arXiv subjects

Joseph E. Lawrence

Publications and source records attributed to Joseph E. Lawrence.

21 records · Page 2Linked to original sources

arXiv2019

On the calculation of quantum mechanical electron transfer rates

We present a simple interpolation formula for the rate of an electron transfer reaction as a function of the electronic coupling strength. The formula only requires the calculation of Fermi Golden Rule and Born-Oppenheimer rates and so can be combined with any methods that are able to calculate these rates. We first demonstrate the accuracy of the formula by applying it to a one dimensional scattering problem for which the exact quantum mechanical, Fermi Golden Rule, and Born-Oppenheimer rates are readily calculated. We then describe how the formula can be combined with the Wolynes theory approximation to the Golden Rule rate, and the ring polymer molecular dynamics (RPMD) approximation to the Born-Oppenheimer rate, and used to capture the effects of nuclear tunnelling, zero point energy, and solvent friction on condensed phase electron transfer reactions. Comparison with exact hierarchical equations of motion (HEOM) results for a demanding set of spin-boson models shows that the interpolation formula has an error comparable to that of RPMD rate theory in the adiabatic limit, and that of Wolynes theory in non-adiabatic limit, and is therefore as accurate as any method could possibly be that attempts to generalise these methods to arbitrary electronic coupling strengths.

physics.chem-ph↗

arXiv2017

Analytic continuation of Wolynes theory into the Marcus inverted regime

The Wolynes theory of electronically nonadiabatic reaction rates [P. G. Wolynes, J. Chem. Phys. 87, 6559 (1987)] is based on a saddle point approximation to the time integral of a reactive flux autocorrelation function in the nonadiabatic (golden rule) limit. The dominant saddle point is on the imaginary time axis at $t_{\rm sp}=iλ_{\rm sp}\hbar$, and provided $λ_{\rm sp}$ lies in the range $-β/2\leλ_{\rm sp}\leβ/2$, it is straightforward to evaluate the rate constant using information obtained from an imaginary time path integral calculation. However, if $λ_{\rm sp}$ lies outside this range, as it does in the Marcus inverted regime, the path integral diverges. This has led to claims in the literature that Wolynes theory cannot describe the correct behaviour in the inverted regime. Here we show how the imaginary time correlation function obtained from a path integral calculation can be analytically continued to $λ_{\rm sp}<-β/2$, and the continuation used to evaluate the rate in the inverted regime. Comparisons with exact golden rule results for a spin-boson model and a more demanding (asymmetric and anharmonic) model of electronic predissociation show that the theory it is just as accurate in the inverted regime as it is in the normal regime.

physics.chem-ph↗

arXiv2016

Magnetoelectroluminescence in organic light emitting diodes

The magnetoelectroluminescence of conjugated organic polymer films is widely accepted to arise from a polaron pair mechanism, but their magnetoconductance is less well understood. Here we derive a new relationship between the experimentally measurable magnetoelectroluminescence and magnetoconductance and the theoretically calculable singlet yield of the polaron pair recombination reaction. This relationship is expected to be valid regardless of the mechanism of the magnetoconductance, provided the mobilities of the free polarons are independent of the applied magnetic field (i.e., provided one discounts the possibility of spin-dependent transport). We also discuss the semiclassical calculation of the singlet yield of the polaron pair recombination reaction for materials such as poly(2,5-dioctyloxy-paraphenylene vinylene) (DOO-PPV), the hyperfine fields in the polarons of which can be extracted from light-induced electron spin resonance measurements. The resulting theory is shown to give good agreement with experimental data for both normal (H-) and deuterated (D-) DOO-PPV over a wide range of magnetic field strengths once singlet-triplet dephasing is taken into account. Without this effect, which has not been included in any previous simulation of magnetoelectroluminescence, it is not possible to reproduce the experimental data for both isotopologues in a consistent fashion. Our results also indicate that the magnetoconductance of DOO-PPV cannot be solely due to the effect of the magnetic field on the dissociation of polaron pairs.

physics.chem-ph↗