Analytical Model for the Molecular Ionization Energy in an External Electric Field

A model for the molecular ionization energy in an applied electric field is presented based on a perturbation expansion in the electric field. The leading term arises from the Frenkel approach, which is the same for all molecules, normally used in the Poole-Frenkel model for the conductivity in an electric field. For a set of test molecules, the results are of comparable quality to previous results using constrained density functional theory. It is concluded that the Frenkel term is dominant and sufficient at relatively low fields and that the dipole and polarizability terms, the leading terms dependent on the properties of the individual molecule, give a significant contribution only at high fields and for relatively large molecules. Since the presented model is analytical, quantum chemical calculations are avoided for a variety of electric field strengths and molecular orientations, and the model can therefore be applied directly in coarse-grained models for electronic processes in dielectric condensed phases.