Polarization Dependence of the Twohyphen;Photon Absorption of Tumbling Molecules with Application to Liquid 1hyphen;Chloronaphthalene and Benzene

摘要

The twohyphen;photon absorption cross sectiondgr;for photons of any polarization (linear, circular, or elliptical) is averaged over all orientations of the absorbing molecule. The result is given bylang;dgr;rang;thinsp;equals;thinsp;dgr;FFthinsp;plus;thinsp;dgr;GGthinsp;plus;thinsp;dgr;HH, wheredgr;F, dgr;Ganddgr;Hare molecular parameters andF, G, andHare simple functions of the polarization vectors. It is shown how the dgr;'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 dgr;'s; hence, circularly polarized light will play an essential role in this spectroscopy. For absorption of two linearly polarized photons with angle thgr; between their polarization vectors, the angular dependence islang;dgr;rang;thinsp;equals;thinsp;Athinsp;plus;thinsp;Bcos2thgr;, whereAandBare simple combinations of thedgr;'s. We obtain two exact symmetry rules which permit allowed twohyphen;photon transitions of different symmetries to be distinguished. For transitions from totally symmetric ground states the rules are: (1) If the excited state transforms likexy, yz, orzx, thendgr;Fthinsp;equals;thinsp;0. (2) If the excited state transforms likex2, y2, orz2, thendgr;Gthinsp;equals;thinsp;dgr;H. In cases of near resonance, when a single intermediate state dominates the formula for the cross section, we show thatdgr;Fthinsp;equals;thinsp;dgr;H, and that linearly polarized light suffices for a complete investigation. These results are applied to liquid 1hyphen;chloronaphthalene. We find two allowed twohyphen;photon transitions which are assigned1B1g(perpendicular nodes) at 37 700 cmminus;1and1Ag(total symmetry) at 42 600 cmminus;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 twohyphen;photon absorption, setting an upper limit of about 10minus;51cm4middot;sec/photonmiddot;molecule on itslang;dgr;rang;. This leads to an unequivocal assignment of1B1ufor this state according to calculations of Jortner. In an Appendix we examine the effect of ldquo;hot spotsrdquo; 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.