CHEMICAL ALGEBRA .4. LENGTH OF TRANSFORMATION PATHWAYS BETWEEN SKELETAL ANALOGS

Even if the eq. (E) of completely G-invariant distance extensions deri ved from a pairing product is not resolved, a distance is defined by m eans of a metric obtained by differential resolution. Under specified conditions, the linear element solution dsigma2 is homogeneous to squa re coordinate differentials. Integration of dsigma along a curve of E affords a length relative to dsigma2. Boundaries of the curve represen t skeletal analogs u and v, whereas inner points represent intermediat es in the transformation u --> v, where the ligand parameters are supp osed to vary continuously: a stereogenic pairing equilibrium between i nfinitesimally close skeletal analogs is assumed. If the curve runs or thogonal to a unit representation space of G, the length is infinite a nd the curve might be regarded as a ''fractal'' transformation pathway . The ''thermodynamic gap'' D(p) is always shorter than the ''kinetic' ' distance of the metric dsigma2.