  The rate constants required to model the OH$^+$ observations in different
regions of the interstellar medium have been determined using state of the art
quantum 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 using
a quantum wave packet method. The calculations have been compared with
time-independent results to asses the accuracy of reaction probabilities at
collision energies of about 1 meV. The good agreement between the simulations
and the existing experimental cross sections in the $0.01-$1 eV energy range
shows the quality of the results.
  The calculated state-to-state rate constants have been fitted to an
analytical form. Second, the Einstein coefficients of OH$^+$ have been obtained
for 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 transition
moments for seven electronic states of OH$^+$ are calculated with {\it ab
initio} methods at the highest level and including spin-orbit terms, and the
rovibrational levels have been calculated including the empirical spin-rotation
and spin-spin terms. Third, the state-to-state rate constants for inelastic
collisions between He and OH$^+(X ^3\Sigma^-)$ have been calculated using a
time-independent close coupling method on a new potential energy surface. All
these rates have been implemented in detailed chemical and radiative transfer
models. Applications of these models to various astronomical sources show that
inelastic collisions dominate the excitation of the rotational levels of
OH$^+$. In the models considered the excitation resulting from the chemical
formation of OH$^+$ increases the line fluxes by about 10 % or less depending
on the density of the gas.
