Second-order Electron Research Articles

Semiempirical Approach to the Fukui Function Analysis of Uric Acid under Different pH Conditions.

Analytic Fukui functions calculated at a first-principles level are combined with experimental pKa values and the calculation of tautomerization energies to obtain the effective regioselectivity of uric acid toward electron-transfer reactions under different pH conditions. Second-order electron binding energies are also computed to determine which of the tautomers is more likely to participate in the electron transfer. A comparison of vertical and adiabatic proton detachment energies allows us to conclude that tautomerization is not mediating deprotonation and that two monoanionic species are of comparable relevance. The main difference between these monoanionic species is the ring that has been deprotonated. Both monoanionic species are produced from a single neutral tautomer and mainly produce a single dianionic tautomer. As a method for the analysis of systems affected by pH such as uric acid, we propose to plot condensed Fukui functions versus pH, allowing us to draw the effect of pH on the regioselectivity of electron transfer in a single image.

Theoretical Study on CO<sub>2</sub>/SO<sub>2</sub> Absorption Using <i>N</i>- Alkylethylenediaminium Protic Ionic Liquid

The protic ionic liquids (PILs) comprising with N-2-ethylhexylethylenediaminium cation (HEtHex+) and bis (trifluoromethanesulfonate) imide anion (TFSA-) forming [HEtHex][TFSA] which has two amines in the polar group and available to absorbs acid gases such as CO2 and SO2. In order to study the CO2/SO2 absorption mechanism of [HEtHex][TFSA], the stable configurations of [HEtHex][TFSA]-nCO2 (n=1, 2, 3, 4) and [HEtHex][TFSA]-nSO2 (n=1, 2, 4, 6) are investigated using the density functional theory at the M06-2X/6-311G (d, p) level, then the interaction energy, molecular vibration frequency, second-order perturbation energy, electron density and Laplace value are calculated and analysed for the most stable configurations. The results show that N–H...O type weak or medium hydrogen bonding are mainly formed between [HEtHex][TFSA] and CO2/SO2 molecules. The hydrogen bonding interaction is stronger for [HEtHex][TFSA]-nSO2 comparing with [HEtHex][TFSA]-nCO2 and increases with increasing the number of CO2/SO2 molecules.

Theoretical investigation of the electronic absorption spectra of the glucosides

n-alkyl-1X-β-D-glucopyranosides (X = O, S) contain a glucosidic bond joining a glucose moiety and n-alkyl group. We have elucidated the optical properties of the O-/S-glucosidic bond of n-alkyl-β-D-glucopyranosides under aqueous solution by using time-dependent density functional theory (TD-DFT) on the base of the fully relaxed geometries of (model) compounds. For thio-glucopyranosides, a broadening absorption bands with the delocalizations of the sulfur lone pair electrons under UV light are predicted, which is in good agreement with the experimental observations. The main delocalization interaction is found to be the donation of the lone pair of the sulfur atom into σ* orbital of the C-Opyran bond that enhances the S-C-Opyran bond and efficiently raises the electron distribution of the glucose moiety, which is confirmed by the second-order perturbation NBO and electron density difference (EDD) analyses. Such n→σ* character is detected in X = O case either which, however, is basically excluded from any transitions. In addition, we have also investigated the derived X-C-Opyran (X = N(H), P(H)) bond. The n(N)→σ*(C-Opyran) electron donation is found to be less, although still main, delocalization interaction, while there is even no delocalization of n(P)→σ*(C-Opyran) character due to the distant from each other. The absorption characteristics of C-/Si-glucosidic bonds are also discussed.

Size-Dependent πg + πu Combination Band Intensities of Polyynes C2nH2 (n = 1-9) Analyzed by the Local CCH Bending and the Linear Response Functions.

Polyynes (C2nH2) show the unusually strong πg + πu combination bands in the infrared absorption spectra. We calculated them as the first overtone of the local CCH bending; the strong intensities are interpreted as a consequence of the large-amplitude bending vibration of the acidic acetylenic hydrogen combined with the size-dependent π electron conjugation. Our theoretical calculations show that the absorption intensity increases steadily and their increase rate is gradually slowed down by increasing the number of acetylene units up to n = 9. However, the calculated vibrational wavenumber converges quickly in agreement with the experimental observation. The second-order electron density deformation caused by the local CCH bending was analyzed using the linear response functions, including the linear and nonlinear contributions, to explain the n dependence. The easily polarizable π electron density caused two kinds of deformation-dominant but dark δxx-yy type and minor but bright σ type. Both of them exhibit interesting zigzag sign alternations, consistent with the law of alternating polarity of Coulson and Longuet-Higgins. The electron density polarization in these intra- and interacetylene units induces a large axial component molecular dipole moment, contributing to the intensity that increases with n. The difference between the curvilinear and rectilinear bending coordinates is interpreted within the present theoretical scheme.

Structure and hydrogen bonding of mono-protic ionic liquids composed of N-alkylethylenediaminium cations and trifluoromethanesulfonate anion

The stabilities of some of the possible molecular structures, intermolecular hydrogen bonding interactions, and protonation sites of chelating mono-protic ionic liquids composed of N-alkyl (= Hexyl, Octyl, and 2-Ethylhexyl) ethylenediaminium cations with a trifluoromethanesulfonate anion (TFS), forming [HHex][TFS], [HOct][TFS] and [HEtHex][TFS] were studied using DFT calculations with the M06-2X functional and 6-311G(d, p) basis set. The BSSE-corrected interaction energies (∆E0BSSE) for the investigated structures range from − 98.3 to − 108.3 kcal mol−1. NBO and AIM analyses were applied to quantify the relative strengths of the hydrogen bonding interactions and to account for their effect on the stability of various molecular structures. The values of ∆E0BSSE decrease with increasing alkyl chain length and upon introduction of an ethyl branch in the cation. The second-order perturbation energy and electron density indicate that [HAlkyl]1＋[TFS] (protonated at the primary amine, Form A) are more stable than [HAlkyl]2＋[TFS] (protonated at the secondary amine, Form B).

Switching of second-order nonlinear response effected by different acceptors: The impacts of environment and frequency dispersion

In this work, the second-order nonlinear optical (NLO) switch features and electron transition properties for a series of donor-acceptor Stenhouse adducts (DASAs) were explored. The systems we studied contain of a given diethylamine donor and different acceptors, which can be photoinduced from open form to closed form. The calculation results show a remarkable difference in the first hyperpolarizability (β) value between two configurations for each of studied systems, revealing a conspicuous NLO switch feature. Interestingly, in the conditions of gas phase, solid phase polarization effects or frequency dispersion effects, the introduction of indandione acceptor demonstrates the most significant NLO switch feature due to the largest βopen/βclose ratio of compound 5. In general, the differences in the degree of π-electron conjugation and electron transition property between two configurations are responsible for the contrast of NLO response. Our work reveals the features of NLO switch on structure and electron transition property, which will provide some guidance for designing high performance NLO materials.

Electronic Structure and Properties of Silicon-Doped Boron Clusters BnSi withn= 15–24 and Their Anions

We investigated the structures and properties of medium size silicon-doped boron clusters in both neutral and anionic states BnSi0/– with n = 15–24. While geometries were optimized using DFT with both TPSSh and PBE functionals, energies were determined using the coupled-cluster theory (U)­CCSD­(T) with the 6-311+G­(d) basis set, with a calibration using the 6-311+G­(3df) basis set. Average binding energies, second-order energy differences, dissociation energies, and electron detachment energies were predicted by using the (U)­CCSD­(T) + ZPE energies for the entire series. The growth of the BnSi series considered does not follow a regular pattern, but a few trends can be established as follows: (i) most of the lowest-energy isomers of BnSi0/– clusters arise from a replacement of a B atom of the Bn+1 species by an Si atom or an addition of one Si atom into the neutral, anionic, or dianionic Bn species; (ii) the predominance of the planar structures for BnSi0/– clusters can be interpreted as a result of an effect of either the pure boron clusters or the Si dopant or also an effect of the negative charge; and (iii) the Si dopant prefers to be placed at an outer place of the Bn framework in order to exchange for, or to connect to, the peripheral B atoms in forming a low coordination number. The B19Si– anion whose planar motif, MOs shapes, electron distribution, and magnetic ring current are similar to those of the pure anions, B182–, B19–, and B202–, can be considered as a disk aromatic species involving 12 valence π-electrons. The MOs and electron distribution of the pseudotubes B20Si, B22Si, and B24Si can be interpreted by the hollow cylinder model. The first stable pseudotubular shape was found for the size B24Si whose thermodynamic stability is enhanced by both σ and π aromatic characters.

Asymmetric Density Fitting with Modified Cholesky Decomposition Applied to Second-Order Electron Propagator.

Computation of molecular orbital electron repulsion integrals (MO-ERIs) as a transformation from atomic orbital ERIs (AO-ERIs) is the bottleneck of second-order electron propagator calculations when a single orbital is studied. In this contribution, asymmetric density fitting is combined with modified Cholesky decomposition to generate efficiently the required MO-ERIs. The key point of the presented algorithms is to keep track of integrals through partial contractions performed on three-center AO-ERIs; these contractions are stored in RAM instead of the AO-ERIs. Two implementations are provided, an in-core, which reduces the arithmetic and memory scaling factors as compared to the four-center AO-ERIs contraction method, and a semidirect, which overcomes memory limitations by evaluating antisymmetrized MO-ERIs in batches. On the numerical side, the proposed approach is fast and stable. The bad effects due to ill conditioning, namely, several negative and close to zero eigenvalues due to machine round off errors of the matrix associated with the density fitting process, are effectively controlled by means of a modified Cholesky factorization that avoids the matrix inversion needed to perform the asymmetrical density fitting implementation. The numerical experience presented shows that the in-core implementation is highly competitive to perform calculations on medium and large basis sets, while the semidirect implementation has small variations in time by changes in the available memory. The general applicability is illustrated on a set of selected relatively large-size molecules.

Behavior of Ionic Liquids Around Charged Metal Complexes: Investigation of Homogeneous Electron Transfer Reactions Between Metal Complexes in Ionic Liquids

The second-order electron transfer reaction between the photo-excited triplet state of [Zn(TPP)]* (TPP = 5,10,15,20-tetraphenylporphyrin) and [Co(sep)]3+ (sep = sepulchrate = 1,3,6,8,10,13,16,19-octaazabicyclo[6.6.6]eicosane) was investigated in three ionic liquids (ILs, 1-R-3-methylimidazolium bis(trifluoromethylsulfonyl)imide with R = butyl, pentyl, and hexyl) and in acetonitrile. Results of electrochemical and kinetic measurements indicated that ILs dissociate in the vicinity of charged metal complexes and at electrodes, although the dissociated anionic and cationic components of the ILs seem to exist as pairs around the metal complexes. Second-order rate constants for the electron transfer reaction are 1.88 × 109, 3.65 × 107, 2.63 × 107, and 2.01 × 107 kg·mol−1·s−1 in acetonitrile and in the butyl, pentyl and hexyl ILs, respectively, at 298 K, after correction of the contribution of diffusion. The average slope of the plot of the logarithmic second-order rate constants observed in acetonitrile and ILs against the logarithmic viscosity of each solvent was − 0.84. However, the slope of the same plot was much steeper (− 4.1) when data for only the three ILs were used. Detailed analyses of the experimental results on the basis of the Latner–Levin cross relation and the Marcus theory lead to the conclusion that the solvent properties such as the dielectric constant and refractive index around the polarized/charged transition states are different from those for the bulk ILs: observed self-exchange rate constants did not exhibit the Pekar factor dependence when dielectric constants and refractive indices for bulk ILs are used.

Optimization of the spin-component-scaled factor for electron propagator method

A cost-free modification of second-order electron propagator theory (ex-SCS-EP2) to improve the description of ionization energies based on spin-component-scaled approximation is proposed. The relaxation part (PRX) and correlation part (PRM) in second-order self-energy are partitioned into parallel- and anti-parallel-spin component then scaled separately. The scaling factors are optimized with 23 valence orbital energies and results shown that ex-SCS-EP2 performs significantly better than regular EP2, SCS-EP2 and OVGF with 0.22eV of mean absolute error (MAE) and 0.11eV of mean absolute deviation (MAD). The effects of SCS parameters on self-energy are also examined to ensure better description in total correlation energy.

Kinetics of the outer-sphere oxidation of thiourea by heteropoly-α2-17-tungsto-1-vanadodiphosphate anion

Kinetics of the oxidation of thiourea (tu) by heteropoly-α2-17-tungsto-1-vanadodiphosphate anion, α2-[P2VVW17O62]7−, have been studied spectrophotometrically in aqueous acidic medium at 25 °C. At low pH (2.4–3.0), the neutral form of tu is the only reactive species. At higher pH (4.2–4.9), both neutral and deprotonated forms of tu participate in the reaction. The observed mixed-order kinetics suggest two parallel reactions: one in which the order in [tu] is unity, and a second in which it is two. In both cases, the order in [α2-[P2VVW17O62]7−] is unity. Based on the kinetic studies, a mechanism is proposed, in which a second-order proton-coupled electron transfer involving NH2CSNH2 and α2-[P2VVW17O62]7− proceeds through a sequential electron transfer, followed by proton transfer such that the reaction is an “activation-controlled” outer-sphere electron transfer process. By applying the Marcus equation, the self-exchange rate constants for the couples $${\text{NH}}_{2} {\text{CSNH}}_{2}^{ \cdot + }$$ /NH2CSNH2 and α2-[P2VVW17O62]7−/α2-[P2VIVW17O62]8− were evaluated.

A theoretical model of the interaction between phosphates in the ATP molecule and guanidinium systems

In order to understand the interaction between adenosine-5′-triphosphate (ATP) and guanidinium, as recently hypothesized in protein kinase type III inhibitors, a theoretical study has been carried out. First, the intrinsic interactions established between these two systems were studied using a model of ATP; thus, the interactions between a phosphate anion and differently substituted phenylguanidinium cations have been analysed. Then, considering the most stable complexes found with this simplified model, those formed between the phosphate groups of ATP and diaromatic guanidinium derivatives have been studied. All the calculations have been performed using ab initio MP2/6-311++G(d,p)//MP2/6-31+G(d,p) computational level utilizing the polarizable continuum model mimicking water solvation. Besides, only for ATP complexes the geometry optimization has been modified, and thus, DFT-D calculations with the ωB97XD functional were carried out. The Atoms in Molecules analysis of the electron density, natural bond orbital second-order orbital energies and electron density shift maps have been used to better understand the intermolecular interactions.

Composite electron propagator methods for calculating ionization energies.

Accurate ionization energies of molecules may be determined efficiently with composite electron-propagator (CEP) techniques. These methods estimate the results of a calculation with an advanced correlation method and a large basis set by performing a series of more tractable calculations in which large basis sets are used with simpler approximations and small basis sets are paired with more demanding correlation techniques. The performance of several CEP methods, in which diagonal, second-order electron propagator results with large basis sets are combined with higher-order results obtained with smaller basis sets, has been tested for the ionization energies of closed-shell molecules from the G2 set. Useful compromises of accuracy and computational efficiency employ complete-basis-set extrapolation for second-order results and small basis sets in third-order, partial third-order, renormalized partial-third order, or outer valence Green's function calculations. Analysis of results for vertical as well as adiabatic ionization energies leads to specific recommendations on the best use of regular and composite methods. Results for 22 organic molecules of interest in the design of photovoltaic devices, benzo[a]pyrene, Mg-octaethylporphyrin, and C60 illustrate the capabilities of CEP methods for calculations on large molecules.

Competition between intramolecular hydrogen and pnictogen bonds in protonated systems

A theoretical study of the competition between hydrogen (HB) and pnictogen bonds (ZB) in three different families of compounds, (Z)-1,2-disubstituted ethenes (Eth), 1,2-disubstituted benzenes (Phe) and 1,8-disubstituted naphthalenes (Naph), with a charged group, ZH3 + and a neutral one, Z′H2 (Z, Z′ = N, P, As) as interacting moieties, has been carried out. In those structures with a NH3 + motif, intramolecular hydrogen bond structures are minima while pnictogen interactions are transition states. The opposite is true for PH3 + and AsH3 + moieties. An analysis of isodesmic energies (E iso), interaction energies (E b) and deformation energies (E def) shows that in Eth derivatives, the most stable compound corresponds to P+–N ZB while in the Phe and Naph ones, the N+–N HB interaction presents the largest negative isodesmic energy. Also, Eth and Phe derivatives show negative E iso values for all the compounds under study; however, in some cases of Naph derivatives positive isodesmic energies have been found. The Atoms in Molecules (AIM) analysis of the electron density, natural bond orbital (NBO) second-order orbital energies and electron density shift maps (EDS) have been used to better understand these intramolecular interactions.

Reactions of the halonium ions of carenes and pinenes: An experimental and theoretical study

The reactions of vinylcyclopropane (+)-2-carene (1) and vinylcyclobutanes (-)-β-pinene (7), (-)-α-pinene (11), and (-)-nopol (12) with electrophilic halogens in the presence of oxygen and nitrogen nucleophiles in various solvents have been investigated. The halonium ion intermediates that were presumably formed were very reactive and led to opening of the conjugated cyclopropane or cyclobutane. Reactions of chloramine-T trihydrate with compound 1 in acetonitrile gave amidine 13 and diazepine 14. Reactions of chloramine-T trihydrate with pinenes in methylene chloride gave allylic tosylamines 22, 16B and 24. Mechanisms to explain the observations are proposed and supported by ab initio and Density Functional Theory calculations on the carenes and pinenes in this report and their bromonium ion intermediates. For comparisons, the relative extent of conjugation with the bromonium ion moiety of these, as well as select cyclohexene and cyclohexadiene systems and their corresponding bromonium ions, were optimized at the B3LYP/cc-pVDZ level of theory, and then these geometries were analyzed using the absolute hardness index at the Hartree-Fock/aug-cc-pVDZ and B3LYP/aug-cc-pVDZ levels of theory. Additionally, Natural Population Analysis charges were calculated for these systems using Moller-Plessett Second-Order Perturbation Theory electron densities and the aug-cc-pVDZ basis set. Combining the results of these theoretical methods with analysis of structural details of their optimized geometries gives much electronic structure insight into the extent of conjugation of bromonium ions of the carenes and pinenes reported here, and places them in relative context of more traditional conjugated and non-conjugated bromonium ion systems. In particular, bromonium ions of compounds 1, 7, and 11 display structural distortions, charge delocalizations and hardness values comparable with those of traditional conjugated cyclohexadienes, with possible reasons for subtle differences presented.

Voltage and Dopant Concentration Measurements of Semiconductors using a Band-Pass Toroidal Energy Analyzer Inside a Scanning Electron Microscope.

This paper presents experimental results obtained from a scanning electron microscope (SEM) second-order focusing toroidal electron energy analyzer attachment. The results demonstrate that the analyzer can be used to obtain high signal-to-noise voltage and dopant concentration measurements on semiconductors in the presence of different electric field conditions at the sample. The experimentally calculated relative error of measurement typically varies from 31 to 63, corresponding to secondary electron (SE) signal mean shifts of 9-18 mV. The millivolt accuracy of these results is over one order of magnitude better than earlier quantitative dopant concentration measurements made by a retarding field analyzer.

Direct ΔMBPT(2) method for ionization potentials, electron affinities, and excitation energies using fractional occupation numbers

A direct method (D-ΔMBPT(2)) to calculate second-order ionization potentials (IPs), electron affinities (EAs), and excitation energies is developed. The ΔMBPT(2) method is defined as the correlated extension of the ΔHF method. Energy differences are obtained by integrating the energy derivative with respect to occupation numbers over the appropriate parameter range. This is made possible by writing the second-order energy as a function of the occupation numbers. Relaxation effects are fully included at the SCF level. This is in contrast to linear response theory, which makes the D-ΔMBPT(2) applicable not only to single excited but also higher excited states. We show the relationship of the D-ΔMBPT(2) method for IPs and EAs to a second-order approximation of the effective Fock-space coupled-cluster Hamiltonian and a second-order electron propagator method. We also discuss the connection between the D-ΔMBPT(2) method for excitation energies and the CIS-MP2 method. Finally, as a proof of principle, we apply our method to calculate ionization potentials and excitation energies of some small molecules. For IPs, the ΔMBPT(2) results compare well to the second-order solution of the Dyson equation. For excitation energies, the deviation from equation of motion coupled cluster singles and doubles increases when correlation becomes more important. When using the numerical integration technique, we encounter difficulties that prevented us from reaching the ΔMBPT(2) values. Most importantly, relaxation beyond the Hartree-Fock level is significant and needs to be included in future research.

Second-order Hartree–Fock conditional electron densities of atoms

The second-order conditional electron density c(2)N(r1|r2) associated with the electron-pair radial density D(2)N(r1, r2) is studied in the Hartree–Fock theory of atoms with N ( ⩾ 2) electrons. In particular, it is shown that when r2 → ∞, 2c(2)N(r1|r2) becomes DN − 1(r1) which is the single-electron radial density of the (N–1)-electron system arising from the removal of the outermost electron from the original system under the frozen orbital approximation. Namely, we can extract the electron density dh(r) of the outermost subshell h from the total electron-pair density D(2)N(r1, r2). Conditional expectations of multiplicative radial operators have the same properties as above. These results apply not only to the spherically averaged densities but also to the densities with angular variables though in some cases we have to specify angular values of the outgoing electron. A numerical illustration is given for the Kr atom.

Electrical Resistance and Seebeck Coefficient in PbTe Nanowires

We address a physics-based simplified analytical formulation of the diffusive electrical resistance ( (Omega)) and Seebeck coefficient () in a PbTe nanowire dominated by acoustic phonon scattering under the presence of a low static longitudinal electric field. The use of a second-order nonparabolic electron energy band structure involving a geometry-dependent band gap has been selected in principle to demonstrate that the electron mean free path (MFP) in such a system can reach as low as about 8 nm at room temperature for a 10-nm-wide PbTe nanowire. This is followed by the formulation of the carrier back-scattering coefficient for determination of (Omega) and as functions of wire dimensions, temperature, and the field, respectively. The present analytical formulation agrees well with the available experimental data and may find extensive use in determination of various electrothermal transport phenomena in PbTe-based one-dimensional electron devices.

NMR Study of Ligand Exchange and Electron Self-Exchange between Oxo-Centered Trinuclear Clusters [Fe3(μ3-O)(μ-O2CR)6(4-R′py)3]+/0

The syntheses, single crystal X-ray structures, and magnetic properties of the homometallic μ₃-oxo trinuclear clusters [Fe₃(μ₃-O)(μ-O₂CCH₃)₆(4-Phpy)₃](ClO₄) (1) and [Fe₃(μ₃-O)(μ-O₂CAd)₆(4-Mepy)₃](NO₃) (2) are reported (Ad = adamantane). The persistence of the trinuclear structure within 1 and 2 in CD₂Cl₂ and C₂D₂Cl₄ solutions in the temperature range 190-390 K is demonstrated by ¹H NMR. An equilibrium between the mixed pyridine clusters [Fe₃(μ₃-O)(μ-O₂CAd)₆(4-Mepy)(3-x)(4-Phpy)(x)](NO₃) (x = 0, 1, 2, 3) with a close to statistical distribution of these species is observed in CD₂Cl₂ solutions. Variable-temperature NMR line-broadening made it possible to quantify the coordinated/free 4-Rpy exchanges at the iron centers of 1 and 2: k(ex)²⁹⁸ = 6.5 ± 1.3 × 10⁻¹ s⁻¹, ΔH(‡) = 89.47 ± 2 kJ mol⁻¹, and ΔS(‡) = +51.8 ± 6 J K⁻¹ mol⁻¹ for 1 and k(ex)²⁹⁸ = 3.4 ± 0.5 × 10⁻¹ s⁻¹, ΔH(‡) = 91.13 ± 2 kJ mol⁻¹, and ΔS(‡) = +51.9 ± 5 J K⁻¹ mol⁻¹ for 2. A limiting D mechanism is assigned for these ligand exchange reactions on the basis of first-order rate laws and positive and large entropies of activation. The exchange rates are 4 orders of magnitude slower than those observed for the ligand exchange on the reduced heterovalent cluster [Fe(III)₂Fe(II)(μ₃-O)(μ-O₂CCH₃)₆(4-Phpy)₃] (3). In 3, the intramolecular Fe(III)/Fe(II) electron exchange is too fast to be observed. At low temperatures, the 1/3 intermolecular second-order electron self-exchange reaction is faster than the 4-Phpy ligand exchange reactions on these two clusters, suggesting an outer-sphere mechanism: k₂²⁹⁸ = 72.4 ± 1.0 × 103 M⁻¹ s⁻¹, ΔH(‡) = 18.18 ± 0.3 kJ mol⁻¹, and ΔS(‡) = -90.88 ± 1.0 J K⁻¹ mol⁻¹. The [Fe₃(μ₃-O)(μ-O₂CCH₃)₆(4-Phpy)₃](+/0) electron self-exchange reaction is compared with the more than 3 orders of magnitude faster [Ru₃(μ₃-O)(μ-O₂CCH₃)₆(py)₃](+/0) self-exchange reaction (ΔΔG(exptl)(‡298) = 18.2 kJ mol⁻¹). The theoretical estimated self-exchange rate constants for both processes compare reasonably well with the experimental values. The equilibrium constant for the formation of the precursor to the electron-transfer and the free energy of activation contribution for the solvent reorganization to reach the electron transfer step are taken to be the same for both redox couples. The larger ΔG(exptl)(‡298) for the 1/3 iron self-exchange is attributed to the larger (11.1 kJ mol⁻¹) inner-sphere reorganization energy of the 1 and 3 iron clusters in addition to a supplementary energy (6.1 kJ mol⁻¹) which arises as a result of the fact that each encounter is not electron-transfer spin-allowed for the iron redox couple.