Subshell configuration

The zeroth-order antisymmetric wave functions of closed-subshell states, states that have only one electron outside a closed-subshell configuration, and states that are one electron short of having a closed-subshell configuration can be expressed as a single Slater determinant [e.g. (1.259)]. However, for open-subshell states in general, one has to take an appropriate linear combination of a few Slater determinants to get a state that is an eigenfunction of L2 and S2. 

Because of the contraction and stabilization of the 6s orbital, the outermost, or valence, shell of Au is formed by both the 5d and 6s orbitals. Indeed, electronically, Au is halogen-like, with one electron missing from the pseudo noble gas (closed subshell) configuration. Hence, similar to the existence of halogen X2 molecule, gold also forms the covalent Au2 molecule. In addition, gold also forms ionic compounds such as RbAu and CsAu, in which the Au- anion has the pseudo noble gas electronic configuration. 

Both the first and the second ionization processes remove electrons from the 4s orbital of these atoms, with the exception of Cr. In general, the 4s electrons are poorly shielded by the 3d electrons, so Zen(4s) increases from left to right and 4 also increases from left to right. While the 7) process removes the sole 4s electron for Cr, the 72 process must remove a 3d electron. The higher value of h for Cr relative to Mn is a consequence of the special stability of half-filled subshell configurations and the higher Zeff of a 3d electron vs. a 4s electron. 

It is not necessary to consult Table 11.2a to find the lowest terra of a partly filled subshell configuration. We simply put the electrons in the orbitals so as to give the greatest number of parallel spins. Thus, for a dF configuration, we have... 

For a closed-subshell configuration, (a) show that the double sum in (11.80) equals... 

We begin with the ground state of He2. The separated helium atoms each have the ground-state configuration Is. This closed-subshell configuration does not have any unpaired electrons to form valence bonds, and the VB wave function is simply the antisymmetrized product of the atomic-orbital functions ... 

Mulliken atom populations in Table 5 reveal that the platinum in PtM" (M = Cu, Ag, Au) has an approximate 5d configuration similar to PC, and Cu, Ag, and Au have an approximate (n — l)d ° structure and partial ns populations. Such almost closed d subshell configurations suggest that the Cu, Ag, and Au terminals are inert toward methane in their ground states. Thus, the terminal platinum with the open d subshell in PtM" is still the active site for the C-H bond activation. 

If we want to predict all the terms (5,F ) from a given number q of electrons in a partly filled d shell, we may either consider all the possible L,S terms in spherical symmetry and enumerate their octahedral levels according to Eq. (10), or we may consider the subshell configurations yfy with an integral number 0 a 6 and 0 6 4 of electrons in each of the two subshells. The latter process is a little complicated in the case of a partly filled subshell, in close analogy with the formation of L,S terms in spherical symmetry [cf. Eq. (5)]. However, it can be proved that it is only necessary to know the following results... 

They were disappointed that broad absorption bands of the ruby at 18.000 and 24.500 cm masked the predicted position of the spin-allowed transitions to Fg and F4 (of the subshell configuration yiyg). 

Many years later it was realized that the broad absorption bands are simply caused by the spin-allowed transitions. OrgeF explained the great difference in band-width expected from the Franck-Condon principle when the excited level belongs to another subshell configuration with changed intemuclear distances for the minimum of the potential curve, compared to the single lines produced by internal transitions in a subshell configuration. 

Determine the expected ground state of an atom of Ni, which has a d valence subshell configuration. 

Assuming that the Russell-Saunders system applies, determine the term symbols and which is the ground-state term symbol for a hypothetical element having an electron subshell configuration for its ground state. 

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