We present a verification and significant algorithmic improvement of the quasi-correlation tight-binding (QCTB) scheme (a Hückel-Hubbard-type model mimicking electron correlation) for describing effectively unpaired electrons in the spirit of Head-Gordon’s approach [M. Head-Gordon, Chem. Phys. Lett. 380, 488 (2003)]. For comparison purposes, results based on the high-level ab initio multireference averaged quadratic coupled cluster method previously computed in our works are invoked. In doing so, typical polyaromatic hydrocarbons (polyacenes, periacenes, zethrenes, and the Clar goblet) are studied. The evaluation shows that the QCTB Hückel-like scheme extended for electron correlation effects provides a qualitatively and in several cases also quantitatively good picture of the unpairing electrons in formally closed-shell electronic systems. Additionally, fairly large nanographene systems of triangulene structure (C426) and a perforated nanoribbon (C8860) have been treated at QCTB level. Two analytical model problems in the framework of QCTB prove the ability of this approximation to give a correct description of natural orbital occupancy spectra. For the studied QCTB scheme, an efficient algorithm is elaborated, and large-scale calculations of radical characteristics for nanographene networks with thousands of carbon atoms are possible.