A quantum mechanical approach to treat diatom-diatom exchange processes of the type AB+CD-->ABC+D is presented. The approach is based on three types of wave functions psi(0 nu), psi(0 lambda) and chi, where the first two are (asymptotic) elastic distorted wave functions for the two arrangement channels nu and lambda, and chi is a short range (square integrable) wave function describing the system in the dose interaction region. The functions psi(0 nu) and psi(0 lambda) are presented within the j(Z) approximation, and to calculate chi, a perturbative-type Schrodinger equation which contains negative imaginary potentials (to form absorbing boundary conditions) is solved. The variationally stable solution is obtained employing Gaussians and local adiabatic basis sets. The actual calculation of chi is done employing the quasibreathing sphere model, where the relevant angular coordinates are selected. randomly (about 50 sets like that were used) employing a Monte Carlo approach. With this approach, most detailed state-to-state cross sections were calculated for the reaction H-2(n(1)=0, j(1)=0)+OH(n(2)=0, j(2)=0)-->H2O(upsilon ($) over bar j upsilon K Omega(K))+H, where (upsilon ($) over bar j upsilon) are the usual vibrational-bending states of the water molecule, and K and Omega(K) are, respectively, the overall rotational quantum number and the corresponding magnetic component. The results were compared with those due to other treatments and with experiment.