arXiv subjects

Lachlan P. Lindoy

Publications and source records attributed to Lachlan P. Lindoy.

22 records · Page 2Linked to original sources

arXiv2019

Electron spin relaxation in radical pairs: Beyond the Redfield approximation

Relaxation processes can have a large effect on the spin selective electron transfer reactions of radical pairs. These processes are often treated using phenomenological relaxation superoperators or with some model for the microscopic relaxation mechanism treated within Bloch-Redfield-Wangsness theory. Here, we demonstrate that an alternative perturbative relaxation theory, based on the Nakajima-Zwanzig equation, has certain advantages over Redfield theory. In particular, the Nakajima-Zwanzig equation does not suffer from the severe positivity problem of Redfield theory in the static disorder limit. Combining the Nakajima-Zwanzig approach consistently with the Schulten-Wolynes semiclassical method, we obtain an efficient method for modeling the spin dynamics of radical pairs containing many hyperfine-coupled nuclear spins. This is then used to investigate the spin-dependent electron transfer reactions and intersystem crossing of dimethyljulolidine-naphthalenediimide (DMJ-NDI) radical ion pairs. By comparing our simulations with experimental data, we find evidence for a field-independent contribution to the triplet quantum yields of these reactions which cannot be explained by electron spin relaxation alone.

physics.chem-ph↗

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↗

arXiv2018

Simple and accurate method for central spin problems

We describe a simple quantum mechanical method that can be used to obtain accurate numerical results over long time scales for the spin correlation tensor of an electron spin that is hyperfine coupled to a large number of nuclear spins. This method does not suffer from the statistical errors that accompany a Monte Carlo sampling of the exact eigenstates of the central spin Hamiltonian obtained from the algebraic Bethe ansatz, or from the growth of the truncation error with time in the time-dependent density matrix renormalization group (t-DMRG) approach. As a result, it can be applied to larger central spin problems than the algebraic Bethe ansatz, and for longer times than the t-DMRG algorithm. It is therefore an ideal method to use to solve central spin problems, and we expect that it will also prove useful for a variety of related problems that arise in a number of different research fields.

quant-ph↗

arXiv2018

Spin-selective electron transfer reactions of radical pairs: beyond the Haberkorn master equation

Radical pair recombination reactions are normally described using a quantum mechanical master equation for the electronic and nuclear spin density operator. The electron spin state selective (singlet and triplet) recombination processes are described with a Haberkorn reaction term in this master equation. Here we consider a general spin state selective electron transfer reaction of a radical pair and use Nakajima-Zwanzig theory to derive the master equation for the spin density operator, thereby elucidating the relationship between non-adiabatic reaction rate theory and the Haberkorn reaction term. A second order perturbation theory treatment of the diabatic coupling naturally results in the Haberkorn master equation with an additional reactive scalar electron spin coupling term. This term has been neglected in previous spin chemistry calculations, but we show that it will often be quite significant. We also show that beyond second order in perturbation theory, i.e., beyond the Fermi golden rule limit, an additional reactive singlet-triplet dephasing term appears in the master equation. A closed form expression for the reactive scalar electron spin coupling in terms of the Marcus theory parameters that determine the singlet and triplet recombination rates is presented. By performing simulations of radical pair reactions with the exact Hierarchical Equations of Motion (HEOM) method, we demonstrate that our master equations provide a very accurate description of radical pairs undergoing spin-selective non-adiabatic electron transfer reactions. The existence of a reactive electron spin coupling may well have implications for biologically relevant radical pair reactions such as those which have been suggested to play a role in avian magnetoreception.

physics.chem-ph↗