Ellinger Y., Defranceschi M. (eds.) Strategies and applications in quantum chemistry (Kluwer, 200

As the main point is the relative positions of these bands with respect to the vibrational origin, the results of the first calculated frequency can be directly adjusted to the observed one(see below). Thus, we find rather regular progressions of about 50

Many celestial objects show a distinctive set of emission features in the infrared, known as the unidentified infrared emission bands (UIR bands) [21,22]. Since 1981 when Duley and

Williams [23] pointed out that a few of the bands fell at the frequencies characteristic of polycyclic aromatic hydrocarbon molecules (PAHs) and suggested that these bands were produced by aromatic units in thermally excited dust grains, a number of arguments coming from observations, experiments and calculations, converge towards the hypothesis that the features eventually arise from free molecular PAHs rather than dust grain [24-27]. Each

vibrational mode of this class of molecules, respectively the CH stretch, the C=C stretch, C=C deformation modes of the skeleton, the CH in-plane and finally the CH out-of-plane bending vibrations.

region as shown for example in Figure 2. The whole structure, including three newly discovered features at 3.46, 3.51, and (2890, 2850 and was first observed by DeMuizon et al. [28] in two IRAS sources who mentioned also the presence of possible satellites at shorter wavelengths. In the "hot band hypothesis", some of these

lines should originate from transitions between upper vibrational levels in PAH molecules[ll].

Since no experimental work is available to confront the theoretical model designed to describe excited states correctly, test calculations had to be done in a preliminary step. For that purpose, we have chosen ethylene, for which extensive calculations of the vertical spectrum as well as experimental measures are available. It is well known indeed that a correct quantitative and even qualitative description of small systems, is still a challenge for theoretical chemistry. The difficulties are found at each step of the computational approach:

-extended basis sets are needed in order to account for the diffuse character of the valence excited states and for the differential correlation effects;

-dynamic correlation effects, important for s orbitals in excited states, can only be

recovered by including high levels of excitations in the configuration interaction (CI), which rapidly leads to untractable expansions;

- strong interactions between excited valence and Rydberg states often result in orbitals which are much too diffuse to properly describe the former states; electronic densities are thus badly described and difficult to correct even with large CI calculations.

4.1. TEST CALCULATIONS ON

In terms of Lewis orbitals, the electronic configuration of ethylene can be written as

The extensive calculations of Serrano-Andres et al [31] have shown a spurious valenceRydberg mixing in the CASSCF wave functions when valence and Rydberg orbitals are optimized all together in a state average calculation; it was shown that these orbitals loose their diffuse character and instead tend to provide an extra correlation to valence orbitals. To avoid such interaction, the orbitals used for the CI treatment of the electronic spectrum were obtained by a two step procedure :

1 - We decided to first optimize C2H4 bonding and antibonding orbitals through an MCSCF procedure where all single and double excitations of the 12 valence electrons from the 6 occupied orbitals to the 6 antibonding orbitals were allowed. This procedure, hereafter referred to as MCSCF/SD, was applied using a triple zeta basis set augmented by polarisation functions (6-31+G*).

2- To account for Rydberg states, the MCSCF/SD set of orbitals was extended by atomic diffuse functions of s,p and d type (3s=0.023, 4s=0.015, 3p=0.021, 3d=0.015) which were Schmidt-orthogonalized.

Correlation effects were recovered in CI calculations in which the wavefunction was expanded in the N-particule space of Table 6. The internal space was partitioned in two subspaces, the first one containing all the valence occupied orbitals and the second one the corresponding correlating functions plus the Rydberg orbitals. Such a repartition was designed to give an even-handed treatment for both types of valence and Rydberg states.

The orthogonal complement composed the third set of MOs.

The CI space was gradually augmented, each level of calculation being referred to as according to the classes of configurations i and j incorporated in the CI expansion. The evolution of the vertical excitation energies with regard to this systematic building of the N- particle space has been investigated for the Ag symmetry which is well known to be

representative of the difficulties encountered in calculations of electronic spectra.

Table 7 shows the crucial importance of triple excitations. They have to be considered for a balanced and quantitative evaluation of the energies for both ground and excited states. The vertical excitation energy for the first excited state of Ag symmetry, which presents a strong

agreement with the recent two electron REMPI experimental value of 8.28 eV[32] and compares favorably to the 8.40 eV found in the CASPT2 approach [31] for the same

geometry and basis set.

The atomic basis consists in a double-zeta set expanded with polarization functions (DZP) and augmented by diffuse functions (DZPR). Exponents and contraction coefficient are from McLean and Chandler 1980 [18]; diffuse functions, centered on the heavy atoms with exponents of 0.023 for the s orbitals and 0.021 for the p orbitals are from Dunning and Hay 1977 [34]. Extension of the DZP basis set with two sets of diffuse s (0.0437, 0.0184) and p (0.0399, 0.0168) functions (DZPRR) has also been tested.

followed by Schmidt orthogonalization of Rydberg functions), a systematic search was conducted by progressively incorporating groups of orbitals in the active space. Two types of wave functions proved well adapted to the problem, one for in-plane excitations, the

serve as an illustration of the general approach done for all symmetries and wave functions.

4.2.1. In-plane excited states

one electron from the carbene lone pair orbital to 3s and 3p Rydberg orbitals, are better represented by orbitals generated by a MCSCF/SD treatment (Table 9).

The corresponding vertical excitation energies calculated with the DZPR basis set with 5 references are reported Table 10. The same type of energy convergence as observed for appears for when configuration classes, noted by indices, are added to the CI expansion. As energy calculations for excited states of electron systems are sensitive to the "diffusseness" of the basis set, we have tested the DZPRR basis at the level.

The results (in brackets in Table 10) closely resemble those obtained when only one series of diffuse functions (DZPR) is considered, justifying the use of the DZPR basis set for the rest of our calculations.

Because Rydberg states are peculiar states with a core resembling the positive ion and one electron in a diffuse orbital, the Rydberg states have been recalculated with orbitals optimized for the ion, with the same MCSCF/SD expansion. An improvement of 0.2 eV is