A computer-algebraic approach to the study of the symmetry properties of molecules and clusters

This thesis work is dedicated to use the computer-algebraic approach for dealing with the group symmetries and studying the symmetry properties of molecules and clusters. The Maple package Bethe, created to extract and manipulate the group-theoretical data and to simplify some of the symmetry applications, is introduced. First of all the advantages of using Bethe to generate the group theoretical data are demonstrated. In the current version, the data of 72 frequently applied point groups can be used, together with the data for all of the corresponding double groups. The emphasize of this work is placed to the applications of this package in physics of molecules and clusters. Apart from the analysis of the spectral activity of molecules with point-group symmetry, it is demonstrated how Bethe can be used to understand the field splitting in crystals or to construct the corresponding wave functions. Several examples are worked out to display (some of) the present features of the Bethe program. While we cannot show all the details explicitly, these examples certainly demonstrate the great potential in applying computer algebraic techniques to study the symmetry properties of molecules and clusters. A special attention is placed in this thesis work on the flexibility of the Bethe package, which makes it possible to implement another applications of symmetry. This implementation is very reasonable, because some of the most complicated steps of the possible future applications are already realized within the Bethe. For instance, the vibrational coordinates in terms of the internal displacement vectors for the Wilson's method and the same coordinates in terms of cartesian displacement vectors as well as the Clebsch-Gordan coefficients for the Jahn-Teller problem are generated in the present version of the program. For the Jahn-Teller problem, moreover, use of the computer-algebraic tool seems to be even inevitable, because this problem demands an analytical access to the adiabatic potential and, therefore, can not be realized by the numerical algorithm. However, the ability of the Bethe package is not exhausted by applications, mentioned in this thesis work. There are various directions in which the Bethe program could be developed in the future. Apart from (i) studying of the magnetic properties of materials and (ii) optical transitions, interest can be pointed out for (iii) the vibronic spectroscopy, and many others. Implementation of these applications into the package can make Bethe a much more powerful tool.

Femtosecond real-time probing of reactions. 12. Vectorial dynamics of transition states

Femtosecond time-resolved techniques with KETOF (kinetic energy time-of-flight) detection in a molecular beam are developed for studies of the vectorial dynamics of transition states. Application to the dissociation reaction of IHgI is presented. For this system, the complex [I---Hg---I](++)* is unstable and, through the symmetric and asymmetric stretch motions, yields different product fragments: [I---Hg---I](++)* -> HgI(X^2/sigma^+) + I(^2P_3/2) [or I*(^2P_l/2)] (1a); [I---Hg---I](++)* -> Hg(^1S_0) + I(^2P_3/2) + I(^2P_3/2) [or I* (^2P_1/2)] (1 b). These two channels, (1a) and (1b), lead to different kinetic energy distributions in the products. It is shown that the motion of the wave packet in the transition-state region can be observed by MPI mass detection; the transient time ranges from 120 to 300 fs depending on the available energy. With polarized pulses, the vectorial properties (transition moments alignment relative to recoil direction) are studied for fragment separations on the femtosecond time scale. The results indicate the nature of the structure (symmetry properties) and the correlation to final products. For 311-nm excitation, no evidence of crossing between the I and I* potentials is found at the internuclear separations studied. (Results for 287-nm excitation are also presented.) Molecular dynamics simulations and studies by laser-induced fluorescence support these findings.