Theoretical approaches to intramolecular electron transfer processes

Theoretical issues that must be considered for calculating rates of intramolecular electron transfer are discussed. The process itself is well defined only if the ground state is well approximated by a localized electronic function (Robin–Day class I or II). Under those conditions, the linear-response formalism yields the rate as the Fourier transform of the particle–hole propagator. We discuss the validity of electron propagators as approximations to particle-hole propagators, and find that they are valid, for simple models, within the stability range of the Hartree–Fock procedure. The vibronic nature of the transfer process is stressed, and formal schemes are given for calculating direct and through-bridge transfer rates. Outstanding difficulties, and applications to biological systems, are very briefly noted.     

Theoretical investigation of electron transfer transition in tetracyanoethylene-contained organic complexes

In this work, the authors use complete active space self-consistent field method to investigate the photoinduced charge-separated states and the electron transfer transition in complexes ethylene-tetracyanoethylene and tetramethylethylene-tetracyanoethylene. Geometries of isolated tetracyanoethylene, ethylene, and tetramethylethylene have been optimized. The ground state and the low-lying excited states of ethylene and tetracyanoethylene have been optimized. The state energies in the gas phase have been obtained and compared with the experimentally observed values. The torsion barrier of tetracyanoethylene has been investigated through the state energy calculation at different conformations. Attention has been particularly paid to the charge-separated states and the electron transfer transition of complexes. The stacked conformations of the donor-acceptor complexes have been chosen for the optimization of the ground and low-lying excited states. Equilibrium solvation has been considered by means of conductor-like screening model both in water and in dichloromethane. It has been found that the donor and tetracyanoethylene remain neutral in complexes in ground state (1)A(1) and in lowest triplet state (3)B(1), but charge separation appears in excited singlet state (1)B(1). Through the correction of nonequilibrium solvation energy based on the spherical cavity approximation, pi-->pi* electron transfer transition energies have been obtained. Compared with the experimental measurements in dichloromethane, the theoretical results in the same solvent are found higher by about 0.5 eV.     

Solvent friction effect on intramolecular electron transfer

U-shaped donor-bridge-acceptor molecules with different electronic couplings have been investigated as a function of temperature in solvents with slow polarization relaxation, in particular, N-methylacetamide (NMA) and N-methylpropionamide (NMP). At high temperature, the electron-transfer rate is well described by a nonadiabatic model; however, the rate at low temperature is controlled by the solvent friction. The change of the electron-transfer mechanism is discussed and compared with theoretical models.     

Theoretical studies of intramolecular electron transfer reactions: Distance and free energy dependences

Electron tunneling through a square potential energy barrier is used to calculate the distance-dependent factors of electron transfer (ET) processes in metal-monolayer-metal junctions, donors and acceptors dispersed in rigid organic glasses, intramolecular ET in rigid donorbridge—acceptor species in solution and redox centers attached to electrodes through adsorbed monolayers. This tunneling model of distancedependent non-adiabatic factors is incorporated in the intersecting state model (ISM). The result is a simple semiclassical theory which is used to calculate the rates of non-adiabatic ET reactions. When the electron is originally located in a π* molecular orbital of the donor and the reaction free energy is no lower than approximately −50 kJ mol⁻¹, no adjustable parameters are necessary to calculate the intramolecular ET rates from a donor, through a rigid bridge, to an acceptor. Such calculated rates are within an order of magnitude of the experimental values. The model can also account for the ET rates of more exothermic reactions provided that the value of an empirical parameter, which is constant for structurally related reactants and solvents of similar polarity, is estimated. The physical meaning of this parameter is related to the dynamics of the reactions. The profiles of the distance and free energy dependences of photoinduced ET rates are closely reproduced. The occurrence of distance-dependent non-adiabatic factors in intermolecular σ*-d ETs is rationalized.     

A single-molecule probe based on intramolecular electron transfer

Detecting structure, dynamics, and chemical reactions at the single-molecule level represents the ultimate degree of sensitivity for sensing and imaging. There is a tremendous need to develop new molecular systems and methodology for single-molecule-based sensing. This work presents for the first time the single-molecule spectroscopy of a new molecular probe which uses an intramolecular electron transfer mechanism to detect binding, local structure, and interfacial processes. Moreover, we show how information about the interaction of these probes with their environment is obtained from an analysis of the intensity, duration and time-varying behavior of the single-molecule fluorescence.     

Theoretical investigation on dual fluorescence and intramolecular charge transfer of 5-phenyl-5H-phenanthridin-6-one

Quantum-chemical calculations with the time-dependent density function theory (TDDFT) have been carried out for 5-phenyl-5H-phenanthridin-6-one (PP). For this molecule, dual fluorescence and in- tramolecular charge transfer (ICT) were experimentally observed. The B3LYP functional with 6-311 G (2d, p) basis set has been used for the theoretical calculations. The solvent effects have been described within the polarizable continuum model (PCM). Ground-state geometry optimization reveals that the phenyl/phenanthridinone dihedral angle equals 90.0°, a nearly perpendicular structure. Vertical ab- sorption energy calculations characterize the lower singlet excited states both in gas phase and in solvents. It can be found that the lower excited states have locally excitation (LE) feature. Through constructing the potential energy curves of both isolated and solvated systems describing the LE→ICT reaction and fluorescence emission, we obtain the enthalpy difference ΔH between the LE and ICT states, energy barrier Ea, and energy difference δEFC, indicating the structural changes taking place during the ICT reaction. Potential curve and calculated emission energies for both isolated and sol- vated systems show a dual fluorescence phenomenon, consisting of a LE emission band and a red-shifted ICT band. Our calculations including the solvent effects indicate that the dual fluorescence is brought about by the change in molecular structure connected with the planarization of the twisted N-phenylphenanthridinone during the ICT reaction.     

Dynamics of intramolecular electron transfer in dinitrodibenzodioxin radical anions

The activation energy for intramolecular electron transfer in radical anions of 2,7-dinitrodibenzodioxin and 2,8-dinitrodibenzodioxin, obtained by simulation of their temperature-dependent EPR spectra, are well predicted by the values calculated by the two-state Marcus-Hush model from the optical charge-transfer bands using quartic-adjusted energy surfaces. The electronic coupling is higher in the 2,8-dinitrodibenzodioxin (H(ab) = 485 cm(-1)) than in the 2,7-dinitrodibenzodioxin radical anion (H(ab) = 250 cm(-1)), but for each solvent the reorganization energy, taken as the maximum of the optical band, is only slightly higher in the latter. These values are consistent with the fact that the reaction is faster in the 2,8-dinitrodibenzodioxin radical anion isomer, as determined by EPR spectroscopy. The pre-exponential factors obtained combining the EPR-derived rate constants and the activation energies calculated from the optical bands fit well the theoretical (modified) nonadiabatic values in the less viscous solvents. However, for the more viscous solvents, the trend of the pre-exponential values with solvent can only be explained if dynamical solvent effects increasingly influence their value. The influence of solvent dynamics in the 2,8-dinitrodibenzodioxin radical anion starts in the less viscous solvents DMF and DMSO, but in the 2,7-dinitrodibenzodioxin isomer this is only fully evident for the more viscous PhCN and HMPA. The influence of solvent dynamics is higher in the radical with the lowest activation barrier.     

Theoretical study of intramolecular proton transfer of perylenequinone

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Photoinduced intramolecular electron transfer between fluorescein and carbazole

Several dyads consisting of a fluoreseein covalently linked with a carhazole at site 2 or site 6 have been synthesized and characterized.Studies of absorption spectra,emission spectra and fluorescence lifetime quern hing Indicate that the ground-state interaction between fluorescein and carhazole in dyads is negligible and the intramolecular electron transfer (ET) reactions are mainly of dynamic process.Moreover,the efficiency and raie conslam of lectron transfer reactions in ZFO4 (carbazole linked at site 2'of fluorescein) are larg er than those in 4FOZ (carbazole linked at site 6 of fluorescein) 0 74; KET 11×108S-1),because the mutual orientation of donor and acceptor in ZFO4 is nearly face-to-face,which is more favorable to the process than the shoulder-to-shoulder mutual orientation in 4FOZ.Estimations are also formed of the free energy change of the photomduced electron transfer and the back reactions in the dyads.     

Directed,intramolecular electron and energy transfer in mixed-valence dimers

Laser flash photolysis on a series of unsymmetrical ruthenium dimers has provided evidence for directed, intramolecular excitation energy transfer by a one-electron pathway for mixed-valence, Ru^II-Ru^III, dimers and by simple energy transfer for Ru^II-Ru^II dimers.     

Computational study of topological effects on intramolecular electron transfer in mixed-valence compounds

The constrained density functional theory (CDFT) was used to investigate the topological effects on intramolecular electron transfer processes that have been reported in previous experimental work [Inorg. Chem., 1997, 36 (22), pp 5037–5049]. The computation mainly focused on three isomers of diferrocenylbenzenes (ortho, para, and meta) and 5-substituted derivatives of m-diferrocencylbenzenes with R = NH₂, Cl, CH₃, CN, NO₂, NeCH₃)₃³⁺, and N₂⁺. The influence of a third group R′ (R′ = NH₂ and N₂⁺) was introduced to the ortho and para isomers. The calculations were compared with the experimental results. The relation between the substituted functional groups and the effectiveness of intramolecular electron transfer was discussed on the basis of CDFT computational results.     

Unprecedented optically induced long-lived intramolecular electron transfer in cobalt-dioxolene complexes

The observation of very long lifetimes of the metastable states of two cobalt-dioxolene complexes undergoing photoinduced and high T(c) thermally-induced valence tautomer interconversion opens new research perspectives.     

Photoinduced intramolecular electron transfer and triplet energy transfer in a steroid-linked norbornadiene-carbazole dyad

Bichromophoric compound 3 beta-((2-(methoxycarbonyl)bicyclo[2.2.1]hepta-2,5-diene-3-yl)carboxy)androst-5-en-17 beta-yl-[2-(N-carbazolyl)acetate] (NBD-S-CZ) was synthesized and its photochemistry was examined by fluorescence quenching, flash photolysis, and chemically induced dynamic nuclear polarization (CIDNP) methods. Fluorescence quenching measurements show that intramolecular electron transfer from the singlet excited state of the carbazole to the norbornadiene group in NBD-S-CZ occurs with an efficiency (Phi SET) of about 14 % and rate constant (kSET) of about 1.6 x 10(7) s-1. Phosphorescence and flash photolysis studies reveal that intramolecular triplet energy transfer and electron transfer from the triplet carbazole to the norbornadiene group proceed with an efficiency (TET + TT) of about 52 % and rate constant (kTET + kTT) of about 3.3 x 10(5) s-1. Upon selective excitation of the carbazole chromophore, nuclear polarization is detected for protons of the norbornadiene group (emission) and its quadricyclane isomer (enhanced absorption); this suggests that the isomerization of the norbornadiene group to the quadricyclane proceeds by a radical-ion pair recombination mechanism in addition to intramolecular triplet sensitization. The long-distance intramolecular triplet energy transfer and electron transfers starting both from the singlet and triplet excited states are proposed to proceed by a through-bond mechanism.     

Theoretical investigation of large kinetic isotope effects for proton-coupled electron transfer in ruthenium polypyridyl complexes

A theoretical investigation of proton-coupled electron transfer in ruthenium polypyridyl complexes is presented. The three reactions studied are as follows: (1) the comproportionation reaction of [(bpy)(2)(py)Ru(IV)O](2+) and [(bpy)(2)(py)Ru(II)OH(2)](2+) to produce [(bpy)(2)(py)Ru(III)OH](2+); (2) the comproportionation reaction of [(tpy)(bpy)Ru(IV)O](2+) and [(tpy)(bpy)Ru(II)OH(2)](2+) to produce [(tpy)(bpy)Ru(III)OH](2+); and (3) the cross reaction of [(tpy)(bpy)Ru(III)OH](2+) and [(bpy)(2)(py)Ru(II)OH(2)](2+) to produce [(tpy)(bpy)Ru(II)OH(2)](2+) and [(bpy)(2)(py)Ru(III)OH](2+). This investigation is motivated by experimental measurements of rates and kinetic isotope effects for these systems (Binstead, R. A.; Meyer, T. J. J. Am. Chem. Soc. 1987, 109, 3287. Farrer, B. T.; Thorp, H. H. Inorg. Chem. 1999, 38, 2497.). These experiments indicate that the second reaction is nearly one order of magnitude faster than the first reaction, and the third reaction is in the intermediate regime. The experimentally measured kinetic isotope effects for these three reactions are 16.1, 11.4, and 5.8, respectively. The theoretical calculations elucidate the physical basis for the experimentally observed trends in rates and kinetic isotope effects, as well as for the unusually high magnitude of the kinetic isotope effects. In this empirical model, the proton donor-acceptor distance is predicted to be largest for the first reaction and smallest for the third reaction. This prediction is consistent with the degree of steric crowding near the oxygen proton acceptor for the three reactions. The second reaction is faster than the first reaction since a smaller proton donor-acceptor distance leads to a larger overlap between the reactant and product proton vibrational wave functions. The intermediate rate of the third reaction is determined by a balance among several competing factors. The observed trend in the kinetic isotope effects arises from the higher ratio of the hydrogen to deuterium vibrational wave function overlap for larger proton donor-acceptor distances. Thus, the kinetic isotope effect increases for larger proton donor-acceptor distances. The unusually high magnitude of the kinetic isotope effects is due in part to the close proximity of the proton transfer interface to the electron donor and acceptor. This proximity results in strong electrostatic interactions that lead to a relatively small overlap between the reactant and product vibrational wave functions.     

Theoretical investigation of intramolecular vibrational energy redistribution in highly excited HFCO

The present paper is devoted to the simulations of the intramolecular vibrational energy redistribution (IVR) in HFCO initiated by an excitation of the out-of-plane bending vibration [nnu(6)=2,4,6,...,18,20]. Using a full six-dimensional ab initio potential energy, the multiconfiguration time-dependent Hartree (MCTDH) method was exploited to propagate the corresponding six-dimensional wave packets. This study emphasizes the stability of highly excited states of the out-of-plane bending mode which exist even above the dissociation threshold. More strikingly, the structure of the IVR during the first step of the dynamics is very stable for initial excitations ranging from 2nu(6) to 20nu(6). This latter result is consistent with the analysis of the eigenstates obtained, up to 10nu(6), with the aid of the Davidson algorithm in a foregoing paper [Iung and Ribeiro, J. Chem. Phys. 121, 174105 (2005)]. The present study can be considered as complementary to this previous investigation. This paper also shows how MCTDH can be used to predict the dynamical behavior of a strongly excited system and to determine the energies of the corresponding highly excited states.     

Solvent effects on competitive intramolecular electron transfer and energy transfer in a covalently linked porphyrin-phthalocyanine heterodimer

Photophysical properties of a porphyrin-phthalocyanine heterodimer covalently linked with a dipentoxy chain have been studied.Absorption spectra show that there is weak exciton coupling between the two chromophores in the ground state.Fluorescence spectra show that intramolecular energy transfer from porphyrin to phthalocyanine moiety occurs in competition with electron transfer.The efficiency of these two processes depends upon the mutual orientation of the two chromophores.The effect of solvent polarity on the intramolecular processes is also discussed.     

Theoretical investigation of the effects of intramolecular electron-spin relaxation on Stern-Gerlach deflections

The exact solution of a random walk model for electron spin flips in a magnetic field is presented and applied to the Stern-Gerlach (SG) deflection of a spin-1/2 molecule. It is found that when the intramolecular spin-relaxation time τ is much longer than t, the residence time of the molecule in the magnetic gradient, the SG deflection spectrum is unaffected, whereas when τ is much shorter than t, the two-line splitting pattern collapses to that of a single line, neither shifted nor broadened with respect to the line profile at zero field gradient. SG band profiles at intermediate values of λ = τ/t are especially interesting. In the range 2.0> λ > 0.5, the M_s = ± 1/2 SG bands are not shifted from their peak position at large λ, however they are strongly broadened asymmetrically toward zero deflection. This broadening assumes the nature of a broad peak at λ ≈ 0.5, which then narrows substantially and rapidly shifts to the position of zero deflection for λ between 0.3 and 0.01. Examples are given of the SG spectra of molecules exhibiting extreme values of λ.     

Computational methods for intramolecular electron transfer in a ferrous-ferric iron complex

The limitations of common theoretical and molecular computational approaches for predicting electron transfer quantities were assessed, using an archetypal bridged ferrous-ferric electron transfer system in aqueous solution. The basis set effect on the magnitude of the electronic coupling matrix element computed using the quasi-diabatic method was carefully examined, and it was found that the error related to a poor basis set could exceed the thermal energy at room temperature. A range of approaches to determining the external (solvent) reorganization energy were also investigated. Significant improvements from the Marcus continuum model can be obtained by including dipolar Born-Kirkwood-Onsager correction. In this regard, we also found that Klamt's Conductor-Like Screening Model (COSMO) yields estimations of the external reorganization energy similar to those obtained with explicit solvent molecular dynamics simulations if the fast-frequency modes are neglected, which makes it an attractive alternative to laborious umbrella sampling simulations. By using the COSMO model, we also confirm that a decrease in curvature of the potential energy surface is a manifestation of the dielectric saturation observed in the first solvation layer. The linearity of solvent response to the charge redistribution was assessed by analyzing the energy gap autocorrelation function as well as the solvent density and dipole moment fluctuations. Molecular dynamics was also used to evaluate the sign and magnitude of the solvent reorganization entropy and to determine its effect on the predicted electron transfer rate. Finally, we present a simple way of estimating the vibration frequency along the reaction coordinate, which also enables prediction of the mass-dependent isotopic signature of electron transfer reactions.