Wave function analysis with Shavitt graph density in the graphically contracted function method

The goals of electronic structure theory are to make quantitative predictions of molecular properties and to provide qualitative insight into bonding as well as features of potential energy surfaces. Oftentimes, the two goals are at odds as an accurate treatment requires a complicated wave function that obscures chemical insight. The multifacet graphically contracted function (MFGCF) method offers a new approach that allows both goals to be addressed simultaneously. The recursive product structure of the MFGCF wave function reduces the exponential scaling of the exact wave function and allows the computation of molecular properties with polynomial scaling with respect to system size. Additionally, the graph density concept provides an intuitive tool for visualizing and analyzing the qualitative features of the wave function. In this work, the graph densities for model systems are examined to demonstrate their utility in analyzing the changes in wave function character along potential energy surfaces and near avoided crossings. Finally, we demonstrate that the graph density exposes the structure of the exact wave function for a system of noninteracting molecules as a product of the fragment wave functions.