Vladimir Hizhnyakov, University of Tartu
Ernst Sigmund, Technical University of Brandenburg, Germany
Mihhail Klopov, Tallinn University of Technology
Quantum mechanics has given us a insight into the world of small things. Still there are a number of problems that have not been solved. One of these is the dimer in a solid which exhibits the pseudo-Jahn-Teller effect. Dimer is a molecule with two structurally similar building blocks in interaction with each other. The pseudo-Jahn-Teller effect states that two (energetically close) states of a electron are in interaction through the movement of the nuclei in the case of such a molecule. A solid contains many lattice vibrations or movements of the nuclei, which makes this problem hard to solve.
The aim of this thesis was to find a quantitative model that can describe the fore-mentioned systems. The main idea was to reduce the coupling of the electronic states with all vibrations to the coupling with one vibration and to take all vibrational effects into account approximately. The rewriting of the equations of the system in an numerically easily solvable way was also important. Th system was described in two ways. First, the calculated optical spectra of the dimer were found. The results show that the influence of vibrations must be clearly observable through the addition of a band spectrum - the so called phonon wing - to each spectral line. It turns out that a phonon wing associated with a spectral line has a unique shape which implies that the vibrations couple to the electrons unequally. The other contribution of this work was the non-radiative decay of the excited state of the dimer. This means that in the excited state the system does not emit light but loses energy by creating vibrations of the lattice. As mentioned earlier the interaction of each energy level with the lattice vibrations is different which means the system loses energy in a nonuniform way. This means that the electron distribution must have longer and shorter lived configurations during the transition to the lowest energy level of the excited state which plays an important role for example in photochemical processes.