A weighted quasi-Newton algorithm for function minimization and a variable-order, variable-step Adams algorithm for ordinary differential equations were combined to solve site-specific gas-phase reaction rate constants. If the systems appear to be "stiff", smaller steps were taken in Adams method to search for the solution. A user supplied error tolerance was used to determine the accuracy of the solution. Upon the return of each solution, a weighted algorithm is introduced into the calculation of X-2 to minimize interference from noise. Lower and upper bounds for reagent fraction and rate constants were applied to ensure the validity of the results. The search direction is calculated by a quasi-Newton algorithm. When a saddle point is suspected, a local search is carried out with a view to moving away from the saddle point. The information obtained from site-specific rate constants may provide further insight into the reaction mechanism as well as gasphase structure. It can be applied to gas-phase H/D exchange, deprotonation, and other reactions.