Estructura electrónica y vibracional de moléculas con interés astrofísico.

Abstract

In this work we study the properties of certain molecules related to astrophysics. Since the first diatomic molecules were discovered, a lot of molecules have been discovered throughout the space by using infrared wavelength observations. These observations showed the great variety of complex molecules in the universe besides the little diatomic molecules. The complex molecules are important components inside the galaxy interstellar medium. One example of these complex molecules are the PAHs (Polycyclic Aromatic Hydrocarbons), such as naphthalene, anthracene or pirene, which are organic compounds containing only hydrogen and carbon. These molecules are composed of multiple aromatic rings. Signatures of these PAHs are found in the spectral bands of the cosmic infrared emission. A variation in the central wavelength of these bands in different space regions have been related with diverse components of the carriers. For instance, if we are considering a HII region, the central wavelength drops to a lower wavelength; and if we consider a planetary nebula, the central wavelength rises to a higher value. Then, the observations of such differences allow us to know the components of the spectral regions. This work studies the electronic structure of three different polycyclic aromatic hydrocarbons: the coronene (C24H12), the corannulene (C20H10) and the C20. The latter has not been found yet in the space but we include it because we also want to study how the curvature influence in the molecular properties of the polycyclic aromatic hydrocarbons. The three molecules have different geometric structures: the coronene is a planar molecule with six rings of benzene, the corannulene has a slight curvature with a central cyclopentane surrounded by five rings of benzene. Each molecule has its own particular symmetry, so the simmetry groups of these three molecules are not the same. The symmetry group of the coronene is the symmetry group D6h, the simmetry group C5v is the one corresponding to the corannulene, and finally, the C20 has a simmetry group Ih. In order to calculate some electronic and vibrational properties of these molecules, we use a package of programs called MOLPRO, which allows us to know the total electronic energy of the molecules, as well as the energy of a lot of monoelectronic levels (occupied or unoccupied). MOLPRO is a set of ab initio program for standard computational chemistry applications. We have used it using different methods, like Hartree-Fock (HF), Møller-Plesset methods (MP2) or coupled cluster theory (CCS) and density functional theory programs (DFT). We have started with the coronene, and we have used these methods to get the energy and comparing the energies calculated between them and with some papers we have read. The energies of the corannulene and of the C20 have been calculated in the same way. After that, we have assigned a symmetry element to several energy levels of the three molecules according to the simmetry near the gap dividing the occupied (HOMO) and the unoccupied (LUMO) levels. Nevertheless, the MOLPRO program is not able to identify properly the simmetry groups of the three molecules because it is only able to work with abelian point groups, so we had to assign the energy levels by using some equivalence tables. This assignment has been partially confirmed in the bibliography, including the degeneration of the energy levels. However, the C20 levels have been more difficult to assign due to the differences of energy, which were higher than the differences we saw in the coronene and the corannulene. That is why the assignment has not been made. Afterwards, we have paid special attention to the highest ocuppied molecular orbital (HOMO) and to the lowest unocuppied molecular orbital (LUMO). That is because, as we have stated before, we want to know how the curvature influence in the energy levels and the gap between ocuppied and unocuppied levels in these three molecules. Again, we can compare the calculations made with the MOLPRO program with others made before in order to know if our calculations were right. In addition, the normal modes of vibration of the molecules in the ground electronic state have been calculated. The goal of these calculations is, using the harmonic approximation, to know how the atoms in the molecule are moving. We have assigned these normal modes with the aid of the group theory in order to discover what normal modes are active to infrared (IR) or Raman. The frequencies of these IR active modes are closely related with the peaks of the infrared interstellar bands. Our results show that the HOMO – LUMO gap seems to increase as the curvature increases. It is remarkable in the case of C20, whose curvature is bigger because it is a spheroidal-like molecule, and the gap is quite greater. In fact, we wanted to study the C60, which has been found in the space and therefore their characteristics and properties may be more interesting, but the memory of the computer we have used was not big enough in order to get these calculations.