By C. K. Jorgensen
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Extra info for Absorption Spectra and Chemical Bonding in Complexes
3 3 2 8 4 4 3 \5B between F and P of d and d and between F and P of d 7 n and d . g. the parameter E analogous to Β is defined =^ Ε3 Μ9 -^ + <> ρί 36 Table 2 gives some of the term distances, relative to the lowest n term, of the d -systems. We may use this theory in two senses, a k strong sense, where F is calculated according to eqn. (32) from the TABLE 2. EXCITATION ENERGIES OF SOME MULTIPLET TERMS IN SPHERICAL SYMMETRY, EXPRESSED IN RACAH'S PARAMETERS OF INTERELECTRONIC REPULSION. ). 2 d and d *D 3p *G 0 5B + 2C 15 Β 12B + 2C 22B + 7C 3 8 d and d 2 G 4p 2p 2 H 7 0 4B + 3C 15B 9B + 3C 9B + 3C d 5 e 4S G 4p 4 D 4 F 105 IB 175 225 0 + + + + 5C 7C 5C 7C THE ENERGY LEVELS OF A C O N F I G U R A T I O N 41 Hartree-Fock self-consistent (HFSC) radial functions R and compared with the experimental values (as calculated for the levels compiled in Charlotte Moore's tables of atomic energy levels), and a weak sense, where agreement with experiment is obtained by a k reasonable choice of F as numerical parameters without any reference to the wave function.
Not only for a hydrogen atom, but for any of the central fields v 28 ORBITALS IN ATOMIC S P E C T R O S C O P Y found in atoms, the number of zero points of R (excluding those at r = 0 and r -> oo) is « — / — 1. Thus, the lowest value of η for a given /(Is, 2p, 3d, 4f, . ) has only one maximum, and the orthogonality with the other orbitals is secured from the angular dependence alone. The following values of η produce their orthogonality with the first orbital by having different domains with alternating positive and negative values of R.
Actually, they are mixed in such a way that a triplet and a singlet state results. Most text-books describe perturbation theory in a number of steps which leads to some confusion in terminology. These steps are: (1) "Zero-order" perturbation, where a set of "degenerate" wave functions ΨΆ, Ψκ, . . ¥ n having the same energy before the perturbation are used for forming linear combinations Ψ1 = k a ^ a + . . + k n ^ n appropriate for step (2) (securing vanishing nondiagonal elements between two such different linear combinations under the perturbation).
Absorption Spectra and Chemical Bonding in Complexes by C. K. Jorgensen