Complete basis set, Gaussian, and hybrid density functional theory evaluation of the proton affinities of water and ammonia

An ab inito computation of reorganization energy for the electron transfer (ET) reactions between metal–benzene and metal ion–benzene complexes is presented. The geometry optimization of the metal–benzene complexes was performed. The metal atoms (or metal ions)– benzene molecule separation distances computed using an ab initio method were found to agree with earlier reported results. Values of reorganization energies using George-Griffith Marcus (GGM) method (the contribution from only diagonal elements of force constant matrix) and Hessian matrix method (including the contribution from both diagonal and off-diagonal elements) were computed. Results of reorganization energy show that the GGM method gives much lower values compared to those obtained using the Hessian method, suggesting that the coupling interactions between different vibrational modes are important to the inner-sphere reorganization energy for the ET reactions in gaseous phase.     

Reply to “contribution of inner-sphere reorganization in electron transfer reaction in solution” by S.U.M. Khan and J.O'M. Bockris

Equations and interpretations in the Khan—Bockris Comment are the same as in the author's paper except for the valid objection to the computation of literature values of force constants. The argument that inner-sphere reorganization energies are dominant is rather pointless since the opposite view is equally supported by experiment. The Khan—Bockris force constants are inaccurate because of the method of computing reduced masses and the use of metal—ligand distances superseded by more recent values.     

Theoretical studies on the inner-sphere reorganization energies for the self-exchange reactions of gas-phase diatomic molecules HA (A = Mg,Al, Si,P, S,Cl)

On the basis of the recently proposed accurate calculation scheme of the inner-sphere reorganization energies (RE ) of the reactants in gas-phase electron-transfer xprocesses, the inner-sphere RE values for the AH + AH⁺ (A = Mg, Al, Si, P, S, Cl) self-exchange systems are calculated in terms of an ab initio Hartree–Fock self-consistent-field MO method at different basis-set levels (6-31G **, 6-31 +G **, DZ , and DZP ). The structural parameters involved are also determined via the perturbation theory and the Dunham expansion of the Morse function and compared with the experimental values. Dissociation energies are corrected by electron correlation at the MP 2/6-31G * level. Results of the inner-sphere REs obtained from different models via ab initio calculations for these systems discussed here are in full agreement with the corresponding experimental data. © 1995 John Wiley & Sons, Inc.     

An inner-sphere reorganization model of hetero-exchange electron transfer reaction of diatomic reactants

An accurate theoretical scheme for obtaining directly the inner-sphere reorganization energies of the hetero-exchange electron transfer reactions from ionization potentials and electron affinities is first reported in this paper. Ionization potentials and electron affinities are alternatively obtained from the Rydberg spectroscopic data via a numerical procedure for some diatomic molecules. The inner-sphere reorganization energy values are calculated for the hetero-exchange electron transfer reactions (AB + CD⁺ → AB⁺ + CD) of diatomic molecules and are compared with those from other approximate methods.     

The inner-sphere reorganization energies for AH2 + AH (A = Al,Si, P,S) electron self-exchange reactions in electron-transfer processes from ab initio calculations

This article presents an application of the accurate calculation scheme proposed recently for the inner-sphere reorganization energies of molecules of the type AH₂ (A = Al, Si, P, and S). A reasonable extension has been made. The inner-sphere reorganization energies for the title thermal electron self-exchange reactions are calculated in terms of ab initio MO self-consistent field method (HFSCF ) at different basis-set levels (6-31G **, 6-31 + G **, DZ , and DZP ) and the involved parameters are also determined. These calculated results have been calibrated by comparing optimized molecular geometrical parameters and corresponding energy properties with the experimental findings or other theoretical values. An approximation, in which the contribution from the bond length–bond angle to the potential energy surface is neglected, is adopted in constructing the calculation formulas via the function model. Its adequacy is discussed. Agreement among different calculation schemes is analyzed. © 1995 John Wiley & Sons, Inc.     

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.     

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.     

Effect of the Ligand Nature in Zinc(II) Complexes on the Inner-Sphere Reorganization in the Electron Transfer Reactions

The effect of the ligand surrounding on the character and degree of the inner-sphere reorganization during electroreduction of aqua, aquahydroxy, hydroxy, and Edta complexes of zinc(II) is studied in the framework of a quantum-chemical approach. It is established that the most substantial intramolecular reorganization occurs during the transfer of the first electron onto [Zn(Edta)]^2–. The solvent's reorganization energy is estimated.     

Direct calculation of electron transfer parameters through constrained density functional theory

It is shown that constrained density functional theory (DFT) can be used to access diabatic potential energy surfaces in the Marcus theory of electron transfer, thus providing a means to directly calculate the driving force and the inner-sphere reorganization energy. We present in this report an analytic expression for the forces in constrained DFT and their implementation in geometry optimization, a prerequisite for the calculation of electron transfer parameters. The method is then applied to study the symmetric mixed-valence complex tetrathiafulvalene-diquinone radical anion, which is observed experimentally to be a Robin-Day class II compound but found by DFT to be in class III. Constrained DFT avoids this pitfall of over-delocalization and provides a way to find the charge-localized structure. In another application, driving forces and inner-sphere reorganization energies are calculated for the charge recombination (CR) reactions in formanilide-anthraquinone (FA-AQ) and ferrocene-formanilide-anthraquinone (Fc-FA-AQ). While the two compounds have similar reorganization energies, the driving force in FA-AQ is 1 eV larger than in Fc-FA-AQ, in agreement with experimental observations and supporting the experimental conclusion that the anomalously long-lived FA-AQ charge-separated state arises because the electron transfer is in the Marcus inverted region.     

ELECTRON TRANSFER REACTIONS OF METAL CARBONYL ANIONS

Abstract

Metal carbonyl anions exhibit one- and two-electron reactions. The two-electron processes involving transfer of groups (hydrogen, alkyl, and halogen) between metal centers are related to the nucleophilicity. The one-electron processes are primarily outer-sphere electron transfer for the metal carbonyl anions. These reactions are observed in the presence of oxidants such as coordination complexes, pyridinium salts, metal carbonyl dimers and metal carbonyl clusters. However, in contrast to organic reactions, the metal carbonyl anions may undergo inner-sphere electron transfer. Reactions of metal carbonyl anions of low nucleophilicity with metal carbonyl cations or halides are best interpreted as inner-sphere, one-electron transfer.     

Inner-sphere electron-transfer reorganization energies of zinc porphyrins

Inner-sphere electron-transfer reorganization energies of Zn(protoporphyrin IX) and Zn(octaethylporphyrin) are determined from band-shape analyses of the first ionization obtained by gas-phase valence photoelectron spectroscopy. The experimentally determined total inner-sphere reorganization energies for self-exchange (120-140 meV) indicate that structural changes upon oxidation are largely confined to the porphyrin ring, and substituents on the ring or solvent and other environmental factors make smaller contributions. Computational estimates by different models vary over a wide range and are sensitive to numerical precision factors for these low reorganization energies. Of current computational models that are widely available and practical for molecules of this size, functionals that contain a mixture of Hartree-Fock exchange and DFT exchange-correlation appear to be the most applicable.     

Quantum mechanical investigation of the inner-sphere reorganization energy of cyclooctatetraene/cyclooctatetraene radical anion. Part I

The inner-sphere reorganization energy of the electron self-exchange of the couple cyclooctatetraene/cyclooctatetraene radical anion has been investigated by quantum mechanical calculations. The more stable Jahn Teller distorted B2g conformation of the radical anion has been used in this study. Two different theories have been applied in this first part. The harmonic approximation in the classical Marcus scheme has been modified by using projected force constants, which are obtained from the complete force constant matrix and the geometry changes of the molecule during the ET (introduced by Mikkelsen). A different approach (introduced by Nelsen) combines the different energies of the neutral and radical anion with and without relaxation corresponding to the vertical ionization potential and the vertical electron affinity. The electronic energies of the neutral molecule and the radical anion differ dramatically applying three different levels of quantum mechanical calculations (UAM1, UB3LYP, PMP2 with three different basis sets with and without diffuse functions). Nevertheless the Nelsen method gives almost consistent results for the inner-sphere reorganization energies: 120.1 kJ/mol for semiempirical UAM1 method, 159.3 kJ/mol, 156.4 kJ/mol and 158.3 kJ/mol for density functional UB3LYP/6-31G*, UB3LYP/6-31++G* and UB3LYP/AUG-cc-pVDZ calculations and 192.5 kJ/mol for ab-initio PMP2/6-31G* investigations, respectively. These values are in agreement with earlier experimental work supposing the total reorganization energy to be larger than 38 kcal/mol assuming an electron self-exchange rate of 10(4) M(-1) s(-1). The simple harmonic approximation of Marcus relation has not yet been applied for a molecule like cyclooctatetraene with large torsional geometry changes. Using the projected force constants after scaling, considerably different results for the inner-sphere reorganization energy have been calculated: 738.1 kJ/mol for the UB3LYP/6-31G*, 743.3 kJ/mol for UB3LYP/6-31++G* and 759.1 kJ/mol for UB3LYP/AUG-cc-pVDZ level of theory. Comparison with our concentration dependent EPR experiments are controversial to the earlier experimental results, but the latter supports the assumption that the electron self-exchange occurs in a time scale so that the molecules cannot complete their vibrational motions. Therefore the projected Marcus relation is not valid for cyclooctatetraene/cyclooctatetraene radical anion including a large torsional change during the electron transfer.     

Adsorption mechanisms of selenium oxyanions at the aluminum oxide/water interface

Sorption processes at the mineral/water interface typically control the mobility and bioaccessibility of many inorganic contaminants such as oxyanions. Selenium is an important micronutrient for human and animal health, but at elevated concentrations selenium toxicity is a concern. The objective of this study was to determine the bonding mechanisms of selenate (SeO4(2-) and selenite (SeO3(2-) on hydrous aluminum oxide (HAO) over a wide range of reaction pH using extended X-ray absorption fine structure (EXAFS) spectroscopy. Additionally, selenate adsorption on corundum (alpha-Al2O3) was studied to determine if adsorption mechanisms change as the aluminum oxide surface structure changes. The overall findings were that selenite forms a mixture of outer-sphere and inner-sphere bidentate-binuclear (corner-sharing) surface complexes on HAO, selenate forms primarily outer-sphere surface complexes on HAO, and on corundum selenate forms outer-sphere surface complexes at pH 3.5 but inner-sphere monodentate surface complexes at pH 4.5 and above. It is possible that the lack of inner-sphere complex formation at pH 3.5 is caused by changes in the corundum surface at low pH or secondary precipitate formation. The results are consistent with a structure-based reactivity for metal oxides, wherein hydrous metal oxides form outer-sphere complexes with sulfate and selenate, but inner-sphere monodentate surface complexes are formed between sulfate and selenate and alpha-Me2O3.     

Ab initio calculation of inner-sphere reorganization energies of arenediazonium ion couples

The geometries of a series of substituted arenediazonium cations (p-NO2, p-CN, p-Cl, p-F, p-H, m-CH3, p-CH3, p-OH, p-OCH3, p-NH2) and the corresponding diazenyl radicals were optimized at the HF/6-31G, MP2/6-31G, B3LYP/6-31G, B3LYP/TZP, B3PW91/TZP, and CASSCF/6-31G levels of theory. Inner-sphere reorganization energies for the single electron-transfer reaction between the species were computed from the optimized geometries according to the NCG method and compared to experimental values determined by Doyle et al. All levels of theory predicted a CNN bond angle of 180 degrees in the cation. A bent neutral diazenyl radical was predicted at all levels of theory excepting B3LYP/TZP and B3PW91/TZP for the p-Cl-substituted compound. Inner-sphere reorganization energies determined at the HF, MP2, and CASSCF levels of theory correlated poorly with both experimental results and calculated geometries. Density functional methods correlated best with the experimental values, with B3LYP/6-31G yielding the most promising results, although the ROHF/6-31G survey also showed some promise. B3LYP/6-31G calculations correctly predicted the order of the inner-sphere reorganization energies for the series, excluding the halogen-substituted compounds, with values ranging from 42.8 kcal x mol(-1) for the p-NO2-substituted species to 55.1 kcal x mol(-1) for NH2. The magnitudes of these energies were lower than the experimental by a factor of 2. For the specific cases examined, the closed-shell cation geometries showed the expected geometry about the CNN bond, with variations in the CN and NN bond lengths correlating with the electron-donating/withdrawing capacity of the substituent. As predicted by Doyle et al., a large geometry change was observed upon reduction. The neutral diazenyl radicals showed a nominal CNN bond angle of 120 degrees and variations in the CN and NN bond lengths also correlated with the electron-donating/withdrawing capacity of the substituent. Changes in theta(CNN) and r(CN) both correlated well with calculated lambda(inner). The key parameters influencing inner-sphere reorganization energy were the CN and NN bond lengths and the CNN bond angle. This influence is explained qualitatively via resonance models produced from NRT analysis and is related to the amount of CN double bond character. Based on these observations, B3LYP/6-31G calculations are clearly the most amenable for calculating inner-sphere reorganization energies for the single electron-transfer reaction between cation/neutral arenediazonium ion couples.     

Inner-sphere reorganization energy of iron-sulfur clusters studied with theoretical methods

Models of several types of iron-sulfur clusters (e.g., Fe(4)S(4)(SCH(3))(4)(2-/3-/4-)) have been studied with the density functional B3LYP method and medium-sized basis sets. In a vacuum, the inner-sphere reorganization energies are 40, 76, 40, 62, 43, and 42 kJ/mol for the rubredoxin, [2Fe-2S] ferredoxin, Rieske, [4Fe-4S] ferredoxin, high-potential iron protein, and desulfoferrodoxin models, respectively. The first two types of clusters were also studied in the protein, where the reorganization energy was approximately halved. This change is caused by the numerous NH.S(Cys) hydrogen bonds to the negatively charged iron-sulfur cluster, giving rise to a polar local environment. The reorganization energy of the iron-sulfur clusters is low because the iron ions retain the same geometry and coordination number in both oxidation states. Cysteine ligands give approximately the same reorganization energy as imidazole, but they have the advantage of stabilizing a lower coordination number and giving more covalent bonds and therefore more effective electron-transfer paths.     

Chemodynamics of metal complexation by natural soft colloids: Cu(II) binding by humic acid

The chemodynamics of Cu(II) complexation by humic acid is interpreted in terms of recently developed theory for permeable charged nanoparticles. Two opposing electric effects are operational with respect to the overall rate of association, namely, (i) the conductive enhancement of the diffusion of Cu(2+), expressed by a coefficient f(el), which accounts for the accelerating effect of the negative electrostatic field of the humic particle on the diffusive transport of metal ions toward it, and (ii) the ionic Boltzmann equilibration with the bulk solution, expressed by a factor f(B), which quantifies the extent to which Cu(2+) ions accumulate in the negatively charged particle body. These effects are combined in the probability of outer-sphere metal-site complex formation and the covalent binding of the metal ion by the complexing site (inner-sphere complex formation) as in the classical Eigen mechanism. Overall "experimental" rate constants for CuHA complex formation, k(a), are derived from measurements of the thermodynamic stability constant, K*, and the dissociation rate constant, k(d)*, as a function of the degree of metal ion complexation, θ. The resulting k(a) values are found to be practically independent of θ. They are also compared to theoretical values; at an ionic strength of 0.1 mol dm(-3), the rate of diffusive supply of metal ions toward the particles is comparable to the rate of inner-sphere complex formation, indicating that both processes are significant for the observed overall rate. As the ionic strength decreases, the rate of diffusive supply becomes the predominant rate-limiting process, in contrast with the general assumption made for complexes with small ligands that inner-sphere dehydration is the rate-limiting step. The results presented herein also resolve the discrepancy between experimentally observed and predicted dissociation rate constants based on the above assumption.     

Mechanistic aspects of transition metal-catalyzed hydrogen transfer reactions

In this tutorial review recent mechanistic studies on transition metal-catalyzed hydrogen transfer reactions are discussed. A common feature of these reactions is that they involve metal hydrides, which may be monohydrides or dihydrides. An important question is whether the substrate coordinates to the metal (inner-sphere hydrogen transfer) or if there is a direct concerted transfer of hydrogen from the metal to substrate (outer-sphere hydrogen transfer). Both experimental and theoretical studies are reviewed.     

The unusual extraction behavior of americium(III) and dioxouranium(VI) from picric acid medium using neutral oxodonors II. A thermodynamic study

The role of temperature on the distribution of Am³⁺ and UO₂ ²⁺ was investigated in the extraction systems involving TBP and DOSO as the neutral oxodonors and picrate as the organophilic counter anion. The inner-sphere water molecules and their substitution by the oxodonor molecules appeared to influence the extraction constants of these metal ions. The conditional extraction constants for Am³⁺ were found to be larger (about 3 order of magnitude) than those for UO₂ ²⁺. From the thermodynamics data it appeared that both TBP as well as DOSO bind Am³⁺ ion through outer-sphere coordination. In presence of 1M NaCl, though the interaction with TBP remains unaltered DOSO tend to form an inner-sphere complex. On the other hand, UO₂ ²⁺ forms inner-sphere complexes with DOSO and outer-sphere complex with TBP in the absence of salt. In the presence of 1M NaCl, both TBP and DOSO form inner-sphere complexes. The effect of ionic strength on metal ion extraction was also investigated. For Part I see Ref. 9.     

非金属氧化-还原对MO2/MO2-(M=N,S,Cl)的电子转移反应动力学

以Marcus-Hush电子转移理论为基础,提出了用量子化学密度泛函方法研究自交换和异交换电子转移反应的理论方案.在DFTB3LYP/6-311+G(2D)水平上研究了溶液中NO₂/NO₂^-,SO₂/SO₂^-和ClO₂/ClO₂^-等3个氧化-还原对的自交换以及它们之间的6个交叉电子转移反应的动力学性质,获得了与实验较为一致的结果.     

Palladium Complexes of Corroles and Sapphyrins

Palladium complexes of corrole and sapphyrin were prepared in high yield and fully characterized. The corrole provides a tetradentate/trianionic square planar coordination sphere for Pd^II, charge balanced by pyridinium. Both one and two Pd^II ions may be accommodated by the pentapyrrolic skeleton of the sapphyrin, and in each case the macrocycle acts as bidentate/monoanionic ligand and the inner-sphere square planar geometry is completed by allyl anions coordinated in an η³ fashion. NMR spectroscopy and X-ray crystallography data analyses uncovered the presence of interesting stereoisomers due to the flexibility of the ally ligands and also the pyrrole ring(s) that is/are not involved in metal binding.