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

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

Exciton surface states in molecular crystals

A new Hamiltonian partition method, used previously for cooperative excitations in molecular crystals, has been adopted for the treatment of surface exciton states in molecular crystals. The formation of surface excitons depends on the relative magnitude of the exciton transfer integrals, J terms, as compared to the environmental shift integrals, D terms. This was established for a sample calculation on a simple cubic molecular crystal. It was found that when the absolute value of the nearest neighbor D term exceeds the corresponding J term two localized states emerge for each value of a two dimensional wavevector. The two localized states are degenerate in the limit of an infinitely thick crystal. The localization of the surface states increases with an increase in the magnitude of the D term.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/69728/2/JCPSA6-61-1-330-1.pd

Percolation analog for a two-component liquid-vapor system

Generalized site-bond percolation theory is utilized to provide an analog for a two-component liquid-vapor system in the phase transition region. The percolation model exhibits a behaviour typical of a non-ideal real liquid-vapor system with features such as separate curves for the liquid and vapor phases, and minimum and maximum azeotrope formation.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/23122/1/0000046.pd

Molecular Exciton Cluster States and Spectra with Application to Benzene

A cluster expansion is introduced for the determination of the optical absorption properties of cluster states in substitutionally disordered molecular crystals. This method is based on the Green's function expansion in terms of the localized cluster states in the energy region of the guest sub-band. The general features of the method are illustrated by calculations for a simple two-dimensional molecular crystal. The physical parameters for the calculation are based on the v 11 benzene vibrational exciton. Both polarized and unpolarized cluster optical absorptions display strong asymmetries, with respect to the isolated guest spectral line. Calculations are performed on the monomer, dimer, trimer, and tetramers (three kinds) of the benzene crystal ac -plane.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/50373/1/2220810208_ftp.pd

SURFACE STATES IN MOLECULAR CRYSTALS

$^{1}$ Electronic Vibrational Cooperative Excitation in Molecular Crystals, J. Hoshen and J. Jortner, to be published.Author Institution: Department of Chemistry, University of MichiganSurface states in cubic molecular crystals were determined, utilizing the Hamiltonian partition $method.^{1}$ The crystal Hamiltonian was split into an unperturbed term which can be diagonalized, and a perturbation term. The perturbation term involved exciton transfer terms (J-terms) and environmental shift terms (D-terms). The pertinent results are: a) when the absolute value of the D-term exceeds the absolute value of the J-term a localized state splits out of the exciton band; b) two localized states are formed for thin crystals; however, the splitting between the localized states decreases rapidly, as the ratio D/J or the thickness of the crystal increases. The two localized states form a pair of degenerate states in the limit of an infinite crystal; and c) the localization of the exciton on the surface of the crystal is increased with the increase of D/J. The exciton is partially localized on crystal planes adjacent to the surface plane. However this localization falls off rapidly with the increase of distance from the surface plane

OPTICAL PROPERTIES OF CLUSTERS IN MIXED MOLECULAR CRYSTALS AND APPLICATION TO BENZENE

$^{1}$J. Hoshen and J. Jortner, J. Chem. Phys. 56, 4138 (1972).""Author Institution: Department of Chemistry, The University of MichiganA new formalism is given for the optical absorption spectra generated by clusters of guest molecules in substitutionally disordered molecular crystals. The cluster method presented is an extension of the formalism given by Hoshen and $Jortner^{1}$ for calculating the density of states for clusters in mixed molecular crystals. Optical properties are calculated for a one and two dimensional cluster. Results will be compared with experimental data for benzene vibrational excitons

On the application of group theory to molecular excitons

In this paper a group theoretical approach was employed for the classification and construction of molecular exciton wavefunctions for two important crystal structures (naphthalene--anthracene and benzene), utilizing the representation theory of finite groups. The generally valid scheme requires only cyclic boundary conditions (being explicitly imposed on all space group operations, including rotations and reflections). Even though these symmetry considerations are insufficient to determine crystal wavefunctions belonging to a general k vector, it is still possible to write a simple expression for such wavefunctions. This is achieved for cases where the nonvanishing exciton transfer integrals are confined to molecular interactions along symmetry axes and/or planes.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/22009/1/0000424.pd