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The rate constants required to model the OH$^+$ observations in differentregions of the interstellar medium have been determined using state of the artquantum methods.  First, state-to-state rate constants for the H$_2(v=0,J=0,1)$+ O$^+$($^4S$)$\rightarrow$ H + OH$^+(X ^3\Sigma^-, v', N)$ reaction have been obtained usinga quantum wave packet method. The calculations have been compared withtime-independent results to asses the accuracy of reaction probabilities atcollision energies of about 1 meV. The good agreement between the simulationsand the existing experimental cross sections in the $0.01-$1 eV energy rangeshows the quality of the results.  The calculated state-to-state rate constants have been fitted to ananalytical form. Second, the Einstein coefficients of OH$^+$ have been obtainedfor all astronomically significant ro-vibrational bands involving the$X^3\Sigma^-$ and/or $A^3\Pi$ electronic states.  For this purpose the potential energy curves and electric dipole transitionmoments for seven electronic states of OH$^+$ are calculated with {\it abinitio} methods at the highest level and including spin-orbit terms, and therovibrational levels have been calculated including the empirical spin-rotationand spin-spin terms. Third, the state-to-state rate constants for inelasticcollisions between He and OH$^+(X ^3\Sigma^-)$ have been calculated using atime-independent close coupling method on a new potential energy surface. Allthese rates have been implemented in detailed chemical and radiative transfermodels. Applications of these models to various astronomical sources show thatinelastic collisions dominate the excitation of the rotational levels ofOH$^+$. In the models considered the excitation resulting from the chemicalformation of OH$^+$ increases the line fluxes by about 10 % or less dependingon the density of the gas.

OH+ in astrophysical media: state-to-state formation rates, Einstein coefficients and inelastic collision rates with He