Page 64 - Strategies and Applications in Quantum Chemistry From Molecular Astrophysics to Molecular Engineer

A COUPLED MCSCF-PERTURBATION TREATMENT OF ELECTRONIC SPECTRA 49

4.3. RESULTS AND DISCUSSION
The analysis of the variational wavefunctions clearly shows admixtures of valence and
Rydberg characters in many states, either at the orbital level or at the CI level. We will not
discuss this point here, but will focuse on transition energies.
The transition energies from the ground state to the lowest 60 vertical excited states
considered in this study are reported in Table 2 (30 singlets) and in Table 3 (30 triplets)
where they are compared to the avalaible experimental results and to some previous
theoretical calculations [45,60,65,68].
It is immediately seen that the agreement of our computed values with experimental
transitions is excellent for both valence and Rydberg states. The discrepancies vary from
0.00 eV to 0.40 eV for the largest of them. An exact value of the deviation is however
difficult to obtain due to both the experimental band widths and the fact that many observed
transitions are not necessary vertical so that structural effects and vibrational shifts are
involved. However, the calculated root-mean-square deviation of the computed values from
their experimental assignment is found to be, for the whole spectrum, about . To
our knowledge, there has been no report, whatever might have been the theoretical method
used, of such a small deviation between theory and experiment when dealing with so many
excited states together.

Within a few exceptions, all singlet states can be correlated to an observed experimental
feature. Especially, the high density of states around 11.8 and 12.7 eV is compatible with
the observation of unresolved broad peaks in the 11.6-11.9 eV and 12.5-12.8 eV spectral
intervals [60]. Unfortunately, the lack of spectroscopic resolution makes any unambiguous
one-to-one assignment impossible in these regions.
The situation is more favorable at lower energies: up to about 11 eV, each calculated singlet
state correlates unambiguously to a well-resolved experimental line, and the deviation from
the experiment does not exceed 0.35 eV which is the largest discrepancy observed.
Compared to the calculations by Harding and Goddard [60], the agreement between both
methods is excellent. Each state reported by these authors is found in our calculations. In
addition, we report some new singlet states of Rydberg character whose description has
been made possible essentially because of the larger flexibility of both our MCSCF
calculation and one-particle space (basis set including semi-diffuse orbitals that were not in
reference [60]). Our calculations provide a clear-cut assignment for the
states which were not reported previously. It is
important to notice that most of these new states correlate to the recent experimental results
obtained in the study by Brint and Sommer [62] which is devoted to the Rydberg series. It
is worth to emphasize that all their lower terms of the ns (3 states), np (6 states) and nd (4
terms) series can be related to a calculated state. Getting a correct description of the higher
terms of these series would however require the inclusion of a Rydberg orbital progression
in the basis set, so as the consideration of f functions as suggested in reference [62].
The same comments apply to the triplet states, although comparison to experiments is more
difficult due to the lack of experimental determinations, even in the low energy region.
However, as seen in Table 3, the agreement with avalaible data is excellent, and shows the
same quality as for singlet states. So is the correlation with the results by Harding and
Goddard [60]. In the triplet manifold, as in the singlet one, the largest flexibility of the
present method allows for more states to be found: as an example, we tentatively assign the
or the state, missing in reference [60], to a peak reported at 9.59 eV [69].