Recently, I found the Clementi & Raimondi table of effective nuclear charges for different orbitals and atoms: http://dx.doi.org/10.1063/1.1712084
To my understanding, the effective nuclear charge Z_eff tells us the strength of the atomic potential that is "felt" by a given electron. And I would assume that one puts the Z_eff into the well-known equation for hydrogen-like systems in order to reproduce the binding energy of the electron/orbital under investigation.
However, looking at the Clementi & Raimondi values I find that the Z_eff value for 2s orbitals is significantly smaller than the one for 2p orbitals. This is in contrast to my intuitive understanding of Z_eff, but also with all the approximate rules for estimating Z_eff that one is taught at university.
Obviously, I am missing an important point of the Clementi & Raimondi table. I would be really grateful for any explanation on that topic. Thank you very much.
Actually, in some cases the 2p electrons are closer to the nucleus than the 2s ones. For example, look at the ionization energies of these electrons in highly charged atomic cations (NIST's web).
In the tables published by Clementi (400+ citations) nearly all the (neutral) atoms show a similar behavior: Much larger Z_eff for the 2p orbital than for the 2s orbital. So, it is not just a pathologic case.
You must start with the Slater's idea on how to use exponential basis functions for atomic and molecular calculations. Then the paper you quote makes sense and the parameters used too.
In the paper they explain that their approach is very similar to the one used by Slater.
They first obtain the Slater exponent (zeta) by using slater type radial orbitals (R(r)=N r^{n-1} e^{\zeta}) with n the first quantum number, and solve the Roothan self-consistent field equations to obtain the "correct" energies.
Then they find the screening constant (sigma) by solving \zeta=(Z-\sigma)/n.
At first sight I would say that because they are just using radial functions, the orbitals other than s ones would have completely wrong exponents, and the value of such orbitals would also be very wrong. This however does not explain why the 2s values are SO MUCH different from the ones I calculate with Multi Configuration Dirac Fock.
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