Spin effects on spur kinetics. Re-encounters and the indepedent pairs approximation

Abstract

Recent developments in the theory of reaction kinetics in multi-pair spurs have incorporated the possibility that spin correlations may affect the chemistry in a complex manner. The analyses published so far have employed two distinct approximations: that pairs evolve independently, except on encounter, and that a non-reactive (e.g. triplet) encounter does not affect the subsequent encounter rates. This paper presents tests of these two approximations, both separately and in combination, using two Monte Carlo simulation techniques: a random-flights method, in which spin effects can be incorporated without either approximation, and a modification of the independent reaction times method, which is subject to the independent pairs approximation, but treats reencounters properly. The accuracy of both approximations is assessed, separately and in combination; both result in small errors in opposite directions. As a result of this cancellation the predictions of random-flights simulations and the master equation model, where both approximations are used in combination, agree to within 2%. This error is considerably smaller than the spin effects under investigation, and is also much smaller than errors incurred by using either (i) the prescribed diffusion approximation for the encounter rate coefficient (rather than the independent pairs approximation) or (ii) a deterministic diffusion-kinetic analysis of the spur chemistry employing a macroscopic reaction rate coefficient without explicit consideration of spin correction effects.