溶液中M(H_2O)_6~(2+/3+)(M=V,Cr,Mn,Fe,Co)自交换电子转移体系内层重组能和活化能的理论研究

通过建立电子转移过程的活化模型和重组模型,提出了用量子化学从头算方法研究电子转移过程内层重组能和活化能的新方法．在ＵＭＰ２／６－３１１Ｇ水平上获得了５对过渡金属水合离子体系Ｍ（Ｈ２Ｏ）２＋／３＋６（Ｍ＝Ｖ,Ｃｒ,Ｍｎ,Ｆｅ,Ｃｏ）自交换反应的内层重组能和活化能,获得了与Ｍａｒｃｕｓ电子转移理论相一致的结果     

Theoretical study of the inner‐sphere energy barrier of the transition‐metal complex M(H2O) in electron‐transfer process

Two theoretical models, a reorganization model and an activation model, are presented for accurately determining the energy barrier of the type M(H₂O) of the transition‐metal complexes in the electron‐transfer process. Ab initio calculations are carried out at UMP2/6‐311G level for several redox pairs M(H₂O) (M=V, Cr, Mn, Fe, and Co) to calculate their inner‐sphere reorganization energies and activation energies according to the models presented in this article. The values of theoretical inner‐sphere reorganization energies and activational energies are comparable with the experimental results obtained from the vibration spectroscopic data. The theoretical reorganization energy of the every redox pair is four times as much as its activation energy, which agrees with Marcus' electron‐transfer theory. The fact proved that the theoretical models presented in this article are scientific and available for studying the electron‐transfer process of the transition‐metal complex. ©1999 John Wiley & Sons, Inc. Int J Quant Chem 75: 119–126, 1999     

Inner‐sphere reorganization for redox pairs M(NH3)62+/3+ (M=Mn,Fe, and Co): Models and calculations

The inner‐shell reorganization and activation models of the electron‐transfer reactions of transition‐metal hexammine complexes are presented. The inner‐shell reorganization and activation energies of several hexammine redox pairs M(NH₃)₆^2+/3+ (M=Mn, Fe, and Co) in self‐exchange reactions are studied by different formalisms. The extent of the anharmonicities in the vibration between the metal–ion and the ligands in the reorganization process of these complexes is determined. The inner‐shell barriers of these redox pairs are dependent on reorganization model used. The contribution of the individual reactants to the inner‐shell barrier is sensitive to the model used. © 2001 John Wiley & Sons, Inc. Int J Quantum Chem, 2001     

Theoretical study of self‐exchange electron‐transfer reactions for the M(H2O)\documentclass{article}\pagestyle{empty}\begin{document}$^{2+/3+}_{6}$\end{document} (M = V,Cr, Mn,and Fe) systems

Based on an activation model, a available scheme to calculate the rate of the electron‐transfer reaction between transition‐metal complexes in aqueous solution is presented. Ab initio technique is used to determine the electron‐transfer reactivity of the type M(H₂O)$^{2+/3+}_{6}$ of transition‐metal complexes at the UMP2/6‐311G level. The activation parameters and activation energies of the electron‐transfer systems are obtained via the activation model. An alternative determining method of the potential energy surface (curve) slope at the crossing point is given in which the inner‐sphere contribution of potential energy surface slope is expressed as the sum of two separate reactants. Theoretical self‐exchange rate constants for M(H₂O)$^{2+/3+}_{6}$ (M = V, Cr, Mn, and Fe) systems are obtained at 298 K and zero ionic strength. The calculated results of the activation energy, electronic transmission factor, and electron‐transfer rate are compared with the corresponding quasi‐experimental values as well as those obtained from other methods, and better agreements are found. The present results indicate that the scheme can adequately describe the self‐exchange reactions involved in this study. © 2000 John Wiley & Sons, Inc. Int J Quant Chem 78: 32–41, 2000     

Nonempirical ab initio studies on inner-sphere reorganization energies of M2+(H2O)6/M3+(H2O)6 redox couples at valence basis level

On the basis of the basic feature of the electron transfer reactions, a new theoretical scheme and application of a nonempirical ab initio method in computing the inner-sphere reorganization energies (RE) of hydrated ions in electron transfer processes in solution are presented at valence STO basis (VSTO) level. The potential energy surfaces and the various molecular structural parameters for transition metal complexes are obtained using nonempirical molecular orbital (MO) calculations, and the results agree very well with experimentally observed ones from vibrational spectroscopic data. The results of inner-sphere REs obtained from these calculations via this new scheme give a good agreement with photoemission experimental findings and those from the improved self-exchange model proposed early for M²⁺(H₂O)₆/M³⁺(H₂O)₆(M = V, Cr, Mn, Fe, and Co) redox couple systems and are better than those from semiempirical INDO/II MO method and other classical methods. Further, the observed agreement of the optimized structural data and the results of inner-sphere REs of complexes with experimental findings confirms the following: (1) the validity of nonempirical MO calculation method to get accurate structural parameters and inner-sphere RE for the redox systems for which reliable vibrational spectroscopic data are not available, (2) the validity of the improved self-exchange model proposed early for inner-sphere RE, and (3) the reasonableness of some approximations adopted in this study. © 1997 John Wiley & Sons, Inc.     

Inner Sphere Reorganization Energy for the Electron Transfer Reactions between M-C_6H_6 and M~ -C_6H_6 Complexes in Gaseous phase: An ab initio Computation

IntroductionTheelectrontransfer(ET)reactionisanfundamentalchemicalprocessandhasbecomethefocusoftheoreticalandexperimentalstudies1-3.AsuitableapproachtowardunderstandingtheETreactivitypatternsistoseparatethevariouscontributionsintoexponentialandpre-exponentialfactors.Theexponentialparts,i.e.,theFrank-Condonfactor,isacompositeofthestructuralreorganizationofthereactingsystemimmediate1yaftertheelectrontransfered.Basedonthecharacteristicsofthereactingsystem'sstructure,thereorganizationenergy(RE…     

苯硝化反应中电子转移反应重组能的计算

提出了重组能的量子化学算法,在用CISD/6-31G基组水平上,得到苯硝化反应中反应物及过渡态的结构.并计算了各自交换电子转移反应以及交叉电子转移反应的重组能,同实验重组能进行了比较.计算用了Gaussian 94程序.从重组能的角度分析了苯硝化反应.结果表明,对于NO2++NO2→NO2+NO2+的自交换电子转移反应,重组能较大,结论为: 在芳烃硝化反应中,存在以NO2+为氧化剂的电子转移步骤的可能性很小,而从动力学的角度上,用NO+作反应的氧化剂更有可能.     

Theoretical Study on Electron Transfer Matrix Element in Oxidation of α—Amino Carbon—Centered Radical by O2

As a successive work of our previous paper,^1the electron transfer matrix element(Vrp)in the oxidation of the simplified model molecule of α-amino carbon-centered radical by O2 has been investigated with ab initio calculation at the level of UHF/6-31 G**.Based on the optimized geometries of the reactgant and the ion-pair complex obtained previously,the reaction heat and the iuner reorganization energy have been obtained by constructing the potential energy curves of reactant and product states considering the solvent effect with the conductor-like screening model(COSMO).The solvent reorganization energy has been estimated using Lippert-Mataga relationship.The calculated results show that the value of Vrp is several times larger than that of RT,which means that the model reaction is an adiabatic one.Theoretical investigation indicates that the solvent effect on the direct electron transfer (ET) process of oxidation of α-amino carbon-centered radical by oxygen is remarkable.     

Ab initio prediction of MnOH2/MnOH2 electron transfer reactivity at electron correlation level

An ab initio calculation of electron transfer reactivity of Mn²⁺OH₂/Mn³⁺OH₂ redox system, in gas and in solution, has been made in this paper. The detailed geometry optimization and the scanning of the potential energy surfaces have been carried out at UMP2 (full)/6-311+G^* level. The relevant energy quantities (such as the activation energy and the binding energy) are calculated at different levels of theory (HF, MP2, MP3, MP4 and QCISD and corresponding spin-projection PUHF, PMP2 and PMP3) with the same basis set (6-311+G^*). Both all-electrons and valence electrons have been correlated in energy calculations. The electronic transmission coefficient is calculated using the ab initio potential energy surface slopes and the coupling matrix element determined from the two-state model and the Slater-type d-electron wave functions. The pair distribution function is obtained using both a classical sphere approximation scheme and a novel scheme. The relevant kinetic parameters are obtained at different ab initio levels in terms of the new model. The contact-distance dependence of these parameters and the applicability of the presented models are also discussed.     

Aerobic Damage to [FeFe]‐Hydrogenases: Activation Barriers for the Chemical Attachment of O2

[FeFe]‐hydrogenases are the best natural hydrogen‐producing enzymes but their biotechnological exploitation is hampered by their extreme oxygen sensitivity. The free energy profile for the chemical attachment of O₂ to the enzyme active site was investigated by using a range‐separated density functional re‐parametrized to reproduce high‐level ab initio data. An activation free‐energy barrier of 13 kcal mol^?1 was obtained for chemical bond formation between the di‐iron active site and O₂, a value in good agreement with experimental inactivation rates. The oxygen binding can be viewed as an inner‐sphere electron‐transfer process that is strongly influenced by Coulombic interactions with the proximal cubane cluster and the protein environment. The implications of these results for future mutation studies with the aim of increasing the oxygen tolerance of this enzyme are discussed.     

Co(H2O)62+/3+体系电子转移反应动力学的理论研究

A theoretical scheme is presented which is based on an activation model for calculating the rate of the electron- exchange reaction between transition metal complexes in aqueous solution and applies to Co(H2O)6 2+/3+ electron transfer system. The activation parameter and activation energy of the system are obtained via the activation model. The slopes of the potential energy surfaces (curves) of the reacting system at the separated reactants are calculated from the fitted potential energy curves. The coupling matrix element is determined by using the perturbation theory and numerical integral method. Theoretical rate constants are obtained for the system at both UHF/6-311G and UMP2/6-311G levels. The agreement of the theoretical results with experimetal values is excellent. This fact indicates the scheme proposed is feasible and accurate in studying the self- exchange eletron transfer reaction.     

Distance dependence analysis of the electron transfer reactivity for the metastable FeOH2/FeOH2 system: an ab initio investigation

A novel theoretical scheme and ab initio application in discussing the electron transfer (ET) reactivity are presented in this paper, and are also calibrated in terms of the mono-hydrated iron ion system, Fe²⁺–OH₂/Fe³⁺–OH₂. The detailed geometry optimizations have been made at UMP2(full)/6-311+G^* level, and the activation geometrical configuration and the energy have been obtained at this level of theory using the activation model and the ab initio potential energy surface fitted from MP2(full)/6-311+G^* single point energies. The corresponding energy quantities (such as the activation energy, and dissociation energy) have also been obtained at different levels of theory (HF, MP2, MP3, MP4, QCISD and PUHF, PMP2 and PMP3 with the spin-projection) and a same basis set (6-311+G^*). The electron correlation calculations include the all electron correlation and the valence electron correlation. The electronic transmission coefficient is calculated using the ab initio potential energy surface slopes and the coupling matrix element determined from the two-state model and the Slater-type d-electron wave functions. The pair distribution function is calculated using two different schemes. Taking the pair distribution function and the local ET rate into account, a statistically averaged overall observed ET rate scheme and a spherically averaged local ET rate scheme are proposed. The relevant kinetic parameters are obtained in terms of these new schemes at different ab initio calculational levels. The contact distance dependence of these parameters and the applicability of the presented models and ab initio calculational method are also discussed.     

Co(H_2O)_6~(2 /3 )体系电子转移反应动力学的理论研究

电子转移过程在化学、生命科学、材料科学等领域普遍存在,几十年来一直受到国际学术界的广泛关注,是当前化学研究的前沿课题之一[1－6].过渡金属络合物间的电子转移是一类重要的电子转移过程,其动力学行为是理论和实验研究的热点[7－12].根据过渡态理论,这类自交换反应速率可表示为ket=κeZeffexp(－ΔE/RT)(1)其中,Zeff为核频率因子,对于溶液中的双分子反应其值约为1011dm3·mol－1·s－1[11];ΔE是活化能;κe称为电子因子,对于绝热反应κe=1.显然,活化能和电子因子是影响电子转移速率的两个关键因素.根据络合物的结构特点,一…     

Cepa calculations of potential energy surfaces for open-shell systems. I. The reaction of O(3P) with H2(1Σg+)

Ab initio calculations including electron correlation effects (mainly on CEPA-PNO level) have been performed for the potential energy surface of the reaction of ³P oxygen atoms with molecular hydrogen. The collinear abstraction reaction (C_∞v symmetry) and the vertical insertion reaction (C_2v) have been investigated with particular emphasis.The influence of the orbital basis size and of electron correlation both on the reaction energy and on the barrier height and location for the abstraction reaction has been studied in some detail. Our extrapolated value for the barrier for this reaction is 13.4 ± 1.0 kcal/mol, in fair agreement with the experimental activation energy, while the insertion reaction has to pass over a barrier of =48 kcal/mol. The analysis of electron correlation effects reveals that it is compulsory to include all singly and doubly substituted configurations, to correct for unlinked cluster contributions and to use fairly large basis sets if one wants to get accurate ab initio potential surfaces for the reactions of triplet oxygen atoms.     

Cyclic M(SO2) (M=Zn,Cd) and its Anions: Matrix Infrared Spectra and DFT Calculations

Reaction of laser ablated zinc and cadmium atoms with SO₂ molecules was studied by low temperature matrix isolation infrared spectroscopy. Cyclic M(SO₂) and anion M(SO₂)^- (M=Zn, Cd) were produced in excess argon and neon, which were identified by ³⁴SO₂ and S¹⁸O₂ isotopic substitutions. The observed infrared spectra and molecular structures were confirmed by density functional theoretical calculations. Natural charge distributions indicated significant electron transfer from s orbitals of zinc or cadmium metal atom to SO₂ ligand and cyclic M(SO₂) complexes favored “ion pair” M⁺(SO₂)^- formation, which were trapped in low temperature matrices. In addition Zn-O or Cd-O bond in M(SO₂) exhibited strong polarized covalent character. Reaction of Hg atom with SO₂ was also investigated, but no reaction product was observed, due to the relativistic effect that resulted in the contraction of 6s valence shell and high ionization potential of Hg atom     

Ab initio calculations on the clustering energies and stable structures of H(M)+ + M → H(M)2+ (M = CO and N2)

The clustering energies of the reactions, H(M)⁺+ M → H(M)⁺₂ (M = CO and N₂), were calculated by ab initio single configuration LCAO SCF MO and SCEP methods. The calculated energies are in good agreement with the experimental enthalpies.     

Electron transfer in uranyl(VI)-uranyl(V) complexes in solution

The rates and mechanisms of the electron self-exchange between U(V) and U(VI) in solution have been studied with quantum chemical methods. Both outer-sphere and inner-sphere mechanisms have been investigated; the former for the aqua ions, the latter for binuclear complexes containing hydroxide, fluoride, and carbonate as bridging ligand. The calculated rate constant for the self-exchange reaction UO(2)(+)(aq) + UO(2)(2+)(aq) <=>UO(2)(2+)(aq) + UO(2)(+)(aq), at 25 degrees C, is k = 26 M(-1) s(-1). The lower limit of the rate of electron transfer in the inner-sphere complexes is estimated to be in the range 2 x 10(4) to 4 x 10(6) M(-1) s(-1), indicating that the rate for the overall exchange reaction may be determined by the rate of formation and dissociation of the binuclear complex. The activation energy for the outer-sphere model calculated from the Marcus model is nearly the same as that obtained by a direct calculation of the precursor- and transition-state energy. A simple model with one water ligand is shown to recover 60% of the reorganization energy. This finding is important because it indicates the possibility to carry out theoretical studies of electron-transfer reactions involving M(3+) and M(4+) actinide species that have eight or nine water ligands in the first coordination sphere.     

Electron transfer reactions of iron(III)-polypyridyl complexes with organic sulfoxides

The redox reactions of four iron(III)-polypyridyl complexes with six aryl methyl sulfoxides have been investigated by spectrophotometric technique. The reaction follows clean second order kinetics and proceeds through rate determining electron transfer (ET) from organic sulfoxides to iron(III). The Marcus cross-reaction relation has been applied to obtain the self exchange rate constant for the ArSOR/ArS⁺(O)R couple as 1.3×10⁷ M⁻¹ s⁻¹. The application of Marcus theory to this ET reaction shows that the contribution of inner sphere reorganization energy is 0.4 eV. The rate constant and reaction constant values observed with organic sulfoxides are small compared with organic sulfides towards the same oxidant Fe(NN)₃³⁺.     

Free Energy Relationships for the Outer-Sphere Anion–Anion and Anion–Cation Optical Electron Transitions Involving Common Cyanometalate (II) and (IV) Donors: Evidence for the Frequency-Distorted Reorganization Dynamics

This work is an extension of the research project on the outer-sphere optical charge transfer (CT) initiated by Prof. R.R. Dogonadze at the Laboratory founded by him in Tbilisi, Georgia. We report the band deconvolution procedures and accomplished free energy relationships for recently observed novel outer-sphere anion–anion and anion–cation optical electron transitions involving common cyanometalate II and IV ions, viz. [M(CN) _x ]^4–, M = Fe, Ru, Os (x = 6) and M = Mo, W (n = 8) as electron donors, and [Fe^III(CN)₆]^3– and [Ru^III(NH₃)₆]³⁺ as electron acceptors, respectively. The CT band maximum vs. the redox asymmetry free energy relationships, constructed through the consideration of spin-orbit splitting effects, exhibit linear character with slopes close to unity as predicted theoretically, and fully confirm the assignment of these transitions to outer-sphere optical electron transitions as outlined in the preceding works. The preliminary comparative analysis of presented relationships based on the contemporary charge transfer theory and recent differential DO-D stretching overtone data strongly suggests the essential redox asymmetry for the reorganization free energy increments attributed to first solvating shells of cyanometalate ions involved.     

电场对金属串配合物M3(dpa)4Cl2 (M=Co,Rh, Ir; dpa=dipyridylamide)结构的影响

应用密度泛函理论PBE0 方法研究具有分子导线潜在应用的金属串配合物M₃(dpa)₄Cl₂ (1: M=Co, 2: M=Rh, 3: M=Ir; dpa=dipyridylamide)在电场作用下的几何和电子结构. 结果表明: 配合物基态均是二重态. 1和2的M₃⁶⁺金属链形成三中心三电子σ键, 3 中M₃⁶⁺形成三中心四电子σ键且存在弱的δ键. 随金属原子周期数增大其M―M键增强、LUMO与HOMO能隙减小、金属原子的反铁磁耦合减弱以至消失且自旋密度向配体的离域增强. 在Cl4→Cl5 电场作用下, 低电势端的M3－Cl5 键缩短, 高电势端的M2―Cl4 键增长, M―M平均键长略为缩短, M―M键增强, 有利于分子线的电子传递; 分子能量降低, 偶极矩线性增大. 低电势端Cl5的负电荷向高电势端Cl4 转移, 且3 中金属原子的正电荷由高电势端向低电势端的转移较明显, 自旋电子由低电势端向高电势端金属原子移动, 但桥联配体dpa^-与M和Cl 所在的分子轴间没有电荷转移. 电场使LUMO与HOMO能隙减小, 有利于分子的电子输运. 随金属原子周期数增大, 电场作用下M―M平均键长变化减小, LUMO、HOMO的能级交错现象减少.