On the theory of tunnelling in electron and proton transfer reactions

The concept of tunnelling in the theory of electron and proton transfer reactions has recently been questioned on the ground that the situation is a non-stationary one. It has been suggested that time-dependent perturbation theory should be applied to obtain the quantum mechanical transition probability. We have done this for a square barrier. The result for most reactions is the same as obtained by the WKB approximation.     

An electron density based analysis to establish the electronic adiabaticity of proton coupled electron transfer reactions

Electrons and protons are the main actors in play in proton coupled electron transfer (PCET) reactions, which are fundamental in many biological (i.e., photosynthesis and enzymatic reactions) and electrochemical processes. The mechanism, energetics and kinetics of PCET reactions are strongly controlled by the coupling between the transferred electrons and protons. Concerted PCET reactions are classified according to the electronical adiabaticity degree of the process. To discriminate among different mechanisms, we propose a new analysis based on the use of electron density based indexes. We choose, as test case, the 3-Methylphenoxyl/phenol system in two different conformations to show how the proposed analysis is a suitable tool to discriminate between the different degree of adiabaticity of PCET processes. The very low computational cost of this procedure is extremely promising to analyze and provide evidences of PCET mechanisms ruling the reactivity of many biological and catalytic systems.     

Dissociative electron transfer reactions

We consider recent data on dissociative electron transfer reactions in which the electron transfer causes practically concerted dissociation of the chemical bond in the reagent. We discuss considerable experimental data on reactions in the gas phase and in solutions, and also existing theoretical models for describing the kinetics of these complex processes. Translated from Teoreticheskaya i éksperimental’naya Khimiya, Vol. 34, No. 2, pp. 67–78, March–April, 1998.     

Light-induced electron transfer reactions

The reactions of the luminescent excited states of the polypyridine-ruthenium(II) complexes (^*RuL₃²⁺) with electron acceptors and donors are discussed. These electron transfer reactions convert the excited state into RuL₃³⁺ and RuL₃⁺, respectively. The former ruthenium complex is a more powerful oxidant and the latter is a more powerful reductant than the excited state itself. Some applications of these complexes in the conversion and storage of solar energy are presented. Theoretical models for electron transfer reactions are described and the implications of these models for the quenching and back electron transfer reactions are discussed. It is pointed out that the exploitation of the inverted region may provide a useful means of slowing down back electron transfer reactions.     

Correlation balance in basis sets for electronic structure calculations

The balanced addition of polarization functions to the 6–31G and 6–311G basis sets for correlated wave functions is evaluated using bond energy predictions at the MP 2 and full MP 4 levels as a measure of correlation-balanced basis sets. The homolytic dissociations of the XH bonds in H₂, CH₄, NH₃, H₂O, and HF and the XY bonds in C₂H₆, NH₂NH₂, HOOH, and CH₃OH are used as the basis for the evaluation. It is found that correlation balance is achieved for HH, XH, and XY bonds, particularly at the MP 2 level, only if at least as many polarization sets, and sometimes more, are added to the hydrogens as are added to the heavy atoms.     

Photochemical electron transfer reactions in alkylcobaloximes

It is shown that photolysis with visible light (λ > 420 nm) of any alkylcobaloxime procedes via a mechanism involving an initial electron transfer reaction from an equatorial ligand to the central metal to produce a cobalt(II) species which retains both original axial ligands. In a subsequent rearrangement of the equatorial ligand a hydrogen atom is ejected.     

The theory of electron transfer

This article provides an overview of the theory of electron transfer. Emphasis is placed on the history of key ideas and on the definition of difficult terms. Among the topics considered are the quantum formulation of electron transfer, the role of thermal fluctuations, the structures of transition states, and the physical models of rate constants. The special case of electron transfer from a metal electrode to a molecule in solution is described in detail.     

Nonadiabatic theory of electron transfer

Tunneling between potential wells is considered as affected by random nonadiabatic change in the resonance condition. A general expression is derived for the transition probability on the assumption that the process involves only two states of the discrete spectrum. Detailed consideration is given to the case of an electron localized by the polarized layer it produces.     

Activation entropy of electron transfer reactions

We report microscopic calculations of free energies and entropies for intramolecular electron transfer reactions. The calculation algorithm combines the atomistic geometry and charge distribution of a molecular solute obtained from quantum calculations with the microscopic polarization response of a polar solvent expressed in terms of its polarization structure factors. The procedure is tested on a donor–acceptor complex in which ruthenium donor and cobalt acceptor sites are linked by a four-proline polypeptide. The reorganization energies and reaction energy gaps are calculated as a function of temperature by using structure factors obtained from our analytical procedure and from computer simulations. Good agreement between two procedures and with direct computer simulations of the reorganization energy is achieved. The microscopic algorithm is compared to the dielectric continuum calculations. We found that the strong dependence of the reorganization energy on the solvent refractive index predicted by continuum models is not supported by the microscopic theory. Also, the reorganization and overall solvation entropies are substantially larger in the microscopic theory compared to continuum models.     

Pathway analysis of super-exchange electronic couplings in electron transfer reactions using a multi-configuration self-consistent field method

We present a novel pathway analysis of super-exchange electronic couplings in electron transfer reactions using localized molecular orbitals from multi-configuration self-consistent field (MCSCF) calculations. In our analysis, the electronic coupling and the tunneling pathways can be calculated in terms of the configuration interaction (CI) Hamiltonian matrix obtained from the localized MCSCF wave function. Making use of the occupation restricted multiple active spaces (ORMAS) method can effectively produce the donor, acceptor, and intermediate configuration state functions (CSFs) and CIs among these CSFs. In order to express the electronic coupling as a sum of individual tunneling pathways contributions, we employed two perturbative methods: L?wdin projection-iteration method and higher-order super-exchange method. We applied them to anion couplings of butane-1,4-diyl and pentane-1,5-diyl. The results were (1) the electronic couplings calculated from the two perturbative methods were in reasonable agreement with those from a non-perturbative method (one-half value of the energy difference between the ground and first excited states), (2) the main tunneling pathways consisted of a small number of lower-order super-exchange pathways where bonding, anti-bonding, or extra-valence-shell orbitals were used once or twice, and (3) the interference among a huge number of higher-order super-exchange pathways significantly contributed to the overall electronic coupling, whereas each of them contributed only fractionally. Our method can adequately take into account both effects of non-dynamical electron correlation and orbital relaxation. Comparing with the analyses based on the Koopmans' theorem (ignoring both effects) and the ORMAS-CIs from frozen localized reference orbitals (ignoring the effect of orbital relaxation), we discuss these effects.     

Photochemical electron transfer reactions of tirapazamine

The absorption and fluorescence spectra of 3-aminobenzo-1,2,4-triazine di-N-oxide (tirapazamine) have been recorded and exhibit a dependence on solvent that correlates with the Dimroth ET30 parameter. Time-dependent density functional theory calculations reveal that the transition of tirapazamine in the visible region is pi-->pi* in nature. The fluorescence lifetime is 98+/-2 ps in water. The fluorescence quantum yield is approximately 0.002 in water. The fluorescence of tirapazamine is efficiently quenched by electron donors via an electron-transfer process. Linear Stern-Volmer fluorescence quenching plots are observed with sodium azide, potassium thiocyanate, guanosine monophosphate and tryptophan (Trp) methyl ester hydrochloride. Guanosine monophosphate, tyrosine (Tyr) methyl ester hydrochloride and Trp methyl ester hydrochloride appear to quench the fluorescence at a rate greater than diffusion control implying that these substrates complex with tirapazamine in its ground state. This complexation was detected by absorption spectroscopy.     

Protein dynamics and electronic fluctuation effects in electron transfer reactions of membrane-bound proteins and metalloprotein complexes

We have analyzed specific long-range features of the electron transfer reactions in the cytochrome c/cytochrome b₅ complex, and the bacteriopheophytin/quinone and quinone/bacteriochlorophyll special pair cation radical long-range electron transfers. The analysis rests on an electron transfer theory which incorporates vibrational dispersion in the protein and solvent environments, and environmental fluctuation effects on the electronic transmission coefficient.The dispersion represents broadly the “inverse” temperature dependence of the photosynthetic reactions, but an explicit temperature dependence of the rate parameters is needed for quantitative data agreement. The data suggest that the transmission coefficient may exhibit some reaction free energy and temperature dependence caused by fluctuations in the environmental nuclear motion. The data are presently insufficiently diagnostic in this respect, but transmembrane potential induced rate variations over wide temperature ranges could lead to its clarification.     

Salt effects in photoinduced electron transfer reactions

Metal salts and oxygen react synergistically to inhibit back-electron-transfer in photoinduced reactions.     

Using many-particle basis sets for electronic energy calculations of molecules

A method of calculating the electronic energies of molecules using a many-particle basis set is proposed. In this case, the many-particle Schrödinger equation may be solved without resorting to the one-electron approximation. The results of the electronic energy calculations of some two-electron systems are in good agreement with experimental results.     

Optimized effective potentials from electron densities in finite basis sets

The Wu-Yang method for determining the optimized effective potential (OEP) and implicit density functionals from a given electron density is revisited to account for its ill-posed nature, as recently done for the direct minimization method for OEP's from a given orbital functional [T. Heaton-Burgess, F. A. Bulat, and W. Yang, Phys. Rev. Lett. 98, 256401 (2007)]. To address the issues on the general validity and practical applicability of methods that determine the Kohn-Sham (local) multiplicative potential in a finite basis expansion, a new functional is introduced as a regularized version of the original work of Wu and Yang. It is shown that the unphysical, highly oscillatory potentials that can be obtained when unbalanced basis sets are used are the controllable manifestation of the ill-posed nature of the problem. The new method ensures that well behaved potentials are obtained for arbitrary basis sets.     

Barrierless electron transfer bond fragmentation reactions

The ultrafast N-O bond fragmentation in a series of N-methoxypyridyl radicals, formed by one-electron reduction of the corresponding N-methoxypyridiniums, has been investigated as potentially barrierless electron-transfer-initiated chemical reactions. A model for the reaction involving the electronic and geometric factors that control the shape of the potential energy surface for the reaction is described. On the basis of this model, molecular structural features appropriate for ultrafast reactivity are proposed. Femtosecond kinetic measurements on these reactions are consistent with a kinetic definition of an essentially barrierless reaction, i.e., that the lifetime of the radical is a few vibrational periods of the fragmenting bond, for the p-methoxy-N-methoxypyridyl radical.     

Energetics of electron transfer reactions in polar solvents

The free energy change of an electron transfer reaction in a polar solvent is rigorously analyzed within the framework of the dielectric continuum model. An appropriate expression for the electrostatic energy between the two product ions separated by R is derived. The present result does not support a recent claim by Suppan that, if R is close to the contact distance, the electrostatic energy should be much larger in magnitude than estimated from the usual expression −e²/ε_sR.