Derivation of femtosecond pump–probe dissociation transients from frequency resolved data.

We present a theoretical synthesis of Zewail’s femtosecond transition state (FTS) experiments. The FTS transients are obtained by convoluting the continuous wave, bound–free, and free–free frequency-resolved spectra with the pump and probe laser pulses. We accomplish this by deriving a simple semiclassical expression for the free–free (as well as the bound–free) matrix elements and regularizing the divergent integrals occurring in the free–free integrals, by subtracting a δ-function singularity. This method allows us to write the FTS transient signal as a coherent superposition of a ‘‘molecular’’ term and an ‘‘atomic’’ term, which shows clearly the effects of the interaction between the on-resonance and off-resonance transients observed in Zewail’s experiments. Our method, which achieves essentially the same accuracy as the purely numerical wave-packet propagation techniques, is much more efficient. It enables an easy exploration of all possible pump–probe configurations and clearly confirms the fact that quantum mechanics does not allow a unique definition of a ‘‘bond-breaking’’ time. In fact, we show that the observed transients are a strong function of the laser preparation and probing. In addition, we demonstrate that the assumption that the initial wave packet is localized after absorption of a 50–100 fs pulse is wrong, and that the classical approximation that there exists a one-to-one correspondence between the probe frequency and the internuclear distance of the photofragments is inaccurate. We show that the parameters obtained by the use of these classical approximations for the free–free spectrum lead to the extraction of the wrong potential parameters which, in turn, leads to a discrepancy between the calculated and measured bound–free absorption spectrum. This discrepancy does not exist... [ABSTRACT FROM AUTHOR]