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

Arrhenius parameters has been observed with several cationic cyanine dyes in low- polarity solvents, and has been attributed to the extensive formation of dye-counterion ion pairs on the basis of conductivity measurements [60]. Support for this interpretation comes from some calculations on cyanine model system which indicate a catalytic effect of ion-pairing on the ground state isomerization [67]. In the two most polar solvents, where ion pairs are not formed, a decrease of dielectric constant causes a significant, though not very large, increase of the activation energy. It is not clear whether chlorobenzene should be considered in the analysis of this trend or if the formation of some kind of ion pairs, looser than those formed in toluene, is responsible for the slight decrease of activation energy in this solvent relative to the more polar dichloromethane. However, apart from phenomena traceable to ion pair formation, both the value of the activation energy and its increase with a decrease of the solvent polarity (already observed with DOC and DTC [55]) are in good agreement with those theoretically

In summary, all the experiments expressly selected to check the theoretical description provided fairly clear evidence in favour of both the basic electronic model proposed for the BMPC photoisomerization (involving a TICT-like state) and the essential characteristics of the intramolecular and potential surfaces as derived from CS INDO CI calculations. Now, combining the results of the present investigation with those of previous studies [24,25] we are in a position to fix the following points

cis planar isomer, as well as recovery of the trans one, through a perpendicular CT-like minimum of intramolecular origin, 2) a small intramolecular barrier (1.-1.2 kcal

effects come into play primarily around the perp conformation, due to localization of the

our recent theoretical work and for inviting us to join in the study of cyanine photophysics and photochemistry. We wish also thank Prof. E.Castelluci for his generous help in the picosecond measurements carried out using the facilities provided by the LENS laboratory of Florence. The sample of BMPC perchlorate used in this work was donated by Prof. Sheves, Rehovot, to whom we are very grateful. This research was supported by the Ministero della Ricerca Scientifica e Tecnologia (Rome), the Consiglio Nazionale delle Ricerche (Rome) and the Centro Interdipartimentale di Calculo Automatico e Informatica

Applicata (University of Modena).

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and Defrees and McLean in 1986 [2], calculated the harmonic IR spectra of confirming Reisenauer et al. attributions; however, IR spectra for the corresponding deuterated molecules are not available to discuss Huang and Graham experimental measurements.

In the stellar environment where PAHs are supposed to be at the origin of the observed IR emission, satellite bands have been observed around the feature. In the PAHs model, one of the hypothesis for these bands is what is called the "hot band hypothesis", which states that some of these lines are transitions from upper vibrationally excited levels

existing in space; consequently, the calculation of its anharmonic IR spectra should be helpful for testing the hot band hypothesis.

Concerning the electronic spectra, very little has been done. No experimental work is

However, because the transitions towards these triplet states are not allowed, they are of no help for the astrophysical observations and a much more complete vertical spectrum is needed in order to assist in the search of from its electronic transitions. Till now, the few attempts to find signatures of the molecule in the Visible-UV region have been unsuccessful. But this search has still to be done systematically when data are available, based on the fact that a molecule seen widely in radio and possibly in IR, should necessarily absorb energy at shorter wave length, somewhere in the UV or visible. Considering the real lack of information about this spectrum, we might assume that the observational windows currently chosen for such a search could be erroneous.

From this brief review of the data available, it is obvious that more theoretical work is

spectrum is known with a good precision from experimental work, we found it useful to perform calculations of the rotational constants in order to compare with the observational or experimental values and illustrate the ab-initio approach. Then, we calculated the IR spectrum, vibrations and intensities, for the molecule and its deuterated isomers, allowing to answer the pending questions in the experimental spectra; taking anharmonicity into account showed interesting features for the interpretation of the satellite bands observed at

in space. Finally, in order to decide the window to be used for a search of the molecule in the Visible-UV area, we determined its electronic spectrum, i.e. transition energies and transitions moments at a highly sophisticated level of wave functions.

2. Radio signature

Directly linked to the geometry and dipole moment of a molecule, the rotational spectrum is an unambiguous fingerprint that has enabled the radioastronomers community to identify

of theory (from RHF to MP4 [12]) are presented in Table 1. The rotational constants

The molecule appears close to cyclopropene [4] with geometrical parameters (C=C = 1.296

aromatic values. We note the lengthening of the double bond opposite to the carbene center and the shortening of the other two bond lengths to a value close to that of aromatic compounds; at the same time, the angles relax to be closer to a regular triangle in order to accomodate the possible conjugation of the two electrons in the system over the threemembered ring.

These calculations also show a systematic behaviour of the MP3 calculations to provide bond lengths slightly shorter than MP2 due to the correction of an overestimated correlation by third-order terms.

Despite little differences between the geometries, especially those taking correlation effects into account, it can be seen that the rotational constants calculated from the frozen geometries are not accurate enough for a search of the molecule on a radiotelescope.

At that point, it should also be kept in mind that the values of bond lengths and angles are not directly accessible from experiments but are indirectly determined so as to reproduce the rotational constants which are themselves deduced from microwave experiments. Thus, comparison are always subject to some controversy since there is no biunivoque correspondence between the geometry and the rotational parameters.

At all events, the rotational constants have to be corrected for the electronic correlation still missing in the electronic wave function and for the contribution of the nuclear vibrations. These effects are to be taken into account with a precision depending on the error bar to be admitted. A now classic way to proceed is to perform calculations on model compounds to determine the error in theoretical bond lengths and angles as a function of the level of theory and to use it as a correcting factor for the corresponding parameters in the molecule under consideration [13-15]. It has to be noted that such a strategy is designed to account, not only for the errors inherent to the theoretical model but also for the zero-point

In this study where we are interested in isotope substituted systems, that is in systems with the same electronic wave function, a more global approach can be used. From Table 2 it is obvious that MP3 calculations give the best overall results. The compensation of errors that we find here is a general characteristic of this level of wave function, as illustrated by previous calculations on various series of molecules [16]. Thus, we will use the MP3 level of theory together with the formula

for the estimation of the rotational constants of the deuterated isomers from the experimental values of the hydrogenated species. The present values should be precise enough to help in the laboratory search of these deuterated isomers.

3. IR signature and interstellar UIR bands

3 . 1 . HARMONIC IR SPECTRUM

and MP4/6-31 l++G(d,p) levels are reported in Table 3. The results are nicely converging as electronic correlation is progressively included in the wave function. Excellent agreement between theory and experiment is thus obtained at the MP4 level, which allows for a correct treatment of simultaneous correlation effects in coupled vibrations. The only discrepancies which could show up, would proceed from anharmonicity, as illustrated by the CH stretching vibrations which are found shifted to higher frequencies than anticipated.

For larger systems, where MP4 calculations are no longer tractable, it is necessary to use scaling procedures. The present results make it possible to derive adapted scaling factors to be applied to the force constant matrix for each level of wave function. They can be determined by comparison of the raw calculated values with the few experimental data, each type of vibration considered as an independent vibrator after a normal mode analysis.

A least square fitting leads to the following values:

CH stretching : 0.80 (RHF); 0.87 (MP2) ; 0.89 (MP4)

CC stretching : 0.85 (RHF); 0.95 (MP2) ; 1.0 (MP4)

CH in-plane bending : 0.80 (RHF) ; 0.94 (MP2) ; 0.96 (MP4)

CH out-of-plane bending : 0.80 (RHF); 0.96 (MP2) ; 1.0 (MP4)

Corrected frequencies are then obtained following Pulay's procedure [17] and the intensities recalculated from the scaled force constants matrix. It can be seen on Table 3 that neither the basis set extension, nor the inclusion of part of the correlation change the results significantly if corrections are adapted to the method of calculation, which is particularly encouraging for an application to larger systems. Frequencies, once corrected by the above scaling procedure or by uniform scaling using an averaged value should then be accurate within a few percent for molecules of the same family, except for the presence of strong coupling between vibrations. An example of such situation can be found here for the asymmetric CH bending and CC stretching vibrations, which, from the composition of the

experimental value by 2% of its value.