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. arXiv:1909.09882v1 [physics.chem-ph]

We describe a fast implementation of the quasi-centroid molecular dynamics (QCMD) method in which the quasi-centroid potential of mean force is approximated as a separable correction to the classical interaction potential. This correction is obtained by first calculating quasi-centroid radial and angular distribution functions in a short path integral molecular dynamics simulation and then using iterative Boltzmann inversion to obtain an effective classical potential that reproduces these distribution functions in a classical NVT simulation. We illustrate this approach with example applications to the vibrational spectra of gas phase molecules, obtaining excellent agreement with QCMD reference calculations for water and ammonia and good agreement with the quantum mechanical vibrational spectrum of methane.

Binary collision expansion is applied to the space-tinic memory function associated with the single particle density correlation function. Thc ilsc of the potential of mean force as the interaction potential in the determination of two particle dynamics, thus taking into account the structural corrclations of the fluid, is found to yield significantly improved results for thc correlation function. Comparison of oilr results with molccular dynamics and experimental values shows very good agrecmcnt over a wide range of densities and wave vectors.Un dcvcloppemcnt en tcrmes de collisions binaires cst applique la fonction dc mCmoirc spatio-tcmporellc associCe avec la fonction dc corrdlation dc dcnsitc unc seulc partieulc. On trouve quc I'utilisation du potcnticl de force moycnnc comme potenticl d'intcraction dans la determination de la dynamiquc i deux partieulcs, de faqon a tenir comptc dcs corrdlations structurales du tluiclc, donne tine amelioration notable dcs rCsultats pour la fonction dc corrdlation. La comparaison dc nos rcsultats avcc des calculs dc dynamique mol6eulaire ct Ics valeurs cxpdrimentales indique un accord excellent pour une gammc Ctendue de dcnsitis ct de veeteurs d'onde.[Traduit par Ic journal]Can. J. Phys 61. 926 (1983) i