Free Energy Of Electron Transfer Research Articles

Molecular modelling of fullerene C60 functionalized by nitric oxide for use in biological environment

The unique potential of fullerene C60 for various biological applications has ignited significant interest. However, its inherent non-polarity poses a critical challenge for its effective integration within biological systems. This study delves into the intricate physicochemical characteristics of the innovative [C60 + NO] complex using density functional theory and time-dependent density functional theory. The computational analyses encompass molecular charge, surface electrostatic potential, and dipole moment evaluations. Impressively, the dipole moment of the [C60 + NO] complex significantly increases to 12.92 D. Meticulous surface analysis reveals a subtle interplay between molecular structures, indicating weak interactions. The analysis of the absorption spectrum unveils a noteworthy red-shift of 200 nm subsequent to complex formation. To elucidate the electron transfer mechanisms, we explore photo-induced electron transfer through CAM-B3LYP. This exploration elucidates intricate pathways governing electron transfer, with complementary insights gleaned from Marcus theory's outputs, especially the Gibbs free energy of electron transfer. Changes in the physicochemical properties of approaching C60 and NO molecules reveal interesting results compared to separate molecules. These findings resonate profoundly in the context of potential biological and pharmaceutical utilization. With implications for the biomedical area, the outcomes linked to the [C60 + NO] complex kindle optimism for pioneering biomedical applications.

Kinetics of Initial Charge Separation in the Photosynthetic Reaction Centers of Rhodobacter sphaeroides.

A stochastic kinetic study of the initial electron transfer reaction in the reaction centers of wild-type and different mutants of photosynthetic bacterium Rhodobacter sphaeroides is suggested. The present approach to the disorder-driven complex kinetics skilfully offers an alternative to the earlier dynamic analyses. Exploiting a rational description of the reaction coordinate, effected by the relaxation of the surrounding protein environment, the measured kinetics were reproduced quantitatively. Notably, comparisons of the extracted relative free energies of electron transfer for the selected mutants and the available independent electrochemical estimates show exact agreement in some cases.

Theoretical studies on photo-induced electron transfer process on [Thioridazine].C60 nano-complex; a first principle DFT and TD-DFT

In this study, using the density functional theory (DFT) and time dependent density functional theory (TD-DFT) methods, the physical and chemical properties of the Thioridazineand fullerene C60 nano complex were studied. The most important goal was increasing C60 dipolar moment as a novel drug delivery system to carry Thioridazineand. Several descriptors were used in the ground state, including electrochemical properties based on the HOMO and LUMO orbital energy, hardness, softness, chemical potential, and Mulliken charge. The dipole moment of this nano-complex is about 2.61D, which indicates its moderate solubility in polar solvents. The UV-Vis spectrum obtained with the CAM-B3LYP method shows that the absorption spectrum has blue-shifted by about λ = 24 nm after formation of the complex. Based on the calculations in the excited state and the hole-electron theory in the first three modes, a photo-induced electron transfer (PET) phenomenon was observed at different absorption wavelengths for the complex. Using the Marcus theory of electron transfer, the free energy of activation for electron transfer and the free energy of electron transfer for all PETs were calculated.

New insights into quantifying the solvatochromism of BODIPY based fluorescent probes

A simple semiempiric phenomenological approach is developed for quantifying the solvent effect on the absorption and emission properties of BODIPYs. It is based on a new rule describing the linear relationship between the difference (Stokes shift) and the sum (double Gibbs free energy of electron transfer) for absorption and emission wavenumbers derived from a combination of solvent functions of Liptay theory. This rule is correspondent to changes of dipole moments in the ground and excited states. High reliability and advantages of the developed approach in comparison with traditional methods of the analysis of the solvatochromism based on Dimroth-Reichardt and Lippert-Mataga solvent scales are illustrated for selected BODIPYs exhibiting positive, negative, and near-zero solvatochromism.

Charge-transfer or excimeric state? Exploring the nature of the excited state in cofacially arrayed polyfluorene derivatives

It is well known that upon electronic excitation various π-stacked dimers readily exhibit excimer formation, facilitated by a perfect sandwich-like arrangement between the chromophores. However, it is unclear whether such a dimer is also capable of electron transfer upon excitation, if a strong electron-donating group is covalently attached. In this work, we probe the nature of the excited state in a series of cofacially arrayed polyfluorene derivatives with electron-rich aromatic donor attached via a methylene linker. Our studies show that in all cases excimer formation is energetically favorable, and promotion of a charge-transfer state in such systems is possible but requires a free energy for electron transfer far exceeding 1 V. These findings shed light on important design principles for molecular scaffolds capable of stabilizing both excimeric and charge-transfer states upon their excitation.

Direct Measurement of Charge Regulation in Metalloprotein Electron Transfer.

Determining whether a protein regulates its net electrostatic charge during electron transfer (ET) will deepen our mechanistic understanding of how polypeptides tune rates and free energies of ET (e.g., by affecting reorganization energy, and/or redox potential). Charge regulation during ET has never been measured for proteins because few tools exist to measure the net charge of a folded protein in solution at different oxidation states. Herein, we used a niche analytical tool (protein charge ladders analyzed with capillary electrophoresis) to determine that the net charges of myoglobin, cytochrome c, and azurin change by 0.62±0.06, 1.19±0.02, and 0.51±0.04 units upon single ET. Computational analysis predicts that these fluctuations in charge arise from changes in the pK a values of multiple non‐coordinating residues (predominantly histidine) that involve between 0.42–0.90 eV. These results suggest that ionizable residues can tune the reactivity of redox centers by regulating the net charge of the entire protein–cofactor–solvent complex.

Direct Measurement of Charge Regulation in Metalloprotein Electron Transfer

AbstractDetermining whether a protein regulates its net electrostatic charge during electron transfer (ET) will deepen our mechanistic understanding of how polypeptides tune rates and free energies of ET (e.g., by affecting reorganization energy, and/or redox potential). Charge regulation during ET has never been measured for proteins because few tools exist to measure the net charge of a folded protein in solution at different oxidation states. Herein, we used a niche analytical tool (protein charge ladders analyzed with capillary electrophoresis) to determine that the net charges of myoglobin, cytochrome c, and azurin change by 0.62±0.06, 1.19±0.02, and 0.51±0.04 units upon single ET. Computational analysis predicts that these fluctuations in charge arise from changes in the pKa values of multiple non‐coordinating residues (predominantly histidine) that involve between 0.42–0.90 eV. These results suggest that ionizable residues can tune the reactivity of redox centers by regulating the net charge of the entire protein–cofactor–solvent complex.

Electron Transfer through the Acceptor Side of Photosystem I: Interaction with Exogenous Acceptors and Molecular Oxygen.

This review considers the state-of-the-art on mechanisms and alternative pathways of electron transfer in photosynthetic electron transport chains of chloroplasts and cyanobacteria. The mechanisms of electron transport control between photosystems (PS) I and II and the Calvin-Benson cycle are considered. The redistribution of electron fluxes between the noncyclic, cyclic, and pseudocyclic pathways plays an important role in the regulation of photosynthesis. Mathematical modeling of light-induced electron transport processes is considered. Particular attention is given to the electron transfer reactions on the acceptor side of PS I and to interactions of PS I with exogenous acceptors, including molecular oxygen. A kinetic model of PS I and its interaction with exogenous electron acceptors has been developed. This model is based on experimental kinetics of charge recombination in isolated PS I. Kinetic and thermodynamic parameters of the electron transfer reactions in PS I are scrutinized. The free energies of electron transfer between quinone acceptors A1A/A1B in the symmetric redox cofactor branches of PS I and iron-sulfur clusters FX, FA, and FB have been estimated. The second-order rate constants of electron transfer from PS I to external acceptors have been determined. The data suggest that byproduct formation of superoxide radical in PS I due to the reduction of molecular oxygen in the A1 site (Mehler reaction) can exceed 0.3% of the total electron flux in PS I.

Unsolicited Photoexcited-State Pathways Relegate the Long-Lived Charge Separation in Self-Assembled Nucleobase–Arene Conjugate

We report a comprehensive analysis of the ultrafast photoexcited-state processes of a nucleobase-arene conjugate, 9-(adenin-9-yl)anthracene (AdAn), in organic solvents. By virtue of the strong base-pairing and π-π interactions, AdAn forms an alternate distichous assembly, wherein the adenines are near-orthogonally flanked to the columnar anthracene-on-anthracene (An-An) stacks. The preliminary photophysical and redox analysis of AdAn in organic solvent reveals a summation of adenine (Ad) and anthracene (An) spectral features with minimal perturbation in the ground state properties. The frontier molecular orbital analysis suggests a favorable charge transfer characteristics in the dyad which is further corroborated by the negative value of the free energy for electron transfer from 1Ad* to An (△Get = -1.25 eV) and Ad to 1An* (△Get = -0.12 eV) obtained via Weller analysis. Upon photoexcitation (λex = 266 and 355 nm), self-assembled AdAn reveals the formation of radical ion-pair intermediates (τcrA = 120 ms)...

Effect of solvent nature on the photoreduction kinetics of substituted benzoquinones

Effect of the solvent nature on the kinetics of photoreduction of substituted benzoquinones in the presence of hydrogen donors has been studied. It has been found that the effective photoreduction rate constant (kH) for quinones decreases with an increase in solvent polarity. For the 3,6-di-tert-butylbenzoquinone–1,2-N,N-dimethylaniline pair, the dependence of ln kH on the difference of the reciprocals of optical and static solvent permitivities (1/e ∞–1/e0) is stepwise with a break point corresponding to CH2Cl2. A similar relationship lnkH = f(1/e ∞–1/e0) is observed for the p-chloranil–mesitylene pair. In the study of the photoreduction kinetics for a series of seven o-benzoquinones in the presence of p-derivatives of N,N-dimethylaniline in CH2Cl2, it has been found that the dependence of kH on the free energy of electron transfer (ΔGe) has a maximum for the 3,6-di-tert-butylquinone-1,2–N,N-dimethylaniline pair at ΔGe = 0.11 eV.

NIR-Sensitized Photoinitiated Radical Polymerization and Proton Generation with Cyanines and LED Arrays

Abstract Photoinitiated radical polymerization using as photoinitiator system a combination of NIR-sensitizer (Sens) and a radical initiator (RI) was investigated in different multifunctional monomers derived from the multifunctional acrylic esters HDDA, TPGDA, PEGDA, and TMPTA. NIR-LEDs were applied for exposure exhibiting their emission maximum either at 750 nm, 790 nm, 830 nm or 940 nm. Solubility of Sens in the respective monomers, their absorption data (λabsmax, emax), fluorescence data (Φf, λfmax), electrochemical data (Eox, Ered) and the free energy of electron transfer (ΔGel) between the excited state of Sens and RI were compiled. It showed for many systems an exothermic behavior, which does not always correlate with reactivity. Iodonium salts with low coordinating anions ([B(Ph)4]−, [B(Ph-F5)4]−, [(CF3SO2)2N]-, PF6−) and Triazine A (2,4-Bis(trichloromethyl)-6-(4-methoxy)phenyl-1,3,5-triazine) were applied as RI. Sens was selected from the group of cyanines in which neutral compounds exhibited the highest reactivity. Cationic sensitizers showed almost no initiating reactivity. Furthermore, the sensitizer (5-(6-(2-(3-Ethyl-1,1-dimethyl-1H-benzo[e]indol-2(3H)-ylidene)ethylidene)-2-(2-(3-ethyl-1,1-dimethyl-1H-benzo[e]indol-3-ium-2-yl)vinyl)cyclohex-1-en-1-yl)-1,3-dimethyl-2,6-dioxo-1,2,3,6-tetrahydropyrimidin-4-olate) (S9) was taken to study the effect of wavelength dependent LED excitation. The highest reactivity was found for the LED emitting at 850 nm where the system possesses the highest excitation volume and the lowest absorption of photoproducts. Furthermore, thermal investigation approved that the combination S9 and iodonium salt can be considered as a thermal initiation system either. Thus, these systems can be seen as hybrid initiator systems. Finally, we show for the first time the generation of solvated protons using different iodonium salts and sensitizers in acetone as surrounding. The activity of solvated protons was evaluated showing a certain reactivity tendency. The number of solvated protons with respected to the number of sensitizer molecules was lower than unity showing their consumption by nucleophilic centers.

Theoretical study of electron transfer process between fullerenes and neurotransmitters; acetylcholine, dopamine, serotonin and epinephrine in nanostructures [neurotransmitters].C n complexes.

Neurotransmitters are the compounds which allow the transmission of signals from one neuron to the next across synapses. They are the brain chemicals that communicate information throughout brain and body. Fullerenes are a family of carbonallotropes, molecules composed entirely of carbon, that take the forms of spheres, ellipsoids, and cylinders. Various empty carbon fullerenes (Cn) with different carbon atoms have been obtained and investigated. Topological indices have been successfully used to construct effective and useful mathematical methods to establish clear relationships between structural data and the physical properties of these materials. In this study, the number of carbon atoms in the fullerenes was used as an index to establish a relationship between the structures of neurotransmitters (NTs) acetylcholine (AC) 1, dopamine (DP) 2, serotonin (SE) 3, and epinephrine (EP) 4 as the well-known redox systems and fullerenes C n (n = 60, 70, 76, 82, and 86) which create [NT].Cn; A-1 to A-5 up to D-1 to D-5. The relationship between the number of carbon atoms and the free energy of electron transfer (ΔG et(n); n = 1-4) is assessed using the Rehm-Weller equation for A-1 to A-5 up to D-1 to D-5 supramolecular [NT].Cn complexes. The calculations are presented for the four reduction potentials ( (Red.) E 1 to (Red.) E 4 ) of fullerenes C n . The results were used to calculate the four free energy values of electron transfer (ΔG et(1) to ΔG et(4)) of the supramolecular complexes A-1 to A-8 up to D-1 to D-8 for fullerenes C60 to C120. The first to fourth free activation energy values of electron transfer and the maximum wavelength of the electron transfers, ΔG (#) et(n) and λ et (n = 1-4), respectively, were also calculated in this study for A-1 to A-8 up to D-1 to D-8 in accordance with the Marcus theory.

Comparative antioxidant potency and solvent polarity effects on HAT mechanisms of tocopherols

The antioxidant activity of the four forms of tocopherol has been investigated in gas phase and in different solvents using PBE0/6-31+G(d) level of theory. The three main working mechanisms, homolytic hydrogen atom transfer (HAT), single electron transfer-proton transfer (SET-PT) and sequential proton loss electron transfer (SPLET) have been considered. The O–H bond dissociation free energy (BDFE), ionization potential (IP), proton dissociation free energy (PDFE), proton affinity (PA) and electron transfer free energy (ETFE) parameters have been calculated in gas phase and solvents. The theoretical results show the effect of the substituent position with respect to the phenolic O–H group on the reactivity. The methyl group, in ortho position, lends additional inductive and steric stability to the tocopheroxyl radical and therefore, increases antioxidant activity. α-tocopherol is shown to be the most reactive form in gas phase with the lowest BDFE, IP, and PA values, whereas in all solvents, γ-tocopherol has the lowest PA and PDFE values.The solvent effects are evaluated using an implicit solvation model (IEF-PCM). We have used a good model to calculate the solvation free energy of proton and electron in different media, where proton or electron was attached to one molecule of solvent and the obtained species were optimized using IEF-PCM approach in the same solvent. In gas phase, and non-polar solvents like benzene and toluene, BDFE value is lower than PA and IP, this suggested that HAT would be the most favorable mechanism for explaining the antioxidant activity of tocopherols, whereas SPLET mechanism is thermodynamically preferred in polar solvents like water, DMSO and methanol, where PA value of all forms of tocopherol is considerably lower than BDFE and IP.

Structural relationships and theoretical study of the free energies of electron transfer, electrochemical properties, and electron transfer kinetic of cephalosporin antibiotics derivatives with fullerenes in nanostructure of [R]·C n (R = cefadroxil, cefepime, cephalexin, cefotaxime, cefoperazone and ceftriaxone) supramolecular complexes

Various empty carbon fullerenes (C n ) with different carbon atoms have been obtained and investigated. Cephalosporin antibiotics and its derivatives have important medicinal properties. The β-lactam class of antibiotics has a broad spectrum of antimicrobial properties. Their antibacterial and pharmacokinetic properties have wide therapeutic applications. Topological indices have been successfully used to construct effective and useful mathematical methods to establish clear relationships between structural data and the physical properties of these materials. In this study, the number of carbon atoms in fullerenes was used as an index to establish a relationship between the structures of cefadroxil, cefepime, cephalexin, cefotaxime, cefoperazone and ceftriaxone (β-lactam antibiotics) and fullerenes (C n , n = 60, 70, 76, 82 and 86), which create [cefadroxil]·C n , [cefepime]·C n , [cephalexin]·C n , [cefotaxime]·C n , [cefoperazone]·C n and [ceftriaxone]·C n . The relationship between the number of fullerene carbon atoms and the free energies of electron transfer (ΔG et(1)–ΔG et(4)) are assessed using the Rehm-Weller equation for A-1 to A-5, B1 to B-5, C-1 to C-5, D-1 to D-5, E-1 to E-5 and F-1 to F-5 of the supramolecular complexes [R]·C n (where R = cefadroxil, cefepime, cephalexin, cefotaxime, cefoperazone and ceftriaxone) complexes. The calculations are presented for the four reduction potentials (Red. E 1–Red. E 4 ) of fullerenes C n . The results were used to calculate the four free energies of electron transfer (ΔG et(1)–ΔG et(4)) of the cephalosporin-fullerene supramolecular complexes A-1 to A-5, B1 to B-5, C-1 to C-5, D-1 to D-5, E-1 to E-5 and F-1 to F-5 for fullerenes C60–C120. The free energies of activation for electron transfer, Δ $$ G_{{_{{{\text{et}}\left( n \right)}} }}^{{^{\# } }} $$ (n = 1–4) were also calculated for these complexes in accordance with the Marcus theory. In this study, was presented the calculated wavelengths (λ(n); n = 1–4; in nm) of the photoelectron transfer process as well in the nanostructure complexes.

Exciplexes versus Loose Ion Pairs: How Does the Driving Force Impact the Initial Product Ratio of Photoinduced Charge Separation Reactions?

Many donor–acceptor systems can undergo a photoinduced charge separation reaction, yielding loose ion pairs (LIPs). LIPs can be formed either directly via (distant) electron transfer (ET) or indirectly via the dissociation of an initially formed exciplex or tight ion pair. Establishing the prevalence of one of the reaction pathways is challenging because differentiating initially formed exciplexes from LIPs is difficult due to similar spectroscopic footprints. Hence, no comprehensive reaction model has been established for moderately polar solvents. Here, we employ an approach based on the time-resolved magnetic field effect (MFE) of the delayed exciplex luminescence to distinguish the two reaction channels. We focus on the effects of the driving force of ET and the solvent permittivity. We show that, surprisingly, the exciplex channel is significant even for an exergonic ET system with a free energy of ET of −0.58 eV and for the most polar solutions studied (butyronitrile). Our findings demonstrate that exciplexes play a crucial role even in polar solvents and at moderate driving forces, contrary to what is usually assumed.

Long-Range Electron Transfer with Myoglobin Immobilized at Au/Mixed-SAM Junctions: Mechanistic Impact of the Strong Protein Confinement

Horse muscle myoglobin (Mb) was tightly immobilized at Au-deposited ~15-Å-thick mixed-type (1:1) alkanethiol SAMs, HS-(CH₂)₁₁-COOH/HS-(CH₂)₁₁-OH, and placed in contact with buffered H₂O or D₂O solutions. Fast-scan cyclic voltammetry (CV) and a Marcus-equation-based analysis were applied to determine unimolecular standard rate constants and reorganization free energies for electron transfer (ET), under variable-temperature (15-55 °C) and -pressure (0.01-150 MPa) conditions. The CV signal was surprisingly stable and reproducible even after multiple temperature and pressure cycles. The data analysis revealed the following values: standard rate constant, 33 s⁻¹ (25 °C, 0.01 MPa, H₂O); reorganization free energy, 0.5 ± 0.1 eV (throughout); activation enthalpy, 12 ± 3 kJ mol⁻¹; activation volume, -3.1 ± 0.2 cm³ mol⁻¹; and pH-dependent solvent kinetic isotope effect (k(H)⁰/k(D)⁰), 0.7-1.4. Furthermore, the values for the rate constant and reorganization free energy are very similar to those previously found for cytochrome c electrostatically immobilized at the monocomponent Au/HS-(CH₂)₁₁-COOH junction. In vivo, Mb apparently forms a natural electrostatic complex with cytochrome b₅ (cyt-b₅) through the "dynamic" (loose) docking pattern, allowing for a slow ET that is intrinsically coupled to the water's removal from the "defective" heme iron (altogether shaping the biological repair mechanism for Mb's "met" form). In contrary, our experiments rather mimic the case of a "simple" (tight) docking of the redesigned (mutant) Mb with cyt-b₅ (Nocek et al. J. Am. Chem. Soc. 2010, 132, 6165-6175). According to our analysis, in this configuration, Mb's distal pocket (linked to the "ligand channel") seems to be arrested within the restricted configuration, allowing the rate-determining reversible ET process to be coupled only to the inner-sphere reorganization (minimal elongation/shortening of an Fe-OH₂ bond) rather than the pronounced detachment (rebinding) of water and, hence, to be much faster.

Photophysical investigations on supramolecular fullerene/phthalocyanine charge transfer interactions in solution

The photophysical features of non-covalently linked fullerenes C60 and C70 with a designed free-base phthalocyanine, namely, 2,3,9,10,16,17,23,24-octakis-(octyloxy)-29H,31H-phthalocyanine (1) have been investigated employing various spectroscopic tools like UV–vis absorption spectrophotometry, steady state and time resolved fluorescence along with proton NMR measurements in toluene. The ground state interaction between fullerenes and 1 is nicely demonstrated with the appearance of well defined charge transfer absorption bands in the visible region of the electronic spectra. Steady state fluorescence experiment reveals efficient quenching of the excited singlet state of 1 in presence of both C60 and C70. The average values of binding constants for the non-covalent complexes of C60 and C70 with 1 are determined to be ∼18,150 and ∼32,000dm3mol−1, respectively. The magnitude of K suggests that 1 preferentially binds C70 in comparison to C60 although average value of selectivity in binding is measured to be low (∼1.75). Time resolved emission measurements establish photoinduced energy transfer from the excited singlet state of 1 to fullerene in toluene. Measurements of free energy of electron transfer and free energy of radical ion-pair formation elicit that C70/1 complex is stabilized more in comparison to C60/1 complex regarding generation of charge-separated state. Proton NMR studies provide very good support in favor of effective ground state complexation between fullerenes and 1. Semi empirical theoretical calculations on fullerene/1 systems in vacuo substantiate the stronger binding between C70 and 1 in comparison to C60/1 system in terms of heat of formation value of the respective complexes, and determine the orientation of bound guest (here C70) towards the plane of 1 during complexation.

Designed azurins show lower reorganization free energies for intraprotein electron transfer

Low reorganization free energies are necessary for fast electron transfer (ET) reactions. Hence, rational design of redox proteins with lower reorganization free energies has been a long-standing challenge, promising to yield a deeper understanding of the underlying principles of ET reactivity and to enable potential applications in different energy conversion systems. Herein we report studies of the intramolecular ET from pulse radiolytically produced disulfide radicals to Cu(II) in rationally designed azurin mutants. In these mutants, the copper coordination sphere has been fine-tuned to span a wide range of reduction potentials while leaving the metal binding site effectively undisrupted. We find that the reorganization free energies of ET within the mutants are indeed lower than that of WT azurin, increasing the intramolecular ET rate constants almost 10-fold: changes that are correlated with increased flexibility of their copper sites. Moreover, the lower reorganization free energy results in the ET rate constants reaching a maximum value at higher driving forces, as predicted by the Marcus theory.

Free energies, kinetics, and photoelectron-transfer properties, and theoretical and quantitative structural relationship studies of [SWCNT(5,5)-armchair-C n H20][R] (R = η2-C m Pd(dppf), η2-C m Pd(dppr), and η2-C m Pd(dppcym)2, n = 20 to 300 and m = 60 and 70) nanostructure complexes

Metal complexes containing one or several bis(triorganylphosphine)palladium fragments attached to the C60 core and coordinated in olefinic η2 mode have been previously described. The number of carbon atoms of the single-walled carbon nanotubes (SWCNTs) is the useful numerical and structural electrochemical properties contributing to the relationship between the structures of the η2_C m Pd(dppf), η2_C m Pd(dppr), and η2_C m Pd(dppcym)2 (m = 60 and 70) ligands (A to E) and [SWCNT(5,5)-armchair-C n H20] (n = 20 to 190) 1 to 18 and the production of the [SWCNT(5,5)-armchair-C n H20][R] (R = η2-C m Pd(dppf), η2-C m Pd(dppr), and η2-C m Pd(dppcym)2, n = 20 to 300 and m = 60 and 70) complexes 30 to 174. In this study, the relationship between the number of carbon atoms index and the first and second free energies of electron transfer (ΔGet(n), n = 1,2) using the Rehm-Weller equation based on the first and second oxidation potentials (oxE1 and oxE2) of A to E for the predicted complexes 30 to 174 between 1 and 29 with exohedral metallofullerenes A to E, as [SWCNT(5,5)-armchair-C n H20][R] (R = η2-C m Pd(dppf), η2-C m Pd(dppr), and η2-C m Pd(dppcym)2, n = 20 to 300 and m = 60 and 70) 30 to 174 was assessed. Here, the first and second free activation energies of electron transfer and the wavelengths of the electromagnetic photons in the photoelectron transfer process, ΔG#et(n) and λ(n) (nm), respectively, for 30 to 174 in accordance with the Marcus theory and Planck's equation were also calculated.

Theoretical Study and Structural Relationships of Free Energies of Electron Transfer, Electrochemical Properties and Electron Transfer Kinetics of Ferrocene Derivatives with Fullerenes in Nanostructures of [(R)2Cp2-Fe].Cn Supramolecular Complexes

Ferrocene (Cp2-Fe) and its derivatives are part of a broad-spectrum of organometallic compounds that are commonly used in electronics and semiconductors. Fullerenes are a family of carbon allotropes composed entirely of carbon in the form of spheres, ellipsoids and cylinders. Various empty carbon fullerenes (Cn) have been obtained and investigated. The Cp2-Fe derivatives have exhibited important electron-transfer properties. Topological indices have been proposed to correlate structures with properties. They have been successfully employed to construct effective and useful mathematical methods to establish clear relationships between structural data and the physical properties of these materials. In this study, the number of carbon atoms in the fullerenes was used as an index to establish a relationship between the structures of ferrocenyl derivatives (1–15), ferrocenyl fullerene complexes 1–15 (the most well-known redox systems) and fullerenes Cn (n = 60, 70, 76, 82 and 86) A-1 to O-5, which are commonly denoted as [Fc-x].Cn. The Rehm-Weller equation was applied to build the relationship between the structures and the free energies for electron transfer (ΔGet(1) to ΔGet(4) ) of the complexes [Fc-x].Cn (A-1 to O-5). The calculations are presented for the four reduction potentials ( Red.E1 to Red.E4 ) of the fullerenes Cn . The reduction potentials of the fullerenes Cn have been applied to calculate the four free energies of electron transfer (ΔGet(1) to ΔGet(4) ) of supramolecular complexes [Fc-x].Cn (A-1 to O-5). Based on Marcus theory and Planck's equation, the first four free activation energies of electron transfer and the wavelengths (ΔGet(1) # to ΔGet(4) # and λ et , n = 1–4, respectively) for the photoelectron transfer process were also calculated for [Fc-x].Cn (A-1 to O-5).