The kernel energy method: Construction of 3- and 4-tuple kernels from a list of double kernel interactions

The kernel energy method (KEM) provides a way to calculate the ab initio energy of very large biological molecules. The results are accurate, and the computational time reduced. However, by use of a list of double kernel interactions a significant additional reduction of computational effort may be achieved, still retaining ab initio accuracy. A numerical comparison of the indices that name the known double interactions in question, allow one to list higher order interactions having the property of topological continuity within the full molecule of interest. When, that list of interactions is unpacked, as a kernel expansion, which weights the relative importance of each kernel in an expression for the total molecular energy, high accuracy, and a further significant reduction in computational effort results. A KEM molecular energy calculation based upon the HF/STO3G chemical model, is applied to the protein insulin, as an illustration.