The matrix elements of spin-orbit interaction are obtained for polyatomic molecules using M.O. wave functions, taking account of configurational interaction. These results are then applied to the calculation of singlet-triplet transition probabilities in aromatic compounds. It is shown without evaluation of integrals that intercombination transitions in these compounds should be much weaker than in most other classes of organic compounds. This is in agreement with experimental results on the phosphorescence lifetimes of these compounds.

The emission lifetimes of the metastable triplet states (phosphorescent states) of a large variety of organic molecules have been measured. The lifetimes are in the range from 10−4 to about 10 seconds. It is shown that the transition probabilities corresponding to the shorter lifetimes are of the same magnitude as found in the light atoms of which the molecule is composed. The longer lifetimes, on the order of seconds, are found only among the aromatic compounds. A consideration of the perturbing singlet states in aromatic compounds shows that the matrix elements for the intercombination must be very much smaller than those responsible for the intercombination in the free carbon atoms. Direct evidence that the long-lived states of the aromatic compounds are triplet states is obtained by showing that as the atomic number of chemically similar substituents is increased (e.g. substitute Br for Cl), the transition probability increases approximately in proportion to the increase in the square of the spin-orbit interaction energy of the substituent atom. The luminescences are usually observable only when the substance is dissolved in a rigid solvent, and the effect of such a solvent on the lifetimes is discussed. Experimental data relating singlet-triplet absorption strength to triplet state lifetime is presented.

The polarized optical spectra of the ions Ti3+, V3+, Cr3+, Mn3+, Co3+, and Ni3+ in corundum single crystals have been studied at temperatures from 4.2° to 1200°K. A theory of the band strength based on the point-charge model and p-d mixing has been developed and applied to the data with results in fair agreement with experiment. The effects of temperature show that the vibrational-electronic contribution to band strength is quite small at low temperature but may be appreciable at high temperatures. The crystal-field parameters have been calculated as convergent lattice sums. The observed trigonal-field parameter has the opposite sign from that calculated by the point-charge model if the impurity ion is assumed to occupy an Al3+ ion position in the lattice, but has the same sign as calculated for an ion 0.1 Å displaced along the c3 axis toward the empty octahedral site. Details of the spectra have been interpreted as showing that the surroundings of an ion are distorted in some electronic states.

The rare-earth ions may exist in the divalent state in suitable host crystals such as CaF2. All of the trivalent ions from Ce to Yb (and probably also La) are reduced in situ to the divalent state in CaF2 by gamma irradiation. The spectra of most of these ions show that the ground and first few excited states derive fromfn configurations, but the weak absorption due to these is masked at higher energies by strong broad bands of the parity-permitted f"->fn-'d transitions. The excitation energy of these spectra have been calculated in a first approximation as the energy difference between the "Hund rule," single-determinant states of the configurationsr-'d andf". This procedure satisfactorily accounts for the remarkable variations in the excitation energy in passing from one ion to the next in the series with the exception of Gd++ Ce++ and Tb++. Gd++ probably has Fa for its ground configuration, while Ce++ and Tb++ are borderlin~ cases: !he spectral str:uc~ure probably arises chiefly from the crystal-field splitting of the a orbital, since each ion m CaF2 has a Similar spectrum, and the spectra change drastically in sites of other than cubic symmetry.

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