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 mutually exclusive 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, introduced in earlier work on the GCF wave function, provides an intuitive tool for visualizing and analyzing the qualitative features of the wave function in terms of the nodes and arcs of the Shavitt graph. Formally, the node(arc) density is equal to the sum of the squares of the configuration interaction coefficients for those configuration state functions that pass through that node(arc). Thus it is a measure of the importance of that node(arc) in describing the wave function. In this work, we discuss the general features of the MFGCF wave function and the recursive algorithm for computing the graph densities using the MFGCF wave function. The algorithm scales polynomially with the number of orbitals and allows the analysis of wave functions for which traditional analysis approaches based on individual configuration state function coefficients become intractable. 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.

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

248th National Meeting (2014)

The official archive and repository for all ACS Meetings & Expositions abstracts and select posters or presentations.