Models for Quantum Effects in Electron Transfer:  Co(Cp)₂⁺|V(CO)₆^-

Abstract

We model the absolute electron transfer (ET) rate and the vibrational quantum effects on ET rate previously observed experimentally for the ion pair complex Co(Cp) 2 + |V(CO) 6 -. We find that the absolute rate and vibrational rate effects cannot be predicted by the standard ET methods. In this work we analyze new resonance Raman, absorption, and infrared spectra and combine these results with density functional (DFT) quantum calculations of structure, vibrational modes, and solvent effects to predict absolute electron-transfer rates and vibrational quantum effects for ET. Related DFT calculations on Na + |V(CO) 6are used to support a spectroscopic identification of the ion pair geometry. The ET is from the radical pair state reached by chargetransfer absorption of the ion pair Co(Cp) 2 + |V(CO) 6 -. The weak coupling rate model based on the golden rule model of ET predicts absolute ET rates that are 135 times too large. From our DFT calculations on Co(Cp) 2 |V(CO) 6 we conclude that a small Jahn-Teller geometry change in both radicals can reduce the orbital overlap and electronic coupling in the radical pair state so that the effective coupling matrix element is much smaller than the 417 cm -1 inferred from the absorption spectrum. A new study of the electronic coupling versus geometry is required to test this suggestion versus the possibility that the weak coupling model is inappropriate for our molecule. The standard model, which emphasizes totally symmetric vibrations, also cannot explain prior experimental ET rates for quantum populations (V ) 0, 1, 2) in the nontotally symmetric CO stretching mode. These rate effects likely involve a fast IVR conversion from totally symmetric vibrations to IR active CO stretching motions followed by ET. The vibrational quantum effect on ET probably is caused by a breakdown in the Condon approximation, where an increase in the quantum number of vibration increases the electronic coupling matrix element. The models suggest a number of new experiments to probe the mechanism of ET in weak coupled molecules.

Using Resonance Raman Spectroscopy To Examine Vibrational Barriers to Electron Transfer and Electronic Delocalization

“…These problems would seem to invite the discovery and development of improved, or altogether new, experimental probes. A partial list of candidate problems could include the following: (a) mode-specific reorganizational energetics of the solvent, (b) breakdown of the Born−Oppenheimer approximation (separability of nuclear and electronic motion), (c) “down stream” structural changes, i.e., changes that are initiated only after the photoexcited system moves out of the Franck−Condon region, and (d) the role of coherent vibrational and electronic phenomena …”

Vibrational State Dependence of Interfacial Electron Transfer: Hot Electron Injection from the S1 State of Azulene into TiO2 Nanoparticles

“…In nearly all reported cases isolated molecular systems in the gas phase were investigated . Only a handful of successful examples in the condensed phase exists, among which the most instructive is the elegant demonstration of vibrational quantum state-specific photoinduced electron transfer reaction in the [V(CO) 6 – /Co(Cp) 2 + ] ion pairs by Spears et al ,, In the case of interfacial processes, it has been realized for some time on kinetic grounds that electron transfer from molecular donors to wide bandgap semiconductors may occur from vibrationally hot states because the commonly observed 10 13 –10 14 s –1 electron injection rates exceed the vibrational relaxation (IVR) rates of small molecules by at least 1 order of magnitude. − Injection of electrons from vibrationally hot donor states is of great interest because it offers the possibility of generating photovoltaic potentials that are higher than those predicted by the equilibrium thermodynamic parameters of the system. More broadly, charge separation occurring faster than the IVR of the excited donor opens the fascinating prospect of state-specific interfacial chemistry in the condensed phase with various degrees of vibrational excitation leading to different products.…”

Giant Cobalticinium Dendrimers

“…Since their first synthesis by Wilkinson in 1952, cobalticinium salts (also named cobaltocenium) have been the subject of attention, because their redox robustness provides a useful electrochemistry and electron-transfer chemistry including very stable (although air -sensitive and reactive) neutral cobaltocene, a so-called “19-electron” complex, and a very electron-rich species, the 20-electron cobaltocene anion . The cobalticinium moiety has been used inter alia to design coordination polymers, organic-organometallic crystals, and metal-containing polymers, for ion pairing with metal−carbonyl anions, for anion recognition, to induce radical polymerization, and as a starting point to build polyolefin and polybenzyl dendritic cores . Although many ferrocenyl dendrimers are known, , there are only few reports on cobalticinium dendrimers, , and the known cobalticinium dendrimers are relatively small.…”