Graphically Contracted Function Construction with the Recursive Pairwise Merge Algorithm

Abstract

A new implementation of a recursive pairwise merge algorithm to construct a GCF from a list of CSF expansion coefficients is presented. The essential new feature is the preallocation of some work arrays used within the intermediate steps of the merge procedure. This results in roughly an order of magnitude improvement in overall efficiency and also approximately eliminates a factor of n, the molecular orbital dimension, from the original implementation. Initial application of this merge procedure to a series of H m molecules shows that the GCF wave functions can be represented well both with delocalized canonical Hartree-Fock orbitals and with localized molecular orbitals. Finally, for a given wave function complexity, as measured by the average facet count, $\bar{\text {f}}$, the delocalized Hartree-Fock orbitals show smaller errors for small $\bar{\text {f}}$ values, while the localized orbitals show smaller errors for larger $\bar{\text {f}}$ values.