  We present an exhaustive study of more than 250 ab initio potential energy
surfaces (PESs) of the model dipeptide HCO-L-Ala-NH2. The model chemistries
(MCs) used are constructed as homo- and heterolevels involving possibly
different RHF and MP2 calculations for the geometry and the energy. The basis
sets used belong to a sample of 39 selected representants from Pople's
split-valence families, ranging from the small 3-21G to the large
6-311++G(2df,2pd). The reference PES to which the rest are compared is the
MP2/6-311++G(2df,2pd) homolevel, which, as far as we are aware, is the more
accurate PES of a dipeptide in the literature. The aim of the study presented
is twofold: On the one hand, the evaluation of the influence of polarization
and diffuse functions in the basis set, distinguishing between those placed at
1st-row atoms and those placed at hydrogens, as well as the effect of different
contraction and valence splitting schemes. On the other hand, the investigation
of the heterolevel assumption, which is defined here to be that which states
that heterolevel MCs are more efficient than homolevel MCs. The heterolevel
approximation is very commonly used in the literature, but it is seldom
checked. As far as we know, the only tests for peptides or related systems,
have been performed using a small number of conformers, and this is the first
time that this potentially very economical approximation is tested in full
PESs. In order to achieve these goals, all data sets have been compared and
analyzed in a way which captures the nearness concept in the space of MCs.
