Knowledge Bank

To facilitate interpretation of intensity experiments and to determine higher order molecular properties, the theory of angular and polarization $correlation1$ of radiation has been extended to include (1) higher multipole transitions (2) interference $effects2$ in molecules of arbitrary symmetry. For oriented molecules the intensities at two arbitrary directions related by given Euler angles are derived in terms of rotation matrices and the molecular multipole transition moments. This allows the interpretation of experiments with arbitrarily chosen propagation directions of the incoming (to interact with the parent molecule) and the outgoing (to observe the daughter molecule) radiation. It will also permit quantum averages for molecular rotation in a solid matrix. For random systems, it is shown that one should not neglect cross terms'' of matrix elements such as that in the electric dipole transition intensity for the parent molecule, $(x)_{p} (y)_{p}$. The product of the above with the corresponding cross term'' in the daughter molecule, $(x)p(y)p(x)d(y)d$ may not have vanishing coefficient (in terms of the product of four direction cosines) on average over random molecular orientation. This is because the parent and daughter molecules are correlated and the space average must be taken together, not separately. General intensity formulas are derived for viewing of the photoselected molecules along the same direction of the incoming radiation. Average over space is performed over the product of four rotation matrices. From the different coupling possibilities of these rotation matrices, the intensities are expressed in terms of different kinds of bipolar harmonics of the transition moments. The coupling of these bipolar harmonies in turn gives the angular correlation between the molecular multipole transition moments of the parent and the daughter molecules. Explicit examples up to electric and magnetic quadrupole radiation are given for viewing along and perpendicular to the incident light direction. The meaning of higher multipole correlation and the molecular information that can be inferred will be discussed.