|MadSci Network: Chemistry|
What a good question! I will try to answer it, although a lot of what I am going to say could be found in text books (ie. Huheey, Inorganic Chemistry, 4 Ed.) and it may be easier to read it there or, hopefully, integrate my comments with the text to better explain it. Do the Slater's Rules for screening constants take into account the stability of filled and half-filled orbitals? Simple answer, no. Slater was working on development of his rules in the 1920's and 30's, when there were no computers and quantum mechanics was just beginning. The ideas about orbitals and such were just being formulated. Slater's Rules were developed to explain the concept and, to a first approximation, allow for some rationalization of the observable trends in the periodic table. They work and they don't. They work in that they can help to explain such broadly observed phenomenon as the periodicity of ionization energy (which is, from Bohr, a function of nuclear charge squared and should increase exponentially) and ionic radii. They don't work in that Slater's Rules don't take into account some of the subtleties of the table, like half-filled and filled orbitals. What other things did Clementi and Raimondi take into account when the calculated their values for effective nuclear charge? Clementi and Raimondi did their work on effective nuclear charges in the early 1960s. By this time, there was a great deal of background work that had been done on orbitals and molecules. And the computer had been invented! This gave them the ability to incorporate self-consistent field (SCF) wave functions for the hydrogen to krypton atoms into their calculations. They didn't have to rely on Slater-type orbitals which, for simplicity of calculation, didn't contain nodes. They were thus able to go to a greater depth with a refined mathematical model, and this allowed them to clearly distinguish the s-orbitals from the p-orbitals in determining their set of rules. Specifically, they had a better model for dealing with electron penetration of the inner core. How does the special stability of half-filled orbitals relate to the effective nuclear charge, and is it ever considered when calculating Zeffective? Again, the simple answer would be: it doesn't and no, it is not considered. But that doesn't help us much. As you have pointed out, the unexpected electronic configuration is a consequence of exchange energy and the calculation of the effective nuclear charge by SCF doesn't include that in considering the atom. The result is that Zeff is a linear progression across "Cr". But Clementi and Raimondi's model does take into account the filled orbitals. That is, their rules are able to distinguish the s-orbitals and p-orbitals, and appear to have steps that would accomodate the filling of all orbitals. In other words, they include some of the effects but not all. One article I found on SCF points out that Clementi and Raimondi's results were still not great because it is difficult to "estimate repulsion from a wide-ranging electron by treating it as a fractional static electron at the nucleus, but it's better than nothing." They go on to point out that in more sophisticated SCF approaches, that each electron is treated as existing in a static electric field - due to the fixed nucleus and a static cloud of electron density given by the superposition of their assumed densities. This potential allows you to calculate a new set of densities, which are used as input to improve the orbitals, again and again until a self-consistency is reached. If the exchange integral is not included in the calculation, then all of the measurements will be missing this effect and it would appear that that is the case. I am not an expert on the latest measurements and calculations around effective nuclear charge, but I suspect that there has been little improvement on the SCF results and hence, the answer to the second part is "no". I hope this helps! Good question and there is a fair amount of information out there. It is likely that your University has access to the original articles by Clementi and Raimondi (J. Chem. Phys. 1963, 38, 2686; J. Chem. Phys. 1967, 47, 1300) and might have some of the more "recent" work by Froese-Fischer (Atomic Data 1972). And, of course, there is always the classic paper by Slater (Physical Rev. 1930).
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