Non-negligible Outer-Shell Reorganization Energy for Charge Transfer in Nonpolar Systems

Many charge-transporting molecular systems function as ordered or disordered arrays of solid state materials composed of nonpolar (or weakly polar) molecules. Due to low dielectric constants for nonpolar systems, it is common to ignore the effects of outer-shell reorganization energy (lambda(out)). However, ignoring lambda(out) has not been properly supported and it can severely impact predictions and insights derived. Here, we estimate lambda(out) by two means: from experimental ultraviolet photoelectron spectra, in which vibronic progression in these spectra can be fitted with the widths of peaks determining the low-frequency component in reorganization energy, regarded to be closely associated with lambda(out), and from molecular dynamic (MD) simulation of nonpolar molecules, in which disorder or fluctuation statistics for energies of charged molecules are calculated. An upper bound for lambda(out) was obtained as 505 and 549 meV for crystalline anthracene (140 K) and pentacene (50 K), respectively, by fitting of experimental data, and 212 and 170 meV, respectively, from MD simulations. These values are comparable to the inner-sphere reorganization energy (lambda(in)) arising from intramolecular vibration. With corresponding spectral density functions calculated, we found that lambda(out) is influenced both by low- and high-frequency dynamics, in which the former arises from constrained translational and rotational motions of surrounding molecules. In an amorphous state, about half of the lambda(out)'s obtained are from high-frequency components, which is quite different from the conventional polar solvation. Moreover, crystalline systems exhibit super-Ohmic spectral density, whereas amorphous systems are sub-Ohmic.