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Register a new userOn the calculation of quantum mechanical electron transfer rates
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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.
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We present quantum mechanical calculations of Auger decay rates for two Rubidium Rydberg atoms with weakly overlapping electron clouds. We neglect exchange effects and consider tensor products of independent atom states forming an approximate basis of the two-electron state space. We consider large sets of two-atom states with randomly chosen quantum numbers and find that the charge overlap between the two Rydberg electrons allows one to characterise the magnitude of the Auger decay rates. If the electron clouds overlap by more than one percent, the Auger decay rates increase approximately exponentially with the charge overlap. This finding is independent of the energy of the initial state.
We study a simple quantum mechanical symmetric donor-acceptor model for electron transfer (ET) with coupling to internal deformations. The model contains several basic properties found in biological ET in enzymes and photosynthetic centers; it produces tunnelling with hysteresis thus providing a simple explanation for the slowness of the reversed rate and the near 100% efficiency of ET in many biological systems. The model also provides a conceptual framework for the development of molecular electronics memory elements based on electrostatic architectures.
The effect of solvation on the electron transfer (ET) rate processes is investigated on the basis of the exact theory constructed in J. Phys. Chem. B Vol. 110, (2006); quant-ph/0604071. The nature of solvation is studied in a close relation with the mechanism of ET processes. The resulting Kramers turnover and Marcus inversion characteristics are analyzed accordingly. The classical picture of solvation is found to be invalid when the solvent longitudinal relaxation time is short compared with the inverse temperature.
We perform the fixed-node diffuse Monte Carlo (FN DMC) calculations to determine the barrier height and reaction energy of a critical reaction, the H-transfer reaction from syn-CH3CHOO to vinyl hydroperoxide. The FN DMC barrier height is found to be 16.60+/-0.35 kcal/mol which agrees well with the experimental measurement within a few tenths of kcal, justifying the reliability of the FN DMC method for predicting barrier height of the rapid unimolecular reaction of Criegee intermediates. By comparing the predictions from the CCSD(t), G3 (MCG3), DFT and MP2 methods with respect to the FN DMC results and available experiment measurement, we found that the CCSD(t) barrier heights agree with the FN DMC counterpart within statistical errors, and is within a closer agreement with experiment and FN DMC prediction than the G3(MCG3) models. Barrier heights predicted from the relatively more economic DFT methods are within a few tenths kcal of the FN DMC prediction. MP2 method severely underestimates the barrier height. FN DMC prediction for the reaction energy is -17.25+/-0.31 kcal/mol, setting an upper limit for the reaction energies predicted by the post Hartree-Fock methods and a lower limit for the DFT reaction energies. We provide FN DMC input for clarifying the energetic uncertainties in the critical H-transfer reaction of syn-CH3CHOO. The quantitatively close agreements between the FN DMC barrier height and experimental measurement, and between the predictions from the FN DMC and G3 model for the reaction energy provide a theoretical basis for resolving the energy uncertainty in this reaction.
We used molecular dynamics simulations and the path sampling technique known as forward flux sampling to study homogeneous nucleation of NaCl crystals from supersaturated aqueous solutions at 298 K and 1 bar. Nucleation rates were obtained for a range of salt concentrations for the Joung-Cheatham NaCl force field combined with the SPC/E water model. The calculated nucleation rates are significantly lower than available experimental measurements. The estimates for the nucleation rates in this work do not rely on classical nucleation theory, but the pathways observed in the simulations suggest that the nucleation process is better described by classical nucleation theory than an alternative interpretation based on Ostwalds step rule, in contrast to some prior simulations of related models. In addition to the size of NaCl nucleus, we find that the crystallinity of a nascent cluster plays an important role in the nucleation process. Nuclei with high crystallinity were found to have higher growth probability and longer lifetimes, possibly because they are less exposed to hydration water.
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