4. Survey of Novel Multiphoton Active Materials 1257 4.1. Multiphoton Absorbing Systems 1257 4.2. Organic Molecules 1257 4.3. Organic Liquids and Liquid Crystals 1259 4.4. Conjugated Polymers 1259 4.4.1. Polydiacetylenes 1261 4.4.2. Polyphenylenevinylenes (PPVs) 1261 4.4.3. Polythiophenes 1263 4.4.4. Other Conjugated Polymers 1265 4.4.5. Dendrimers 1265 4.4.6. Hyperbranched Polymers 1267 4.5. Fullerenes 1267 4.6. Coordination and Organometallic Compounds 1271 4.6.1. Metal Dithiolenes 1271 4.6.2. Pyridine-Based Multidentate Ligands 1272 4.6.3. Other Transition-Metal Complexes 1273 4.6.4. Lanthanide Complexes 1275 4.6.5. Ferrocene Derivatives 1275 4.6.6. Alkynylruthenium Complexes 1279 4.6.7. Platinum Acetylides 1279 4.7. Porphyrins and Metallophophyrins 1279 4.8. Nanoparticles 1281 4.9. Biomolecules and Derivatives 1282 5. Nonlinear Optical Characterizations of Multiphoton Active Materials 1282

Multiphoton Absorbing Materials : Molecular Designs, Characterizations, and Applications

We consider the effect of molecular symmetry on the two‐photon absorption constants of a randomly oriented sample of molecules. It is shown that a complete polarization study of an allowed two‐photon transition of a fluid generally yields enough information to permit an unequivocal identification of the symmetry species of the excited state. Ambiguities occur in only a few cases. Thus, oriented molecule studies for symmetry assignment will be largely unnecessary in two‐photon molecular spectroscopy. Symmetry assignment rules are given for all of the 32 crystallographic point groups and for the two groups of linear molecules. It is shown that certain transitions, which are allowed for two photons of different energies, are forbidden for two photons of the same energy. The application of this formalism to Raman scattering problems is discussed.

Excited State Symmetry Assignment Through Polarized Two‐Photon Absorption Studies of Fluids

Resonant X-ray Raman scattering

Explicit forms for the two-photon absorption cross section in linearly and circularly polarized light for rotating diatomic molecules have been developed. The ratio (σλλ/σ cc ) of the cross sections for individual rotational transitions is precisely two-thirds for all branches of ΔΩ = 0, ±1, ±2 transitions except for the unique case—the Q branch of a ΔΩ=0 transition. In the latter case the ratio becomes J-dependent and may range from infinity to 4/1 (for high J) for different relative contributions to the absorption cross section of intermediate states having either the same or different electronic symmetry. These contributions are thus experimentally accessible in this favourable situation.

Two-photon absorption by rotating diatomic molecules

In theories which describe the response of freely rotating molecules to externally imposed stimuli it is frequently necessary to average rotationally a product of direction cosines relating space‐fixed and molecular coordinate frames. In this paper a systematic method for deriving the required tensor averages is presented, and results up to the seventh rank are explicitly shown. Where appropriate both reducible and irreducible expressions are given and their equivalence is demonstrated. Finally, some useful identities relating rotational averages of different ranks are noted.

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On three‐dimensional rotational averages

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 1B1g (perpendicular nodes) at 37 700 cm−1 and 1 Ag (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 1B1u 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.

P. R. Monson

Papers

Polarization Dependence of the Two-Photon Absorption of Tumbling Molecules with Application to Liquid 1-Chloronaphthalene and Benzene