Two-photon absorption in solution by means of time-dependent density-functional theory and the polarizable continuum model

Abstract

We present the first study of two-photon absorption (TPA) of solvated molecules based on direct evaluation of TPA cross sections from the quadratic response of time-dependent perturbations. A set of prototypical two-photon (TP) chromophores has been selected and analyzed: a pure pi system (t-stilbene) and its substituted homologs obtained employing a donor (D) and an acceptor (A) group to probe the solvent effects along the series pi, D-pi-D, A-pi-D, and A-pi-A. For the selected systems we have calculated the TPA cross sections in different environments by means of the polarizable continuum model. The data have been analyzed to evaluate how the structural and environmental parameters contribute to the final two-photon absorption cross section. These include molecular structure, geometry relaxation in solution, polarity, and refractive index of the solvent. The performances of the three common functionals SVWN, BLYP, and B3LYP have been compared. The results show a significant solvent dependence of the TPA cross section and an unusual trend when passing from cyclohexane to water. The data have also been rationalized in terms of the main orbital excitations leading to the transitions. Finally, trends along the series have been described and comparison with experiments and previous calculations has been drawn.

Theoretical study of one- and two-photon absorption spectra of azoaromatic compounds

“…͑4͔͒ is twice the Birge's formula. In summary, it is expected that our results for the 2PA cross-sections would differ by the factor of two in total, i.e., twice smaller, from the results of the works by Day et al 11 and Frediani et al 13 A second important aspect affecting the comparison between theoretical values for the 2PA cross-sections, and even between theoretical results and experimental data, is the distinct values used for the damping constant ⌫ f to describe the line broadening of the excited final state.…”

“…For DIAMINO, Cronstrand et al 40 reported a value of 260 GM obtained using a few-state model and the B3LYP functional. More recently, Frediani et al 13 calculated a value of 765 GM for the higher energy transition of DIAMINO in vacuo. In spite of the energy difference ͑about 0.4 eV͒, we believe that the S 0 → S 3 transition determined in this work accesses the same 3 1 Ag state reported by Frediani et al 13 For DO3, a value of 84 GM was reported by Day et al 11 through a TDDFT/B3LYP study applying the two-state approximation and a Lorentzian line-shape for the S 0 → S 2 transition.…”

“…More recently, Frediani et al 13 calculated a value of 765 GM for the higher energy transition of DIAMINO in vacuo. In spite of the energy difference ͑about 0.4 eV͒, we believe that the S 0 → S 3 transition determined in this work accesses the same 3 1 Ag state reported by Frediani et al 13 For DO3, a value of 84 GM was reported by Day et al 11 through a TDDFT/B3LYP study applying the two-state approximation and a Lorentzian line-shape for the S 0 → S 2 transition. Frediani et al 13 also studied this compound using the B3LYP functional and reported values of 327 and 247 GM for S 0 → S 2 and S 0 → S 4 transitions in vacuo, respectively.…”

“…͑4͔͒. In this work the two-photon transition matrix element is defined considering single beam 2PA measurements, and therefore it is one fourth of the Birge's formula, 41 defined considering double-beam 2PA measurements and which was used by Day et al 11 and Frediani et al 13 On the other hand, while in these works the 2PA cross-section was defined dividing the transition rate by the square of photon flux, here it is defined dividing the dissipation rate of the photons of the incident light single beam by the square of photon flux, what make consistent the comparison of our theoretical results with the experimental data obtained by De Boni et al 6 using the Z-scan technique. 19 Therefore, our definition for 2PA cross-section ͓Eq.…”

“…[7][8][9] More recently, theoretical methods have been employed to support the understanding of experimental 2PA spectrum of several compounds, 8,[10][11][12] including azoaromatic compounds, which have also been the target of theoretical studies. [11][12][13] Among several theoretical methods used to study electronic transitions of compounds, the density functional theory ͑DFT͒ combined with linear response function formalism 14 has been shown to provide accurate excitation energies particularly when employing hybrid exchange-correlation functionals. Likewise, application of quadratic response function can be used to study the 2PA process.…”