Photo-Ionization Time Delay in Linearly Extended π-Conjugated Molecular Systems

We calculate the photo-ionization time delay for extended, linear, π-conjugated molecules. Ionization can be realized as scattering of an electron from bound to continuum states due to interaction with an ionizing radiation field. This allows us to use the Wigner method, whereby the rate of change in phase of the scattered electron wave packet with respect to the electron energy gives a measure of the ionization time delay. An analytical expression for ionization time delay is obtained using a model system that shows how interference between different ionization pathways leads to a finite time delay, even if there is a zero time delay corresponding to individual pathways. It is observed that the ionization time delay increases linearly as the size of the chain increases. We compute the ionization time delay also using computational chemistry and compare the results with those obtained from the model system. In qualitative agreement with the model calculation, we find that the ionization time delay increases linearly with increasing conjugation.