Calculations of rate constants are presented for fast neutral reactions between polar diatomic and polyatomic molecules. The method applies the infinite-order sudden approximation to treat the rotations of the diatomic molecule and a rotationally adiabatic approximation with asymmetric top wavefunctions to describe the rotations of the polyatomic. A capture approximation is used to calculate reaction cross sections and rate constants. The interaction potential is expressed as a sum of dipole-dipole and dispersion contributions. The calculated rate constants compare well with analytical formulas derived for the limits of high and very low temperatures. The NaO + H2O, NaO + O3, CH + CH2O, and SH + NO2 reactions are considered as examples and calculated rate constants are compared with experiment for these four fast reactions. Quite good agreement is obtained for the NaO + O3 and CH + CH2O reactions. © 1992 American Chemical Society.