Dynamics of two-photon two-color transitions in flurophores excited by femtosecond laser pulses

We present the results of theoretical and experimental studies of the polarized fluorescence in fluorophores excited by two-photon two-color (2P2C) femtosecond laser pulses. Quantum mechanical expressions describing the fluorescence polarization have been derived using the spherical tensor technique for asymmetric top molecules under the condition of isotropic rotation diffusion for arbitrary polarization of each of the three photons involved in the photoprocess. The expressions are presented in terms of the molecular parameters MK(R, R´, t) which contain all information about the photoprocess dynamics and can be directly determined from experiment. Ab initio computations of the flurophore structure and two-photon dynamics have been performed for p-terphenyl and indole in vacuum and in solutes using the polarizable continuum model and TD-DFT method, respectively. In case of p-terphenyl, full geometry optimization of the low-lying excited singlet electronic of the D2h symmetry has been performed. The results obtained indicate that that the solute molecules do not affect noticeably the position of the p-terphenyl energy levels which conclusion nicely fits the results reported elsewhere. In case of indole, the energy of low-lying molecular states, their permanent dipole moments, and transition dipole moments to the ground state have been computed both for non-relaxed and relaxed geometries. The results obtained manifests strong influence of the polar solute (methanol) on the position of the lowlying molecular energy levels and on the dipole moments. Using the results of the computation obtained three molecular parameters of the zero-th order, M0(0,0), M0(2,0), M0(2,2) have been calculated and compared with their values obtained experimentally. The comparison shows excellent agreement between the theory and experiment.