Exchange Rules for Diradical π-Conjugated Hydrocarbons

Abstract

A variety of planar π-conjugated hydrocarbons such as heptauthrene, Clar's goblet and, recently synthesized, triangulene have two electrons occupying two degenerate molecular orbitals. The resulting spin of the interacting ground state is often correctly anticipated as S = 1, extending the application of Hund's rules to these systems, but this is not correct in some instances. Here we provide a set of rules to correctly predict the existence of zero mode states, as well as the spin multiplicity of both the ground state and the low-lying excited states, together with their open-or closed-shell nature. This is accomplished using a combination of analytical arguments and configuration interaction calculations with a Hubbard model, both backed by quantum chemistry methods with a larger Gaussian basis set. Our results go beyond the well established Lieb's theorem and Ovchinnikov's rule, as we address the multiplicity and the open-/closed-shell nature of both ground and excited states.

Topological frustration induces unconventional magnetism in a nanographene

“…The MFH solution predicts an antiferromagnetic (open-shell singlet) ground state of 1 (Fig. 2c), which is in agreement with previous theoretical reports [33][34][35] and our spin-polarised density functional theory (DFT) calculations, wherein for 1 both in the gas phase and on Au(111), the open-shell singlet state is the ground state, with the ferromagnetic (open-shell triplet) state 25.4 meV (gas phase) and 13.2 meV (on-surface) higher in energy ( Supplementary Fig. 2).…”

Clar Goblet and Aromaticity Driven Multiradical Nanographenes

“…[6,7] Our models reproduce this trend with DFT and CASSCF with dynamic correlations matching previous studies (see Ta ble S2 in the Supporting Information). [13,14] It is remarkable that the larger the amount of dynamic electron correlation introduced in the calculation the larger the relative stabilityo ft he singlet state. This can be inferred from the data collected in Table S2, including the resultso btained in this work and those published in Refs.…”

“…[18] This methodology shows remarkable accuracy [19] and has been used in relateds tudies. [9][10][11][12][13][14]20] Also, for completeness, [21][22][23][24] we performed calculations with the M06-2X [25] functional on the CG obtainings imilar results( Ta ble S2). Energies for different spin states werec omputed with DFT and CASSCF and corrected by dynamical correlation effects using CASPT2, which has been shownt ob ea ccurate for low-spins tates in non-KekulØan systems.…”

“…Multiconfigurational studies to date have been limited to CG and similar-size molecules, [13,14] while the studyo fl arger bowtie nanographenes has been restricted to density functional theory (DFT). [5,6,9,10,12] However,i nn anographenes, low-spin states computed with DFT are usually contaminated with higher-spin states, and this limits the accuracyo nt he relative energetics.…”

Theoretical Insights for Materials Properties of Cyclic Organic Nanorings

“…Note also that any deformation, distortion, or doping of the perfect loop indeed breaks that degeneracy and thus reduces the radical character of the systems facilitating indeed their synthesis. Interestingly, the ultimate origin of these zero‐energy modes relies on the structural symmetry, commuting with the sublattice operator, [ 162 ] which can be lifted upon local distortions. Furthermore, the radical nature of linear acenes is known to also increase with the system size, but the cyclic topology seems to exacerbate this character.…”