The present work investigates the performance of exchange-correlation functionals in the prediction of two-photon absorption (2PA) strengths. For this purpose, we considered six common functionals used for studying 2PA processes and tested these on six organoboron chelates. The set consisted of two semilocal (PBE and BLYP), two hybrid (B3LYP and PBE0), and two range-separated (LC-BLYP and CAM-B3LYP) functionals. The RI-CC2 method was chosen as a reference level and was found to give results consistent with the experimental data that are available for three of the molecules considered. Of the six exchange-correlation functionals studied, only the range-separated functionals predict an ordering of the 2PA strengths that is consistent with experimental and RI-CC2 results. Even though the range-separated functionals predict correct relative trends, the absolute values for the 2PA strengths are underestimated by a factor of 2-6 for the molecules considered. An in-depth analysis, on the basis of the derived generalized few-state model expression for the 2PA strength for a coupled-cluster wave function, reveals that the problem with these functionals can be linked to underestimated excited-state dipole moments and, to a lesser extent, overestimated excitation energies. The semilocal and hybrid functionals exhibit less predictable errors and a variation in the 2PA strengths in disagreement with the reference results. The semilocal and hybrid functionals show smaller average errors than the range-separated functionals, but our analysis reveals that this is due to fortuitous error cancellation between excitation energies and the transition dipole moments. Our results constitute a warning against using currently available exchange-correlation functionals in the prediction of 2PA strengths and highlight the need for functionals that correctly describe the electron density of excited electronic states.
A study of the influence of the solvent on the electronic contributions to the two-photon absorption cross
section (δ) of the simplest pyridinium-N-phenolate betaine dye molecule is presented. The calculations of δ,
for the first excited singlet state (connected with the intramolecular charge transfer), were performed as a
function of the interplanar angle between the pyridinium and the phenolate ring. It was found that in the gas
phase the two-photon absorption cross section is enhanced several times near 80° as compared to the planar
structure. The calculations show that in aqueous solution there is no distinct maximum value of δ. The
computations of the first- (β) and second-order (γ) hyperpolarizabilities performed for the gas phase have
shown that the angle at which δ has its maximum value is exactly the same for β and γ. The behavior of
these two parameters in water resembles that of δ. The demeanor of all three nonlinear parameters in the gas
phase as well as in aqueous solution has been successfully explained using the two-level model, accounting
the lowest-lying charge-transfer state only. The solute/solvent interaction was included within Langevine
dipoles/Monte Carlo formalism. All parameters were evaluated by applying the semiempirical GRINDOL
method based on the NDO-like Hamiltonian.
The static and frequency-dependent first hyperpolarizabilities ( ) of Reichardt's betaine dye and two simplest pyridinium-N-phenoxide betaines were computed in the gas phase and in aqueous solution. The sum-overstate formalism was used to calculate individual components of the -tensors. The solvent effect was included via the Langevin dipoles/Monte Carlo approach. The influence of the molecular geometry on the values of the betaine dyes was investigated as well. The calculations demonstrate that the values strongly depend on the interplanar angle between the pyridinium and the phenoxide ring. Moreover, we observed dramatically decreased values of (for all investigated betaines) in aqueous solution as compared to the gas phase.
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