A more refined approach would then be to cast the strains in terms of the normal modes of the system. These normal modes define a complete orthonormal basis for all possible intra-molecular deformations and the decrease in activation barrier can be expressed as a summation over those modes. However, each mode will not, in general, project onto a single component of the tensorial description, but can be subdivided into its contributions to multiple orders of strain. Hence, for the intra-molecular strain effects on the reaction rate constant, we write: