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By C. K. Jorgensen

ISBN-10: 0080096271

ISBN-13: 9780080096278

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The one-electron operators (determining, for example, orbital energies according to eqn. (5) as diagonal elements) take over all the results of the discussion above, substituting ψ for Ψ in all expressions. The only two-electron operator of consequence for our treatment is the electrostatic interaction between two electrons, D 38 THE ENERGY LEVELS OF A C O N F I G U R A T I O N 2 r being a potential of the form g = e / i 2 . The non-diagonal elements of this operator affect at most four orbitals and are expressed (abgcd) = (ac:bd) = J ί Φ ^ φ ^ τ ^ φ ^ φ α ^ ά τ ^ (27) The first notation was used by Condon and Shortley for conforming to the traditional order of wave functions before and after the operator g.

The latter picture is only correct for the mass ratio between the nucleus and the electrons and to some extent for the very low density in the volume outside the nucleus. On the other hand, the planets are individually different, tangible bodies, while the electron density in an atom is described by the cloudy wave function mentioned above. One further important difference is that while the gravity interactions between the planets are very small, compared to the interaction with the sun, the electrostatic interactions between the electrons in an atom with several electrons are by no means negligible, compared to the attraction by the nucleus.

Hence, the deviations between semi-empirical and HFSC-calculated values of the interelectronic repulsion parameters (eqn. 38) might be partly explained by a deviation of the partly filled shell (defined, for example, from the density of uncompensated electron spin) in the actual ion from the HFSC-radial function. Actually, the radial and angular correlation effects invalidate to some extent the whole concept of electron configurations, since a 44 THE ENERGY LEVELS OF A CONFIGURATION given configuration inevitably has some non-vanishing non-diagonal elements of the two-electron operator g with other configurations, and therefore, the actual wave functions must be intermixings of many configurations.

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Absorption Spectra and Chemical Bonding in Complexes by C. K. Jorgensen


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