ABSTRACT
Our qualitative understanding of molecular structure strongly relies on the
notion of the minimal basis set. We think in terms that the atoms enter the
molecules with their 1s, 2s, 2p, etc. orbitals (or their hybrids), while we do
our calculations by using larger and larger basis sets. To resolve this con-
tradiction, we should find proper connections between the simple qualitative
picture and the results obtained in the large-scale ab initio calculations using
extended basis sets. There are some very simple cases in which the Hartree-
Fock (or DFT) wave function of a molecule can trivially be described in terms
of some distorted atomic minimal basis, provided that atom-centered basis
sets were used in the calculations. (The term “distorted” is understood with
respect to the free atoms’ orbitals.) Thus, in the H2 molecule there is only a
single MO and it consists of basis functions belonging to either of the atoms.
Therefore, one half of that MO is in the subspace defined by the basis set of
one hydrogen atom, and another half is in that of the other hydrogen. That
means that there is only a single effective AO on each atom, irrespective of
how many basis functions were used-the structure of the basis influences
only the detailed form of that effective AO. Similarly, one has only five MOs
in the 10-electron water or methane molecules, so their “truncations” on the
oxygen and carbon atom, respectively, define five effective atomic orbitals,
i.e., as many as the number of functions in a classical minimal basis. This
property ceases to exist in a strict sense when one turns to larger systems (al-
ready in the water or methane molecules one gets up to five effective AOs
also on the hydrogens) but one can find a good connection with the concept
of the minimal basis also in a general case. As will be shown below, one
can recognize as many significantly populated effective AOs on each atom of
ordinary compounds, as many orbitals are in the respective minimal basis set,
even if large basis sets are used in the calculations [40-42].
