A Molecular "Thermometer" for Measuring Effective Non-Local Exchange

Non-local exchange (NLX) is a key ingredient for accurate density functional calculations, but its effective strength is often hard to quantify beyond simple global hybrids. To this end, we introduce a molecular probe based on the isomerization of hexaethynylbenzene to carbo-benzene, a reaction with exceptional sensitivity to exchange effects. Using the isomerization energy, we define a simple relative measure, $t_X$ , that gauges the effective NLX of a method on a scale ranging from 0 for the local density approximation to 100 for Hartree-Fock. Across a broad set of density functional approximations, $t_X$ closely tracks the formal Hartree-Fock exchange content of global hybrids, while revealing that most common GGAs, meta-GGAs, and global hybrids still provide too little effective exchange. Several range-separated hybrid, double hybrid, and some local hybrid functionals perform much better and closely approach the near-basis-set-limit coupled-cluster reference value of $t_X=60$ . The $t_X$ values of various semiempirical quantum mechanical and machine-learned interatomic potential methods indicate that they empirically account for NLX effects to a varying degree. Thus, the proposed reaction serves as a compact thermochemical benchmark for assessing and developing methods that aim to reliably describe NLX.