Vibronic coupling in icosahedral systems

Due to the high symmetry of the icosahedron, many of the electronic and vibrational levels of the C_6_0 molecule and its rela.ted compounds are highly degenerate. Therefore in dealing with properties of the C_6_0 and the related compounds, the Jahn-Teller (JT) interaction must be considered. The C_6_0 molecule is known to exhibit a strong electron-phonon interaction. Hence studies of the Jahn-Teller (JT) effect are important in understanding the properties of C_6_0 and related molecules. Many kinds of JT effects are possible in icosahedral symmetry which the C_6_0 molecule possesses. The high degeneracies that occur in this symmetry generate problems which are not seen in cubic systems, such as the JT G x (g + h) and H x (g + h) systems. Depending on the ratio of the vibronic coupling constants, the wells on the lowest adiabatic potential energy surface (APES) for the G x (g + h) JT system, are of T or D_3 symmetry; for the H x (g + h) JT system, the wells on the lowest APES are of D_5_d or D_3_d symmetry. For the case of D_3_d minima in the simpler H x h JT system, it has previously been found unexpectedly that, above a certain coupling strength, the A-type level has a lower energy than the H-state. This is the first known example of a linear JT system in which the JT effect effectively alters the symmetry of the ground state. However, a physical explanation of why this crossover occurs deserves further consideration. In this thesis, an explanation based on the competition between the two tunneling paths on the lowest APES is proposed. It is assumed that tunneling occurs along paths of steepest descent. The reversal in sign of the tunneling splitting, calculated using the WKB method, in the icosahedral H x h Jahn-Teller system is explained in terms of different tunneling paths along which the system moves as the strength of the vibronic coupling K_h__1 changes. It is found that this sign reversal occurs when K_h__1/(h/2#pi#)w #approx# 4.1. This result is very near to the original result of K_h__1/(h/2#pi#)w #approx# 3.8 obtained using a totally different method. This reversal can be explained as follows; for weak vibronic coupling, the H symmetry state is dominated by tunneling along the steepest descent path of C_1 symmetry which connects two D_3_d wells via one point on the D_3 symmetry saddle trough; for strong coupling, the A symmetry state is dominated by tunneling along the steepest descent path of C_2 symmetry winch connects two different D_3_d wells via a point on a saddle trough of T symmetry. Reduction factors (RFs) are needed when modeling vibronic systems by an effective Hamiltonian in an electronic basis. The results of analytical calculations of the second-order RFs are presented in this thesis for the ground states of the icosahedral G x (g + h) and H x (g + h) JT systems in analyticaI form. These second-order RFs are calculated for the isotropic case using simple excited states in the wells. Details are given for the G x g JT system from wells of T symmetry, for the G x h JT system from wells of D_3_d symmetry and for the G x (g + h) JT system for wells of D_3_D symmetry. Also, second order RFs for the H x g JT system for wells of D_3_d symmetry, for the H x h_1 JT system for wells of D_3_d symmetry and for the H x h_2 JT system for wells of D_5_d symmetry. These results are particularly useful in investigations of the vibronic coupling effects in C_6_0 molecules. (author)SIGLEAvailable from British Library Document Supply Centre-DSC:DXN052504 / BLDSC - British Library Document Supply CentreGBUnited Kingdo