A study designed to refine the procedure for performing ab initio molecular dynamics calculations (AIMD) on chemical reactions is presented. Of key interest is the calculation of changes in free energy along the entire reaction path. Several simple elementary reactions are studied with the Car-Parrinello projector augmented-wave (CP-PAW) density-functional theory (DFT) methodology. The illustrative gas-phase bimolecular addition reactions are (i) a sigma complexation of BH3 + H2O.H2O-BH3, (ii) the Diels-Alder reactions of butadiene with ethene, C4H6 + C2H4 --> cyclohexene, 1,3-cyclopentadiene (CP) and ethene, CP + C2H4 --> norbornene, and the stereoselective reaction of 5-amino-CP with ethene, amino-CP + C2H4 --> amino-norbornene, (iii) the carbene cyclopropanation Cl2C + C2H4 --> Cl2C3H4, and (iv) the dimerization of ketene. These reactions were used to test both the slow-growth and point-wise thermodynamic integration (STI and PTI) methods of phase-space sampling as well as the Nose-Hoover and Andersen thermostats. It is found that the PTI technique is potentially superior to the slow-growth method in terms of computational expense and is at least as accurate. The Nose-Hoover thermostat appears to be inadequate for most of the reactions modeled here, whereas the stochastic Andersen thermostat affords more accurate results.