Superexchange and sequential mechanisms in charge transfer with a mediating state between the donor and acceptor

The rate of intramolecular charge transfer from biphenyl to naphthalene was determined for the radical anions and radical cations of molecules with the general structure: (2-naphthyl)-(steroid spacer)-(4-biphenylyl). Varied degrees of unsaturation (one double bond, NSenB; two double bonds, NSen(2)B; and the b-ring completely aromatized, NSarB) were incorporated into the steroid spacer to examine the effect it would have on the charge transfer rate. The charge transfer rate, as inferred from the decay of the biphenyl radical ion absorption, increased in all cases relative to the completely saturated 3-(2-naphthyl)-16-(4-biphenylyl)-5alpha-androstane (NSB) reference molecule. For the anion charge transfer, the decay rates increased by factors of 1.4, 4.2, and 5.1, respectively, and for the cation, the decay rates increased by factors of 5, 276, and 470. To explain the results, the charge-transfer process was viewed as a combination of two independent mechanisms: a single-step, superexchange mechanism, and a two-step, sequential charge transfer. Using a low level of theory, simple models of the superexchange and two-step mechanisms were developed to elucidate the nature and differences between the two mechanisms. The critical variable for this analysis is the free energy of formation (DeltaG(I) degrees ) of the intermediate state: (2-naphthyl)-[spacer](1)+/--(4-biphenylyl). The conclusion from this treatment is that superexchange is the dominant mechanism when DeltaG(I) degrees is large, but at small DeltaG(I) degrees , the sequential mechanism will dominate. This is because the superexchange rate is shown to have a weak dependence on DeltaG(I) degrees , changing 10-fold for a change in DeltaG(I) degrees of 2 eV, compared to the sequential mechanism in which the rate can change over 10(3) for 0.5 V.     

Physical aspects of charge transfer theory

The possible shapes of the ground (U_I) and first excited (U_II) adiabatic potentials are discussed in connection with the electron transfer problem. If U_I has two minima the electron transfer process is adiabatic, regardless of the value of the gap 2Γ between U_I and U_II; the transfer rate W has the form W = B exp(?E_A/T), the pre-exponential factor B can be influenced by the size of the gap, especially when Γ is small. For the fluctuation model of the medium in the case of purely adiabatic transfer (large Γ) the value of W corresponds to diffusional penetration through the potential barrier. A barrier of arbitrary shape is considered and an expression for W obtained, which matches with the corresponding expression for the “hindered adiabatic” case of small Γ.     

Quantum effects in energy and charge transfer in an artificial photosynthetic complex

We investigate the quantum dynamics of energy and charge transfer in a wheel-shaped artificial photosynthetic antenna-reaction center complex. This complex consists of six light-harvesting chromophores and an electron-acceptor fullerene. To describe quantum effects on a femtosecond time scale, we derive the set of exact non-Markovian equations for the Heisenberg operators of this photosynthetic complex in contact with a Gaussian heat bath. With these equations we can analyze the regime of strong system-bath interactions, where reorganization energies are of the order of the intersite exciton couplings. We show that the energy of the initially excited antenna chromophores is efficiently funneled to the porphyrin-fullerene reaction center, where a charge-separated state is set up in a few picoseconds, with a quantum yield of the order of 95%. In the single-exciton regime, with one antenna chromophore being initially excited, we observe quantum beatings of energy between two resonant antenna chromophores with a decoherence time of ～100 fs. We also analyze the double-exciton regime, when two porphyrin molecules involved in the reaction center are initially excited. In this regime we obtain pronounced quantum oscillations of the charge on the fullerene molecule with a decoherence time of about 20 fs (at liquid nitrogen temperatures). These results show a way to directly detect quantum effects in artificial photosynthetic systems.     

Electronic energy transfer in mixed organic solids: Anderson localization or delocalization?

A simple Anderson transition model, ignoring guest clusterization, excitation lifetime, sensor concentration, exciton-phonon coupling and thermalization, appears to be incompatible with the critical concentrations observed for triplet exciton transport in several ternary crystal systems. Dynamic percolation, involving hopping or tunneling through long-range clusters, remains our suggested model.     

Approximations in the theory of charge transfer through bridged systems

Using Laplace transforms, analytical approximations are obtained in a simple way for the probabilities of charge transfer between donor and acceptor states coupled by a bridge. As a test, these are compared with accurate and numerical calculations when the bridge is treated as a standard diatomic Huckel chain, whose energies lie in two separate bands, the lower (upper) band being completely full (empty). The analytical approximations are found to be generally accurate and provide useful insight into the charge transfer process. ©1999 John Wiley & Sons, Inc. Int J Quant Chem 72: 207–220, 1999     

Undoing static correlation: long-range charge transfer in time-dependent density-functional theory

Long-range charge-transfer excited states are notoriously badly underestimated in time-dependent density-functional theory (TDDFT). We discuss how exact TDDFT captures charge transfer between open-shell species: in particular, the role of the step in the ground-state potential, and the severe frequency dependence of the exchange-correlation kernel. An expression for the latter is derived, that becomes exact in the limit that the charge-transfer excitations are well separated from other excitations. The exchange-correlation kernel has the task of undoing the static correlation in the ground state introduced by the step, in order to accurately recover the physical charge-transfer states.     

Intramolecular energy transfer through charge transfer state in lanthanide compounds: a theoretical approach

A theoretical approach for the intramolecular energy transfer process involving the ligand-to-metal charge transfer (LMCT) state in lanthanide compounds is developed. Considering a two-electron interaction, both the direct Coulomb and exchange interactions are taken into account, leading to expressions from which selection rules may be derived and transfer rates may be calculated. These selection rules show that the direct Coulomb and exchange mechanisms are complementary, in the same way as obtained in previous works for the case of ligand-lanthanide ion energy transfer processes. An important result from numerical estimates is that the channel ligand-LMCT state is by far the dominant case, leading to transfer rates higher than for the channel lanthanide ion-LMCT state by several orders of magnitude. The analysis of the emission quantum yield as a function of the relative energy position of the LMCT state in a typical Eu(3+) compound allows the identification of two quenching regions, the most pronounced one occurring close to the lower ligand triplet level.     

Control over directional metal-metal charge transfer in cyanide-bridged dimanganese complexes: effects of mu-CN linkage isomerism and ancillary ligand set

Synthesis and characterisation of cyano-bridged complexes of the form [(eta-C5R4Me)L(ON)Mn(mu-XY)Mn(CO)2-L'(dppm)]z (X,Y = C,N; z = 1-3) shows that systematic variation of the orientation of the CN bridge and the nature and geometric arrangement of the ancillary ligands affords control of the direction and energy of metal-metal charge transfer in the mixed valence dications.     

Controlling energy and charge transfer in linear chlorophyll dimers

A series of linkers constructed from combinations of phenyl and ethynyl groups is shown to permit ultrafast energy transfer between two chlorophylls, while allowing control over radical cation migration between them.     

Tuning the metal-to-metal charge transfer energy of cyano-bridged dinuclear complexes

The metal-to-metal charge transfer (MMCT) transitions of a series of Class II mixed valence dinuclear complexes bearing cyano bridging ligands may be varied systematically by variations to either the hexacyanometallate(II) donor or Co(III) acceptor moieties. Specifically, the new dinuclear species trans-[L(14S)CoNCFe(CN)(5)](-)(L(14S)= 6-methyl-1,11-diaza-4,8-dithia-cyclotetradecane-6-amine) and trans-[L(14)CoNCRu(CN)(5)](-)(L(14)= 6-methyl-1,4,8,11-tetraazacyclotetradecane-6-amine) have been prepared and their spectroscopic and electrochemical properties are compared with the relative trans-[L(14)CoNCFe(CN)(5)](-). The crystal structures of Na(trans-[L(14S)CoNCFe(CN)(5)]).51/2H(2)O.1/2EtOH, Na(trans-[L(14)CoNCRu(CN)(5)]).3H(2)O and Na(trans-[L(14)CoNCRu(CN)(5)]).8H(2)O are also reported. The ensuing changes to the MMCT energy have been examined within the framework of Hush theory, and it was found that the free energy change between the redox isomers was the dominant effect in altering the energy of the MMCT transition.     

Time-dependent density functional theory study of charge transfer in collisions

We study the charge transfer between colliding ions, atoms, or molecules, within time-dependent density functional theory. Two particular cases are presented, the collision between a proton and a Helium atom, and between a gold atom and a butane molecule. In the first case, proton kinetic energies between 16?keV and 1.2?MeV are considered, with impact parameters between 0.31 and 1.9 ?. The partial transfer of charge is monitored with time. The total cross-section is obtained as a function of the proton kinetic energy. In the second case, we analyze one trajectory and discuss spin-dependent charge transfer between the different fragments.     

Estimating and modeling charge transfer from the SAPT induction energy

Recent studies using quantum mechanics energy decomposition methods, for example, SAPT and ALMO, have revealed that the charge transfer energy may play an important role in short ranged inter‐molecular interactions, and have a different distance dependence comparing with the polarization energy. However, the charge transfer energy component has been ignored in most current polarizable or non‐polarizable force fields. In this work, first, we proposed an empirical decomposition of SAPT induction energy into charge transfer and polarization energy that mimics the regularized SAPT method (ED‐SAPT). This empirical decomposition is free of the divergence issue, hence providing a good reference for force field development. Then, we further extended this concept in the context of AMOEBA polarizable force field, proposed a consistent approach to treat the charge transfer phenomenon. Current results show a promising application of this charge transfer model in future force field development. © 2017 Wiley Periodicals, Inc.     

Advanced theory of excitation energy transfer in dimers

Previously, we developed a unified theory of the excitation energy transfer (EET) in dimers, which is applicable to all of the cases of excitonic coupling strength (Kimura, A.; Kakitani, T.; Yamato, T. J. Phys. Chem. B 2000, 104, 9276). This theory was formulated only for the forward reaction of the EET. In the present paper, we advanced this theory so that it might include the backward reaction of the EET as well as the forward reaction. This new theory is formulated on the basis of the generalized master equation (GME), without using physically unclear assumptions. Comparing the present result with the previous one, we find that the excitonic coupling strengths of criteria between exciton and partial exciton and between hot transfer and hopping (F?rster) mechanisms are reduced by a factor of 2. The critical coherency eta c is also reduced significantly.     

Thermal energy charge transfer reactions of acetone and biacetyl

Rate coefficients up to a factor of 2.5 times larger than the capture collision rate are reported for a series of thermal energy, positive ion-molecule reactions of acetone and biacetyl. These rapid rates are interpreted in tems of a dissociative charge transfer process in which an electron is transferred in a non-spiralling collision from outside the classical capture limit. The factor which lead to this type of mechanism are discussed briefly.     

Photo-induced energy and charge transfer dynamics in Y6 dimers

Y6 (BTP-4F) is one of the novel non-fullerene acceptors and its photo-physics significantly affects the efficiency of organic solar cells. Here, the photo-induced energy and charge transfer (CT) dynamics in four typical dimers (Y, C, S1, and S2)-TYPE from Y6 films are revealed by combining electronic structure theory calculations, rate theories, and quantum dynamics simulations. The rate theories show that in ground-state CT processes the Y-TYPE is bipolar with the largest rate among all dimers, and in excitation energy transfer the triplet rates are about 10⁵ smaller than the singlet ones, however, the singlet rates can reach 10¹³s⁻¹, which may lead to the rate theories invalid. The stochastic Schrödinger equation based on the diabatic Hamiltonian is thus adopted to reveal excited-state dynamics. The results show that three of the four dimers are H-aggregate except for S1-TYPE with J-aggregate property. However, these J/H-aggregate properties are excited-state dependent, for instance, the Y-TYPE becomes J-aggregate in the second excited-state. Furthermore, CT states are strongly mixed with the first two excited states, which can dramatically impact the energy transfer. Indeed, the dynamic simulations clarify that the excited-state energy relaxation mediated by CT states can be performed in the first 20 fs, and the CT-state population is even non-negligible in the quasi-stationary distribution.     

Ergodic collision theory of intermolecular energy transfer

We present a simple theory of collisional energy transfer between molecules based on the assumption of ergodic collisions, i.e., the final state distri     

A schematic model for energy and charge transfer in the chlorophyll complex

A theory for simultaneous charge and energy transfer in the carotenoid-chlorophyll-a complex is presented here and discussed. The observed charge transfer process in these chloroplast complexes is reasonably explained in terms of this theory. In addition, the process leads to a mechanism to drive an electron in a lower to a higher-energy state, thus providing a mechanism for the ejection of the electron to a nearby molecule (chlorophyll) or into the environment. The observed lifetimes of the electronically excited states are in accord/agreement with the investigations of Sundstr?m et al. and are in the range of pico-seconds and less. The change in electronic charge distribution in internuclear space as the system undergoes an electronic transition to a higher-energy state could, under appropriate physical conditions, lead to oscillating dipoles capable of transmitting energy from the carotenoid-chlorophylls chromophore to the reaction center by sending an electromagnetic wave (a photon) which provides a novel new mechanism for energy production. In the simplest version of the F?rster?CDexter theory, the excitation energy of a donor is transferred to an acceptor and then de-excited to the ground state by fluorescence with no electron being transferred. In the process proposed herein, charge and energy both are transferred from donor to acceptor which can further de-excite by fluorescence. The charge transfer time scale involving an actual transfer of electron is in the pico-second range.