The author replies to Bills.
We are glad that Bills has calculated (ed' - es) for the two cases, Cr and Cu, for which we did not have the optimized orbitals of the
4s23dn configuration. It now seems
that the (ed' - es) is positive throughout the series when determined from 4s23dn wavefunctions. In one respect the new results make our conclusion wider. Since (ed" -
es') is also positive for the
4s13dn+1
configurations, it can now be said that the substitution 4s --> 3d gives a less stable
configuration in every case, and not just when the original configuration was the one suggested by the spectroscopic ground state.
On the other hand, the new results, combined with the fact that (ed' -
es) can be negative when determined from the orbitals of the
4s13dn+1
configuration, show that the subtle question as to when the
4s13dn+1
configuration has lower average energy is beyond the frozen-orbital approximation. Bills is also correct in pointing out that the configuration with lowest average energy is not necessarily
the one that contains the lowest state of all.
The value of the frozen orbital approximation lies in revealing the factors that affect the stability of a configuration in the absence of orbital relaxation. Thus the substitution 4s --> 3d in both 4s23dn and
4s13dn+1
configurations is opposed by a large increase in 3d orbital energy and favored by the
3d - 4s orbital energy difference in the original configuration. The reverse substitution 3d --> 4s in the 4s13dn+1
configuration is favored by the decrease in the 4s orbital energy and opposed by the orbital energy difference in the original configuration. It seems less surprising when the latter factor prevails.
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