Many problems in quantum chemistry deal with the computation of fundamental or excited states of moleules and lead to the resolution of eigenvalue problems. One of the major dificulties in these computations lies in the very large dimension of the systems to be solved. Indeed these eigenfuntions depend on 3n variables where n stands for the number of partiles (electrons and/or nucleari) in the moleule. In order to diminish the size of the systems to be solved, the chemists have proposed many interesting ideas. Among those stands the adiabatic variable method; we present in this paper a mathematical analysis of this approximation and propose, in particular, an a posteriori estimate that might allow for verifying the adiabaticity hypothesis that is done on some variables; numerical simulations that support the a posteriori estimators obtained theoretically are also presented.