Reorganization energies and spectral densities for electron transfer problems in charge transport materials

In describing the dynamics of electron transfer or charge transport, the reorganization energy and the spectral density function describe the influence of nuclei motion to the transporting electron. The spectral density can be obtained using various theoretical approaches: from a model of dielectric response, or calculated with various computational means. With the vast advancement of modern computational techniques, many details in vibronic coupling can be obtained, including those described in the early literature. In this work, we provide a comprehensive understanding of the nature of vibronic coupling in light of some early literature. The theoretical connection among different quantities for vibronic coupling is discussed, followed by a brief review of the spectral density function. Various approaches and some of the results for the spectral density function are also reviewed. The importance of low-frequency bands in nonpolar systems that can be overlooked is also discussed, for both Holstein and Peierls types of electron-phonon couplings.