Predicting the Radical Character of Open-Shell Nanographenes with the GVB-Based Block-Correlated Coupled Cluster Theory

Abstract

Open-shell nanographenes (NGs) possess unique electronic properties that hold promise for next-generation carbon-based materials, yet their rational design is hampered by the lack of quantitative tools to predict their radical character. Empirical rules such as Clar’s aromatic sextet rule and the Fries rule provide useful qualitative guides for closed-shell systems but inherently fail for open-shell NGs, where the ground state is better described as a resonance hybrid of closed-shell and open-shell structures. Here, we present a further development of the generalized valence-bond-based block-correlated coupled cluster (GVB-BCCC) theory and demonstrate its application in qualitative and quantitative predictions of the radical character in open-shell NGs. Four methodological advances are reported: (1) a systematic search procedure of multiple GVB solutions that enables the computational identification of distinct resonance structures (closed-shell, diradical, and tetraradical forms) through tailored initial orbital guesses; (2) the first implementation of GVB-BCCC4 for triplet ground states, extending the framework to systems with triplet ground states; (3) the first implementation of the unrelaxed one-particle density matrix for singlet GVB-BCCC4, enabling the extraction of natural orbital occupation numbers (NOONs) as a rigorous, quantitative measure of radical character directly from the GVB-BCCC4 wavefunction; and (4) the introduction of a relative local correlation energy (RLCE) index for evaluating local aromaticity in individual benzene-like rings. By exploiting the fact that distinct GVB solutions map to chemically intuitive resonance forms, our approach is able to identify the dominant resonance structure through accurate GVB-BCCC4 calculations on top of the respective GVB references. Critically, by comparing the uncorrelated GVB solutions with the fully correlated GVB-BCCC4 results, we can unambiguously determine whether the radical character of a given system originates from the π-skeleton topology (a resonance-driven effect) or from interpair electron correlation─a distinction that remains inaccessible to empirical rules or conventional methods. Our approach is then applied to 11 representative NGs, including systems with up to 66 π orbitals. The radical character indices from GVB-BCCC4 show excellent agreement with DMRG-CASCI reference data, while broken-symmetry DFT is found to be unreliable for systems with pronounced polyradical character. The singlet–triplet energy gaps calculated at the GVB-BCCC4 level also agree well with available experimental values. This work establishes GVB-BCCC as a predictive tool for understanding the structure–property relationships of open-shell systems and for guiding the rational design of carbon-based functional materials.