Edge counts for the auxiliary pair graph within the graphical unitary group approach. (17th November 2021)

• Record Type: Journal Article
• Authors: Brozell, Scott R.; Shepard, Ron
• Is Part Of: Molecular physics. Volume 119:Number 21/22(2021)
• Publication Date: 2021-11-17
• Subjects: Shavitt graph statistics -- graphical unitary group approach -- full configuration interaction -- particle-hole symmetry -- bra–ket symmetry; Molecules -- Periodicals; Chemistry, Physical and theoretical -- Periodicals; Molécules -- Périodiques; Chimie physique et théorique -- Périodiques; 539.6.05
• DOI: 10.1080/00268976.2021.1950858
• Languages: English
• ISSNs: 0026-8976

Abstract

Abstract : Closed-form expressions are presented for the numbers of edges in the auxiliary pair graphs (APGs) associated with non spin–orbit and spin–orbit Shavitt graphs for full configuration interaction expansions. A Shavitt graph is a visual representation of a configuration state function expansion space constructed via the graphical unitary group approach (GUGA). An APG is an organisational aid and a programmatic tool generated from a Shavitt graph. The number of edges in an APG determines bounds on the computational scaling as a function of the total numbers of electrons, orbitals, and spin multiplicities. The edge counts extend a suite of Shavitt graph statistics based on these functional parameters. The derivation and the presentation of the formulas for the edge counts has been assisted by the bra–ket interchange symmetry and the particle-hole interchange symmetry in the GUGA formalism. These symmetry operators produce one-to-one correspondences between various sets of edges, and this yields identities among some edge count formulas. There are 208 possible edge types. Of these, some do not contribute to two-electron operators, some are related by bra–ket interchange symmetry, and some are related by particle-hole interchange symmetry. For the remaining unique edge types, explicit expressions are derived for the numbers of edges. GRAPHICAL ABSTRACT: UF0001