Numerical calculations of multiphoton molecular absorption

Motivated by the possibility of multiphoton-driven pump-probe experiments, such as time-resolved photoelectron spectroscopy, we carry out essential states's calculations of strong-field molecular excitation by solving the time-dependent Schrödinger equation for a molecule in a high-intensity laser field. Usually such calculations rely on adiabatic elimination, but here we make direct use of a large number of energies and transition dipole moments obtained from electronic structure calculations. In this way, we capture a range of multiphoton absorption orders, from 2 to 5, and include dynamic Stark shifts naturally. We consider a range of laser frequencies and intensities to characterize several multiphoton resonances and dynamic Stark shifts. The calculations also include averaging over molecular orientation and geometry, but are carried out for frozen nuclei, which is relevant in the limit of very short laser pulses (<10 fs). Here we focus on the molecule thiophene; however, these calculations can easily be implemented for other molecules with appropriate electronic structure input.