R.W. Munn

Polarization energy of a localized charge in a molecular crystal

Abstract A method is developed which gives an explicit self-consistent algebraic expression for the polarization energy of a point charge localized in a perfect molecular crystal in terms of Fourier transformed lattice multipole sums. An exact macroscopic expression is derived for the long-range contribution. Calculations of the polarization energy in anthracene and naphthalene are presented for several molecular polarizabilities. The results confirm those obtained by the self-consistent polarization field method and agree with experiment, though the point-molecule approximation is not strictly adequate. The method may be extended to calculate the forces on molecules and the electron-phonon coupling due to polarization fluctuations.

Calculation and spectroscopic assignment of charge-transfer states in solid anthracene, tetracene and pentacene☆

Abstract The Fourier-transform method of calculating polarization energies is used to evaluate the energies of electron-hole pairs in anthracene, tetracene and pentacene crystals as a function of separation, r. Charge-quadrupole interactions are included which refine and extend previous calculations on anthracene. Detailed analysis of the long-range behaviour shows that the total electrostatic energy has the coulombic 1/r dependence, mediated by an apparent dielectric constant which depends on direction, varying more weakly than the dielectric tensor itself and in the opposite sense. The calculated charge-transfer (CT) energies determine the potential for the CT eigenstates of the crystal hamiltonian. Several methods to approximate these states are discussed and a generalization of the Merrifield-Choi model is adopted for their description. It is shown that the lowest CT state is split by electron-transfer interaction between translationally equivalent molecules in the unit cell. By combining the calculated electronic eigenvalues with the expected vibrational structure of the CT states, a satisfactory assignment is obtained for all CT bands observed by Sebastian, Weiser, Peter and Bassler in the electro-absorption spectra of anthracene, tetracene and pentacene. This assignment is shown to be in qualitative agreement with the observed intensity distributions. The results of this spectroscopic analysis are compared with observed yields of optically generated charge carriers produced by isothermal dissociation of CT states. The available experimental results are shown to be consistent with the assumption that this process involves direct optical population of both electronic and vibronic CT levels, the latter relaxing vibrationally before (or independent of) their diffusive dissociation.

Polarization energy of a localized charge in a molecular crystal. II. Charge-quadrupole energy

Abstract The apparent polarization energy of a localized charge in a molecular crystal comprises charge-induced-dipole, charge-permanent-multipole and lattice relaxation contributions. An expression is derived for the charge-quadrupole energy WQ, which includes a macroscopic part. For benzene, WQ is ∓0.037 eV, for naphthalene ∓0.111 eV, for anthracene ∓0.168 eV, and for biphenyl ∓0.116 eV (upper sign for holes, lower for electrons). These values imply significant differences between electron and hole apparent polarization energies.

Polarization energy of a localized charge in a molecular crystal. III submolecule treatment

Abstract The Fourier-transforn method of calculating polarization energies for localized charges is extended to treat molecules as sets of submolecules. This takes account of molecular size, shape and orientation, and is essential to obtain results for highly anisotropic molecules in an internally consistent way. Results are presented for naphthalene and anthracene, and (for the first time) for benzene, biphenyl and p-terphenyl; with each aromatic ring treated as a submolecule, variations between crystals are mostly small. Concentrating the excess charge on one ring gives polarization energies of typically −1.3 to −1.4 eV, whereas spreading the charge uniformly over all rings gives −1.1 to −1.2 eV. Combined with calculatedion-quadropole energies, these results can be compared with experimental values from photoemission and photoconductivity studies. They imply lattice relaxation energies of −0.2 to −0.4 eV.

Effective molecular polarizabilities in some aromatic hydrocarbon crystals

Abstract Two equivalent methods of calculating effective molecular polarizabilities from crystal electric susceptibilities are compared. For monoclinic crystals containing two molecules per unit cell, there is no unique solution. The range of solutions is examined for naphthalene, anthracene, biphenyl, p -terphenyl and phenanthrene, treated as polarizable points. For all these molecules the largest polarizability component is unacceptable, owing to the point molecule approximation. When the interactions between molecules are calculated as averages between aromatic rings, more realistic polarizabilities result, showing variations consistent with the molecular geometry. Comparable results are obtained for benzene (orthorhombic). It is concluded that reliable polarizabilities should become available by developments of such an approach.

Microscopic dielectric theory for molecular crystals

Abstract Explicit expressions are derived for the microscopic electron density response function and the direct and inverse dielectric function of molecular crystals in the point dipole approximation. The results allow specifically molecular treatments to be related to general theories of the solid state. Extensions incorporating a molecular polarizability response distributed over a finite molecular volume are examined. A uniform polarizability response of this kind allows the point dipole algebra to be retained with electric fields averaged over molecular volumes. The submolecule treatment introduced previously is a special case of this approximation.

Raman intensities of lattice vibrations in molecular crystals

Abstract An exact expression within the point-dipole rigid-molecule approximation is derived for the intensity of polarized Raman scattering from lattice modes in molecular crystals. By treating the local electric field properly, the method gives the contribution to the intensity from translational motions as well as rotational ones. The intensity varies as the fourth power of the local field correction for both types of motion. It also depends on the polarization vectors of the lattice modes and the effective molecular polarizability. Methods for obtaining these quantities are discussed. Numerical calculations for the pure rotational modes in hexachlorobenzene and naphthalene crystals show that the intensifies are very sensitive to the input data, making it difficult to draw conclusions from a comparison with measured intensifies.

Theoretical interpretation of the electroabsorption spectrum of fullerene films

A three-dimensional analogue of the Merrifield model of the coupling between the Frenkel and charge transfer (CT) excitations of a molecular crystal is used to calculate the electroabsorption (EA) spectrum of buckminsterfullerene films. The approach is essentially nonempirical, with most of the input parameters estimated from theoretical calculations or from independent experiments, but in doubtful cases a comparison of the calculated and experimental EA spectra guides the choice between alternative sets of parameters. Semiquantitative agreement between the calculated and experimental EA spectra lends credence to the model, which can therefore be used to draw conclusions concerning the underlying physical mechanisms. The EA signal of the CT states is shown to be substantially affected by the off-diagonal CT interactions, and by interactions with the optically inactive Frenkel excitons, whose intramolecular parentage is tentatively assigned. The results confirm the validity of previous calculations of the ...

Theoretical calculation of the electro-absorption spectrum of the α-sexithiophene single crystal

An extended two-dimensional analogue of the Merrifield model of the mixing between Frenkel and charge-transfer excitons is used to calculate the electro-absorption spectrum of the α-sexithiophene single crystal. The model reflects the symmetry of the crystal and takes into account all the major interactions between the molecules. The input parameters are estimated from independent quantum-chemical and micro-electrostatic calculations. The simulated spectrum is in very good agreement with experiment, both in shape and in absolute amplitude. The results demonstrate that the eigenstates of the crystal between 2.55 and 2.85 eV are primarily of charge-transfer parentage, so that charge-transfer contributions dominate the electro-absorption spectrum in that region. This first successful reproduction of the electro-absorption spectrum of a single crystal is a stringent test of the theoretical description that confirms its validity.

Charge-transfer exciton band structure in the fullerene crystal-model calculations

A three-dimensional analog of the Merrifield model of the coupling between Frenkel and charge-transfer (CT) excitons of the C60 fullerene crystal is presented. The model is based on the nearest-neighbor approximation for the off-diagonal interactions and is essentially nonempirical. The parameters are estimated from free-molecule data and from the results of theoretical calculations published by other authors. The band structure of CT excitons in C60 is calculated and discussed in the context of available experimental evidence. Residual ambiguities in the parametrization are removed by calculation of the electroabsorption spectrum and comparison with experiment, as described in the accompanying paper.