Atomic energy levels isoelectronic sequence

[Lorenzo Lodi]

I am trying to rationalise the behaviour of experimental atomic energy
levels of the potassium atom (Z=19) isoelectronic sequence. Ground-state
potassium has the expected [Ar] 4s^1 configuration (2S term symbol),
while the 4p and 3d configurations (2Po and 2D terms) have relative
energies approximately of 13000 and 21500 cm-1. (Atomic energy levels
for atoms and ions can be obtained from the NIST Atomic Spectra
Database.)

Given that there is only one valence electron, I would naively expect
that the low-energy spectrum of cations isoelectronic to K (ie, Ca+,
Sc++, Ti+++ etc) be somewhat similar, i.e.:
1) Ordering of configurations same as K: 4s < 4p < 3d
2) Increasing Z energy separations increase as Z^2, as this is the
behaviour of hydrogen-like atoms.

Both my suppositions are wrong:
1) The energy ordering of Sc++ are: 3d < 4s < 4p (ions more highly
ionized than Sc++ also show this ordering).
2) The energy separations between energy levels increase much faster
than Z^2, more like Z^8 (I've checked up to Mn^6+). For example, the
energy spacing E(4p)-E(3d) is ~128300cm-1 for Ti^3+ (Z=22) and
~395700cm-1 for Mn^6 (Z=25), implying a scaling Z^8.81.

I would be very grateful if anyone could rationalize these observations.
Fell free to point out any reference from the scientific literature.

L.