We present accurate fully quantum calculations of thermal rate constants for a symmetric double well system coupled to a dissipative bath. The calculations are performed using the quasiadiabatic propagator path integral (QUAPI) methodology to evaluate the flux–flux correlation function whose time integral determines the rate coefficient. The discretized path integral converges very rapidly in the QUAPI representation, allowing efficient calculation of quantum correlation functions for sufficiently long times. No ad hoc assumption is introduced and thus these calculations yield the true quantum mechanical rate constants. The results presented in the paper demonstrate the applicability of the QUAPI methodology to practically all regimes of chemical interest, from thermal activation to deep tunneling, and the quantum transmission factor exhibits a Kramers turnover. Our calculations reveal an unusual step structure of the integrated reactive flux in the weak friction regime as well as quantum dynamical enhancement of the rate above the quantum transition state theory value at low temperatures, which is largely due to vibrational coherence effects. The quantum rates are compared to those obtained from classical trajectory simulations. We also use the numerically exact classical and quantum results to establish the degree of accuracy of several analytic and numerical approximations, including classical and quantum Grote–Hynes theories, semiclassical transition state theory (periodic orbit) estimates, classical and quantum turnover theories, and the centroid density approximation.

High-level ab initio calculations of the ground and several excited-state adiabatic potential surfaces of the NaFH system are reported. These calculations were performed by multireference configuration interaction on a large grid of geometries which allowed them to be used for constructing an accurate analytic representation of the NaFH potential surfaces. For the ground and first excited states, using a genetic algorithm, an analytic 2×2 matrix fit was obtained corresponding to a diabatic representation. The off-diagonal coupling was obtained by fitting the energy gap between the surfaces in the region of their avoided crossing, and the diagonal elements were then fit to reproduce the ab initio adiabatic energy at 1530 points. The full fit was used to locate the barrier and the van der Waals well on the ground-state potential surface, the exciplex on the first-excited-state potential surface, and the minimum energy path for the ground-state Na+HF→NaF+H reaction. Additional calculations on the van der Waals and saddle point regions were carried out by a variety of ab initio methods as a check on accuracy. Major topological features of the potential energy surfaces representing higher-than-first excited states were examined.

We present a new semiclassical method for electronically nonadiabatic collisions. The method is a variant of the time-dependent self-consistent-field method and is called continuous surface switching. The algorithm involves a self-consistent potential trajectory surface switching approach that is designed to combine the advantages of the trajectory surface hopping approach and the Ehrenfest classical path self-consistent potential approach without their relative disadvantages. Viewed from the self-consistent perspective, it corresponds to “on-the-fly histogramming” of the Ehrenfest method by a natural decay of mixing; viewed from the surface hopping perspective, it corresponds to replacing discontinuous surface hops by continuous surface switching. In this article we present the method and illustrate it for three multidimensional cases. Accurate quantum mechanical scattering calculations are carried out for these three cases by a linear algebraic variational method, and the accurate values of reactive probabilities, quenching probabilities, and moments of final vibrational and rotational distributions are compared to the results of continuous surface switching, the trajectory surface hopping method in two representations, the time-dependent self-consistent-field method, and the Miller–Meyer classical electron method to place the results of the semiclassical methods in perspective.

We present accurate path integral calculations of quantum rate constants for model nonadiabatic reactions in condensed matter. The model is described by two coupled diabatic potential surfaces interacting linearly with a bath of harmonic oscillators. The rate constant is obtained from the time integral of the flux-flux correlation function which is evaluated by the quasi-adiabatic propagator path integral method. We study the dependence of the reaction rate on friction, temperature, and exothermicity and compare with predictions of analytical theories. In particular, we observe a broad golden rule plateau as well as rate enhancement due to quantum resonances for low friction in agreement with the semiclassical analysis of Onuchic and Wolynes.

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