On multipole interaction methods in exciton theory

Three features of the multipole method of treating excited state molecular interactions in crystals are examined. The first is the error caused by treating the interactions as those of point multipoles even for nearest neighbour molecules with some overlapping of electron clouds. The second is the question of the convergence of the multipole series, and of the conditions under which terms higher than the dipole-dipole must be included. The third is the influence of the coupling of the static moments of one molecule with the transition moments between different excited states in another. It is concluded from a discussion of principles, supported by calculations of examples, that `conventional' methods using only dipole-dipole interactions are adequate when (i) the transitions are at least moderately intense and (ii) the dipole lattice sums are not made very small by special conditions of molecular orientation. When these conditions are not satisfied quadrupole and octupole moments must be included. Their effects on factor-group splittings may be many times greater than those of the dipole term; in intensity calculations where the changes occur only in second order, the dipole approximation remains more acceptable but higher moments are not, in general, negligible.