This is a preview of subscription content, log in via an institution to check access.
Preview
Unable to display preview. Download preview PDF.
References
While a symmetry group leaves the Hamiltonian invariant, this is not necessarily the case for a dynamical group [2a], in which case we only require that the Hamiltonian is expressible through its generators. In addition, one sometimes requires [2b] that all of the dynamics of the system is contained in a single irreducible representation (irrep) of the dynamical group. However, in the case of U(n) different irreps are needed for different multiplets of the model systems studied.
W. Miller, Jr., Symmetry Groups and Their Applications (Academic Press, N.Y., 1972), p. 400.
Cf., for example, C.E. Wulfman, in Group Theory and Its Applications, Vol. 2, E.M. Loebl, Ed. (Academic Press, N.Y., 1971), p. 145.
P. Jordan, Z. Phys. 94, 531 (1935).
I.M. Gelfand and M.E. Tsetlin, Dokl. Akad. Nauk SSSR 71, 825, 1070 (1950); G.E. Baird and L.C. Biedenharn, J. Math. Phys. 4, 1449 (1963); 5, 1723, 1730 (1964), 6, 1847 (1965); M. Moshinsky, J. Math. Phys. 4, 1128 (1963).
M. Moshinsky, J. Math. Phys. 7, 691 (1966); Group Theory and the Many-Body Problem (Gordon and Breach, N.Y., 1968).
M. Moshinsky and T.H. Seligman, Ann. Phys. (N.Y.) 66, 311 (1971).
W.G. Harter, Phys. Rev. A8, 2819 (1973).
J. Paldus, J. Chem. Phys. 61, 5321 (1974); Intern. J. Quantum Chem., Symp. 9, 165 (1975).
J. Paldus, in Theoretical Chemistry: Advances and Perspectives, Vol. 2, H. Eyring and D.J. Henderson, Eds. (Academic Press, N.Y., 1976), p. 131.
W.G. Harter and C.W. Patterson, Phys. Rev. A13, 1067 (1976); A Unitary Calculus for Electronic Orbitals (Springer-Verlag, Berlin, 1976).
J. Paldus, in Electrons in Finite and Infinite Structures, P. Phariseau and L. Scheire, Eds. (Plenum Publ. Co., N.Y., 1977), p. 411.
I. Shavitt, Intern. J. Quantum Chem., Symp. 11, 131 (1977); Symp. 12 (in press).
F.A. Matsen, Intern. J. Quantum Chem., Symp. 8, 379 (1974); 10, 525 (1976).
F.A. Matsen, Adv. Quantum Chem. 1, 59 (1964), J. Amer. Chem. Soc. 92, 3525 (1970).
F.A. Matsen, T.L. Welsher and B. Yurke, Intern. J. Quantum Chem. 12, 985 (1977); F.A. Matsen and T.L. Welsher, 12, 1001 (1977).
P.E.S. Wormer and A. van der Avoird, J. Chem. Phys. 57, 2498 (1972); Intern. J. Quantum Chem. 8, 715 (1974); P.E.S. Wormer, Ph.D. Thesis, University of Nijmegen, The Netherlands, 1975.
F.A. Matsen, Advan. Quantum Chem. 11 (in press), Intern. J. Quantum Chem., Symp 12 (in press); Accounts of Chem. Research (in press).
J.-F. Gouyet, R. Schranner and T.H. Seligman, J. Phys. A: Math. Gen. 8 285 (1975); J.-F. Gouyet, Rev. Mex. Fis (in press).
J. Drake, G.W.F. Drake and M. Schlesinger, J. Phys. B8, 1009 (1975); G.W.F. Drake and M. Schlesinger, Phys. Rev. A 15, 1990 (1977).
A.A. Cantu, D.J. Klein, F.A. Matsen and T.H. Seligman, Theoret. Chim. Acta 38, 341 (1975).
I. Shavitt, in Methods of Electronic Structure Theory, H.F. Schaefer III, Ed. (Plenum Publ. Co., N.Y., 1977), p. 189.
G.A. Segal, R.W. Wetmore and K. Wolf, Chemical Physics 30, 269 (1978).
J.D. Louck, Amer. J. Phys. 38, 3 (1970).
We call these matrices tableaus because of the unconventional numbering of rows and columns user the rows are numbered from the bottom upwards and the columns from right to left in order to achieve a simple correspondence with the EGT's.
J. Paldus, Phys. Rev. A14, 1620 (1976).
T. Sebe and J. Nachamkin, Ann. Phys. (N.Y.) 51, 100 (1969); R.R. Whithead, Nucl. Phys. A 182, 290 (1972).
B. Roos, Chem. Phys. Letters 15, 153 (1972); B.O. Roos and P.E.M. Siegbahn, in Methods of Electronic Structure Theory, H.F. Schaefer III, Ed. (Plenum Publ. Co., N.Y., 1977), p. 277.
R.F. Hausman, S.D. Bloom and C.F. Bender, Chem. Phys. Letters 32, 483 (1975), R.H. Hausman and C.F. Bender, in Methods of Electronic Structure Theory, H.F. Schaefer III, Ed. (Plenum Publ. Co., N:Y.,1977), p. 319, C.F. Bender, J. Comput. Phys. (in press).
Cf., for example, Ref. [20] and C. Lanczos, J. Res. Nat. Bur. Stand. 45, 255 (1950); E.R. Davidson, J. Comput. Phys. 17, 87 (1975).
M.J. Downward and M.A. Robb, Theoret. Chim. Acta 46, 129 (1977); D. Hegarty and M.A. Robb, “Direct CI Calculations using the Calculus of the Unitary Group”, preprint. Unfortunately, this work does not fully exploit the simple structure and sparseness of generator matrices.)
M. Kotani, A. Amemiya, E. Ishiguro and T. Kimura, Tables of Molecular Integrals, (Maruzen Co., Ltd., 2nd edition, Tokyo, 1963).
P.E.S. Wormer, unpublished results.
C.R. Sarma and S. Rettrup, Theoret. Chim. Acta 46, 63 (1977); S. Rettrup and C.R. Sarma, Theoret. Chim. Acta 46, 73 (1977), cf., also, C.R. Sarma and K C. Dinesha, J. Math. Phys. 8, 1662 (1978).
A.P. Jucys, I. B. Levinson and V.V. Vanagas, Mathematical Apparatus of the Theory of Angular Momentum (Israel Program for Scientific Translations, Jerusalem, 1962, and Gordon and Breach, N.Y., 1964); A.P. Jucys and A.A. Bandzaitis, The Theory of Angular Momentum in Quantum Mechanics, (Institute of Physics and Mathematics of the Academy of Science of the Lithuanian S. S. R., Mintis Vilnius, 1965, in Russian); E. El Baz and B. Castel, Graphical Methods of Spin Algebras (M. Dekker, N.Y., 1972); D. M. Brink and G.R. Satchler, Angular Momentum, 2nd edition (Clarendon Press, Oxford, 1968).
The “overlapping” part in the product Eij Ekℓ consists of rows k, k + 1,...,j if i ≤ k < j < ℓ (product of two raising generators) or of rows ℓ, ℓz + 1,...,j if i ≤ ℓ < j ≤ k (product of a raising and a 2708 lowering generator).
J. Paldus, unpublished results
J. Downing, unpublished results.
J. Paldus and P. E. S. Wormer, Phys. Rev. A (in press); cf. also J. Paldus, B. G. Adams and J. Čížek. Intern. J. Quantum Chem. 11, 813 (1977).
V. P. Karasev, in Group Theoretical Methods in Physics, D.V. Skobel'tsyn, Ed. (Proc. of the-P.N. Lebedev Physics Institute, Vol. 70, Consultants Bureau, N.Y., 1975), p. 141; V. K Agrawala and J.G. Belinfante, Ann. Phys. (N.Y.) 49, 130 (1968); P.A.M. Guichon, Report LYCEN 7570, University of Lyon, France (1975); M. Kibler and E. El Baz, Report LYCEN 7872, University of Lyon, France (1978).
J. Paldus and M.J. Boyle, unpublished results.
Abelian point groups may be handled quite easily [9], even with an efficient canonical basis storage (IV. 4), [40].
I. Shavitt, unpublished results.
Cf., for example, B. R. Judd, W. Miller, Jr., J. Patera and P. Winternitz, J. Math. Phys. 15, 1787 (1974).
J. Mickelsson, J. Math. Phys. 11, 2803 (1970), 12, 2378 (1971).
J. Flores and M. Moshinsky, Nucl. Phys. A93, 81 (1967).
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1979 Springer-Verlag
About this paper
Cite this paper
Paldus, J. (1979). Unitary group approach to molecular electronic structure. In: Beiglböck, W., Böhm, A., Takasugi, E. (eds) Group Theoretical Methods in Physics. Lecture Notes in Physics, vol 94. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-09238-2_15
Download citation
DOI: https://doi.org/10.1007/3-540-09238-2_15
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-09238-4
Online ISBN: 978-3-540-35345-4
eBook Packages: Springer Book Archive