The competition between thermalization and dissociation in dilute gas-phase unimolecular reactions gives rise to absolute rate constants as a function of temperature and the number density. Such competitive effects are fully modeled using a master equation formalism that accounts for conservation of total angular momentum as well as conservation of total energy. After such modeling, a general functional form of the rate constants is necessary for approximating the temperature- and pressure-dependent behavior. We present a damped pseudospectral functional form for such an approximation. It is a computationally efficient: and an highly accurate approximation. We illustrate the method and demonstrate its advantages by application. Comparison with extant methods of approximation is also given. Given applications pertain to a singe-well, single-channel reaction, which allows for radiative recombination of radicals in interstellar chemistry, to a single-well, multiple-channel chemically activated reaction in chemical vapor deposition, and, a multiple-well, multiple-channel chemically activated reaction in combustion.