Comparative study on the band structures of tetrazaporphin nickel(II) and porphyrinato nickel(II). A crystal-orbital approach based on a semiempirical Hartree-Fock self-consistent-field model

The band structures of (a) tetrazaporphin nickel(II) and (b) porphyrinato nickel(II) have been studied by means of the crystal-orbital (CO) model based on the tight-binding approximation. The CO approach is performed in the self-consistent-field scheme of the Hartree-Fock formalism. The employed Hamiltonian is a semiempirical intermediate neglect of differential overlap operator that has been designed to reproduce the results of high-quality ab initio calculations. Interaction patterns between atomic pairs in the unit cells of the polymers and two-center combinations that belong to different layers of the one-dimensional (1D) systems have been analyzed. As a result of the pronounced charge deficit at the transition-metal centers, highly repulsive interaction energies are derived for the Ni-Ni coupling within the 1D stacks. The destabilizing metal-metal interaction is determined by classical Coulomb forces while covalent one-electron coupling and exchange effects are negligibly small. The interaction between the Ni center and pyrrole nitrogens in neighboring cells is strongly attractive due to the different net charges of the two atomic species. Both unoxidized polymers, (a) and (b), have a finite band gap; the valence and conduction bands are ligand $\pi$ and ${\pi }^{*}$ functions. A large number of ligand $\pi$, lone-pair, and $\sigma$ bands is predicted on top of the transition-metal bands that are formed by the orbitals of the square-planar coordinated Ni centers with $d^8$ configuration. The closely spaced (energy criterion) ligand ($\pi$, lone-pair, $\sigma$) and transition-metal [$3d_{z^2}\left(\sigma \right)$, $3d_{\mathrm{xz}}\left(\pi \right)$, $3d_{\mathrm{yz}}\left(\pi \right)$, $3d_{x^2-y^2}\left(\delta \right)$] basis energies as well as the symmetry reduction $D_{4h}(\overrightarrow{\mathrm{k}}=0, \overrightarrow{\mathrm{k}}=\frac{\pi }{c})\to C_{4v}(\overrightarrow{\mathrm{k}}\ne 0, \overrightarrow{\mathrm{k}}\ne \frac{\pi }{c})$ for nonmarginal values of the wave vector $\overrightarrow{\mathrm{k}}$ leads to a pronounced $\overrightarrow{\mathrm{k}}$ dependence in the composition of the CO wave functions. Correlations between different types of ligand states ($\pi \to n$, $\pi \to \sigma$, $n\to \sigma$, etc.) and between Ni $3d$ and ligand functions are detected in the various dispersion curves. Partially oxidized modifications of (a) and (b) are organic metals with conductive pathways that are confined to the extended ligand frameworks. The computational findings are compared with available experimental results derived for recently synthesized phthalocyanine and porphyrin polymers that show unexpected physical and chemical properties in the solid state.