On the spectral line width broadening for simulation of the two-photon absorption cross-section of para-Nitroaniline in liquid environment

The calculated two-photon absorption (TPA) cross-section amplitude depends on the spectral line width (Γ) of the transition and there is not a consensus on the most appropriate way to obtain the Γ value. Usually it is arbitrarily defined or ambiguously estimated based on experimental data or using a transition energy variation determined from a quantum mechanics/molecular mechanics approach. In this study we compare different procedures to estimate Γ values and different methods of spectral convolution to simulate TPA cross-section for para-Nitroaniline (pNA) in liquid environment. The effects of the liquid environment on the nonlinear absorption were approximated using Monte Carlo and Born-Oppenheimer Molecular Dynamics as well as the commonly used Polarizable Continuum Model. The different procedures adopted here provided large difference in the calculated TPA amplitudes, mainly because of the underestimate/overestimate of the homogeneous and/or inhomogeneous contributions to the spectral line width. Based on these difficulties, we suggest a new procedure in which the value assigned to Γ is the one used to induce the total line width of the simulated TPA spectrum to reproduce the experimental one-photon absorption line width. Within this procedure the Γ value, which becomes a fitting parameter (Γ_fit), represents part of the homogeneous contribution to the spectral line width. Finally, although time dependent density functional theory calculations reproduced only reasonably well the energy of the lowest-energy π → π* transition of pNA, the fitting procedure here proposed provided the calculated TPA cross-section in good agreement with the available experimental data.