Year: 2026
Type: article
Abstract: ABSTRACT Valence‐bond (VB) theory provides a structural language for reasoning about molecular electronic structure, but its practical use is limited by the algebra of matrix elements between non‐orthogonal VB structures. We introduce symvb, a SymPy‐based package that automates this algebra through Löwdin's cofactor expansion and returns symbolic VB Hamiltonian and overlap matrices, closed‐form energies, and Chirgwin–Coulson weights as functions of the atomic‐orbital integrals. In , decreasing overlap shifts the bonding stabilization toward covalent–ionic resonance, which is the hallmark of charge‐shift bonding. In the allyl anion, the long‐bond Rumer weight, a biradical signature, grows from 1/8 to 1/2 with on‐site repulsion. In the mixed‐valence disphenoid , correlation shifts the Robin–Day boundary toward weaker coupling. In benzene, a covalent‐only model gives the wrong sign for the energy response to weakening a single bond, exposing the essential role of ionic structures. Thus, symvb provides a reusable symbolic workflow for constructing and interpreting non‐orthogonal VB models.
DOI: 10.1002/qua.70284
Authors: Punhasa S. Senanayake, Marat R. Talipov
Institution: New Mexico State University
Language: English
Subfield: Atomic and Molecular Physics, and Optics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: bronze
Awards: G1822451126, G620453595, G9000015656
OpenAlex ID: W7204257185