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.     

Contribution of inner-sphere reorganization in electron-transfer reaction in solution

A recently published paper in which the inner- and outer-sphere contributions in redox reactions are compared is incorrect. If one uses the experimental values for the force constants, rather than those calculated from the Urey—Bradley method, one finds R_inner = 1.6 R_out, where R represents the reorganization energy.     

Solvent reorganization energy of electron-transfer reactions in polar solvents

A microscopic theory of solvent reorganization energy in polar molecular solvents is developed. The theory represents the solvent response as a combination of the density and polarization fluctuations of the solvent given in terms of the density and polarization structure factors. A fully analytical formulation of the theory is provided for a solute of arbitrary shape with an arbitrary distribution of charge. A good agreement between the analytical procedure and the results of Monte Carlo simulations of model systems is achieved. The reorganization energy splits into the contributions from density fluctuations and polarization fluctuations. The polarization part is dominated by longitudinal polarization response. The density part is inversely proportional to temperature. The dependence of the solvent reorganization energy on the solvent dipole moment and refractive index is discussed.     

The use of calculated reorganization energies in experimental electrochemical kinetics

Calculated reorganization energies in solution using the polarizable continuum model implemented in Gaussian 03 are compared to experimental values of the heterogeneous rate constants for the reduction of a wide variety of neutral molecules in dimethylformamide. The calculated reorganization energies are fully consistent with the experimental data; the computational procedure may in fact be quite useful for estimating the reorganization energies for outer-sphere electrochemical reactions. From the comparison between the calculated reorganization energy values and the experimental values for the heterogeneous rate constants, the adiabaticity of the redox couples' is discussed.     

Solvent-dependent vibrational frequencies and reorganization energies of two merocyanine chromophores

Absorption and resonance Raman spectra have been measured over a wide range of solvents for two merocyanine dyes containing the indoline ("Fischer" base) electron donor group with different accepting groups. One appears to be near the cyanine limit (equal contributions of the neutral and zwitterionic resonance forms to both ground- and excited-state structures) based on electrooptic absorption data showing a very small dipole moment change upon electronic excitation. The resonance Raman spectra of both molecules show significant frequency shifts and intensity redistributions that evolve monotonically with increasing solvent polarity and are consistent with increasing zwitterionic character of the ground-state structure. The vibrational reorganization energies of both molecules, obtained by simulating the absorption band shapes, are smaller in polar solvents than in nonpolar or weakly polar ones, consistent with a more cyanine-like structure at higher solvent polarities. However, the vibrational reorganization energies of both molecules exceed 700 cm(-1) in all solvents, larger than in many true cyanine dyes, and the optical absorption maxima do not correlate well with either solvent polarity or vibrational reorganization energy. This indicates some limitations to the structural conclusions that can be reached from the two-state model for pi-conjugated donor-acceptor systems.     

Cooperativity in chiroptical sensing with dendritic zinc porphyrins

Zinc porphyrin-appended dendrimers, 12PZn, 18PZn, 24PZn, and 36PZn, containing 12, 18, 24, and 36 zinc porphyrin units, respectively, were synthesized using zinc porphyrin dyad (2PZn) and triad (3PZn) as precursors. Although these dye-functionalized dendrimers all serve as chiroptical sensors for an asymmetric bipyridine (RR- and SS-Py2), the sensing capability is highly dependent on the structure of the dendritic scaffold. 2PZn, which is chiroptically silent toward Py2, turns cooperative and displays a large ICD (induced circular dichroism) response in the visible region when incorporated into 12PZn. Judging from the extents of contribution of each zinc porphyrin unit to the CD amplitudes ([Deltaepsilonmax]), the cooperativity in 24PZn (112 M-1 cm-1) is lower than that in 12PZn (196 M-1 cm-1) and much lower in dendron 4PZn (59 M-1 cm-1). In contrast, 3PZn, which is ICD-active toward Py2, hardly shows such an enhanced cooperativity when incorporated into 18PZn and 36PZn and dendron 6PZn, as well. Absorption spectroscopy suggests some unique conformational characteristics of the zinc porphyrin units in highly cooperative 12PZn.     

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.     

Anomalous reorganization free energies in optical electron transfer in solution

Autoionization bands are observed in the photoelectron emission spectroscopy of aqueous solutions of cyanometalate complexes (Mn, Fe, W, Mo), anions (NO₃, CIO⁻₄ and cations (Ag⁺ TI⁺. Reorganization free energies for autoionization bands are anomalously low in absolute value (by≈1 eV) in comparison with direct transitions to the continuum. Interpretation is based on potential energy profiles and model calculations for the reorganization free energy.     

Ligand reorganization and activation energies in nonadiabatic electron transfer reactions

The activation energy and ligand reorganization energy for nonadiabatic electron transfer reactions in chemical and biological systems are investigated in this paper. The free energy surfaces and the activation energy are derived exactly in the general case in which the ligand vibration frequencies are not equal. The activation energy is derived by free energy minimization at the transition state. Our formulation leads to the Marcus-Hush [J. Chem. Phys. 24, 979 (1956); 98, 7170 (1994); 28, 962 (1958)] results in the equal-frequency limit and also generalizes the Marcus-Sumi [J. Chem. Phys. 84, 4894 (1986)] model in the context of studying the solvent dynamic effect on electron transfer reactions. It is found that when the ligand vibration frequencies are different, the activation energy derived from the Marcus-Hush formula deviates by 5%-10% from the exact value. If the reduced reorganization energy approximation is introduced in the Marcus-Hush formula, the result is almost exact.     

Bond lengths and reorganization energies in fullerenes and their ions

A very simple tight binding method with bond-length-dependent couplings, similar to the Su-Schrieffer-Heeger model, is described and applied to fullerenes in different charge states. The bond lengths, calculated from the π bond orders, are in good agreement with results obtained by ab initio methods which include correlation, where comparisons can be made. The Jahn-Teller distortions are found to be small for the examples C₂₀, C₂₈-T_d, and C₆₀-I_h. Often many possible distortions are found, for example two different D_5d distortions for the C₂₀ spin triplet state. Bond reorganization energies (λ_b) for reduction and oxidation, which are measures for trapping efficiency and vibronic coupling, are obtained using a parabolic approximation of the energy surface. Received: 3 December 1996 / Accepted: 3 March 1997     

Alkylamine sensing using langmuir-blodgett films of n-alkyl-N-phenylamide-substituted zinc porphyrins

Two porphyrin compounds, zinc(II) 5,10,15,20-tetrakis(3,5,5-trimethyl- N-phenylhexanamide)porphyrin and zinc(II) 5,10,15,20-tetrakis(2,2-dimethyl- N-phenylpropanamide)porphyrin, have been investigated as possible candidates for the detection of alkylamines. UV-visible spectroscopy has shown that their solution absorption spectra are significantly modified upon interaction with a range of organic analytes, including acetic acid, butanone, ethylacetate, hexanethiol, octanal, octanol, alkylamines, and trimethylphosphite. Large spectral changes are observed for the family of alkylamines as a result of the specific affinity between zinc and the amine moiety. Langmuir-Blodgett (LB) films of the porphyrins have been fabricated in order to assess their solid-state sensing capability toward amines. The surface pressure-area (Pi- A) isotherms reveal a clear three-phase Langmuir film behavior and show that these monolayer films may be compressed to a relatively high surface pressure ( approximately 40-50 mN m (-1)). The isotherm data alongside molecular modeling suggest a relatively flat orientation of the porphyrin rings of both compounds: that is, a mutually parallel alignment of the plane of the porphyrin ring and that of the water surface. LB films deposited at 15 mN m (-1) have been exposed to alkylamine vapor (carried by N 2). A red shift and increase in intensity of the Soret band absorbance is observed which can be reversed by flowing pure N 2 over the gently heated sample (60 degrees C) after exposure. Primary amines were expected to invoke the greatest sensing response due to (i) their larger association constants with these porphyrins compared to secondary and tertiary amines and (ii) the ease of diffusion of amines which is expected to follow the order primary > secondary > tertiary due to the steric hindrance arising from the bulky secondary and tertiary amines. However, the magnitude of the absorbance change is largest for exposure to the secondary amines, dipropylamine and dibutylamine, for both porphyrins, compared to primary and tertiary amines. This trend follows that observed when the amines were added to solutions of the porphyrins. The rate of response of the porphyrin LB films falls as the molecular weight of the diffusing alkylamine increases. Furthermore, a greater rate of response is observed for the phenylhexanamide porphyrin compared to the phenylpropanamide porphyrin due to its lower molecular density within the LB film and therefore more porous structure.     

Highly sensitive chiral shift reagent bearing two zinc porphyrins

A new type of chiral receptor (R,R)- or (S,S)-1b with C(2) symmetry was synthesized. An induced-fit type of binding behavior of 1b for diamines was revealed by CD spectroscopy. NMR studies demonstrated that 1b can function as a highly sensitive chiral shift reagent for the determination of the enantiomeric purity of chiral diamines, aziridine, and isoxazoline at the microgram level. [structure: see text]     

Water-soluble zinc porphyrins as artificial receptors for amino acids

The binding of amino acids to water-soluble zinc porphyrins in basic aqueous solution was spectrophotometrically analyzed. The amino acids were bound to the porphyrins through the coordination of the N atom with the central zinc ion. Additional attractions arise due to Coulomb interactions between the -COO(-) anion of the amino acids and the -N(CH(3))(3)(+) cation of the porphyrin substituents and due to hydrophobic interactions between the porphyrin plane and the hydrophobic substituents of the amino acids. These attractions could be explained based on the binding data. The compensatory relationships of DeltaS and DeltaH were also discussed.     

Effect of axial ligands and macrocyclic structure on redox potentials and electron-transfer mechanisms of SnIV porphyrins

The electrochemical properties of dichloro- and dihydroxo-SnIV porphyrins with three different macrocycles were examined in CH2Cl2 containing 0.1 or 0.2 M tetra-n-butylammonium perchlorate as supporting electrolyte. The investigated compounds are represented as (TPP)SnX2, (P)Sn(X)2, and (PQ)Sn(X)2, where TPP = 5,10,15,20-tetraphenylporphyrin, P = 5,10,15,20-tetrakis(3,5-di-tert-butylphenyl)porphyrin, PQ = 5,10,15,20-tetrakis(3,5-di-tert-butylphenyl)quinoxalino[2,3-b']porphyrin, and X = Cl or OH. Each porphyrin can be electroreduced in two one-electron-transfer steps with the half-wave potentials and stability of the eletroreduced compounds being dependent upon the type of coordinated axial ligand and specific macrocyclic structure. All reductions of (TPP)Sn(OH)2, (P)Sn(OH)2, and (PQ)Sn(OH)2 are reversible under the given experimental conditions and lead to the expected porphyrin pi-anion radicals and dianions, which were characterized by thin-layer UV-vis spectroelectrochemistry. This contrasts with what occurs upon the reduction of (PQ)SnCl2, which undergoes a chemical reaction with trace H2O in solution, leading to the formation of (PQ)Sn(OH)2 as well as to a protonated form of the quinoxalinoporphyrin, (PQH)Sn(OH)2, under the application of an applied potential. A protonation of the Q group breaks the conjugation between the fused quinoxaline unit and the porphyrin macrocycle, thus effectively giving a compound whose reduction properties resemble that of the metalloporphyrin in the absence of the fused ring. The electrooxidation of each neutral SnIV porphyrin was also investigated, and the effect of axial ligand and fused quinoxaline ring on the redox potentials and products of electron transfer are discussed.     

The reorganization energies in one-electron oxidation of ferrous complexes in aqueous solution

The photoelectron emission method was used to determine the reorganization free energy of nuclear coordinates in one-electron oxidation reactions. The experimental results for eight ferrous complexes, some of which have large organic ligands, in aqueous solution are in excellent agreement with the theoretical ones.     

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.     

Selective extraction of higher fullerenes using cyclic dimers of zinc porphyrins

Higher fullerenes (>/=C76) were selectively extracted from a fullerene mixture obtained from a combustion-based industrial production source by cyclic dimers of beta-unsubstituted porphyrin zinc complexes 2C5-2C7 with C5-C7 alkylene spacers as host molecules. Results of single extraction of the fullerene mixture with 2C5-2C7 together with a beta-substituted analogue of 2C6 (1C6) and spectroscopic titration of 2C6 and 1C6 with C60, C70, and C96 indicated that the host selectivity toward higher fullerenes is much dependent on the structure of the porphyrin units and the size of the host cavity. Sequential three-stage extraction of the fullerene mixture with the best-behaved 2C6 resulted in considerable enrichment in very rare fullerenes C102-C110 (<0.1 abs %) up to 82 abs % (C76-C114, 99 abs %) (356 nm) of total fullerenes.     

Hopping transport in conductive heterocyclic oligomers: reorganization energies and substituent effects

Molecular scale charge motion in disordered organic materials at ambient temperature occurs via a hopping-type mechanism with rates dictated both by the charge transfer integral and by the reorganization energy due to geometric relaxation. This contribution presents a systematic theoretical analysis of cation internal reorganization energies for a broad family of organic oligoheterocycles-variation of reorganization energy with oligomer chain length, heteroatom identity, and a range of heterocycle substituents provides key information on important structural properties governing internal reorganization energies. At room temperature, the range in reorganization energies induced by substituent variations corresponds to a >10(2)-fold variation in intrinsic hole transfer rate, suggesting that changes in reorganization energy dominate variations in charge-transfer rates for many semiconducting/conducting oligomers.