Evolution of spin coherence of radical pairs due to spin-selective recombination: Comparison of three models.

This study looked for a way to evaluate the validity of previously suggested models for describing the spin-selective recombination of radical pairs. As an example, for analysis, we used the conventional model, the model by Jones and Hore [Chem. Phys. Lett. 488, 90 (2010)], and the model by Salikhov [Am. J. Phys. Chem. 11, 67 (2022)]. To do this, analytical solutions to the evolution of the radical pair density matrix due to a radical pair's spin-selective recombination and singlet-triplet transitions in a strong magnetic field were obtained for the conventional model and the Jones and Hore model. Spin interactions included in the Hamiltonian were time-independent exchange interactions as well as Zeeman and hyperfine interactions. The most striking difference between the models' predictions appeared when considering the fraction of singlet pairs among all currently existing ones. In the Jones and Hore model, this ratio has the form of damped oscillations for any values of the spin-hamiltonian parameters. The conventional model and the Salikhov model both predicted that this ratio had the form of undamped oscillations in the absence of exchange interaction and at a sufficiently low recombination rate. Besides, the conventional model predicts the possibility of a resonance-like behavior of this ratio when singlet-triplet transitions in a part of the radical pair ensemble are completely suppressed by tuning the magnetic field strength. Possible experimental conditions in which distinguishing between the models seems to be most straightforward were suggested.

A spin statistical factor in electron transfer to oxygen molecules.

The oxygen molecule in its ground triplet state (3O2) is a strong electron acceptor. Electron transfer to 3O2 to form a superoxide anion is an important elementary step in many chemical and biological processes. If this transfer occurs from a spin 1/2 paramagnetic particle where the total spin of the reactants is equal to 3/2, the reaction is spin-forbidden. In liquids, the significant dipole-dipole electron spin interaction in 3O2 is supposed to mix the non-reactive quartet and reactive doublet states at a time scale of ∼10 ps, thus avoiding the barrier. To elucidate the role of spin effects in the electron transfer to 3O2, we studied this reaction over a range of more than three orders of magnitude of the relative diffusion coefficient (D) of the reactants. It was found that spin effects during electron transfer to 3O2 become insignificant when D < 10-9 m2 s-1. In the range of intermediate D values (10-9 m2 s-1 < D < 10-8 m2 s-1) - which corresponds to some reactions of oxygen with small radicals in aqueous solutions - the effective spin factor decreases with increasing D value. If D > 10-8 m2 s-1, the electron transfer is spin-selective with the spin factor of 1/3 as determined by the spin statistics. At such D values, the reaction encounter time may exceed the expected quartet-doublet mixing time by almost an order of magnitude. The reduced rate of quartet-doublet transitions within the encounter complex in the reaction with 3O2 has been explained by the spin-exchange interaction and chemical Zeno effect.

The role of Heisenberg spin exchange and the quantum Zeno effect in the spin-selective reaction between spin-1/2 and spin-1 particles.

The kinetics of spin-selective reactions involving triplet molecules, such as triplet-triplet annihilation or electron transfer to dioxygen molecules in the ground triplet spin state, are strongly dependent on the dipole-dipole interaction (DDI) of electron spins in spin-1 particles. The effect of this interaction on the intersystem crossing in the reaction encounter complex of the paramagnetic particles was previously considered for some particular cases using oversimplified approaches. In this study, we consider a rigorous kinetic model of the irreversible reaction between the spin-1/2 and spin-1 particles in an encounter complex with the reactive doublet state. This model explicitly includes both isotropic exchange coupling of the reactants and spin dependence of the reaction rate in the form of the Haberkorn reaction term. For the time-independent DDI, an analytical expression for the reaction kinetics was derived. The effect of DDI fluctuations was analyzed using numerical simulations. It was found that increasing both the exchange coupling and the reaction rate constants can significantly slow down the quartet-doublet spin transitions and, as a consequence, the observed spin-selective reaction rate. Additionally, the presence of the irreversible reaction in the doublet states affects a coherent evolution in the non-reactive quartet subsystem.

Simple rules for resolved level-crossing spectra in magnetic field effects on reaction yields.

In this work we derive conditions under which a level-crossing line in a magnetic field effect curve for a recombining radical pair will be equivalent to the electron spin resonance (ESR) spectrum and discuss three simple rules for qualitative prediction of the level-crossing spectra.

Interaction of spin-correlated radical pair with a third radical: Combined effect of spin-exchange interaction and spin-selective reaction.

The reaction of electron transfer between two paramagnetic particles may be strongly dependent on the total spin state of the pair. Such dependence can be used to control electron transfer in a molecular medium via the control of the spin degrees of freedom. In this work, the spin-selective electron transfer has been studied in a three-spin system composed of a spin-correlated radical ion pair (RIP) and the nitroxide radical, TEMPONE. The RIPs were created in an n-hexane solution of tetramethylpiperidine (TMP) and para-terphenyl (p-TP) using X-rays. To monitor the spin evolution of the RIPs with a nanosecond time resolution, the method of time-resolved magnetic field effect in the RIP recombination fluorescence was applied. It was found that increasing the TEMPONE concentration increased the rate of both the radiation-induced fluorescence intensity decay and the paramagnetic relaxation of the spin-correlated RIP. For the three-spin system studied, we developed a theoretical model to calculate the singlet state population of the spin-correlated RIP that described both the spin-selective reaction and the spin-exchange interaction during an encounter between RIP partners and a third radical. It was found that the effect of the spin exchange could be neglected if the rate of the spin-selective reaction is high enough. Based on quantum chemical calculations and experiments, we found that there was a spin-selective distant electron transfer from p-TP radical anions to the TEMPONE radical. Another partner of the RIP, the radical cation formed from TMP, was only involved in the spin exchange interaction with TEMPONE radicals.

Dimer Radical Anions of Polyfluoroarenes. Two More to a Small Family.

While there is a body of experimental data concerning dimers formed by an aromatic molecule and its radical cation, information on the corresponding dimer radical anions (DRAs) is scarce. In this work, evidence for the formation of the DRAs of decafluorobiphenyl and 4-aminononafluorobiphenyl has been obtained by the optically detected electron paramagnetic resonance and the time-resolved magnetic field effect techniques. Theoretical investigation (DFT B3LYP-D3/6-31+G*) of these DRAs and the DRAs of octafluoronaphtalene and 1,2,4,5-tetrafluorobenzene previously detected by Werst has been undertaken to gain greater insight into the structure of the polyfluoroarene DRAs. Without substituents different from a fluorine atom, an extra electron is evenly delocalized over two fragments; the bonding interaction is π stacking. On the potential energy surfaces (PES), there are two minima of nearly equal energy corresponding to the structures of perfect and parallel displaced sandwiches. Such a PES structure is due to a conical intersection between two electronic states of different symmetry. The DRA of 4-aminononafluorobiphenyl is an ion-molecular associate stabilized by electrostatic interactions involving NH2 groups. The complex cyclic structure of the PES of this DRA suits the successive electron transfers between the dimer fragments. The calculated hyperfine coupling constants averaged over the PES minima agree well with the experimental ones.

Structure and Stability of Pentafluoroaniline and 4-Aminononafluorobiphenyl Radical Anions: Optically Detected Electron Paramagnetic Resonance, Time-Resolved Fluorescence, Time-Resolved Magnetic Field Effect, and Quantum Chemical Study.

Radical anions (RAs) are the key intermediates of the selective hydrodefluorination of polyfluoroarenes. We used the techniques of optically detected electron paramagnetic resonance (OD EPR), time-resolved fluorescence, time-resolved magnetic field effect (TR MFE), and the density functional theory to study the possibility of RAs formation from 4-aminononafluorobiphenyl (1) and pentafluoroaniline (2) and estimate their lifetimes and decay channels. To our knowledge, both RAs have not been detected earlier. We have registered the OD EPR spectrum for relatively stable in nonpolar solutions 1(-•) but failed to register the spectra for 2(-•). However, we have managed to fix the 2(-•) by the TR MFE method and obtained its hyperfine coupling constants. The lifetime of 2(-•) was found to be only a few nanoseconds. The activation energy of its decay was estimated to be 3.6 ± 0.3 kcal/mol. According to the calculation results, the short lifetime of 2(-•) is due to the RA fast fragmentation with the F(-) elimination from ortho-position to the amine group. The calculated energy barrier, 3.2 kcal/mol, is close to the experimental value. The fragmentation of 2(-•) in a nonpolar solvent is possible due to the stabilization of the incipient F(-) anion by the binding with the amine group proton.

Spin-selective reaction with a third radical destroys spin correlation in the surviving radical pairs.

The goal of this work is to reveal the effect that an irreversible spin-selective reaction of a partner of the spin-correlated radical pair (SCRP) with a third paramagnetic particle has on the spin state of the surviving SCRPs in the absence of spin exchange interaction. As studied SCRPs, we used the geminate (excess electron/radical cation) pairs generated by ionizing irradiation of tetramethyl-para-phenylenediamine solutions in n-dodecane. As a spin-selective reaction, the scavenging of electrons by nitroxide radicals from the bulk of the solution was used. Both the electron scavenging reaction and the spin correlation in the surviving SCRPs were monitored by measuring the recombination fluorescence decays of the irradiated solutions under the same experimental conditions. It was found that the spin-selective electron scavenging results in the acceleration of spin correlation decay in the remaining unreacted SCRPs. In accordance with the suggested theoretical model, the rate of this additional spin correlation decay is revealed to be equal to the scavenging rate.

Radical cations of branched alkanes in solutions: time-resolved magnetic field effect and quantum chemical studies.

Radical cations of heptane and octane isomers, as well as several longer branched alkanes, were detected in irradiated n-hexane solutions at room temperature by the method of time-resolved magnetic field effect (TR MFE). To identify radical cations, the hyperfine coupling constants as determined by simulation of the TR MFE curves were compared to the constants calculated using the density functional theory (DFT) approach. The g-values of the observed radical cations were close to that of the 2,2,3,3-tetramethylbutane radical cation studied earlier by optically detected electron spin resonance (ESR) and TR MFE techniques. No evidence of the decay of the radical cations of branched alkanes to produce olefin radical cations was found, which was further supported by the observation of positive charge transfer from the observed radical cations to cycloalkane molecules. The lifetimes of the radical cations of the branched alkanes were found to be longer than tens of nanoseconds.

Interaction of 1,3,2,4-benzodithiadiazines and their 1-Se congeners with Ph3P and some properties of the iminophosphorane products.

Interaction between Ph(3)P and 1,3,2,4-benzodithiadiazine (1); its 6,7-difluoro (2), 5,6,8-trifluoro (3) and 5,6,7,8-tetrafluoro (4) derivatives; and 5,6,8-trifluoro-3,1,2,4-benzothiaselenadiazine (5) proceeded via a 1:1 condensation to give Ph(3)P═N-R iminophosphoranes (1a-5a, R = corresponding 1,2,3-benzodichalcogenazol-2-yls), which are inaccessible by general approaches based on the Staudinger and Kirsanov reactions. In contrast, neither Ph(3)As nor Ph(3)Sb reacted with 1 and 4. Molecular structures of 1a-5a and 5 were confirmed by X-ray diffraction (XRD). The crystals formed by chiral molecules of 2a-5a were racemic, whereas the crystal of 1a was formed by a single enantiomer. In all of the Ph(3)P═N-R derivatives, one of the Ph rings is oriented face-to-face to the hetero ring, R. Upon heating to ∼120 °C in squalane (1a, 3a, 4a) or dissolving in chloroform at ambient temperatures (1a, 2a, 4a), the Ph(3)P═N-R derivatives generated the 1,2,3-benzodithiazolyls (1b-4b, respectively) whose identity was confirmed by electron paramagnetic resonance (EPR). 2,1,3-Benzothiaselenazolyls 5b and 6b were detected by EPR as the main paramagnetic products of solution thermolysis of 5 and its 5,6,7,8-tetrafluoro congener (6), respectively. Passing a chloroform solution of 4a through silica column unexpectedly gave 5-6-6-6 tetracyclic (9) and 6-10-6 tricyclic (10) sulfur-nitrogen compounds, which were characterized by XRD.

Longitudinal electron spin relaxation induced by degenerate electron exchange as studied by time-resolved magnetic field effects.

T(1) paramagnetic relaxation of radical ions induced by degenerate electron exchange (DEE) reactions is studied theoretically and experimentally. Our theoretical analysis shows that T(1) relaxation time is well described by the Redfield theory at arbitrary values of the characteristic DEE time tau. Longitudinal relaxation of norbornane (NB) radical cation is studied by means of the time-resolved magnetic field effects (TR-MFE) technique; the rate constant of DEE involving NB(*+) radical cation and NB neutral molecule is obtained. Advantages of the TR-MFE technique and its potential for measuring the short DEE times are discussed in detail.

Intramolecular dynamics of 1,2,3-trifluorobenzene radical anions as studied by OD ESR and quantum-chemical methods.

Ab initio UMP2, RMP2, DFT/UB3LYP, and CBS-QB3 calculations have shown that the adiabatic potential energy surface (PES) of the 1,2,3-trifluorobenzene radical anion is a pseudorotation surface formed by nonplanar stationary structures. The low (approximately 2-4 kcal/mol) energy barriers in the path of pseudorotation imply manifestations of spectral exchange in the ESR spectra of this radical anion. The optically detected ESR of radical ion pairs was used to obtain the ESR spectrum of 1,2,3-trifluorobenzene radical anion in liquid squalane solution and to study temperature variations in the spectrum over the range of 243-325 K. The spectrum is a doublet of triplets with hfc constants of a(F(2)) = 29 mT and a(2F(1,3)) = 7.6 mT at T = 243 K. The experimental hfc constants are temperature-dependent. Calculations of the temperature dependence of hfc constants in the framework of the model of classical nuclei motion along the pseudorotation coordinate reproduce well the experimental data.