We apply our invertibility of quantum mechanical systems concept to design open loop controls of molecular systems. The inverse quantum-mechanical control of molecules is studied using the equation of motion for the expectation value of an operator. With this method a requisite external field is obtained to exactly track a prescribed molecular objective expectation value as a function of time. Applications to diatomic molecules are formulated. While the method is directly applicable as a test of physical intuition, it can in principle be used to design fields for specific objectives including reactive selectivity. Results are presented for energy tracking in the hydrogen fluoride molecular system. The numerical calculations show that seemingly benign objective tracks may give rise to singularities in the field. However, these singularities do not present problems in the evolution of the dynamical quantities and instead provide useful hints for designing robust fields.