Benzene Vibrational Exciton Spectrum

A critical discussion of the infrared polarization assignments of Zwerdling and Halford, in view of the now accepted benzene crystal structure, leads to acceptance of their results, though with somewhat reduced credibility. The controversial 707‐cm−1 absorption is assigned as the B2 interchange component (b axis polarized) of the a2u fundamental (674‐cm−1 gas‐phase) exciton band. The resulting, unusually large, static and dynamic exciton interaction terms are tabulated. Recent calculations based on atom—atom interactions are in reasonable agreement with the above results.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/71308/2/JCPSA6-47-9-3227-1.pd

Vibrational excitons, resonant energy transfer, and local structure in liquid benzene

The presence of vibrational excitons in liquid benzene has been tested by the method of isotopic dilution. A C6H6/C6D6 concentration study on the infrared and Raman fundamental modes reveals that the umbrella (A2u) vibrational exciton in solid benzene retains its characteristics upon melting and at room temperature. The total liquid exciton bandwidth is about 40 cm−1, practically the same as in the solid. This indicates an instantaneous local liquid structure similar to that of the solid (the Ci crystal site symmetry is also nearly preserved), in general agreement with indications from other methods. The fastest nearest neighbor vibrational resonant transfer takes about 1 psec. The residual linewidth at isotopic dilution is 3–4 cm−1, which is due to inhomogeneous and/or homogeneous broadening. The respective overall reorientational and/or translational relaxation takes about 2 psec or longer. The exciton linewidth is proportional to the square root of the isotopic concentration except for a sudden break at some critical concentration.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/70052/2/JCPSA6-66-11-5035-1.pd

Fractal to Euclidean crossover and scaling for random walks on percolation clusters. II. Three‐dimensional lattices

We perform random walk simulations on binary three‐dimensional simple cubic lattices covering the entire ratio of open/closed sites (fraction p) from the critical percolation threshold to the perfect crystal. We observe fractal behavior at the critical point and derive the value of the number‐of‐sites‐visited exponent, in excellent agreement with previous work or conjectures, but with a new and improved computational algorithm that extends the calculation to the long time limit. We show the crossover to the classical Euclidean behavior in these lattices and discuss its onset as a function of the fraction p. We compare the observed trends with the two‐dimensional case.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/70154/2/JCPSA6-83-6-3099-1.pd

Exciton percolation and exciton coherence

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/69756/2/JCPSA6-66-7-3301-1.pd

Green’s functions for a face centered orthorhombic lattice

Diagonal and off‐diagonal matrix elements of the Green’s functions for a face centered orthorhombic lattice are presented in terms of integrals of complete elliptic integrals of the first and third kind. These Green’s functions are also applicable to structures like that of the benzene crystal (space group D152h, interchange symmetry D2).Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/69909/2/JMAPAQ-17-11-2067-1.pd

Diffusive and percolative lattice migration: Excitons

A microscopic transport theory is developed for stochastic and correlated hopping on ordered and random lattices that contain a small fraction of supertraps and a small number of ’’hoppers’’ (i.e., excitons). It includes short‐time (’’transient’’) behavior, which is of interest for both time‐resolved and steady‐state experiments. The relations with diffusion, percolation, random walk, and rate equations are exhibited and applications to energy transport in disordered molecular aggregates illustrate the approach, which is a combination of a rigorous analytical method and simple computer simulations of general validity. Simple analytical results, derived for special (limiting) cases, are compared with other methods, thus emphasizing the roles of time, dimensionality, anisotropy, clusterization, correlation of hops, and the order parameter of the lattice as well as the suitability of various approaches for dealing with these factors.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/69980/2/JCPSA6-72-5-3053-1.pd

Fractal to Euclidean crossover and scaling for random walkers on percolation clusters

Simulations of random walkers on two‐dimensional (square lattice) percolation clusters were performed for a range of occupation probabilities from critical to unity. The number of distinct sites visited, over 2×105 steps, shows the conjectured scaling, crossover and superuniversaility (ds=4/3, within 1%) behavior over a wide range of site occupation probabilities. Possible deviations from superuniversality and/or scaling are discussed.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/70167/2/JCPSA6-81-2-1015-1.pd

Exciton percolation I. Migration dynamics

The exciton transfer, via migration and trapping, in binary and ternary mixed crystals is formulated in terms of percolation theory and the cluster structure for binary randomly mixed crystals. An important limiting case (exciton supertransfer) is derived for long exciton lifetime, relative to jumping and trapping time. The exciton supertransfer case is solved analytically [in terms of the functions derived by J. Hoshen and R. Kopelman, Phys. Rev. B (in press)] and the solutions involve neither physical parameters nor physical constants. Other limiting cases are derived, as well as an algorithm for the general energy transfer case. This algorithm relates the migration and trapping in binary and ternary systems with the trapping‐free migration in binary systems. The algorithm involves the use of empirical information, i.e., the parameters describing the exciton dynamics in a pure crystal. The various formulations are valid for concentrations both above and below the critical (’’percolation’’) concentration, with due emphasis on small, medium, and large cluster contributions. Sample calculations are given (for the square lattice with site percolation).Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/71176/2/JCPSA6-65-7-2817-1.pd

Fractal behavior of correlated random walk on percolating clusters

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/70722/2/JCPSA6-84-2-1047-1.pd