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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This paper presents the first test of the popular trajectory surface-hopping (TSH) method against accurate three-dimensional quantum mechanics for a reactive system. The system considered is a model system in which an excited atom with an excitation energy of 0.76 eV reacts with or is quenched by the H 2 molecule. The electronically nonadiabatic collisions occur primarily near a conical intersection of an exciplex with a repulsive ground state. The accurate quantal results are calculated using the outgoing wave variational principle in an electronically diabatic representation. Four variants of the TSH method are tested, differing in the criteria for hopping and the component of momentum that is adjusted in order to conserve energy when a hop occurs. Coupling between the ground and excited surface occurs primarily in the vicinity of a conical intersection and is mediated by an exciplex found on the upper surface. We find that the overall TSH quenching probabilities are in good agreement with quantum mechanical results, but the branching ratios between reactive and nonreactive trajectories and many of the state-selected results are poorly reproduced by trajectory calculations. The agreement between trajectory surface hopping and quantal results is on average worse for the relatively more "quantum mechanical" j ) 0 initial state and M + H 2 quenching process and better for the relatively more "classical" j ) 2 initial state and MH + H′ reactive process. We also perform a statistical calculation of overall quenching probability and unimolecular rate of the nonadiabatic decay of the exciplex. We find that only about 10 % of trajectories can be described as "statistical" and that statistical calculation overestimates the total quenching rate significantly.

We present a systematic test of four general semiclassical procedures for the theoretical treatment of multistate molecular processes such as electronically nonadiabatic photochemical reactions. The methods are tested by comparing their predictions to accurate quantal results for three two-state model reactions involving conical intersections. The four methods tested are Tully's fewest-switches version of trajectory surface hopping ͑1990͒, the Blais-Truhlar trajectory surface hopping method ͑1983͒, the Ehrenfest scheme ͑1975-1979͒, and the Meyer-Miller method ͑1979͒.We test the ability of the classical path methods to predict both electronic probabilities and product rovibrational distributions. For each of the four basic approaches we test six options for extracting final-state information from the calculated dynamics. We find that, although in most cases there is qualitative agreement between average quantum mechanical and trajectory results, the overall average error is about 50% for Tully's fewest-switches method, the Ehrenfest method, and the Meyer-Miller method, and even higher, about 60%, for the Blais-Truhlar method. These values do not include additional errors in the below-threshold regions, which are especially large for the Meyer-Miller method because of the electronic zero-point energy in the Meyer-Miller classical analog Hamiltonian.

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