Theoretical model for ultra fast dynamics of vibronic couplings in conjugated polymers

Modulations of the instantaneous frequencies of the stretching modes with an oscillation period around 200 fs have been reported for the non equilibrium vibrational state in the 2 1 A g of PDA. We propose here a model Hamiltonian which allows to study the time evolution of the non equilibrium system towards equilibrium. This includes the electronic, the vibrational, the linear and quadratic electron vibration interaction Hamiltonians of a conjugated polymer. In the off diagonal quadratic interactions the coupling between the high frequency stret ching mode and the low frequency bending mode of the polymers is taken into account. In this framework we study the time evolution of the out of equilibrium system relaxing to the thermalized state and we show that the stretching mode frequencies changes in time in quali tative agreement with the experimental results.