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The solvation free energy difference, ΔG, and reorganization energy, λ, of the electronic transition between the ground and first excited state of formaldehyde are investigated as a function of the solvent electronic polarizability in aqueous solution. Solvent shifts are difficult to measure experimentally for formaldehyde due to oligomer formation; shifts for acetone, which have been measured experimentally, are used instead for comparison with computational results. Predictions of the Poisson–Boltzmann equation of dielectric continuum theory with molecular shaped cavities and charges on atomic sites calculated from ab initio quantum chemistry are compared with direct molecular dynamics simulations using the fluctuating charge model of polarizable water. The explicit molecule simulations agree with the acetone experimental results, but the continuum dielectric calculations do not agree with explicit solvent or with experiment when the default model cavity is used for both the ground and excited state mol...

A dielectric continuum theory for the solvation of a polar molecule in a polar, polarizable solvent is tested using computer simulations of formaldehyde in water. Many classes of experiments, for example those which measure solvent‐shifted vertical transition energies or electron transfer rates, require an explicit consideration of the solvent electronic polarization. Due to the computational cost of simulating a polarizable solvent, many simulation models employ non‐polarizable solute and solvent molecules and use dielectric continuum theory to relate the properties of the non‐polarizable system to the properties of a more realistic polarizable system. We have performed simulations of ground and excited state formaldehyde in both polarizable and non‐polarizable water, and the solvation energies and solvent‐shifted electronic spectra we obtained are used to test dielectric continuum, linear response predictions. Dielectric continuum theory correctly predicts that free energy differences are the same in polarizable and non‐polarizable water. The theory wrongly predicts that the reorganization energy in a polarizable solvent is 30% smaller than the reorganization energy in a polar, non‐polarizable solvent; in the simulations, the reorganization energies differ by only 6%. We suggest that the dielectric continuum theory fails because it assumes that both solute electronic states exist in the same size cavity in the solvent, whereas in the simulation the cavity radius increases by 20% after the electronic transition. We account for the change in the cavity size by adding a non‐linear solute–solvent coupling to the dielectric continuum theory, and find that the resulting predictions are just outside the error bounds from the simulation. The cavity size corrections have the undesired and incorrect side‐effect of predicting fluctuations far smaller than seen in the simulations. This reveals the inherent difficulty in devising a simple, fully self‐consistent dielectric continuum theory for solvation.

We investigate the distribution of energies of thermally activated particles escaping from a metastable well. This energy distribution is connected by detailed balance to the energy‐dependent transmission coefficient, the probability that a particle injected into a well will stick. Theoretical expressions for the energy‐dependent transmission coefficient show good agreement with simulation results for a one‐dimensional reaction coordinate coupled to a frictional bath. Slight deviations from theoretical predictions based on turnover theory [E. Pollak, H. Grabert, and P. Hanggi, J. Chem. Phys. 91, 4073 (1989)] are understood in light of the assumptions of turnover theory. Furthermore, the theoretical expressions for energy distributions also provide good fits for fully three‐dimensional simulations of sticking and desorption of Ar and Xe on Pt(111) [J. C. Tully, Surf. Sci. 111, 461 (1981)]. Finally, we compare the theoretical efficiencies of several reactive flux sampling schemes, including a scheme designed to be optimal.

We have implemented a semiclassical dynamics simulation method to investigate the effects of finite barrier heights and nonlinear potentials on the rate of diffusion of a particle which is coupled to a frictional bath and is traveling on a one‐dimensional potential energy surface. The classical reactive flux method has been modified to account for semiclassical tunneling and above‐barrier reflection. A novel perturbation theory treatment of the semiclassical dynamics is developed to simulate the motion of the particle when the coupling to the frictional bath is small and the particle’s motion is nearly conservative. Our simulation results support the theoretical prediction that the diffusion constant increases as friction decreases. We also find supporting evidence for an inverse isotope effect, as the diffusion constant for a classical particle can be larger than that of a corresponding quantum mechanical particle. The escape rate and the average energy of escaping particles are also found to be in good agreement with theoretical predictions.

The time correlation function for a harmonic quantum mechanical system can be related to the time correlation function for a corresponding classical system. Although straightforward to derive and well known in other contexts, this relationship has been unappreciated in the context of vibrational relaxation, where time correlation functions obtained from classical molecular dynamics have been used to predict relaxation rates for a quantum solute in a classical solvent. This inconsistent treatment—quantum solute, classical solvent—predicts a relaxation rate which is slower than if the entire system, both solute and solvent, were treated classically. We demonstrate that if the classical time correlation functions are rescaled to account for the ratio of quantum to classical fluctuations, providing a quantum mechanical treatment for the solute and the solvent, the relaxation rates and the entire absorption spectrum are the same as for a purely classical treatment. Our conclusions are valid when the solute and...

By computer simulation and also by analytical methods we have computed the nuclear tunneling enhancement of the rate for ferrous–ferric exchange in water. The model we have examined is the one studied earlier where we treated water as a classical liquid [R. A. Kuharski, J. S. Bader, D. Chandler, M. Sprik, M. L. Klein, and R. W. Impey, J. Chem. Phys. 89, 3248 (1988)]. But now we treat water quantum mechanically and find that the tunneling enhancement is a factor of 60 in the rate constant. Further, as observed experimentally, we find that the isotope shift on the rate when changing from D2O to H2O is approximately a factor of 2. The computer simulation aspects of these calculations employ path integral methods and a novel partitioning of the free energy associated with electron transfer. Our results show that it is insufficient to quantize only the atoms composing the ligands. The quantum dynamics of water molecules beyond the first solvation shell prove quite significant.

We present a molecular model for studying the prototypical ferric–ferrous electron transfer process in liquid water, and we discuss its structural implications. Treatment of the nonequilibrium dynamics will be the subject of future work. The elementary constituents in the model are classical water molecules, classical ferric ions (i.e., Fe3+ particles), and a quantal electron. Pair potentials and pseudopotentials describing the interactions between these constituents are presented. These interactions lead to ligand structures of the ferric and ferrous ions that are in good agreement with those observed in nature. The validity of the tight binding model is examined. With umbrella sampling, we have computed the diabatic free energy of activation for electron transfer. The number obtained, roughly 20 kcal/mol, is in reasonable accord with the aqueous ferric–ferrous transfer activation energy of about 15 to 20 kcal/mol estimated from experiment. The Marcus relation for intersecting parabolic diabatic free ene...