Symbolic Valence Bond Theory for Chemists: The symvb Package

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.