Toward a Generalized Hückel Rule: The Electronic Structure of Carbon Nanocones.

Yusuf Bramastya Apriliyanto,Andrea Lombardi,Thierry Leininger,Stefano Battaglia,Noelia Faginas-Lago,Stefano Evangelisti

doi:10.1021/acs.jpca.1c06402

Abstract

In this work, we investigate a particular class of carbon nanocones, which we name graphannulenes, and present a generalized Hückel rule (GHR) that predicts the character of their ground state based on simply the three topological indices that uniquely define them. Importantly, this rule applies to both flat and curved systems, encompassing a wide variety of known structures that do not satisfy the “classic” 4n + 2 rule such as coronene, corannulene, and Kekulene. We test this rule at the Hückel level of theory for a large number of systems, including structures that are convex and flat, with a saddle-like geometry, and at the CASSCF level of theory for a selected representative subset. All the performed calculations support the GHR that we propose in this work.

Highlights

The extraordinary ability of carbon to concatenate with other carbon atoms, forming large stable edifices possibly containing other types of atoms, is at the basis of the unique behavior of this eclectic element, and of life itself
We have found that the ground state wave function was a singlet, and its composition reflected the character predicted by the generalized Hückel rule (GHR), with no exception
In this work, we propose a generalization of the Hückel rule, that is able to predict the nature of the ground state wave function for graphannulene systems solely based on the three topological indices that uniquely define them

Summary

■ INTRODUCTION

The extraordinary ability of carbon to concatenate with other carbon atoms, forming large stable edifices possibly containing other types of atoms, is at the basis of the unique behavior of this eclectic element, and of life itself. Not all curved systems are encompassed by the GHR: a notable example is that of fullerenes, which have a different type of curvature than graphannulenes and are completely different objects In this context, the GHR is complementary to the more famous Hirsch rule[43] and generalization thereof.[44] This GHR predicts correctly the closed-shell character in relation to the aromaticity of circumcoronene (GA6(0, 2)).[26,33,45] It is important to stress out that the GHR predicts the nature of the ground state based on topological features of the graphannulenes structure, whereby a closed-shell wave function usually implies a stable molecule. All SA-CASSCF calculations were carried with the ORCA program package, version 4.2.1.57

■ RESULTS

■ CONCLUSIONS

■ ACKNOWLEDGMENTS

■ REFERENCES