Theory of the Stark Effect in protein systems containing an electron donor–acceptor couple

Mixed-valency can occur in a variety of biological systems, such as the Cu(I)–Cu(II) pair in hemocyanin, Fe(II)–Fe(III) in many iron–oxo and iron–sulfur proteins, and Mn(II)–Mn(III) or Mn(III)–Mn(IV) in the photosynthetic water oxidase. The characterization of the ground states of such systems often has been controversial. Stark Effect spectroscopy is proving to be a valuable tool for the elucidation of systems of this type. The purpose of the present work is to develop theory for the spectral lineshape for the case where the electron donor and acceptor are coupled directly in a strong electric field. A mixed-valence dimer with an applied electric field aligned along the internuclear axis is studied using a two-site small-polaron model. Potential energy surfaces are calculated in the adiabatic (Born–Oppenheimer) approximation. It is shown that two nuclear coordinates (one totally symmetric and one antisymmetric) are coupled to the electronic motion, whereas only the antisymmetric coordinate is coupled in the absence of an electric field. For a strongly localized system, such as a protein system where electron donor and acceptor sites are separated by large distances, the potential surfaces become highly asymmetrical, but coupling to the totally symmetric mode is not significant. For a localized case corresponding to a valence-trapped two-metal cluster, the displacement along the totally symmetric coordinate is directly proportional to the applied field strength. Along the antisymmetric coordinate, the lowest potential surface is an asymmetric double well. For a delocalized (valence-averaged) two-metal cluster, there is significant displacement along the antisymmetric coordinate, an effect which also vanishes in the absence of an applied field. Contributions to the linewidth are estimated. Localized systems show larger field-induced shift in frequency maximum, whereas delocalized systems show greater field-induced line broadening.