The integral encounter theory of multistage reactions containing association-dissociation reaction stages. III. Taking account of quantum states of reactants

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.     

A novel method for calculating rate constants of diffusion-influenced reactions

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.     

CPMG echo amplitudes with arbitrary refocusing angle: explicit expressions, asymptotic behavior, approximations

Exact explicit analytical expression for echoes in the Carr–Purcell–Meiboom–Gill sequence with arbitrary excitation and refocusing angles and resonance offset of RF pulses was obtained, employing the generating functions formalism developed earlier by authors. Asymptotic form and analytical approximation for echoes were derived in an elegant way and analyzed in details. In particular, it was shown that depending on T₁, T₂ and parameters of the pulse sequence, oscillatory behavior of echoes can take place. Accuracy of asymptotic forms and approximations were tested by comparison with exactly calculated echo amplitudes. Besides, it was shown, that the generating function approach can be applied to the consideration of terminated pulse sequences, when after-pulses echoes are registered.     

Analysis of lipid peroxidation kinetics. 1. Role of recombination of alkyl and peroxyl radicals

The kinetics of the lipid peroxidation reaction is only partly understood. Although the set of reactions constituting the overall reaction are believed to be known, it has not been possible to predict how the reaction will respond to a change of one or more of the parameters, e.g., initial concentrations of reactants or different ways of initiating the reaction, nor has it been possible to predict the time dependence of the products. The reason for these problems is the complicated structure of the kinetic scheme, which includes a chain reaction. In this work we perform an in-depth analysis of the importance of the individual reaction steps, and we introduce a new quasi-stationary concentration method based on the assumption that one or more concentrations vary much slower than the others. We show that it is justified to use a quasi-stationary concentration approximation for the alkyl radical L (*), but not for the peroxyl radicals LO 2 (*) as assumed in previous works. The method allows us to derive manageable analytical expressions. On the basis of literature values of the rate constants, we are able to introduce specific simplifications that allow us to obtain simple analytical expressions for the time dependence of all concentrations involved in the process.     

Theory of spin-peierls transitions in chains of exchange clusters

A theoretical approach to the analysis of magnetostructural phase transitions of chain polymeric heterospin complexes is suggested. The approach is based on a model of the spin-Peierls transition in chains of exchange clusters. The chain elasticity parameter is found to be a main factor determining the order of phase transition.     

Spin relaxation parameters in recombining radical ion pair (diphenylsulfide-d10)+/(p-Terphenyl-d14)− obtained by OD ESR and quantum beats techniques

Parameters of paramagnetic relaxation were determined by OD ESR and quantum beats techniques for a recombining pair of radical ions (DPS-d₁₀)⁺/(PTP-d₁₄)^? inn-hexane, isooctane,cis-decalin, and squalane solutions. TheT ₂ relaxation time determined by quantum beats technique is independent of solvent viscosity and magnetic field strength in the range 170–9600 G. These data are in agreement with the results obtained by OD ESR technique assuming fastT ₁ relaxation for radical cation. Neglecting the contribution of radical anion relaxation, we obtainedT _1c=T _2c?50 ns for (DPS-d₁₀)⁺.     

The induction of quantum beats by hyperfine interactions in radical-ion pair recombination

Quantum beats were detected in the recombination of spin-correlated radical-ion pairs. These beats are induced by singlet-triplet transitions in a pair due to hyperfine interactions. Singlet radical-ion pairs were generated by radiolysis of hydrocarbons involving acceptors of electrons and holes. The singlet pair recombination was detected by the luminescence of the product (singlet-excited molecules). The beat frequencies measured for (tetramethylethylene) ⁺/(paraterphenyl-d₁₄)-and (durene)⁺/(paraterphenyl-d₁₄)^? pairs correspond to the hfi constants in the cation radicals. The character of the beats differ in high and zero magnetic fields and their shape depends upon the solvent.     

Singlet and triplet products of the geminate recombination of a radical pair with a single magnetic nucleus (I = 1/2)

The double-channel recombination and separation of the photochemically created singlet radical pair is investigated, taking into account the spin conversion in a zero magnetic field and the arbitrary initial distance between the radicals. The quantum yields of the singlet and triplet products and the free radicals production are found analytically, assuming that the recombination of the diffusing radicals occurs at contact. All the yields are related to the singlet and triplet populations of the recombining radical pair, subjected to spin conversion and contact exchange interaction. The general analytical expressions for the quantum yields are specified for the particular limits of the weak and strong exchange. They are greatly simplified in the case of polar solvents, especially at the contact start. A close similarity is obtained with the results of a previously developed incoherent model of spin conversion, provided that the conversion rate is appropriately related to the hyperfine coupling constant.     

Theoretical Treatment of Degenerate Electron Exchange and Dimerization in Spin Dynamics of Radical Ion Pairs as Observed by Magnetic Field Effects

In this work we have compared manifestations of degenerate electron exchange (DEE) and dimerization reactions in MARY (magnetically affected reaction yield) spectroscopy and time-resolved magnetic field effects (TR-MFE) of radical ion pairs (RIPs). It is shown that dimerization results in phase and frequency changes of the quantum beats in TR-MFE traces, whereas DEE leads to relaxation-type changes in the spin dynamics of RIPs. Dimerization does not change the width of MARY lines considerably, but leads to new lines corresponding to dimer radical ions. In contrast, DEE substantially changes the MARY line widths. Our treatment provides ways to discriminate between both processes from experimental MARY spectra and TR-MFE kinetics. An experimental example dealing with concentration-dependent broadening of the MARY lines is also discussed.