Communication: Optical gap in polyacetylene from a simple quantum chemistry exciton model

A recent virial-theorem-based model of the singlet-triplet splitting in singly excited configurations [A. D. Becke, J. Chem. Phys. 148, 044112 (2018)] offers an accurate and economical tool for the computation of optical gaps in large molecules. Two single-determinant density-functional-theory calculations, one on the (closed-shell) ground state and another on the (restricted open-shell) HOMO → LUMO triplet excited state, followed by a simple two-electron integral evaluation, are all we need. Here the method is used to compute the optical gaps of trans-polyenes containing up to 60 carbon atoms, approaching the polyacetylene limit. Comparisons with previous computations, and experiment, are made. We also explore changes of the exact-exchange mixing fraction in the underlying density functional. Its effect on the optical gap, and also the exciton size, is enormous. Thus we face the vexing, often asked, question: how much exact exchange should be used?