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In their article on 4s/3d occupation (J. Chem. Educ.
1996, 73, 498-503), Melrose and Scerri (MS) had on
hand orbital energies e and Coulomb/exchange integrals J/K
for most of the 3d atoms in the 4s23dn
average-of-configuration (AoC). In an AoC, the lowest state in the
configuration, given by Hund's rules, has its energy averaged with all
the higher energies in the configuration. The data on hand
for Cr and Cu were in the 4s13dn+1
AoC, so they devised their eq 21 solely for Cr and Cu.
Numerical values of the Cr and Cu
4s23dn AoC AO
are available (Fischer, C. F. Atomic Data
1972, 4, 301), as are the e and
Fn for d-d J/K (Fischer, C. F.
Atom. Data Nuc. Tables 1973,
12, 87). The s-d J/K can be found by
numerical integration. The Cu
4s23d9 AoC has only the
2D term, for which analytic orbitals are available (Tatewaki,
H.; Sekiya, M. J. Chem. Phys. 1986, 85, 5895).
These sources were used to obtain the following e for the MS table.
|
es |
ed |
ed' |
(ed' - es) |
| Cr |
-0.242 |
-0.513 |
-0.112 |
0.130 |
| Cu |
-0.285 |
-0.740 |
-0.140 |
0.145 |
Here (ed' - es) is the
4s23dn frozen-orbital
approximation to DeltaEAoC for
4s23dn -->
4s13dn+1. MS hoped that (ed' -
es) would be negative, as it is from their eq 21. For every
atom, frozen 4s23dn AO give a value of
(ed' - es) that is too high, and frozen
4s13dn+1
AO give a value that is too low. The average of the two values is close to the Hartree-Fock
DeltaEAoC plotted by Vanquickenborne, Pierloot, and Devoghel,
Inorg. Chem. 1989, 28, 1805.
For Cr, DeltaEAoC is approx. 0.035. This positive
DeltaE between the two AoC gives no indication that between the
lowest states in Cr
4s23d4 --> 4s13d5,
DeltaE = -0.035. That information comes only from a study of the lowest states.
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