?Algebraic Chemistry? Based on a ?PIRT?
|Title||?Algebraic Chemistry? Based on a ?PIRT?|
|Author(s)||Cynthia Kolb Whitney|
The present paper continues on from my 2004 PIRT paper entitled ?Can Chemical Data Support a ?PIRT???. The present paper first provides more detail on the variation of ionization potentials within the periods of the Period-ic Table. The description developed refers to the standard quantum numbers n,l,s ( n=1 to infinity, l=0 to n−1, s=−1/2,+1/2) for single-electron states that are incorporated into successively larger atoms. The empiri-cal Madelung and Hund rules that are found in today?s chemistry textbooks provide the nominal filling order for sin-gle-electron states. Using this filling order, a simple empirical formula is developed for the local slopes on a log plot of the ionization potentials. The formula is quite accurate for first ionization potentials, but becomes less accurate for higher-order ionization potentials. This fact could well be related to the fact that the filling order that actually occurs in Nature departs from the standard one for about 20% of the known elements. Accordingly, the filling order for single-electron states is itself investigated next. A more efficacious empirical rule is developed. Like the stan-dard one, it involves sums of traditional quantum numbers, but unlike the standard one, judiciously chosen coeffi-cients that are powers of 2 provide the needed improvements. The resulting formulation automatically directs atten-tion to the elements for which the departures from the textbook rules actually do occur. The paper concludes with an indication of future work.