Intermolecular covalent π-π bonding interaction indicated by bond distances, energy bands, and magnetism in biphenalenyl biradicaloid molecular crystal

Density-functional theory (DFT) calculations were performed for energy band structure and geometry optimizations on the stepped π-chain, the isolated molecule and (di)cations of the chain, and various related molecules of a neutral biphenalenyl biradicaloid (BPBR) organic semiconductor 2. The dependence of the geometries on crystal packing provides indirect evidence for the intermolecular covalent π-π bonding interaction through space between neighboring π-stacked phenalenyl units along the chain. The two phenalenyl electrons on each molecule, occupying the singly occupied molecular orbitals (SOMOs), are participating in the intermolecular covalent π-π bonding making them partially localized on the phenalenyl units and less available for intramolecular delocalization. The band structure shows a relatively large bandwidth and small band gap indicative of good π-π overlap and delocalization between neighboring π-stacked phenalenyl units. A new interpretation is presented for the magnetism of the stepped π-chain of 2 using an alternating Heisenberg chain model, which is consistent with DFT total energy calculations for 2 and prevails against the previous interpretation using a Bleaney-Bowers dimer model. The obtained transfer integrals and the magnetic exchange parameters fit well into the framework of a Hubbard model. All presented analyses on molecular geometries, energy bands, and magnetism provide a coherent picture for 2 pointing toward an alternating chain with significant intermolecular through-space covalent π-π bonding interactions in the molecular crystal. Surprisingly, both the intermolecular transfer integrals and exchange parameters are larger than the intramolecular through-bond values indicating the effectiveness of the intermolecular overlap of the phenalenyl SOMO electrons.