Populations and coherence in femtosecond time resolved X-ray crystallography of the photoactive yellow protein

Ultrafast X-ray crystallography of the photoactive yellow protein with femtosecond delays using an X-ray free electron laser has successfully probed the dynamics of an early Franck-Condon species. The femtosecond pump-probe application of protein crystallography represents a new experimental regime that provides an X-ray structural probe for coherent processes that were previously accessible primarily using ultrafast spectroscopy. We address how the optical regime of the visible pump, that is necessary to successfully resolve ultrafast structural differences, affects the motions that are measured using the technique. The sub-picosecond photochemical dynamics in PYP involves evolution of a mixture of electronic ground and excited state populations. Additional to photoisomerisation that is considered to proceed through activated barrier crossing, within the dephasing time structural motion include vibrational coherence arising from excited states, the ground state and a ground state intermediate under experimental conditions used for ultrafast crystallography. Intense optical pulses are required to convert population levels in PYP crystals that allow detection by X-ray crystallography, but the compromise currently needed for the optical bandwidth and power has consequences with regard to the contributions to the motions that are experimentally measured with femtosecond delays. We briefly review the ultrafast spectroscopy literature of the primary photoreactions of PYP and discuss relevant physical models taken from coherent control and femtosecond coherence spectroscopy literature that address both the population transfer as well as the vibrational coherences. We apply linear response theory, with the additional use of a high power approximation, of on-resonance impulsive vibrational coherence in the ground state and the non-impulsive coherence in the excited state and discuss experimental approaches to manipulate the coherence contributions. The results are generalised and extended to discuss the future capabilities of high repetition rate X-ray free electron laser instruments providing enhanced sensitivity to perform the crystallographic equivalent of an impulsive Raman measurement of vibrational coherence.