Many problems in quantum hemistry deal with the omputation of fundamental or ex ited states of mole ules and lead to the resolution of eigenvalue problems. One of the major diÆ ulties in these omputations lies in the very large dimension of the systems to be solved. Indeed these eigenfun tions depend on 3n variables where n stands for the number of parti les (ele trons or protons) in the mole ule. In order to diminish the size of the systems to be solved, the hemists have proposed many interesting ideas. Among those stands the adiabati variable method; we present in this Note a mathemati al analysis of this approximation and propose, in parti ular, an a posteriori estimate that might allow for verifying the adiabati ity hypothesis that is done on some variables.