The Force Concept in Chemistry

The applications, most of which have been developed in the last decade, of the Hellmann-Feynman (H-F) theorem in molecular quantum mechanics are reviewed. In general, the forces (on the nuclei of molecules) calculated with the use of this theorem provide great qualitative insight into the nature of the phenomena investigated; outstanding examples of these are in the concepts of chemical binding and molecular shapes. However, there are serious limitations in quantitative applications of the H-F theorem with approximate wave functions, since the calculated forces are extremely sensitive to small inaccuracies in the wave functions, especially near the nuclei of interest. Nevertheless, in view of the fact that it is difficult to discern general qualitative features in very accurate or ab initio molecular calculations, the H-F theorem is likely to be a highly useful tool for developing much needed qualitative chemical models which will be based on firm quantum mechanical foundations and will also remain open to quantitative extension, at least in principle.