By C. K. Jorgensen
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Extra resources for Absorption Spectra and Chemical Bonding in Complexes
G. in the first row, corresponding to the signs of the products ΨχΨη) have arbitrary signs. There exist only two different polynomials E p , corresponding to a certain third degree secular determinant with arbitrary choice of its three signs of the non-diagonal elements; and only eight different E p's for q = 4. We shall not discuss further the complications of "choice of phases" for wave functions. Until now, we have considered the diagonal or non-diagonal elements of a certain operator Ρ in ^Ψ^ΡΨχ and / Ϊ Ί Ρ Ϊ * We have not specified the number of electrons affected by P, which is highly important for the problem of how to express these elements in terms of Ρ acting on orbitals ψ rather than on the total wave functions Ψ.
The parity is even or odd and combined with one of five values, for which Mulliken has proposed other names, according to their degeneracy number e: Bethe: Γλ Mulliken: Α1 e = 1 Γ2 Α2 1 Γ3 Ε 2 Γ4 Τχ 3 Γ5 Τ2 3 (43) and the orbitals have the analogous names y n (or a 1? a 2, . ). Some English authors also use the five letters α, β, γ, δ, c, and use, for example, άγ and d e electrons for y 3 and y 5. The products of different L-values are: 53 MOLECULAR ORBITALS AND MICROSYMMETRY S I\ Ρ D F A Γ3 + Γ5 Γ2 + Γ 4 + Γ 5 G Γ + Γ +Γ +Γ Η I Γ 3 + 2Γ4 + Γ5 Γτ + Γ2 + Γ 3 + Γ 4 + 2 Γ 5 1 Ζ Α Β (44) combined with even or odd parity (as also in spherical symmetry, 4 3 where, for instance, S from p has odd parity, since 3/ = 3 is odd).
77) are due to an accidental effect of a not too distant configuration and are not connected intimately with the main problem of correlation energy. Until now, we have not mentioned the effects of electrodynamic (magnetic) and relativistic corrections on the energy levels of atomic spectroscopy. These effects can be ascribed in Slater's model to one-electron quantities, the Lande multiplet splitting factors ζ η ΐ, defined from the central field U(r) and the radial function R: 00 (41) 0 The occurrence of the gradient of the central field in the integrals makes it much more difficult to control the "strong sense" validity k of eqn.