Electron transfer at metal surfaces

Abstract

In recent years there has been considerable interest in electrode processes at metal surfaces with alkanethiol monolayers attached to them. One effect of the monolayer is that the electron transfer rate from the redox reagent in solution to the metal (gold or platinum are commonly used) becomes clearly nonadiabatic and the effect of the density of states of the metal on such a rate can be investigated. We develop a way of writing the wave function of a semi-infinite metal using tight-binding matrix elements and the 'Z-transform', a discrete Laplace transform. Using these k-dependent metal wave functions we calculate the coupling matrix element between the metal and the redox reagent and thus the electron transfer rate constant. We then study the effect of changing the density of electronic states at the Fermi level (DOS) of a metal on the rate of nonadiabatic electron transfer by changing the metal. The DOS of platinum is about 7.5 times that of gold, the difference being mainly due to the d-band of Pt. Inspite of this difference, the calculated electron transfer rate constant increases only by a factor of about 1.8. Bands which are weakly coupled (e.g., the d-band of Pt in the present case) contribute much less to the rate constant than is suggested by their density of states. Thereby, the rate constant is approximately independent of the density of states in two cases: adiabatic electron transfer and nonadiabatic electron transfer when the extra density of states is due to weakly coupled bands. Our results are in agreement with experiments performed with systems similar to those used in our calculations. We next employ our method to calculate the temperature dependence of the electronic contribution to the nonadiabatic electron transfer rate constant at metal and semiconductor electrodes. We find that the electronic contribution in metals is proportional to T, and under conditions for the maximum rate constant, that at semiconductor electrodes is also proportional to T, but for different reasons than in the case of metals (Boltzmann statistics and transfer at the conduction band edge for the semiconductor vs. Fermi-Dirac statistics and transfer at the Fermi level, which is far from the band edge, of the metal). On a different topic, we study the inverse photoemission spectra at metal electrode-liquid interfaces. In such experiments, an electron transfer redox agent was used to inject electrons or holes into a metal and create excited electronic states of the metal. Emission thus occurs in competition with energy loss and radiationless transitions. Some of the excited states decay radiatively and gave a frequency-dependent spectrum. The spectrum may be analysed to probe the electronic structure of the metal above and below its Fermi level. The experimental technique, known in the literature as charge transfer inverse photoemission spectroscopy (CTRIPS), is treated theoretically here. We give a possible explanation of the data using a model, experimental band structures (from vacuum inverse photemission) and surface states from solution electroreflectance (ER) experiments and propose experiments that could be performed to further clarify the mechanism of electron transfer.