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A detailed experimental study on reversible photo-induced intramolecular charge separation is presented based on NMR detection of Chemically Induced Dynamic Nuclear Polarization (CIDNP). From variation of such polarization with the external magnetic field the coupling constants of isotropic and anisotropic hyperfine interaction at individual 13C sites are measured in the short-lived charge separated state of dyad molecules composed of donor-bridge-acceptor parts. The objects of study were rigid donor-bridge- acceptor dyads, consisting of triarylamine as a donor, naphthalene diimide (NDI) as an acceptor, and a meta-conjugated diethynyl benzene fragment as a bridge. By systematic variation of side groups in the bridging moiety their influence on the electron withdrawing strength is traced. In combination with similar data for the 1H positions obtained previously for the same compounds (I. Zhukov, et al J. Chem. Phys 2020, 152, 014203) our results provide a reliable basis for determination of the spin density distribution in the charge separated state of such dyads.

Magnetic Field Effects (MFEs) on the recombination of radicals, which diffuse on an infinite plane, are studied theoretically. The case of spin-selective diffusion-controlled recombination of Radical Pairs (RPs) starting from a random spin state is considered assuming uniform initial distribution of the radicals. In this situation, reaction kinetics is described by a time-dependent rate coefficient K(t), which tends to zero at long times. Strong MFEs on K(t) are predicted that originate from the Δg and hyperfine driven singlet-triplet mixing in the RP. The effects of spin relaxation on the magnetic field are studied, as well as the influence of the dipole-dipole interaction between the electron spins of the RP. In the two-dimensional case, this interaction is not averaged out by diffusion and it strongly affects the MFE. The results of this work are of importance for interpreting MFEs on lipid peroxidation, a magnetosensitive process occurring on two-dimensional surfaces of cell membranes.

Previous transient absorption measurements using the magnetically affected reaction yield (MARY) technique for a series of rigidly linked electron donor/electron acceptor dyads (D-X-A) consisting of a triarylamine donor, a naphthalene diimide acceptor, and a meta-conjugated diethynylbenzene unit as a bridge had revealed the presence of electronic exchange interaction, J, in the photoexcited charge separated (CS) state. Here, we present results obtained by photochemically induced dynamic nuclear polarization (photo-CIDNP) that allows for determining the sign of J. By variation of the magnetic field from 1 mT to 9.4 T, pronounced absorptive maxima of CIDNP were detected for more than 20 1H nuclei disregarding the sign of their hyperfine coupling constants in the transient charge separated state, with positions of maxima close to those found by the MARY technique. Quantitative comparison of the observed CIDNP signals for various D-X-A dyads reveals an increase in the CIDNP enhancement factor with increasing population of the triplet state determined by MARY spectroscopy at zero magnetic field. For CIDNP of the methyl groups of the TAA donor dyads, we found in all studies a good linear dependence between the CIDNP signal amplitude and the initial population of the CS triplet state. The linear relationship together with the absorptive CIDNP allows us to conclude that (i) the sign of the electronic exchange interaction Jex is positive, (ii) CIDNP is formed predominantly in the vicinity of level anticrossing between the T+ and S electronic levels, and (iii) coherent triplet-singlet transitions are induced by hyperfine interaction and accompanied by simultaneous electron and nuclear spin flip, T+β→Sα.

Charge recombination in the photoinduced charge separated (CS) state of a rigidly linked donor/bridge/acceptor triad with a triarylamine (TAA) donor, a 1,3-diethynyl-2,5-dimethoxy benzene bridge (OMe), and a perylenediimide (PDI) unit as an acceptor, represents a spin chemical paradigm case of a rigid radical ion pair formed with singlet spin and recombining almost exclusively to the locally excited PDI triplet state (3PDI). The magnetic field dependence of the CS state decay and 3PDI formation kinetics are investigated from 0 to 1800 mT by nanosecond laser flash spectroscopy. The time-resolved magnetic field affected reaction yields spectra of the CS state population and 3PDI population exhibit a sharp and deep resonance at 18.9 mT, indicating level crossing of the S and T+ levels separated by an exchange interaction of J = 18.9/2 mT at zero field. The kinetics are biexponential around the resonance field and monoexponential outside that range. The monoexponential behavior can be simulated by a classical kinetic model assuming a single field dependent double Lorentzian function for the energy gap dependence of all spin conversion processes. The full field dependence of the kinetics has been simulated quantum theoretically. It has been shown that incoherent and coherent hyperfine coupling contribute to S/T+ spin conversion at all fields and that the biexponentiality of the kinetics at resonance is due to a partitioning of the overall kinetics into 2/3 of the singlet hyperfine states exhibiting strong isotropic coupling to T+ and 1/3 of the singlet hyperfine states that do not or only weakly couple isotropically to T+.

In the present work we suggest a method for calculating rate constants of chemical processes affected by mobility of reactants. The method is based on the encounter theory. Unlike the widely accepted model of collision complexes it provides a general formal solution for practically arbitrary reaction scheme.

The formalism developed in Part I [K. L. Ivanov, N. N. Lukzen, A. A. Kipriyanov, and A. B. Doktorov, Phys. Chem. Chem. Phys. 6, 1706 (2004)] of the present contribution is extended to treat the reacting particles with internal quantum states. Initial spatial correlations of reactants are considered in the framework of this formalism as well.

Consistent kinetic description of degenerate electron exchange (ion-molecular charge transfer) reaction in the liquid phase based on the encounter theory has been performed. This has made it possible to allow for re-encounters of reactants and the attendant additional dephasing of electron spin during the encounter. The applicability range of the approximation of noncorrelated spectral migration that is commonly used to describe spectroscopic manifestation of degenerate electron exchange in strong magnetic fields has been refined. It is shown that for radicals with large hyperfine interaction constants the discrepancy between the results obtained, and the approximation of noncorrelated frequency migration may be considerable.

The matrix Integral Encounter Theory (IET) and its modified version (MET) developed earlier are used to study the kinetics of the reversible transitions between two metastable (as singlet and triplet) states of the fluorescent particle. Induced by binary encounters with inert catalysts, these transitions result in either (a) energy quenching or (b) energy conservation, depending on what lifetime of these two states is longer. Integral encounter theory describes adequately the kinetics of energy conservation followed by delayed fluorescence while differential or Markovian versions of the same theory fail. Another advantage of the IET is the natural accounting for arbitrary strong light pumping which makes the Stern–Volmer constant dependent on light intensity, differently for cases (a) and (b).

The matrix kinetic equations for multi-stage reactions in liquid solutions are derived using a newly developed original method based on a many-particle master equation. The method leads to an infinite hierarchy for vector correlation patterns that can be truncated two different ways. The simplest one reproduces the conventional Integral Encounter Theory (IET), while the other allows a general modification of the kernel, resulting in the matrix formulation of so called Modified Encounter Theory (MET). Unlike IET, MET accounts for all binary contributions and correctly restores the long-time asymptotics of bimolecular reactions. The matrix MET, applied in Part II to reversible reactions of inter-molecular energy transfer, significantly improves the results obtained with other methods.

The matrix Modified Encounter Theory (MET), developed in Part I of this work, is applied here to reversible inter-molecular energy transfer in liquid solutions. For fluorescence quantum yield at contact transfer the Stern–Volmer law is confirmed, but the concentration corrections to its constant are diffusion-dependent unlike those obtained earlier with Superposition Approximation. In the particular case of irreversible energy transfer, when the exact solution is available, the latter is used to discriminate between all competing approaches and establishes MET superiority. In the case of reversible energy transfer producing the long-lived or even stable products, the energy is stored there and dissipates due to backward energy transfer in re-encounters. The kinetics of this process, resulting in a delayed fluorescence, is shown to be qualitatively different in cases of short and long encounter times as compared to the excitation lifetime.

Time dependence of the rate coefficients of sterically specific reactions is analyzed theoretically. Generally, such reactions exhibit a non-trivial dependence of their rate constant on the steric factor, f < 1, which is defined as the fraction of reactive surface area. Notably, the rate constant of a diffusion-controlled reaction is proportional not to f but, counter-intuitively, to f due to partial averaging of the reaction anisotropy by translational diffusion. Here we demonstrate that the effective steric factor of a diffusion-influenced reaction is strongly time-dependent, increasing from f to f. When reactants have several active sites, these sites “interfere” each other in the sense that the rate constant depends on their relative positions. We demonstrate that such an interference effect is strongly time-dependent as well: it is absent at t = 0 but builds up with time. We argue that the outlined effects are also of importance for calculating the fluorescence quenching rate constants.

In this work, we treat spin-selective recombination of a geminate radical pair (RP) in a spherical "microreactor," i.e., of a RP confined in a micelle, vesicle, or liposome. We consider the microreactor model proposed earlier, in which one of the radicals is located at the center of the micelle and the other one undergoes three-dimensional diffusion inside the micelle. In addition, we suggest a two-dimensional model, in which one of the radicals is located at the "pole" of the sphere, while the other one diffuses on the spherical surface. For this model, we have obtained a general analytical expression for the RP recombination yield in terms of the free Green function of two-dimensional diffusion motion. In turn, this Green function is expressed via the Legendre functions and thus takes account of diffusion over a restricted spherical surface and its curvature. The obtained expression allows one to calculate the RP recombination efficiency at an arbitrary magnetic field strength. We performed a comparison of the two models taking the same geometric parameters (i.e., the microreactor radius and the closest approach distance of the radicals), chemical reactivity, magnetic interactions in the RP and diffusion coefficient. Significant difference between the predictions of the two models is found, which is thus originating solely from the dimensionality effect: for different dimensionality of space, the statistics of diffusional contacts of radicals becomes different altering the reaction yield. We have calculated the magnetic field dependence of the RP reaction yield and chemically induced dynamic nuclear polarization of the reaction products at different sizes of the microreactor, exchange interaction, and spin relaxation rates. Interestingly, due to the intricate interplay of diffusional contacts of reactants and spin dynamics, the dependence of the reaction yield on the microreactor radius is non-monotonous. Our results are of importance for (i) interpreting experimental data for magnetic field effects on RP recombination in confined space and (ii) for describing kinetics of chemical reactions, which occur predominantly on the surfaces of biomembranes, i.e., lipid peroxidation reactions.