Theory of the Electronic Structure of Excited States in Small Systems with Numerical Applications to Atomic States

  • Donald R. Beck
  • Cleanthes A. Nicolaides
Part of the NATO Advanced Study Institutes Series book series (ASIC, volume 46)


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 We present previously unpublished numerical results on a) the position of the H- 2P2 3P metastable state whose study supports our suggestion that variationally optimized (VO) one-electron basis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.


Excited State Pair Correlation Term Structure Small System Cluster Expansion 
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Copyright information

© D. Reidel Publishing Company, Dordrecht, Holland 1978

Authors and Affiliations

  • Donald R. Beck
    • 1
  • Cleanthes A. Nicolaides
    • 1
  1. 1.Theoretical Chemistry InstituteNational Hellenic Research FoundationAthens 501/1Greece

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