Fast Quasi-Centroid Molecular Dynamics for Water and Ice.

We describe how the fast quasi-centroid molecular dynamics (f-QCMD) method can be applied to condensed-phase systems by approximating the quasi-centroid potential of mean force as a sum of inter- and intramolecular corrections to the classical interaction potential. The corrections are found by using a regularized iterative Boltzmann inversion procedure to recover the inter- and intramolecular quasi-centroid distribution functions obtained from a path integral molecular dynamics simulation. The resulting methodology is found to give good agreement with a previously published QCMD dipole absorption spectrum for liquid water and satisfactory agreement for ice. It also gives good agreement with spectra from a recent implementation of CMD that uses a precomputed elevated temperature potential of mean force. Modern centroid molecular dynamics methods, therefore, appear to be reaching a consensus regarding the impact of nuclear quantum effects on the vibrational spectra of water and ice.

Fast quasi-centroid molecular dynamics.

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.

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 tunneling, zero point energy, and solvent friction on condensed phase electron transfer reactions. Comparison with exact hierarchical equations of motion 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 the nonadiabatic limit, and is therefore as accurate as any method could possibly be that attempts to generalize these methods to arbitrary electronic coupling strengths.