Determination of Two-Photon-Absorption Cross Sections Using Time-Dependent Density Functional Theory Tight Binding: Application to Fluorescent Protein Chromophores

Application of fluorescent proteins (FPs), e.g., as probes for biological imaging, has led to the goal of finding FPs with notable one- and two-photon absorption (OPA and TPA, respectively) features. The variables that affect the TPA cross section are many; e.g., structurally speaking, some studies have shown its magnitude is influenced by the presence of the protein backbone and the molecules of water surrounding the chromophore. However, the impact that the surroundings have on the TPA cross section has not been conclusively determined. One of the main problems that can be faced when trying to account for excited state properties is the cost associated with such computations. Among the methods chosen for this type of computations is time-dependent density functional theory (TD-DFT), commonly used on molecules with no more than 50 atoms due to its computational cost. A cheaper alternative to DFT and, moreover, to TD-DFT is the so-called time-dependent tight binding density functional theory (TD-DFTB), which within the second-order approximation is designated TD-DFTB2. In the present work, TD-DFTB2 was tested to determine whether or not it is an alternative method to TD-DFT for computing excited state properties beyond excitation energies and oscillator strengths such as TPA cross sections. Studies around the performance of TD-DFTB2 on the computation of excitation energies have been previously carried out, and the results show it is comparable to TD-DFT in terms of the computation of excitation energies and oscillator strengths. Despite the latter, what we found is that neither the magnitude nor the trend of the obtained TPA cross sections is preserved with respect to CAM-B3LYP and B3LYP TPA cross sections previously reported by other authors. The computation of TPA cross sections within the two-level model allowed us to determine that among the reasons behind such behavior is the overestimation of the excited state dipole moments. Based on the above, we conclude that TD-DFTB2 is not (yet) a viable route to obtain quantitatively TPA cross sections.