Re the recent query about the 3-21G(*) basis set:
This is discussed in the ab initio bible (Hehre, Radom, Schleyer, Pople)
pp 84-86; see also several of the Tables in this book. On p 86: "...the
3-21G(*) basis set should find considerable use as an alternative to
6-31G* as a means of providing structures and normal-mode frequencies that
closely approximate those of the larger basis representation." In Hehre's
*Practical Strategies for Electronic Structure Calculations*, on e.g.
pp 54-69, it is shown that the 3-21G(*) basis gives relative energies
extraordinarily close tho those of the 6-31G* basis (look at compounds
with the Na--Cl elements, for which the * is relevant).
maybe the point is not whether it's "unbalanced", but whether it
(as far as d-orbital participation goes, Nature is unbalanced).