Thursday, July 19, 2012

more on the 'sloppy aufbau principle'

Eric Scerri,
UCLA, Department of Chemistry & Biochemistry,
Los Angeles.


In a recent posting I mentioned what I called the 'sloppy aufbau', that seems to have taken root in almost all chemistry and physics textbooks which claim to explain how the electronic configurations of atoms develop as one moves through the periodic table.

Although the reception has been encouragingly favorable, a few textbook writers have written to me to say that their book covers the topic adequately and does not fall into the trap that I am trying to highlight.  On checking each of these books I find that although a number of them issue cautions when using the n + l rule or the aufbau principle, none of them actually state explicitly that for scandium, and the following atoms in the first transition, the 3d orbitals are occupied before the 4s.

What I want to do here is to emphasize that what I am urging and what has been discussed in recent articles by Schwarz is nothing new.  It seems to be a matter of 'having to rediscover the wheel'.  In addition to a few old textbooks from the 1940s and 50s that give a full and accurate account, I have found two articles in the Journal of Chemical Education that warn explicitly against the use of the sloppy aufbau even though they don't call it so. 

For example, exactly 50 years ago, R.N. Keller wrote,

In the case of scandium, cited above, the 19th electron assumes a 3d state rather than a 4s state because the Sc+1 ion has lower total energy with  a 3d1 than with a 4s1 configuration.

However, the Sc+ ion is more stable if the 20th electron occupies a 4s orbital rather than a 3d, or,  a 3d14s1 state is more stable for this ion than a 3d2 or a 4s2 state. Similarly the lowest lying state for neutral scandium, 3d14s2, is a more favorable state energetically than any other state such as 3d3, 4s24p1, etc.

Or saying this in a slightly different way, the effective nuclear charge in tri-positive scandium is such as to cause the 19th electron added (i.e., Sc+3 +  e- ---> Sc2+) to occupy the 3d level because this level lies lower energetically than the 4s.

However, once the 19th electron has been added, the whole electronic energy level system for Sc+2 is now slightly different from that for Sc+3.  The interaction of the nucleus of scandium with the 19 electrons in Sc+2 produces a field which favors a 4s state for the 20th electron added (i.e., Sc2+ + e- ---> Sc1+). The resulting field in turn favors a 4s state for the 21st electron added. 

     R.N. Keller, Journal of Chemical Education, 39, 289-293, 1962.

Even earlier, in an article published in 1950 (62 years ago), also in J Chem. Ed., the author D.F. Swinehart also complains of the careless use of the aufbau and among other things says,

It is rather odd to see this clear-cut case of a regression in the teaching of chemistry and physics.  This is not supposed to happen.  So why does it happen?  Or is it just part of the overall downgrading in science education, especially in the US, as described in the latest issue of Scientific American?