Abstract
In this lecture we discuss an approach to the understanding and efficient calculation of electron correlation of valence or inner hole excited states in atoms and small molecules. We start with the formal subshell cluster expansion of the wave-function and we analyze the various correlation effects which appear in the wave-function whose form is dictated by first order perturbation theory. I.e. only single and pair symmetry adapted correlation functions are considered. This analysis allows: 1) The formal decoupling, to a good approximation, of the subshell correlation vectors into groups and their economic computation from small Variational Configuration-Interaction (VCI) procedures. 2) The systematic optimization of the different for each group virtual one-electron functions—expressed in terms of STO’s or GTO’s—by minimizing the corresponding to each group energy functional. 3) The consequent determination of compact but accurate total wave-functions from basis sets which contain the Hartree-Fock and only a few more virtual orbitals. 4) The recognition and isolation of important for electronic spectroscopy and chemical bonding correlation effects from those which contribute mainly to total energies. 5) The recognition of the importance of triple and quadruple correlation effects for certain inner hole excited states, even in small systems. We present previously unpublished numerical results on a) the position of the H- 2P2 3P metastable state whose study supports our suggestion that variationally optimized (VO) one-electron basis sets are competitive with rij dependent basis sets in terms of fast convergence. b) The position of the H-- 2p3 4S° state which is found to be unbound. c) The pair correlations of C where reasonably accurate calculations indicate that VO-GTO virtuals are reasonably competitive with VO-STO virtuals. This suggests that the size of current molecular calculations using Gaussians can be reduced considerably at no expense of accuracy, d) The effect of electron correlation on the term structure of Ni III, of current importance in solid state physics.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
D.R. Beck and C.A. Nicolaides, Int. J. Qu. Chem. S8, 17, (1973).
D.R. Beck and C.A. Nicolaides, Int. J. Qu. Chem. S10, 119, (1976).
R.J. Buenker and S.D. Peyerimhoff, Theor. Chim. Acta 35, 33, (1974).
R.J. Buenker and S.D. Peyerimhoff, this volume.
G. Das and A.C. Wahl, J. Chem. Phys. 50, 3532, (1972)
S.L. Guberman, J. Chem. Phys. 67, 1125 (1977).
R.J. Buenker and S.D. Peyerimhoff, Chem. Phys. Letts. 34, 225, (1975).
C. Froese-Fischer, Comp. Phys. Comm. 4, 107, (1972).
H.J. Silverstone, J. Chem. Phys. 67, 4172, (1977).
C.A. Nicolaides and D.R. Beck, Chem. Phys. Letts. 36, 79, (1975).
D.R. Beck and C.A. Nicolaides, Phys. Letts. 65A, 293, (1978).
C.A. Nicolaides and D.R. Beck, “Time Dependence, Complex Scaling and the Calculation of Resonances in Many-Electron Systems”, to be published in the Volume “Complex Scaling in the Spectral Theory of the Hamiltonian”, ed. by P.O. Löwdin (Int. J. Qu, Chem. supplement volume 1978).
B. Kahn and G.E. Uhlenbeck, Physica 5, 399, (1938); the term “linked cluster” apparently first appeared in this article.
V. Fock, M. Vesselov and M. Petrashen, J. Exp. Theor. Phys. (U.S.S.R.) 10, 723, (1940).
F. Iwamoto and M. Yamada, Prog. Theor. Phys. 17, 543, (1957).
W. Brenig, Nucl. Phys. 4, 363, (1957).
R. Brout, Phys. Rev. 111, 1324, (1958).
O. Sinanoglu, J. Chem. Phys. 36, 706, (1962).
L. Szasz, Phys. Rev. 126, 169, (1962).
H.J. Silverstone and O. Sinanoğlu, J. Chem. Phys. 44, 1898, 3608, (1966).
J. Cizek, J. Chem. Phys. 45, 4256, (1966)
J. Cizek, Adv. Chem. Phys. 14, 35, (1969).
R.K. Nesbet, Phys. Rev. 155, 56, (1957).
C. Møller and M.S. Plesset, Phys. Rev. 46, 618, (1934).
O. Sinanoğlu, Proc. R. Soc. (london) A260, 379, (1961).
C.F. Bender and E.R. Davidson, Phys. Rev. 183, 23, (1969).
A.N. Weiss, Phys. Rev. A3, 126, (1971).
J.W. Viers, F.E. Harris and H.F. Schaefer III, Phys. Rev. A1, 24, (1970).
C.F. Bunge, Chem. Phys. Letts. 42, 141, (1976).
F. Sasaki and M. Yoshimine, Phys. Rev. A9, 26, (1974).
CM. Moser and R.K. Nesbet, Phys. Rev. A6, 1710, (1972).
R. Ahlrichs, H. Lischka, B. Zurawski and W. Kutzelnigg, J. Chem. Phys. 63, 4685, (1975)
W. Meyer, J. Chem. Phys. 58, 1017, (1973) and references therein.
F.W. Byron and C.J. Joachain, Phys. Rev. 157, 7, (1967).
C. Froese-Fischer and K.M.S. Saxena, Phys. Rev. A9, 1498, (1974).
H.P. Kelly and A. Ron, Phys. Rev. A4, 11, (1971).
J. Paldus, J. Cizek and I. Shavitt, Phys. Rev. A1, 50, (1972).
R.J. Buenker, S.D. Peyerimhoff and W. Butscher, Mol. Phys. 35, 771, (1978).
R.E. Knight, Phys. Rev. 183, 45, (1969).
A. Pipano and I. Shavitt, Int. J. Qu. Chem. II, 741, (1968).
C. Froese-Fischer, J. Phys. B6, 1933, (1973).
H.P. Kelly, Phys. Rev. 144, 39, (1966).
I. Oksüz and O. Sinanoğlu, Phys. Rev. 181, 42 (1969).
C.A. Nicolaides and D.R. Beck, J. Phys. B6, 535, (1973).
D.R. Beck and O. Sinanoğlu, Phys. Rev. Letts. 28, 945, (1972).
H.F. Schaeffer III, J. Chem. Phys. 55, 176, (1971).
C.A. Nicolaides and D.R. Beck, J. Chem. Phys. 66, 1982, (1977).
D.R. Beck and C.A. Nicolaides, Phys. Letts. 61A, 227, (1977).
C.A. Nicolaides and D.R. Beck, J. Phys. B9, 1259, (1976).
R.J. Buenker and S.D. Peyerimhoff, Chem. Phys. Letts. 36, 415, (1975).
E.R. Cooper and H.P. Kelly, Phys. Rev. A7, 38, (1973).
E.R. Davidson, in “The World of Quantum Chemistry”, eds. R. Dandel and B. Pullman, Reidel Publ. Co. Dordrecht, (1974).
A. Mennier, B. Levy and G. Berthier, Int. J. Qu. Chem. 10, 1061, (1976).
F. Sasaki, Int. J. Qu. Chem. S11, 125, (1977).
R.J. Bartlett and I. Shavitt, Int. J. Qu. Chem. S11, 165, (1977).
T.A. Carlson and M.O. Krause, Phys. Rev. Letts. 17, 1079, (1966).
Y. Komninos, D.R. Beck and C.A. Nicolaides, unpublished.
L.E. McMurchie and E.R. Davidson, J. Chem. Phys. 66, 2959, (1977).
R.J. Buenker and S.D. Peyerimhoff, Chem. Phys. 8, 324, (1975).
J. Reader, Phys. Rev. A7, 1431, (1973).
D.A. Shirley et.al., “Electron-Correlation Satellites in Electron Spectroscopy”, preprint, presented at the 2nd Int. Conf. on Inner Shell Ionization Phenomena, Preiburg, (1976).
E.K. Viinikka and Y. Ohrn, Phys. Rev. B11, 4168, (1975).
L.E. Nitzsche and E.R. Davidson, J. Chem. Phys. 68, 3103, (1978).
C.C. J. Roothaan and P.S. Bagus, Methods of Comp. Phys. 2, B. Alder, S. Fernbach and M. Rotenberg, eds. Acad. Press (1963).
E.A. McCullough, Jr., J. Chem. Phys. 62, 3991, (1975).
C.A. Nicolaides, Phys. Rev. A6, 2078, (1972)
C.A. Nicolaides, Nucl Inst. Methods 110, 231 (1973).
D.R. Beck and C.A. Nicolaides, Phys. Rev. Letts, submitted May 1978.
C.A. Nicolaides and D.R. Beck, this volume.
E.R. Davidson and L.Z. Stenkamp, Int. J. Qu. Chem. S10, 21 (1976).
L.A. Yaffe and W.A. Goddard III, Phys. Rev. A13, 1682, (1976).
J. Hinze and C.C.J. Roothaan, Supp. Prog. Theor. Phys. 40, 37, (1967).
W.J. Hunt and W.A. Goddard III, Chem. Phys. Letts. 3, 414, (1969).
E.R. Davidson, “Reduced Density Matrices in Quantum Chemistry”, Acad. Press (N.Y.) (1976);
C.F. Bender and E.R. Davidson J. Phys. Chem. 70, 2675 (1966).
C. Edmiston and M. Krauss, J. Chem. Phys. 45, 1833 (1966).
e.g. D.R. Beck, J. Chem. Phys. 51, 2171 (1969).
D.R. Beck and C.A. Nicolaides, unpublished.
D.R. Beck, C.A. Nicolaides and J.I. Musher, Phys. Rev. A10, 1522 (1974).
C.A. Nicolaides and D.R. Beck, Can. J. Phys. 53, 1224 (1975).
H.F. King et. al., J. Chem. Phys. 47, 1936 (1967).
H.F. Schaefer and F.E. Harris, J. Comp. Phys. 3, 217 (1968).
A. Bunge, J. Chem. Phys. 53, 20, (1970).
D.R. Beck and H. Odabasi, Ann. Phys. 67, 274, (1971).
G.W.F. Drake, Phys. Rev. Letts. 24, 126, (1970).
R. Schnitzer and M. Auber, J. Chem. Phys. 64, 2466 (1976).
W. Aberth, J. Chem. Phys. 65, 4329 (1976)
M.L. Vestal, J. Chem. Phys. 65 p. 4331
J. Durup, ibid. p. 4331
R. Schnitzer and M. Aubar, ibid. p. 4432.
J.F. Liebman, D.L. Yeager and J. Simons, (Chem. Phys. Letts. 48, 227, (1977)) have added an attractive external potential to introduce binding, in their study of shape resonances.
S. Huzinaga and A. Hart-Davis, Phys. Rev. 8A, 1734 (1973). Positive eigenvalues were also obtained in certain HF calculations of He- compound states (C.A. Nicolaides, Phys. Rev. A6, 2078 (1972); C.A. Nicolaides, unpublished).
D.R. Yarkony, H.F. Schaefer, III, and C.F. Bender, J. Chem. Phys. 64, 981 (1976).
C.F. Bunge and A.V. Bunge, “Calculations of Atomic Electron Affinities”, preprint.
A.B. Kunz, this volume; Phys. Rev. B7, 5369 (1973).
D.R. Beck and C.A. Nicolaides, this volume.
C. Froese-Fischer, Can. J. Phys. 49, 1205 (1971).
C.E. Moore, “Atomic Energy Levels Vol II”, NBS circular 467 (1952).
R.L. Kelly and L.J. Palumbo, “Atomic and Ionic Emission Lines below 2000 Å”, NRL Reprint 7 599 (1973).
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1978 D. Reidel Publishing Company, Dordrecht, Holland
About this chapter
Cite this chapter
Beck, D.R., Nicolaides, C.A. (1978). Theory of the Electronic Structure of Excited States in Small Systems with Numerical Applications to Atomic States. In: Nicolaides, C.A., Beck, D.R. (eds) Excited States in Quantum Chemistry. NATO Advanced Study Institutes Series, vol 46. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-9902-2_6
Download citation
DOI: https://doi.org/10.1007/978-94-009-9902-2_6
Publisher Name: Springer, Dordrecht
Print ISBN: 978-94-009-9904-6
Online ISBN: 978-94-009-9902-2
eBook Packages: Springer Book Archive