Marcus电子转移理论的科学性探讨

利用科学原理对Marcus电子转移理论的科学性进行了考察, 结果表明Marcus电子转移理论违背了能量守恒定律.     

Activation energy for a model ferrous-ferric half reaction from transition path sampling

Activation parameters for the model oxidation half reaction of the classical aqueous ferrous ion are compared for different molecular simulation techniques. In particular, activation free energies are obtained from umbrella integration and Marcus theory based thermodynamic integration, which rely on the diabatic gap as the reaction coordinate. The latter method also assumes linear response, and both methods obtain the activation entropy and the activation energy from the temperature dependence of the activation free energy. In contrast, transition path sampling does not require knowledge of the reaction coordinate and directly yields the activation energy [C. Dellago and P. G. Bolhuis, Mol. Simul. 30, 795 (2004)]. Benchmark activation energies from transition path sampling agree within statistical uncertainty with activation energies obtained from standard techniques requiring knowledge of the reaction coordinate. In addition, it is found that the activation energy for this model system is significantly smaller than the activation free energy for the Marcus model, approximately half the value, implying an equally large entropy contribution.     

One-dimensional reaction coordinates for diffusive activated rate processes in many dimensions

For multidimensional activated rate processes controlled by diffusive crossing of a saddle point region, we show that a one-dimensional reaction coordinate can be constructed even when the diffusion anisotropy is arbitrary. The rate constant, found using the potential of mean force along this coordinate, is identical to that predicted by the multidimensional Kramers-Langer theory. This reaction coordinate minimizes the one-dimensional rate constant obtained using a trial reaction coordinate and is orthogonal to the stochastic separatrix, the transition state that separates reactants from products.     

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.     

2+3] Cycloaddition of ethylene to transition metal oxo compounds. analysis of density functional results by marcus theory.

Density functional results on the [2+3] cycloaddition of ethylene to various transition metal complexes MO(3)(q) and LMO(3)(q) (q = -1, 0, 1) with M = Mo, W, Mn, Tc, Re, and Os and various ligands L = Cp, CH(3), Cl, and O show that the corresponding activation barriers DeltaE(double dagger) depend in quadratic fashion on the reaction energies DeltaE(0) as predicted by Marcus theory. A thermoneutral reaction is characterized by the intrinsic reaction barrier DeltaE(0) of 25.1 kcal/mol. Both ethylene [2+3] cycloaddition to an oxo complex and the corresponding homolytic M-O bond dissociation are controlled by the reducibility of the transition metal center. Indeed, from the easily calculated M-O bond dissociation energy of the oxo complex one can predict the reaction energy DeltaE(0) and hence, by Marcus theory, the corresponding activation barrier DeltaE. This allows a systematic representation of more than 25 barriers of [2+3] cycloaddition reactions that range from 5 to 70 kcal/mol.     

A one-dimensional energy diffusion approach to multidimensional dynamical processes in the condensed phase

We propose a generalized one-dimensional energy diffusion approach for describing the dynamics of multidimensional dynamical processes in the condensed phase. On the basis of a formalism originally due to Zwanzig, we obtain a one-dimensional kinetic equation for a properly selected relevant dynamical quantity and derive new analytical results for the dynamics of a multidimensional electron-transfer process, nonequilibrium solvation, and diffusive escape from a potential well. The calculated results for electron-transfer reactions in solvent-separated and contact ion pair systems are found to be in good agreement with the experimental results. We are able to explain the rate of the electron-transfer reaction using much smaller and reasonable values of the solvent reorganization energy in contrast to earlier works that had to use a much larger value. The proposed theory is not only conceptually simpler than the conventional approaches but is also free from many of their limitations. More importantly, it provides a single theoretical framework for describing a wide class of dynamical phenomena.     

A quantum chemistry study of the Cl atom reaction with formaldehyde

The elementary vapor-phase reaction between Cl atoms and HCHO has been studied by ab initio methods. Calculations at the MP2, MP3, MP4(SDTQ), CCSD, CCSD(T), and MRD-CI levels of theory show that the reaction is characterized by a low electronic barrier; excluding the effects of spin-orbit splitting in Cl, our best estimate at the MRD-CI/aug-cc-pVTZ//RHF-RCCSD(T)/aug-cc-pVTZ level of theory predicts a Born-Oppenheimer barrier height of 0.7 kJ mol-1. The energies of the lowest six electronic states as resulting from MRD-CI calculations are presented at discrete points along the reaction path, and two avoided crossings are found in the transition state region. The spin-orbit splitting in Cl is also calculated along the reaction path; it is not negligible in the transition state region and is found to increase the barrier by only 1.4 kJ mol-1 at the RCCSD(T)/aug-cc-pVTZ transition state geometry. The minimum energy path of the reaction connects an energetically weakly stabilized adduct on the flat potential surface on the reactant side and an energetically strongly stabilized postreaction adduct. The reaction rate coefficient and the kinetic isotope effects were calculated using improved canonical variational theory with small curvature tunneling (ICVT/SCT), and the results were compared to experimental data. The experimental reaction rate coefficient is reproduced within its uncertainty limits by variational transition state theory with interpolated single-point energy corrections (ISPE) at the MP4(SDTQ) level of theory and by conventional transition state theory with interpolated optimized energies (IOE) at the MRD-CI//RCCSD(T) level of theory and interpolated optimized geometries at the RCCSD(T) level of theory on an MP2/aug-cc-pVTZ potential energy surface when employing scaled vibrational frequencies.     

Light- and heavy-atom tunneling in rearrangement reactions of cyclopropylcarbenes

We investigated both light- and heavy-atom tunneling in the rearrangements of a series of cyclopropylcarbenes using canonical variational transition state theory with multidimensional tunneling corrections (CVT/MT) and the Wentzel-Kramers-Brillouin (WKB) formalism. Halogeno- and hydroxy-substituted cyclopropylcarbenes were found not to undergo carbon tunneling owing to wide reaction barriers. However, while carbon tunneling plays a major role in the ring expansion of parent cyclopropylcarbene yielding cyclobutene, cyclopropylmethylcarbene is prone to undergo hydrogen tunneling to give cyclopropylmethylene.     

Computational study of the reactions of methanol with the hydroperoxyl and methyl radicals. 2. Accurate thermal rate constants

Multistructural canonical variational-transition-state theory with multidimensional tunneling (MS-CVT/MT) is employed to calculate thermal rate constants for the abstraction of hydrogen atoms from both positions of methanol by the hydroperoxyl and methyl radicals over the temperature range 100-3000 K. The M08-HX hybrid meta-generalized gradient approximation density functional and M08-HX with specific reaction parameters, both with the maug-cc-pVTZ basis set, were validated in part 1 of this study (Alecu, I. M.; Truhlar, D. G. J. Phys. Chem. A2011, 115, 2811) against highly accurate CCSDT(2)(Q)/CBS calculations for the energetics of these reactions, and they are used here to compute the properties of all stationary points and the energies, gradients, and Hessians of nonstationary points along each considered reaction path. The internal rotations in some of the transition states are found to be highly anharmonic and strongly coupled to each other, and they generate multiple structures (conformations) whose contributions are included in the partition function. It is shown that the previous estimates for these rate constants used to build kinetic models for the combustion of methanol, some of which were based on transition state theory calculations with one-dimensional tunneling corrections and harmonic-oscillator approximations or separable one-dimensional hindered rotor treatments of torsions, are appreciably different than the ones presently calculated using MS-CVT/MT. The rate constants obtained from the best MS-CVT/MT calculations carried out in this study, in which the important effects of corner cutting due to small and large reaction path curvature are captured via a microcanonical optimized multidimensional tunneling (μOMT) treatment, are recommended for future refinement of the kinetic model for methanol combustion.     

锗烯与甲醛环加成反应的理论研究

用从头算方法研究了单重态锗烯与甲醛环加成反应的机理,找到了反应的中间配合物和过渡态,并讨论了反应机理.在从头算的基础上,用统计热力学方法和过渡态理论计算了该反应在不同温度下的热力学函数的变化和动力学性质.结果表明,此反应由两步组成:(1)锗烯与甲醛反应生成了一中间配合物,是一无势垒的放热反应;(2)中间配合物异构化得到产物锗杂环氧甲烷,此步势垒经零点能校正后只有69.6kJ/mol(MP2/3-21G//3-21G).从热力学和动力学角度综合考虑,该反应在400～500K温度下进行为宜,此时,反应既有较大的自发趋势和平衡常数,又具有较快的反应速率.     

Ab initio molecular dynamics simulation of the aqueous Ru2+/Ru3+ redox reaction: the Marcus perspective

A well-behaved (low spin) transition metal aqua ion, Ru(aq)(2+), is used as a model system in an ab initio molecular dynamics study of a redox half reaction to which the Marcus theory of electron transfer is assumed to apply. Using constraint methods, we show that aqueous Ru(2+) can be reversibly transformed to Ru(3+) under the control of the classical solvent electrostatic potential as order parameter. The mean force is found to vary linearly with the order parameter in accordance with the Marcus theory. As can be expected for a half reaction, the slope in the oxidized and reduced states are asymmetric differing by approximately a factor of two. As a further test, we verify that the corresponding quadratic potential of mean force is in excellent agreement with the free energy profile obtained from the Gaussian distribution of potential fluctuations sampled from free (unconstrained) runs of the reduced and oxidized system. Similar to experimental electrochemical methods, our simulation scheme enables us to manipulate the effective thermodynamic driving force and align the free energy minima of product and reactant state. The activation energy and reaction entropy computed under these conditions are discussed and analyzed from the Marcus perspective.     

Control of kinetics and thermodynamics of [1,5]-shifts by aromaticity: a view through the prism of Marcus theory

The effects of aromatic stabilization on the rates of [1,5]-hydrogen shifts in a series of carbo- and heterocyclic dihydroaromatic compounds were estimated by B3LYP/6-31G computations. The aromatic stabilization energy of the product is directly translated into increased exothermicity of these reactions. Relative trends for a significant range of endothermic and exothermic [1,5]-shifts with different intrinsic activation energies are reliably described by Marcus theory. The effects of aromaticity or antiaromaticity are very large and can lead to dramatic acceleration or deceleration of [1,5]-hydrogen shifts and even to complete disappearance of the reaction barrier. Not only the activation energy but the shape and position of the reaction barrier can be efficiently controlled by changes in the aromaticity of the products, making these systems interesting models for studying hydrogen tunneling. Marcus theory can also be applied successfully to other pericyclic shifts such as [1,5]-shifts which involve chlorine and methyl transfer.     

Semiclassical treatment of thermally activated electron transfer in the intermediate to strong electronic coupling regime under the fast dielectric relaxation

The generalized nonadiabatic transition-state theory (NA-TST) (Zhao, Y.; et al. J. Chem. Phys. 2004, 121, 8854) is used to study electron transfer with use of the Zhu-Nakamura (ZN) formulas of nonadiabatic transition in the case of fast dielectric relaxation. The rate constant is expressed as a product of the well-known Marcus formula and a coefficient which represents the correction due to the strong electronic coupling. In the case of general multidimensional systems, the Monte Carlo approach is utilized to evaluate the rate by taking into account the multidimensionality of the crossing seam surface. Numerical demonstration is made by using a model system of a collection of harmonic oscillators in the Marcus normal region. The results are naturally coincident with the perturbation theory in the weak electronic coupling limit; while in the intermediate to strong electronic coupling regime where the perturbation theory breaks down the present results are in good agreement with those from the quantum mechanical flux-flux correlation function within the model of effective one-dimensional mode.     

锗烯与乙烯环加成反应的理论研究

用RHF/6-31G^*解析梯度方法研究了单重态锗烯与乙烯环加成反应的机理,用二级微扰方法对各构型的能量进行了相关能校正,并用统计热力学方法和过渡态理论计算了该反应在不同温度下的热力学函数的变化和动力学性质。结果表明,此反应历程由两步组成:1)锗烯与乙烯生成了一中间配合物,是一无势垒的放热反应,2)中间配合物异构化为产物锗杂环丙烷,此步势垒经零点能校正后为26.9kJ.mol^-^1(MP2/6-31G^*//6-31G^*);从热力学和动力学的综合角度考虑,该反应在200-300K温度下进行为宜,如此,反应既有较大的自发趋势和平衡常数,又具有较快的反应速率。     

A theoretical study of hydrogen—atom abstraction by methyl radical

The activation energies for the abstraction of a hydrogen atom from each of several hydrocarbons has been calculated using the AM1 molecular orbital method. The calculated barrier for the abstraction from methane is 15.5 kcal/mole, in good agreement with experiment. Calculated barriers for other abstractions are reasonably good. They are much improved when the calculated intrinsic barrier is used together with the experimental heats of reaction in a modified formulation of Marcus theory.     

A product branching ratio controlled by vibrational adiabaticity and variational effects: kinetics of the H + trans-N2H2 reactions

The abstraction and addition reactions of H with trans-N(2)H(2) are studied by high-level ab initio methods and density functional theory. Rate constants were calculated for these two reactions by multistructural variational transition state theory with multidimensional tunneling and including torsional anharmonicity by the multistructural torsion method. Rate constants of the abstraction reaction show large variational effects, that is, the variational transition state yields a smaller rate constant than the conventional transition state; this results from the fact that the variational transition state has a higher zero-point vibrational energy than the conventional transition state. The addition reaction has a classical barrier height that is about 1 kcal∕mol lower than that of the abstraction reaction, but the addition rates are lower than the abstraction rates due to vibrational adiabaticity. The calculated branching ratio of abstraction to addition is 3.5 at 200 K and decreases to 1.2 at 1000 K and 1.06 at 1500 K.     

Methane dissociation on Ni(111): the effects of lattice motion and relaxation on reactivity

The effects of lattice motion and relaxation on the dissociative adsorption of methane on a Ni(111) surface are explored. Electronic structure methods based on the density functional theory are used to compute the potential energy surface for this reaction. It is found that, in the transition state and product regions, there are forces causing the Ni atom over which the molecule dissociates to move out of the surface. In order to examine the extent to which the lattice might pucker during this reaction, high dimensional fully quantum scattering calculations are carried out. It is found that a significant amount of lattice puckering can occur, even at large collision energies, lowering the barrier to reaction and increasing the dissociative sticking probability. This is shown to be in contrast to the predictions of the surface oscillator model. While we observe similar puckering forces for this reaction on Pt(111), our calculations suggest that the puckering on this surface will be considerably less due to the larger metal atom mass. The "laser off" reactivities of CD(3)H on Ni(111) are computed, and it is demonstrated that there can be significant contributions to the reactivity from vibrationally excited molecules, particularly at lower collision energies, or when a large nozzle temperature is required to attain the necessary collision energy for reaction. Comparisons are made with recent experiments with regard to the variation of reactivity with collision energy, vibrational state, and surface temperature.     

First-Principles Investigation of the Electronic and Conducting Properties of Oligothienoacenes and their Derivatives

Herein, we calculated reorganization energies, vertical ionization energies, electron affinities, and HOMO–LUMO gaps of fused thiophenes and their derivatives, and analyzed the influence of different substituents on their electronic properties. Furthermore, we simulated the angular resolution anisotropic mobility for both electron- and hole-transport, based on quantum-chemical calculations combined with the Marcus–Hush electron-transfer theory. We showed that: 1) styrene-group substitution can effectively elevate the HOMO energy level and lower the LUMO energy level, and therefore lower both the hole- and electron-injection barriers; and 2) chemical oxidation of the thiophene ring can significantly improve the semiconductor properties of the fused oligothiophenes through a decrease of the injection barrier and an increase in the charge-transfer mobility for electrons but without lowering their hole-transfer mobilities, which suggests that it may be a promising way to convert p-type semiconductors into ambipolar or n-type semiconductor materials.     

Strongly correlated barriers to rotation from parametric two-electron reduced-density-matrix methods in application to the isomerization of diazene

Recently, parameterization of the two-electron reduced density matrix (2-RDM) has made possible the determination of electronic energies with greater accuracy and lower cost than traditional electron-pair theories including coupled cluster with single and double excitations [D. A. Mazziotti, Phys. Rev. Lett. 101, 253002 (2008)]. We examine the method's performance for strongly correlated barriers to rotation; in particular, we study two distinct pathways in the isomerization of diazene (N(2)H(2)) from cis to trans: (i) a strongly correlated rotational pathway and (ii) a moderately correlated inversion pathway. While single reference wavefunction methods predict that the rotational barrier is higher than the inversional barrier, the parametric 2-RDM method predicts that the rotational barrier is lower than the inversional barrier by 3.1 kcal/mol in the extrapolated basis set limit. The parametric 2-RDM results are in agreement with those from multireference methods including multireference perturbation theory and the solution to the anti-Hermitian contracted Schro?dinger equation. We report energies, optimized structures, and natural orbital occupation numbers for three diazene minima and two transition states.