Spin evolution of radical pair with radical containing two groups of equivalent magnetic nuclei

Geometrization for Energy Levels of Isotropic Hyperfine Hamiltonian Block and Related Central Spin Problems for an Arbitrarily Complex Set of Spin-1/2 Nuclei

Description of interacting spin systems relies on understanding the spectral properties of the corresponding spin Hamiltonians. However, the eigenvalue problems arising here lead to algebraic problems too complex to be analytically tractable. This is already the case for the simplest nontrivial (Kmax−1) block for an isotropic hyperfine Hamiltonian for a radical with spin-12 nuclei, where n nuclei produce an n-th order algebraic equation with n independent parameters. Systems described by such blocks are now physically realizable, e.g., as radicals or radical pairs with polarized nuclear spins, appear as closed subensembles in more general radical settings, and have numerous counterparts in related central spin problems. We provide a simple geometrization of energy levels in this case: given n spin-12 nuclei with arbitrary positive couplings ai, take an n-dimensional hyper-ellipsoid with semiaxes ai, stretch it by a factor of n+1 along the spatial diagonal (1, 1, …, 1), read off the semiaxes of thus produced new hyper-ellipsoid qi, augment the set {qi} with q0=0, and obtain the sought n+1 energies as Ek=−12qk2+14∑iai. This procedure provides a way of seeing things that can only be solved numerically, giving a useful tool to gain insights that complement the numeric simulations usually inevitable here, and shows an intriguing connection to discrete Fourier transform and spectral properties of standard graphs.

Spin-Correlated Radical Ion Pairs Generated in Liquid Haloalkanes Using High-Energy Radiation

The probability of formation of spin-correlated secondary radical ion pairs (RIPs) in diluted solutions of charge acceptors in irradiated haloalkanes is believed to be extremely low due to the dissociative attachment of excess electrons to solvent molecules. Contrary to this, it has been found that spin-correlated RIPs can be formed upon irradiation in some liquid chloroalkanes with yield sufficient to observe the recombination fluorescence of the RIP's partners. This allowed the study of primary radical cations (RCs) as well as radical ionic states of molecules dissolved in haloalkanes using the method of time-resolved magnetic field effect (TR MFE) in radiation-induced fluorescence. With this method, the magnetic resonance characteristics of the solvent RCs in a series of liquid haloalkanes were examined for the first time. For the 1,2-dichloroethane RC, the rate of scavenging by solute molecules and the dominant mechanisms of paramagnetic relaxation were determined. Polysulfone and poly(ethyl methacrylate) were used to demonstrate that due to their high dissolving ability, chloroalkanes can be exploited as solvents to study the magnetic resonance characteristics of radical ionic states of polymeric molecules in solutions with the TR MFE method.

Radical Cations of Branched Alkanes As Observed in Irradiated Solutions by the Method of Time-Resolved Magnetic Field Effect

Spin dynamics in radical ion pairs formed under ionizing irradiation of n-hexane solutions of two branched alkanes 2,3-dimethylbutane and 2,2,4-trimethylpentane has been studied by the method of time-resolved magnetic field effect in recombination fluorescence. Experimental curves of the magnetic field effect are satisfactorily described by assuming that the spin dynamics is determined by the hyperfine interactions in the radical cation (RC) of branched alkane under study with hyperfine coupling (HFC) constants averaged by internal rotations of RC fragments. The HFC constants determined from the magnetic field effect curves are close to those estimated within DFT B3LYP approach. Analysis of the results indicates that at room temperature the lifetimes of the RC of the studied branched alkanes amount to, at least, tens of nanoseconds.

Degenerate Electron Exchange Reaction of n-Alkane Radical Cations in Solution

The degenerate electron exchange (DEE) reaction involving radical cations (RCs) of n-nonane, n-dodecane, and n-hexadecane in n-hexane solution was studied over the temperature range 253-313 K using the method of time-resolved magnetic field effect in recombination fluorescence of spin-correlated radical ion pairs. In the dilute solutions the rate constant of DEE was found to be 200 times slower than the diffusion limit. Using n-nonane as an example, we showed that two reasons are responsible for the low value of the RC self-exchange rate: (1) conformational variability of molecules and RCs and (2) the activation barrier of DEE reaction. The calculations of the reaction enthalpy performed by the B3LYP/6-31G(d) method indicated that electron transfer can be effective only upon collision of RC with a neutral molecule either in the all-trans conformation or in the conformation differing from the latter by rotation of the end ethyl fragment. The activation barrier of the DEE reaction was estimated using the reorganization energy of the internal degrees of freedom calculated at the B3LYP level and was found to be about 6 kcal/mol. A possible influence of the interaction between RC and a neutral molecule in an encounter complex on DEE rate constant is also discussed.

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.