By C. K. Jorgensen
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Additional resources for Absorption Spectra and Chemical Bonding in Complexes
Generally, the second-order perturbations change a given wave 34 THE ENERGY LEVELS OF A CONFIGURATION function Ψ1 by intermixing it with small parts of other wave functions Ψ2, . . with which it has non-diagonal elements. The influence on the wave function Ψχ is inversely proportional to the distance on the energy scale of the other wave functions, while the influence on the energy is proportional to the squares of the non-diagonal elements. On the other hand, only the energy and not the wave function itself is changed by a first-order perturbation.
Eqn. 37), it is possible 2 to write ζη1 as a quadratic function k^Z^ , where the proportionality constant k nI varies surprisingly little within a given p- or d-shell. In this case, Z # is a linear function of the number of electrons q in the partly filled shell, being Z* = Z 0 + 0-5 + 0-7q for 4p<* and Z* = Z 0 — 0-8 + 0-8q for 4d<*. The factors are k 4P ~ 0 1 kK and k 4d ~ 0Ό29 kK, respectively. Z 0 is the ionic charge plus 1. The 2 fundamental reason why £ nl is proportional to Z^ is not as well understood as why Β is proportional to Z^.
The hyperbolic behaviour of two interacting levels. 2 The angle φ is given in eqn. (23). THE ENERGY LEVELS OF A CONFIGURATION 37 Fig. 1 gives E a and Eb as a function of ( E u — E22). It is a hyperbola with the straight lines E u and E22 as asymptotes and the distance 2 E 12 between the two levels for E n — E 22 = 0, agreeing with eqn. (18). The stabilization of the lowest state by intermixing is given by the value of χ from eqn. (19) x = En - ED = _ Eb = E 12 = - E 1 2 tg φ (26) Thus, the result of the intermixing of a small part, a ^ , of a new wave function into Ψλ is exactly the opposite of that expected when E 12 is neglected.
Absorption Spectra and Chemical Bonding in Complexes by C. K. Jorgensen