Many problems in quantum chemistry deal with the computation of fundamental or excited states of molecules and lead to the resolution of eigenvalue problems. One of the major difficulties in these computations lies in the very large dimension of the systems to be solved. Indeed, these eigenfunctions depend on 3n variables, where n stands for the number of particles (electrons or protons) in the molecule. 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 Note 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.