VUV Spectroscopy of Atoms, Molecules and Surfaces

32 Negative ions
feel the repulsion of each other [77]. In the CI approach both types of correlation
are accounted for, but in the MCHF and CC approaches only the static
and dynamic correlations, respectively, are included [83]. By the inclusion of
static correlation only, one is limited to qualitative predictions of the electronic
structure, while quantitative predictions to a ∼0.1 eV accuracy can
be obtained for small molecules when accounting for the dynamic correlation
[76, 83].
The accuracy that can be obtained is, though, not only limited by the
level of approximation applied in the expansion of the total many-electron
wavefunction. Also the molecular orbitals, replacing the atomic orbitals when
building the configurations, must be expanded in a basis set which must include
an infinite number of functions in order to form a complete set. The
path towards the exact solution of the Shrödinger equation is thus one of a
two-dimensional optimization of this one-electron basis set on the one hand
and the total wavefunction expressed in terms of Slater determinants on the
other. Just as there is a hierarchy of many-body models starting at the
Hartree-Fock level, there is a hierarcy of one-electron basis sets starting with
the atomic-like Slater-type orbitals (STO) and proceeding to Gaussian-type
orbitals (GTO) and the numerically more tractable contracted GTO’s representing
linear-combinations of such functions. Using the contracted GTO’s
one can proceed from a minimum basis set, in which the number of oneelectron
functions is chosen in accordance with the actual number of electrons,
to a double- or triple zeta (DZ or TZ) type basis including two- or
three times as many functions. Often, only the functions representing the
valence electrons are doubled or tripled, giving valence double- or triple zeta
basis sets (VDZ or VTZ), respectively. In calculations on highly correlated
systems the inclusion of polarization functions, i.e. functions representing
higher orbital angular momentum, is essential, as denoted by a ”p” (e.g.
pVTZ), and further correlation consistency, denoted by a cc (e.g. cc-pVTZ)
is obtained by including at the same stage of expansion functions that contribute
equal amounts of correlation energy. Finally, especially when dealing
with negative ions, additional diffuse functions may be of relevance, resulting
in an augmention of the basis set, denoted by AUG (e.g. AUG-cc-pTVZ) [76].
2.4.2 The hyperspherical-coordinate approach
The numerical methods discussed above are more or less reminiscent of the
independent-particle approximation and not tailored to deal with the electron
correlation. They are, in principle, capable of predicting a negative-ion
spectrum to an arbitrarily high accuracy, but they do not provide the link
to an understanding, or a visualization, of the underlying electronic struc-