A general classical variational theory of reaction rates [J. Chem. Phys. 87, 5746 (1987)] is applied to the F+H-2-->FH+H reaction for a series of potential-energy functions (PEFs). The variational theory gives the rate as the equilibrium flux of phase points through a trial surface which divides reactants from products and is varied to obtain a least upper bound for the rate. This dividing surface (DS) is defined by a power-series expansion of the H-H internuclear separation (r) in internal coordinates R and theta where R is the distance between atom F and the center-of-mass of H-2 and theta is angle which the H-2 internuclear axis makes with a line from the center-of-mass of H-2 to atom F. The angle-dependent terms in the DS make it possible to describe the dynamical stereochemistry of atom-diatom reactions in a new and useful manner. The profile of the angle-dependent minimum potential energy for reaction versus orientation angle is varied systematically in the PEF series to define a trend toward a "flatter" angle-dependent barrier. Portraits of the dynamical stereochemistry are obtained for each PEF by plotting contours of the density of variational flux on the DS. These reactivity relief maps show how the accuracy of the variational method depends on the expansion order of the DS and how the field of reactivity which surrounds the diatomic reactant expands with increasing temperature and energy. The accuracy of the variational theory was determined by comparing energy-dependent mean reaction cross sections and incremental (angle-dependent) mean reaction cross sections with results obtained by calculating classical mechanical trajectories. The DS was used to show how the accuracy of the no-recrossing assumption of transition state theory depends on orientation angle. Variational and trajectory results were used to calculate energy-dependent transmission and product coefficients.