From cyclic nanorings to single-walled carbon nanotubes: disclosing the evolution of their electronic structure with the help of theoretical methods

Abstract

We systematically investigate the relationships between structural and electronic effects of finite size zigzag or armchair carbon nanotubes of various diameters and lengths, starting from a molecular template of varying shape and diameter, i.e. cyclic oligoacene or oligophenacene molecules, and disclosing how adding layers and/or end-caps (i.e. hemifullerenes) can modify their (poly)radicaloid nature. We mostly used tight-binding and finite-temperature density-based methods, the former providing a simple but intuitive picture about their electronic structure, and the latter dealing effectively with strong correlation effects by relying on a fractional occupation number weighted electron density (ρ FOD ), with additional RAS-SF calculations backing up the latter results. We also explore how minor structural modifications of nanotube end-caps might influence the results, showing that topology, together with the chemical nature of the systems, is pivotal for the understanding of the electronic properties of these and other related systems.

The Low Lying Double-Exciton State of Conjugated Diradicals: Assessment of TDUDFT and Spin-Flip TDDFT Predictions

“…The coefficient of determination R-squared(R 2 ) value is 0.93. In previous works, the N FOD values have been compared with the y 0 values for linear acenes [27] and have been used to demonstrate the poly-radical character of cyclacenes [27] and single-wall carbon nanotubes [28].…”

Emerging DFT Methods and Their Importance for Challenging Molecular Systems with Orbital Degeneracy

“…Finite-Temperature DFT, also called thermally assisted-occupation DFT [22], is a useful tool for systems with a complicated electronic structure [23,24]. Besides its utility to select active orbitals prone to partial occupation, as the first step for more sophisticated multiconfigurational or complete active space self-consistent field (MCSCF/CASSCF) treatments, it has been recently applied to a large set of radical and radicaloid systems [25][26][27][28][29]. It is also conceived as a low-cost tool to explore energy landscapes with varying biradical character, as it may happen in organic chemical reactions, and to discard pathological cases in datasets more effectively than using traditional descriptors [30].…”

Theoretical Insights for Materials Properties of Cyclic Organic Nanorings

“…This is the common case of CPPs and their linear analogues, but not the situation found for CCs or closely related systems. For the latter case, the tight‐binding model already predicts the existence of both zero‐energy states and quasi‐zero‐energy states for even and odd n values of nCCs, [ 106,159 ] or in the language of molecular orbital theories, the frontier orbitals are degenerate for both odd and even systems: CCs with an even (odd) number of rings present two (four) electrons in (a pair of) two completely degenerate orbitals, thus behaving as diradical (polyradical) systems. Theoreticians had studied early the hypothesized structure of cyclacenes in the 1950s and 1960s, together with other cyclic polyenes at the Hückel level, [ 160,161 ] already paving the way toward the understanding of their geometrical and electronic structure.…”

“…Thereof, largely due to the emerging properties recently disclosed and exploited at the nanoscale, we will focus in the following on a set of the most recent (and hopefully novel) prospects of these materials including: 1.The chemical and topological origin of the radical‐like nature of closely related nanorings (i.e., cyclacenes [CCs]) compared with CPPs, [ 103,104 ] and the possible implications for the envisioned growth of armchair or zigzag CNTs [ 105,106 ] ; 2.The comprehension of the driving forces for the supramolecular packing and cohesive energies of these systems as a function of their size, [ 107 ] therefore opening a way to tune their supramolecular structure to access solid‐state CNT‐like structures via the adequate functionalization, [ 108–110 ] and the determination of the preferred charge‐transfer career paths [ 111,112 ] ; …”