We calculate the adiabatic potential energy curves and nonadiabatic first-derivative couplings for the X, A, and C1∑+ states of KH by an ab initio one-electron pseudopotential formalism. The splitting of the X and A curves at the avoided crossing is in good agreement with experiment. The ab initio results are used to calculate the electronically inelastic transition probabilities and cross sections for K+H collisions at low energies by R matrix propagation in the adiabatic representation with exponential sector transformations. Since this method has never been applied before, we made an extensive study of its convergence properties and efficiency. We found it to be a convenient, accurate, and efficient method. The cross sections are changed by about a factor of two when the potential curves are changed by a different treatment of the KH+ core, but only by about 1% when the assumptions about the nonadiabatic second-derivative coupling terms are altered. Our estimate of the 42P→42S quenching cross section at 0.022 eV relative translational energy is 2-4×10 -4 a02. This increases to 8-10×10 -4 a02 by 1.1 eV. The emphasis in this article is on testing and evaluating the new method for solving the scattering problem rather than on the cross sections themselves.