. F. Schaefer III (Plenum, New York, 1977), p. 189.
[7] B. O. Roos, P. E. M. Siegbahn, in Methods of Electronic Structure Theory, ed. H. F. Schaefer III (Plenum, New York, 1977), p. 277.
[8] V. R. Saunders, J. H. van Lenthe, Mol. Phys., 48, 923 (1983).
[9] M. Robb, U. Niazi, Comp. Phys. Reports, 1, 128 (1985).
[10] W. Duch, J. Karwowski, Comp. Phys. Reports, 2, 94 (1985).
[11] J. Olsen, B. O. Roos, P. Jorgensen, H. J, Aa. lensen, J. Chem. Phys., 89, 2185 (1988).
[12] P. J. Knowies, N. C. Handy, J. Chem. Phys., 91, 2396 (1989).
[13] W. Duch, J. Mol. Structure (Theochem), 234, 27 (1991).
[14] J. Karwowski, in Methods in Computational Physics, eds. G. H. F. Diercksen and S. Wilson
(Plenum, New York, 1992), p. 65.
[15] J. Karwowski, in Computational Chemistry. Structure, Interactions and Reactivity, Part A, ed. S. Fraga (Elsevier, Amsterdam 1992), p. 197.
[16] R. Pauncz, Spin Eigenfunctions. Construction and Use, (Plenum, New York 1979).
[17] J. Paldus, in Theoretical Chemistry, Advances and Perspectives, vol. 2. eds. H. Eyring and D. G. Henderson (Academic Press, New York 1976) p. 131.
[18] I. Shavitt, Int. J. Quantum Chem., Sil, 131 (1977); S12, 5 (1978).
[19] M. Kotani et al., Table of Molecular Integrals (Maruzen, Tokyo 1955).
[20] F. E. Harris, J. Chem. Phys., 46, 2769 (1967); 47, 1047 (1967).
[21] K. Ruedenberg, Phys. Rev. Letters, 27, 1105 (1971).
[22] J. Gerrat, Mol. Phys., 33, 1199 (1977).
[23] J. Karwowski, Theoret, Chim. Acta, 29, 151 (1973).
[24] J. Karwowski, Chem. Phys. Lett., 19, 279 (1973).
[25] W. Duch, J. Karwowski, Theoret. Chim. Acta, 71, 187 (1987).
In this article configuration interaction methods of solving the Schrödinger eigenvalue problem are reviewed. In particular computational aspects of the “traditional” and of the direct approach are briefly discussed. A special attention is given to the group-theory based formulations known as the unitary group approach and the symmetric group approach. Recent developments and implementations to relativistic theory of many-electron systems are also described.
[1] E. A. Hylleraas, Z. Phys., 48, 469 (1928).
[2] S. F. Boys, Proc. Roy. Soc. (London), A217 136, 235 (1953).
[3] R. G. Parr, D. P. Craig, I. G. Roos, J. Chem. Phys., 18, 1561 (1950).
[4] A. Meckler, J. Chem. Phys., 21, 1750 (1953).
[5] P. -O. Löwdin, Phys. Rev., 97, 1509 (1955).
[6] I. Shavitt, in Methods of Electronic Structure Theory, ed. H. F. Schaefer III (Plenum, New York, 1977), p. 189.
[7] B. O. Roos, P. E. M. Siegbahn, in Methods of Electronic Structure Theory, ed. H. F. Schaefer III (Plenum, New York, 1977), p. 277.
[8] V. R. Saunders, J. H. van Lenthe, Mol. Phys., 48, 923 (1983).
[9] M. Robb, U. Niazi, Comp. Phys. Reports, 1, 128 (1985).
[10] W. Duch, J. Karwowski, Comp. Phys. Reports, 2, 94 (1985).
[11] J. Olsen, B. O. Roos, P. Jorgensen, H. J, Aa. lensen, J. Chem. Phys., 89, 2185 (1988).
[12] P. J. Knowies, N. C. Handy, J. Chem. Phys., 91, 2396 (1989).
[13] W. Duch, J. Mol. Structure (Theochem), 234, 27 (1991).
[14] J. Karwowski, in Methods in Computational Physics, eds. G. H. F. Diercksen and S. Wilson
(Plenum, New York, 1992), p. 65.
[15] J. Karwowski, in Computational Chemistry. Structure, Interactions and Reactivity, Part A, ed. S. Fraga (Elsevier, Amsterdam 1992), p. 197.
[16] R. Pauncz, Spin Eigenfunctions. Construction and Use, (Plenum, New York 1979).
[17] J. Paldus, in Theoretical Chemistry, Advances and Perspectives, vol. 2. eds. H. Eyring and D. G. Henderson (Academic Press, New York 1976) p. 131.
[18] I. Shavitt, Int. J. Quantum Chem., Sil, 131 (1977); S12, 5 (1978).
[19] M. Kotani et al., Table of Molecular Integrals (Maruzen, Tokyo 1955).
[20] F. E. Harris, J. Chem. Phys., 46, 2769 (1967); 47, 1047 (1967).
[21] K. Ruedenberg, Phys. Rev. Letters, 27, 1105 (1971).
[22] J. Gerrat, Mol. Phys., 33, 1199 (1977).
[23] J. Karwowski, Theoret, Chim. Acta, 29, 151 (1973).
[24] J. Karwowski, Chem. Phys. Lett., 19, 279 (1973).
[25] W. Duch, J. Karwowski, Theoret. Chim. Acta, 71, 187 (1987).
