Efficient calculation of diffracted intensities in the case of nonstationary scattering by biological macromolecules under XFEL pulses

The calculation of diffracted intensities from an atomic model is a routine step in the course of structure solution, and its efficiency may be crucial for the feasibility of the study. An intense X-ray free-electron laser (XFEL) pulse can change the electron configurations of atoms during its action. This results in time-dependence of the diffracted intensities and complicates their calculation. An algorithm is suggested that enables this calculation with a computational cost comparable to that for the time-independent case. The intensity is calculated as a sum of the `effective' intensity and a finite series of `correcting' intensities. These intensities are calculated in the conventional way but with modified atomic scattering factors that are specially derived for a particular XFEL experiment. The total number of members of the series does not exceed the number of chemically different elements present in the object under study. This number is small for biological molecules; in addition, the correcting terms are negligible within the parameter range and accuracy acceptable in biological crystallography. The time-dependent atomic scattering factors were estimated for different pulse fluence levels by solving the system of rate equations. The simulation showed that the changes in a diffraction pattern caused by the time-dependence of scattering factors are negligible if the pulse fluence does not exceed the limit that is currently achieved in experiments with biological macromolecular crystals (10⁴ photons Å^-2 per pulse) but become significant with an increase in the fluence to 10⁶ or 10⁸ photons Å^-2 per pulse.