A generalized higher order kernel energy approximation method.

We present a general mathematical model that can be used to improve almost all fragment-based methods for ab initio calculation of total molecular energy. Fragment-based methods of computing total molecular energy mathematically decompose a molecule into smaller fragments, quantum-mechanically compute the energies of single and multiple fragments, and then combine the computed fragment energies in some particular way to compute the total molecular energy. Because the kernel energy method (KEM) is a fragment-based method that has been used with much success on many biological molecules, our model is presented in the context of the KEM in particular. In this generalized model, the total energy is not based on sums of all possible double-, triple-, and quadruple-kernel interactions, but on the interactions of precisely those combinations of kernels that are connected in the mathematical graph that represents the fragmented molecule. This makes it possible to estimate total molecular energy with high accuracy and no superfluous computation and greatly extends the utility of the KEM and other fragment-based methods. We demonstrate the practicality and effectiveness of our model by presenting how it has been used on the yeast initiator tRNA molecule, ytRN(i)(Met) (1YFG in the Protein Data Bank), with kernel computations using the Hartree-Fock equations with a limited basis of Gaussian STO-3G type.