Marcus theory

Marcus theory is a theory originally developed by Rudolph A. Marcus, starting in 1956, to explain the rates of electron transfer reactions – the rate at which an electron can move or jump from one chemical species (called the electron donor) to another (called the electron acceptor). It was originally formulated to address outer sphere electron transfer reactions, in which the two chemical species only change in their charge with an electron jumping (e.g. the oxidation of an ion like Fe2+/Fe3+), but do not undergo large structural changes. It was extended to include inner sphere electron transfer contributions, in which a change of distances or geometry in the solvation or coordination shells of the two chemical species is taken into account (the Fe-O distances in Fe(H2O)2+ and Fe(H2O)3+ are different). Marcus theory is a theory originally developed by Rudolph A. Marcus, starting in 1956, to explain the rates of electron transfer reactions – the rate at which an electron can move or jump from one chemical species (called the electron donor) to another (called the electron acceptor). It was originally formulated to address outer sphere electron transfer reactions, in which the two chemical species only change in their charge with an electron jumping (e.g. the oxidation of an ion like Fe2+/Fe3+), but do not undergo large structural changes. It was extended to include inner sphere electron transfer contributions, in which a change of distances or geometry in the solvation or coordination shells of the two chemical species is taken into account (the Fe-O distances in Fe(H2O)2+ and Fe(H2O)3+ are different). For electron transfer reactions without making or breaking bonds Marcus theory takes the place of Eyring's transition state theory which has been derived for reactions with structural changes. Both theories lead to rate equations of the same exponential form. However, whereas in Eyring theory the reaction partners become strongly coupled in the course of the reaction to form a structurally defined activated complex, in Marcus theory they are weakly coupled and retain their individuality. It is the thermally induced reorganization of the surroundings, the solvent (outer sphere) and the solvent sheath or the ligands (inner sphere) which create the geometrically favourable situation prior to and independent of the electron jump. The original classical Marcus theory for outer sphere electron transfer reactions demonstrates the importance of the solvent and leads the way to the calculation of the Gibbs free energy of activation, using the polarization properties of the solvent, the size of the reactants, the transfer distance and the Gibbs free energy Δ {displaystyle Delta } G0 of the redox reaction. The most startling result of Marcus' theory was the 'inverted region': whereas the reaction rates usually become higher with increasing exergonicity of the reaction, electron transfer should, according to Marcus theory, become slower in the very negative Δ {displaystyle Delta } G0 domain. Scientists searched the inverted region for proof of a slower electron transfer rate for 30 years until it was unequivocally verified experimentally in 1984. R.A. Marcus received the Nobel Prize in Chemistry in 1992 for this theory. Marcus theory is used to describe a number of important processes in chemistry and biology, including photosynthesis, corrosion, certain types of chemiluminescence, charge separation in some types of solar cells and more. Besides the inner and outer sphere applications, Marcus theory has been extended to address heterogeneous electron transfer. Chemical reactions may lead to a substitution of a group in a molecule or a ligand in a complex, to the elimination of a group of the molecule or a ligand, or to a rearrangement of a molecule or complex. An electron-transfer reaction may, however, also cause simply an exchange of charges between the reactants, and these redox reactions without making or breaking a bond seem to be quite simple in inorganic chemistry for ions and complexes. These reactions often become manifest by a change of colour, e.g. for ions or complexes of transition metal ions, but organic molecules, too, may change their colour by accepting or giving away an electron (like the herbicide Paraquat (N,N-dimethyl-4,4'-bipyridinium dichloride) which becomes blue when accepting an electron, thence the alternative name of methyl viologen). For this type of electron-transfer reactions R.A. Marcus has developed his theory. Here the trace of argument and the results are presented. For the mathematical development and details the original papers should be consulted.