The new theory of electron transfer. Thermodynamic potential profiles in the inverted and superverted regions

In a previous paper (S Fletcher, J Solid State Electrochem 11:965, 2007) a non-Marcus theory of electron transfer was developed, with results applicable to the normal region of thermodynamic driving forces. In the present paper, the theory is extended to highly exergonic reactions (the inverted region) and to highly endergonic reactions (the superverted region). The results are presented mathematically and in the form of Gibbs energy profiles plotted against a charge fluctuation reaction coordinate. The new theory utilizes the concept of donor and acceptor “supermolecules,” which consist of conventional donor and acceptor species plus their associated ionic atmospheres. The key findings are as follows. (1) In the inverted region, donor supermolecules are positively charged both before and after the electron transfer event. (2) In the normal region, donor supermolecules change polarity from negative to positive during the electron transfer event. (3) In the superverted region, the donor supermolecule is negatively charged both before and after the electron transfer event. This overall pattern of events makes it possible for polar solvents to catalyse electron transfer in the inverted and superverted regions. Because this new effect is predicted only by the present theory and not by the Marcus theory, it provides a clear means of distinguishing between them.     

A non-Marcus model for electrostatic fluctuations in long range electron transfer

We propose a new model for the elementary act of electron transfer between two species in solution. The central idea is that the solution in the immediate vicinity of each species may be represented by an equivalent circuit consisting of a Debye circuit shunted by a resistor. Based on this insight, we derive a new formula for the one-dimensional potential energy profile of a coupled donor–acceptor pair at finite (but large) separation d, along a charge-fluctuation reaction co-ordinate, at fixed radii of the transition states. The corresponding reorganisation energy of the reaction is also derived, and it is found to differ from that in the Marcus theory. In particular, the new model predicts that the reorganisation energy is independent of the static dielectric constant of the solution, whereas the old model predicts a strong dependence. The difference is traced to the fact that the Marcus theory omits consideration of the work required to form the charge fluctuations and focuses instead on the work required to localise the charge fluctuations. In general, the equivalent circuit approach permits many of the difficult-to-derive equations of non-equilibrium polarisation theory to be written down by inspection.     

Electron transfer rates and Franck–Condon factors: an application to the early electron transfer steps in photosynthetic reaction centers

Mechanistic aspects of some of the early electron transfer steps occurring in photosynthetic reaction centers are discussed. Starting from the normal modes of the redox cofactors involved in the electron transfer processes, we show how a series of quantities which regulate electron transfer rates, such as (i) the electron transfer active modes, (ii) the intramolecular reorganization energy, and (iii) the mutual couplings between the vibronic states of the donor and the acceptor, can be obtained and used to draw qualitative conclusions on ET rates.     

Kinetic studies on the single electron transfer reaction between 2, 2, 6, 6-tetramethylpiperidine oxoammonium ions and phenothiazines: the application of Marcus theory

Electron transfer reactions take place readily between 2, 2, 6, 6-tetramethylpiperidine oxoammonium ions (1a, 1b) and phenothiazines (2a—2g), giving corresponding nitroxides (3a, 3b) and phenothiazine radical cations (4a—4g). The rate constants for the electron self-exchange reactions between 1 and 3, as well as between 2 and 4, are determined by EPR and ~1H NMR line-broadening effect in acetonitrile. By application of the Marcus theory, the kinetics of the cross-exchange reactions between 1 and 2 is studied.     

Intermolecular electron-self exchange kinetics measured by electron paramagnetic resonance-linebroadening effects: useful rate constants for the application of Marcus theory

The different methods to obtain rate constants of homogeneous intermolecular electron-self exchange reactions in solutions from dynamic linebroadening effects in CW-electron paramagnetic resonance (EPR) spectra are discussed in details. The limitations of the slow and fast exchange region are explained. The medium exchange region is also discussed. Experimental details are given. The exchange rates of the 2-methyl-1,4-naphtoquinone/2-methyl-1,4-napthoquinone radical anion and the 1-nitronaphthalene/1-nitronaphthalene radical anion redox couples are reported to 9.2 · 10⁸ M⁻¹ s⁻¹ (EtOH, 263 K) and 1.8 · 10⁸ M⁻¹ s^-1 (DMF, 266 K), respectively.     

Electrochemical electron transfer and its relation to charge transport in single molecule junctions

Ability to control charge transport at nanometer scale lies in the heart of design of fast reliable electronic devices. Molecular electronics thrive to use functional molecules for such transport. If the molecule contains redox center(s), a diode-like or transistor-like behavior can be easily explored by controlling not only the voltage difference between two metallic contacts of the molecular junction but also the potential of one of the contacting electrodes with respect to some reference. Thus, one needs to understand the relationship between electrochemical electron transfer and charge transport in metal–molecule–metal junctions. This review presents latest theoretical approaches toward understanding of such relationship and discusses pivotal experimental works to validate them. Tunneling and hopping pathways may operate in parallel (two-channel model), but experimental conditions dictate the channel preference.     

Time-dependent bond-current functional theory for lattice Hamiltonians: Fundamental theorem and application to electron transport

The cornerstone of time-dependent (TD) density functional theory (DFT), the Runge-Gross theorem, proves a one-to-one correspondence between TD potentials and TD densities of continuum Hamiltonians. In all practical implementations, however, the basis set is discrete and the system is effectively described by a lattice Hamiltonian. We point out the difficulties of generalizing the Runge-Gross proof to the discrete case and thereby endorse the recently proposed TD bond-current functional theory (BCFT) as a viable alternative. TDBCFT is based on a one-to-one correspondence between TD Peierl’s phases and TD bond-currents of lattice systems. We apply the TDBCFT formalism to electronic transport through a simple interacting device weakly coupled to two biased non-interacting leads. We employ Kohn-Sham Peierl’s phases which are discontinuous functions of the density, a crucial property to describe Coulomb blockade. As shown by explicit time propagations, the discontinuity may prevent the biased system from ever reaching a steady state.     

Theoretical study of the electron transfer reaction of hydrazine with cobalt(II) phthalocyanine and substituted cobalt(II) phthalocyanines

A theoretical model is proposed to explain the trend in reactivity of cobalt(II) phthalocyanine (CoPc) and substituted cobalt(II) phthalocyanines for the oxidation of hydrazine. Our study suggests that the reaction occurs via a through bond charge transfer pathway and not via a through space charge transfer pathway as was shown in previous work for the oxidation of 2-mercaptoethanol by CoPc (G.I. Cárdenas-Jirón and D.A. Venegas-Yazigi, J. Phys. Chem. A. 106, 11398 (2002)). We propose a mechanism for the oxidation of hydrazine based on a four-step energy profile which agrees with a mechanism proposed for the electro-oxidation of hydrazine mediated by cobalt phthalocyanines confined on a graphite electrode. We show that the step in the energy profile that involves formation of a radical of hydrazine seems to be a good starting point for the study of the transfer of the first electron in the oxidation of hydrazine mediated by different substituted cobalt(II) phthalocyanines.     

Nonperturbative quantum simulation of time-resolved nonlinear spectra: Methodology and application to electron transfer reactions in the condensed phase

A quantum dynamical method is presented to accurately simulate time-resolved nonlinear spectra for complex molecular systems. The method combines the nonpertubative approach to describe nonlinear optical signals with the multilayer multiconfiguration time-dependent Hartree theory to calculate the laser-induced polarization for the overall field–matter system. A specific nonlinear optical signal is obtained by Fourier decomposition of the overall polarization. The performance of the method is demonstrated by applications to photoinduced ultrafast electron transfer reactions in mixed-valence compounds and at dye–semiconductor interfaces.     

细菌光合反应中心突变体原初电子转移机理的理 论研究

利用量子化学DFT从头计算方法,计算经过突变的细菌光合反应中心HM202L原始电子给体和其他色素分子的电子结构,然后对其原初电子转移机理进行探讨。结果表明：1)超分子D-2A的HOMO主要是由定域在其组成单元BChl~L分子上的原子轨道组成,而它的LUMO主要是由定域在其组成单元MBPheo~M分子上的原子轨道组成。这表明它在基态的激发态时分别存在超分子内的电荷分离态[BChl~L^--MBPheo~M^+]和[BChl~L^+-MBPheo~M^-]。同时也说明了D-2A阳离子态的正电荷完全分布在组成单元细菌叶绿素分子BChl~L上,与实验事实相符。2)HM202L细菌光合反应中心原初电子转移反应存在由ABCha~L^h^*驱动的电子转移反应。     

Self-consistent reaction field calculation of solvent reorganization energy in electron transfer: a dipole-reaction field interaction model

Based on the continuum dielectric model, this work has established the relationship between the solvent reorganization energy of electron transfer (ET) and the equilibrium solvation free energy. The dipole-reaction field interaction model has been proposed to describe the electrostatic solute-solvent interaction. The self-consistent reaction field (SCRF) approach has been applied to the calculation of the solvent reorganization energy in self-exchange reactions. A series of redox couples, O₂/O⁻ ₂, NO/NO⁺, O₃/O⁻ ₃, N₃/N⁻ ₃, NO₂/NO⁺ ₂, CO₂/CO⁻ ₂, SO₂/SO⁻ ₂, and ClO₂/ClO⁻ ₂, as well as (CH₂)₂C-(-CH₂-) _n -C(CH₂)₂ (n=1 ∼ 3) model systems have been investigated using ab initio calculation. For these ET systems, solvent reorganization energies have been estimated. Comparisons between our single-sphere approximation and the Marcus two-sphere model have also been made. For the inner reorganization energies of inorganic redox couples, errors are found not larger than 15% when comparing our SCRF results with those obtained from the experimental estimation. While for the (CH₂)₂C–(–CH₂–) _n –C(CH₂)₂ (n=1 ∼ 3) systems, the results reveal that the solvent reorganization energy strongly depends on the bridge length due to the variation of the dipole moment of the ionic solute, and that solvent reorganization energies for different systems lead to slightly different two-sphere radii. Received: 19 April 2000 / Accepted: 6 July 2000 / Published online: 27 September 2000     

Leading coordinate analysis of reaction pathways in proton chain transfer: Application to a two-proton transfer model for the green fluorescent protein

The ‘leading coordinate’ approach to computing an approximate reaction pathway, with subsequent determination of the true minimum energy profile, is applied to a two-proton chain transfer model based on the chromophore and its surrounding moieties within the green fluorescent protein (GFP). Using an ab initio quantum chemical method, a number of different relaxed energy profiles are found for several plausible guesses at leading coordinates. The results obtained for different trial leading coordinates are rationalized through the calculation of a two-dimensional relaxed potential energy surface (PES) for the system. Analysis of the 2-D relaxed PES reveals that two of the trial pathways are entirely spurious, while two others contain useful information and can be used to furnish starting points for successful saddle-point searches. Implications for selection of trial leading coordinates in this class of proton chain transfer reactions are discussed, and a simple diagnostic function is proposed for revealing whether or not a relaxed pathway based on a trial leading coordinate is likely to furnish useful information.     

Electronic coupling in electron transfer and the influence of nuclear modes: theoretical and computational probes

Long-range electronic coupling of local donor and acceptor sites is formulated in the context of thermal and optical electron transfer and then illustrated with examples based on electronic structure calculations. The relationship of the calculated results to available experimental kinetic and optical data is discussed in detail. The influence of nuclear modes on the magnitude of the coupling (i.e., departures from the Condon approximation) is investigated in terms of both discrete molecular modes and solvent modes, and a general expression is presented for the modulation of the superexchange tunneling gap by motion along the electron transfer reaction coordinate. AcknowledgementsThe author is grateful to R.J. Cave and M. Rust for making available molecular coordinates for acridinium derivatives, and to R.J. Cave for several valuable discussions. This work was supported by the Division of Chemical Sciences, US Department of Energy, under grant DE-AC02-98CH10886.     

The ring opening of cyclopropylidene to allene: global features of the reaction surface

Summary The global features of the groundstate ring opening of cyclopropylidene to allene are studied by means ofab-initio FORS MCSCF calculations based on a minimal AO basis set. The energy surface is completely mapped out in terms of three reaction coordinates, namely the CCC ring-opening angle and two angles describing the rotations of the CH₂ groups. For each choice of these three variables, the twelve remaining internal coordinates are optimized by energy minimization. In the initial phase of the reaction, as the CCC angle opens, the CH₂ groups rotate in a disrotatory manner, maintainingC _s symmetry. This uphill reaction path leads to a transition region which occurs early, for a CCC angle of about 84°. In this transition region the reaction path branches into two pathways which are each others' mirror images. The system exhibits thus abifurcating transition region. Passed this region, the two pathways are overall conrotatory in character. However, these downhill reaction paths to the products are poorly defined because, from a CCC opening angle of about 90° on,the CH ₂ groups can rotate freely and isoenergetically in a synchronized, cogwheel-like manner and this disrotatory motion can mix unpredictably with the conrotatory downhill motion. There is no preference for any one of the two reaction pathways yielding the two stereoisomers of allene and the reaction is thereforenonstereospecific with respect to the numbered hydrogen atoms. The global surface is documented by means of contour maps representing slices corresponding to constant CCC angles. The bifurcating transition region is mapped in detail.Operated for the U.S. Department of Energy by Iowa State University under Contract No. 7405-ENG-82. This work was supported by the office of Basic Energy Sciences     

The influence of formamide (model of protein unit) on the intramolecular proton transfer in the DNA simple base guanine: A density functional theory study

For the purpose of investigating the influence of protein unit on the intramolecular proton transfer (IPT) reactions in the simple base guanine, a simple model (formamide) of peptides is designed to biological system investigations, and five complexes of formamide–guanine (FG1, FG2, FG3, FG4, and FG5) are determined at the B3LYP/6‐311++G(d,p) level of theory. For comparison, HF and MP2 methods are also used in this paper. The proton transfer (PT) reaction processes of guanine and FGs have been investigated employing the B3LYP/6‐311++G(d,p) level of theory. The selected thermodynamic and kinetic parameters, such as the activation energies (E_a), changes of enthalpy (ΔH) and changes of free energies (ΔG), as well as the equilibrium constants (K_p) for those reaction processes, have also been obtained by calculational means. The calculated results indicate that the assisted and protected effects of formamide on IPT in guanine are site‐dependent. CH1 is the lowest activation energy needed PT process no matter where the formamide molecule is located in. The activation energy of CH1 with formamide in S2 is the lowest one (153.3 KJ/mol), whereas the one of CH5 with formamide in S5 is the highest (318.3 KJ/mol). © 2008 Wiley Periodicals, Inc. Int J Quantum Chem, 2008