VUV Spectroscopy of Atoms, Molecules and Surfaces

30 Negative ions
assignment will then still make sence, but the energy level associated with a
given configuration will split into a multiplet of fine-structure components.
For negative ions in the ground- or doubly-excited states and for neutral
atoms and molecules in highly excited states, the electron correlation is so
large that the above perturbative approach no longer applies. The energy
levels can, however, always be associated with a mixture of different configurations
and the wavefunction written as a linear combination of Slater
determinants. This is the idea behind the configuration interaction (CI) and
multi-configurational Hartree-Fock (MCHF) approaches which can be considered
natural extensions of the Hartree-Fock method. The additional configurations
are often chosen to represent singly-, doubly-, triply- or higher excited
states of the dominant configuration applied in the Hartree-Fock procedure,
as indicated by an additional labelling S, SD, SDT etc. [76, 77]. Since the
singly-excited states do not add to the correlation energy, one has to start out
from at least the SD level. In the MCHF approach the radial wavefunctions
of the single-electron orbitals are optimized variationally in addition to the
coefficients entering the configuration expansion of the total wavefunction.
In the CI approach the radial functions are kept fixed [78].
At a higher level of calculation the configurations (or Slater determiants)
may be chosen independently, i.e. without representing excitations of the
same basic configuration, and the method is then called a multi-reference
(MR) MCHF or -CI (e.g. MRCI). In the frozen-core approximation the excitations
are limited to the outermost bound valence electrons which are then
said to belong to a Complete Active Space (CAS). The method is then called
CASSCF, the MC character being implicitly implied by the presence of the
CAS. In some situations the interactions between the core electrons or between
the valence- and core electrons cannot be ignored, as illustrated by
the importance of these contributions for an accurate (to within a few meV)
prediction of the Ca− binding energy [35, 78]. In principle, energy levels
can be calculated numerically to arbitrarily high accuracy by inclusion of
an arbitrary number of configurations but the calculations quickly become
cumbersome and a large number of configurations is required for reasonable
convergence. The computational efforts may be minimized by including in
the expansion of the total wavefunction terms which depend on the interelectronic
distances, thus from the outset accounting for a larger part of
the electron correlation. This is the idea behind the two-electron Hylleraas
wave-functions and the elaborations towards the development of possible
candidates of correlated wavefunctions applicable to larger systems [79].
The MCHF and MRCI approaches can be applied for calculations of resonance
parameters, in addition to bound state properties, by the inclusion
of continuum states in the configuration expansion [80]. Of widely use, espe-