We analyze here the formula for the rate constant of a chemical reaction provided by the flux-flux correlation function theory. To evaluate this equation, classical trajectories are launched from a surface separating reactants and products, with initial conditions sampled according to the Boltzmann distribution. They are followed until they exit the transition region. We show here that these trajectories have statistical properties that satisfy several nontrivial constraints. We examine the nature of these constraints and explain how they can be used to improve rate constant calculations.