Polyradical character assessment using multireference calculations and comparison with density-functional derived fractional occupation number weighted density analysis

The biradicaloid character of different types of polycyclic aromatic hydrocarbons (PAHs) based on small band gaps is an important descriptor to assess their opto-electronic properties. In this work, the unpaired electron densities and numbers of unpaired electrons (NU values) calculated at the high-level multireference averaged quadratic coupled-cluster (MR-AQCC) method are used to develop a test set to assess the capabilities of different biradical descriptors based on density functional theory. A benchmark collection of 29 different compounds has been selected. The DFT descriptors contain primarily the fractional occupation number weighted electron density (FOD) based on simplified thermally-assisted-occupation density functional theory (TAO-DFT) calculations, but the singlet-triplet energy difference and other descriptors denoted as y0 and nLUNO have been considered as well. After adjustment of the literature-recommended finite temperatures, a very good, detailed agreement between unpaired density and FOD analysis is observed which is also manifested in excellent statistical correlations. The other two descriptors also show good correlations even though the absolute scaling is not satisfactory. A new linear fit of FOD data to the MR-AQCC reference values leads to an improved regression relation for determining the recommended finite temperature value in dependence of the Hartree-Fock exchange. This provides the basis for fast and reliable assessment of the biradical character of many classes of PAHs without the need for performing computationally extended MR calculations.