Dibenzo[ef,kl]heptalene: Nonbenzenoid Organic Magnetism

• Dibenzo[ef,kl]heptalene is a nonbenzenoid π-conjugated hydrocarbon defined by fused heptagons and hexagons, offering a platform for studying open-shell magnetism and unconventional aromaticity.
• Perturbative treatments of its Kekulé structures reveal the influence of supplementary circuits (S1, S2) on stabilization, surpassing traditional benzenoid conjugated-circuit analysis.
• Recent research exploits this molecule as a building block for 2D organic altermagnetic lattices, enabling spin-compensated, spin-split band structures in engineered frameworks.

Dibenzo[ef,kl]heptalene is a non-alternant $\pi$-conjugated hydrocarbon described as consisting of two fused heptagons and two hexagons, with closed-shell and open-shell resonance forms and an electronically nontrivial fused-ring topology (Ortiz et al., 5 Aug 2025). In current research usage it occupies a distinctive position between nonbenzenoid valence-structure theory, graph-theoretic treatments of fused-ring hydrocarbons, and first-principles studies of organic magnetism. It has been analyzed as a platform for perturbative comparison of Kekulé valence structures (Gineityte, 2016), discussed in relation to catacondensed chemical hexagonal complexes and blueprint-map methods (Anstöter et al., 2021), and proposed as a building block for two-dimensional organic altermagnets and related covalent organic frameworks (Ortiz et al., 5 Aug 2025). A high-throughput survey of B,N-substituted polycyclic aromatic hydrocarbons did not include dibenzo[ef,kl]heptalene among its 77 parent PAHs, and therefore reported no direct BN-substitution data for this specific molecule (Chakraborty et al., 2019).

1. Molecular constitution and structural identity

The defining structural feature of dibenzo[ef,kl]heptalene is the presence of fused heptagonal and hexagonal rings in a single conjugated framework. In the altermagnetism study, the molecule is specified as an $S=1$ $\pi$-conjugated hydrocarbon built from two fused heptagons and hexagons, and its spin density is described as delocalized over the molecular framework (Ortiz et al., 5 Aug 2025). The same source emphasizes that the heptagons are chemically decisive because they produce non-alternant character and topological frustration.

This non-alternant topology is central to why dibenzo[ef,kl]heptalene is treated differently from conventional benzenoid nanographenes. Purely hexagonal, alternant nanographenes are described as unable to realize the target $C_4$-symmetric, $\pi/2$-rotated square-lattice connectivity solely through $sp^2$ carbons, whereas dibenzo[ef,kl]heptalene can do so because of its fused heptagons (Ortiz et al., 5 Aug 2025). A plausible implication is that the molecule is important less as an isolated nonbenzenoid curiosity than as a symmetry-enabling organic motif for extended electronic phases.

The provided sources are not fully uniform in their descriptive vocabulary. One summary describes dibenzo[ef,kl]heptalene as a peri-condensed PAH built from a heptalene core fused with two benzene rings (Chakraborty et al., 2019), whereas another places it in the context of catacondensed PAHs and branched cata-fused topologies (Anstöter et al., 2021). The chemically unambiguous point common to the sources is its fused-ring, nonbenzenoid character and the central role of the heptagonal rings.

2. Kekulé structures and perturbative $\pi$-electron stabilization

A perturbative treatment extending the biphenylene framework to dibenzo[ef,kl]heptalene represents each Kekulé valence structure as a set of weakly interacting initially double C=C bonds, with total $\pi$-electron energy written as a power series in the average resonance parameter $\gamma$ for single C–C bonds (Gineityte, 2016):

$\mathcal{E}=\sum_{k=0}^{\infty}\mathcal{E}_{(k)},$

with

$S=1$0

$S=1$1

$S=1$2

and

$S=1$3

Within this framework, the relative importance of individual Kekulé structures is governed by specific conjugated circuits. Standard circuits include $S=1$4 benzene-type six-membered circuits, which contribute $S=1$5 per ring at third order, and destabilizing even-membered circuits such as $S=1$6 and $S=1$7. The treatment further introduces supplementary circuits $S=1$8 and $S=1$9. The $\pi$0 motif, identified with 3,4-dimethylene cyclobutene, contributes $\pi$1 at third order and $\pi$2 at fourth order. The $\pi$3 motif, identified with a [4]radialene-type circuit, contributes $\pi$4 at second order, $\pi$5 at third order, and $\pi$6 at fourth order (Gineityte, 2016).

Applied to dibenzo[ef,kl]heptalene, this circuitry-based analysis distinguishes Kekulé forms that would be indistinguishable in a purely benzenoid Clar-style picture. The supplied treatment ranks $\pi$7-containing structures as the most stable, $\pi$8-containing structures as next most stable, and structures containing either two adjacent C=C bonds between fused benzene rings or two exocyclic C=C bonds attached to the same ring as the least stable (Gineityte, 2016). The stated rationale is that avoidance of $\pi$9 and $C_4$0 destabilization outweighs the residual destabilizing contribution of $C_4$1 or $C_4$2. This places dibenzo[ef,kl]heptalene among the nonbenzenoid hydrocarbons for which aromatic stabilization is not adequately described by conventional benzenoid conjugated-circuit language alone.

3. Graph-theoretic placement and relation to benzenoid generalizations

A mathematically oriented extension of benzenoid theory defines a catacondensed chemical hexagonal complex as a connected flat polygonal complex all of whose polygons are hexagons and each of whose vertices belongs to at most two hexagonal faces; such complexes are proved to be Kekulean, and perfect matchings can be counted for various expansions of cubic graphs (Anstöter et al., 2021). In that framework, blueprint maps encode 1–3-regular branching structure, with labels specifying modes of annulation and distinguishing isomeric complexes.

Dibenzo[ef,kl]heptalene is discussed in that context as a branched cata-fused topology representable by a blueprint map with branching points corresponding to trivalent vertices, and the summary states that the associated counting methods can be applied to its resonance analysis (Anstöter et al., 2021). At the same time, the formal CCHC definition is restricted to complexes made exclusively of hexagons, whereas dibenzo[ef,kl]heptalene is independently described as containing fused heptagons (Ortiz et al., 5 Aug 2025). This suggests that its use in the CCHC discussion is best understood as a topological and combinatorial analogy rather than a literal identification with the hexagon-only class.

That distinction matters because it separates two levels of description. At the graph-theoretic level, dibenzo[ef,kl]heptalene can be compared with branched fused-ring systems through blueprint maps, perfect matchings, and branching/connecting/terminal motifs. At the molecular level, its non-alternant heptagons generate electronic features absent from purely benzenoid, all-hexagon systems. The molecule therefore acts as a bridge between benzenoid combinatorics and nonbenzenoid electronic structure.

4. Isolated-molecule electronic structure and magnetic states

For the isolated planar molecule, DFT and multireference CASSCF-NEVPT2 calculations are reported to confirm a spin-triplet ground state, $C_4$3 (Ortiz et al., 5 Aug 2025). The same study rationalizes this result through sublattice imbalance, invoking Lieb’s theorem for alternant hydrocarbons with $C_4$4, and reports that the resulting spin density is delocalized over several carbon atoms. The coexistence of closed-shell and open-shell resonance descriptions in the graphical analysis is therefore consistent with an open-shell magnetic ground state in the planar geometry.

When two dibenzo[ef,kl]heptalene units are joined through hexagon–hexagon, heptagon–heptagon, or hexagon–heptagon bonds, the magnetic coupling is described as strongly antiferromagnetic, with a singlet ground state ($C_4$5) and triplet and quintet excited states (Ortiz et al., 5 Aug 2025). The interaction is modeled by a Heisenberg Hamiltonian,

$C_4$6

with $C_4$7.

These results establish two separate but related points. First, dibenzo[ef,kl]heptalene is intrinsically magnetic at the monomer level in the planar limit. Second, its dominant intermolecular exchange in simple dimers is antiferromagnetic. The combination is precisely what is needed for the later construction of spin-compensated extended lattices with nontrivial band symmetry.

5. Two-dimensional crystals, symmetry, and organic altermagnetism

The most consequential recent use of dibenzo[ef,kl]heptalene is as a building block for two-dimensional organic altermagnetic crystals. Its connectivity permits each molecule to join to four others and thereby form a square lattice with four-fold rotational symmetry; this is presented as a route to antiparallel local moments related by $C_4$8 rotations, in analogy with symmetry requirements identified for inorganic altermagnets (Ortiz et al., 5 Aug 2025). In this setting the heptagonal, non-alternant character is not incidental but the enabling structural element.

The calculated band structure depends on lattice arrangement. In a $C_4$9 arrangement without $\pi/2$0 rotation between adjacent units, the ground state is a collinear antiferromagnet with zero net magnetization and intact Kramers degeneracy, showing a direct band gap and no spin splitting in the Brillouin zone. In the $\pi/2$1 arrangement, by contrast, DFT yields a spin-compensated ground state with broken time-reversal symmetry and non-relativistic spin splitting across the Brillouin zone (Ortiz et al., 5 Aug 2025). The first valence and conduction bands display $\pi/2$2-wave symmetry, specifically a $\pi/2$3-like angular dependence of the splitting. Reported spin splittings near $\pi/2$4 range from approximately $\pi/2$5 meV to $\pi/2$6 meV.

The same study argues that this splitting originates from lattice symmetry rather than spin–orbit coupling. The two magnetic sublattices are related by a real-space $\pi/2$7 rotation rather than by inversion, and the lack of a symmetry operation such as $\pi/2$8 or translation $\pi/2$9 relating the sublattices lifts Kramers degeneracy at generic $sp^2$0 points, except where symmetry protection remains (Ortiz et al., 5 Aug 2025). In that sense, dibenzo[ef,kl]heptalene supplies an organic implementation of altermagnetic band phenomenology without transition-metal spin centers.

6. Covalent organic frameworks, non-planarity, and relation to BN-substituted PAH design space

To move beyond idealized 2D crystals, covalent organic frameworks based on dibenzo[ef,kl]heptalene units connected by $sp^2$1 or $sp^2$2 diatomic linkers have also been considered (Ortiz et al., 5 Aug 2025). These COFs preserve compensated antiparallel spin alignment and non-relativistic spin splitting, but because the linkers reduce symmetry by breaking mirror symmetry, spin bands are also split at the $sp^2$3 point. The effect is analyzed with a bipartite Hubbard Hamiltonian containing inequivalent on-site energies for the two sublattices, and is presented as a deviation from ideal altermagnetic behavior rather than a loss of the underlying mechanism.

Conformationally, the energetically preferred structure of dibenzo[ef,kl]heptalene is reported to be non-planar, with an $sp^2$4 ground state (Ortiz et al., 5 Aug 2025). Non-planarity modifies inter-unit coupling but does not quench magnetism. Two-dimensional lattices assembled from the non-planar form still favor antiparallel ordering of local $sp^2$5 moments and retain non-relativistic spin splitting, although, as in the lower-symmetry COFs, degeneracy at $sp^2$6 is broken.

A separate but relevant design-space result is negative: dibenzo[ef,kl]heptalene was not included among the 77 Kekulean benzenoid parent PAHs used in a combinatorial survey of B,N-substituted polycyclic aromatic hydrocarbons (Chakraborty et al., 2019). Consequently, no direct enumeration, no direct DFT data, and no direct BN-substituted isomer analysis were reported for this molecule. The survey itself used TPSSh with the def2-SVP basis set in ORCA 4.0.1.2, treating all BN substitution patterns in naphthalene and single BN-pair substitutions in the remaining 76 PAHs, for a total of 33,059 isomers, with optimized geometry, atomization energy per electron, dipole moment, and HOMO–LUMO gap among the calculated properties (Chakraborty et al., 2019). For analogous PAHs, BN substitution was reported to introduce bond-length inhomogeneity, longer BN bonds than CC bonds, broader HOMO–LUMO-gap distributions, and site-dependent non-planarity, with approximately 20% of singly B,N-substituted PAHs exhibiting significant non-planarity defined by $sp^2$7 Å. Because dibenzo[ef,kl]heptalene was not part of that dataset, any transfer of these trends to it remains inferential rather than tabulated.

Taken together, these studies define dibenzo[ef,kl]heptalene as a nonbenzenoid fused-ring hydrocarbon whose importance derives from the interaction of topology, valence-structure multiplicity, open-shell magnetism, and lattice symmetry. Its heptagonal framework differentiates it from ordinary benzenoid PAHs, its Kekulé structures require supplementary circuit analysis beyond standard aromatic-circuit models, and its $sp^2$8 open-shell character enables spin-compensated but spin-split band structures in 2D organic networks (Gineityte, 2016, Ortiz et al., 5 Aug 2025).