This work describes a simple method linking specific rate constants k(E, J) of bond fission reactions AB -> A + B with thermally averaged capture rate constants k(cap)(T) of the reverse barrierless combination reactions A + B -> AB ( or the corresponding high-pressure dissociation or recombination rate constants k (T). Practical applications are given for ionic and neutral reaction systems. The method, in the first stage, requires a phase-space theoretical treatment with the most realistic minimum energy path potential available, either from reduced dimensionality ab initio or from model calculations of the potential, providing the centrifugal barriers E-0(J). The effects of the anisotropy of the potential afterward are expressed in terms of specific and thermal rigidity factors frigid( E, J) and frigid( T), respectively. Simple relationships provide a link between f(rigid)(E,< J >) and f(rigid)(T) where < J > is an average value of J related to J(max)(E), i.e., the maximum J value compatible with E >= E-0( J), and f(rigid)(E,< J >) applies to the transitional modes. Methods for constructing f(rigid)(E, J) from f(rigid)(E, < J >) are also described. The derived relationships are adaptable and can be used on that level of information which is available either from more detailed theoretical calculations or from limited experimental information on specific or thermally averaged rate constants. The examples used for illustration are the systems C6H6+ double left right arrow C6H5+ + H, C8H10+ -> C7H7+ + CH3, n-C9H12+ double left right arrow C7H7+ + C2H5, n-C10H14+ double left right arrow C7H7+ + C3H7, HO2 double left right arrow H + O-2, HO2 double left right arrow HO + O, and H2O2 double left right arrow 2HO.