Articles you may be interested inSolvent perturbations on the excited state symmetry of randomly oriented molecules by twophoton absorption J. Chem. Phys. 88, 7369 (1988); 10.1063/1.454348 Higher excited states of benzene: Polarized ultraviolet twophoton absorption spectroscopy

The two-photon absorption cross section δ for photons of any polarization (linear, circular, or elliptical) is averaged over all orientations of the absorbing molecule. The result is given by 〈δ〉 = δFF + δGG + δHH, where δF, δG and δH are molecular parameters and F, G, and H are simple functions of the polarization vectors. It is shown how the δ's may be calculated from theory and also how they may be measured by experiment. Experiments using only linearly polarized light are insufficient to determine all three δ's; hence, circularly polarized light will play an essential role in this spectroscopy. For absorption of two linearly polarized photons with angle θ between their polarization vectors, the angular dependence is 〈δ〉 = A + Bcos2θ, where A and B are simple combinations of the δ's. We obtain two exact symmetry rules which permit allowed two-photon transitions of different symmetries to be distinguished. For transitions from totally symmetric ground states the rules are: (1) If the excited state transforms like xy, yz, or zx, then δF = 0. (2) If the excited state transforms like x2, y2, or z2, then δG = δH. In cases of near resonance, when a single intermediate state dominates the formula for the cross section, we show that δF = δH, and that linearly polarized light suffices for a complete investigation. These results are applied to liquid 1-chloronaphthalene. We find two allowed two-photon transitions which are assigned Bb11g (perpendicular nodes) at 37 700 cm−1 and A1g (total symmetry) at 42 600 cm−1. This is in reasonable agreement with theoretical predictions of other authors. We have also examined the region of the second excited singlet of benzene, near 6.2 eV. We were not able to detect any two-photon absorption, setting an upper limit of about 10−51 cm4·sec/photon·molecule on its 〈δ〉. This leads to an unequivocal assignment of B11u for this state according to calculations of Jortner. In an Appendix we examine the effect of “hot spots” in the laser beam on the observed cross sections. We show that the elimination of the hot spots is of some importance, contrary to a statement of other authors.

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We examine the polarization dependence of phenomena involving the interaction of three photons and a molecule, in the regime where the interaction is complete before the molecule has time to rotate. We obtain an explicit general formula for the orientation average of the observed intensity, which will be applicable to a randomly oriented sample of molecules. The results apply to simultaneous three-photon absorption, hyper-Raman or double quantum scattering, or other simultaneous three-photon effects in fluids. In viscous media the results apply to sequential three-photon absorptions or to simultaneous two-photon absorption followed by fluorescence, and to three-step photochemical processes in solid matrices. An experimental procedure is given for determining all the available molecular parameters of such processes. Certain simplifications of the general procedure arise in special cases. In all cases the formulas obtained are of the form I=〈|λAμBνCTABC|2〉=Pi(λμν) MijQj(T), where I is the intensity of the effect, (λ, μ, ν) are the polarization vectors, T is the three-photon tensor, the Pi(λ, μ, ν) are a set of polarization parameters, the Qj (T) are a set of molecular parameters, and Mij is an averaging matrix. The Pi, Mij, and Qj are given explicitly for all cases considered. Thus the polarization dependence problem has been reduced to a linear algebra problem.

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