Page 62 - Strategies and Applications in Quantum Chemistry From Molecular Astrophysics to Molecular Engineer

A COUPLED MCSCF-PERTURBATION TREATMENT OF ELECTRONIC SPECTRA 47

4. The vertical electronic spectrum of formaldehyde
4.1. SOME HISTORY ON FORMALDEHYDE STUDIES

Initiated by the pioneering work of Burawoy [51 ], a number of experimental and theoretical
studies were performed on the carbonyl group [52-55]. A complete review is beyond the
scope of this paper. We will mention only some of them that we consider of particular
importance for a comprehensive coverage of the electronic spectrum of formaldehyde for
both the theoretical and experimental points of view.

A review of the early experimental works can be found in references [56-58]. More
recently, Chutjian recorded the electron-impact excitation spectrum of formaldehyde
[59,60] and reported transition energies that are taken as reference values in many other
works. So are the experimental values compiled by Robin [61].
A few years ago, Brint et al. [62] focused on the vacuum high-resolution spectrum,
pointing out a number of well-defined Rydberg series, of special importance for theoretical
benchmarks.

On the theoretical hand, calculations have been performed as soon as in the 50ies [56,63]
since formaldehyde represents the smallest member of the carbonyl series. References to
early works are avalaible in the compilation by Davidson and McMurchie [64] and in
references [56-58,63]. Of particular interest for a comprehensive assignment of the
experimental transitions are the very fine and accurate calculations by Harding and Goddard
using their GVB-CI method [60,65].

4.2. COMPUTATIONAL DETAILS

The MP2/6-311++G** geometry [45] was used for in the present report
(CO=1.2122 Å, CH=1.1044 Å, HCO=121.94°). It is very close to the experimental
geometry [66]. The molecule is supposed to lie in the yz plane; the z axis corresponds to
the axis, as in Figure 1.

The MCSCF and the subsequent perturbation calculations were done using a 6-31+G*
basis set expanded by a set of spd Rydberg functions. Exponents of this additional
gaussians were : 0.032 and 0.028 for the s and p shells for the oxygen atom, and 0.023
and 0.021 for the carbon atom. For the d functions, a common value of 0.015 was chosen
for both heavy atoms.
The MCSCF calculation was performed using the configuration space described in section
3.2. The state-averaging was done for seven and seven states for
both singlet and triplet multiplicities.
The variational calculations were performed using the Alchemy II package [67] while the
further perturbation calculations used a code derived from the original CIPSI module.
Proper interfaces between the two programs were developed.