Ab Initio Calculation of the Dimerization in the Halogen-Bridged Transition-Metal Linear-Chain Compound ${\mathrm{Pt}}_2$${\mathrm{Br}}_6$${\left(\mathrm{N}{\mathrm{H}}_3\right)}_4$

All-electron local-density-approximation electronic-structure calculations show how the ligand structure of a neutral halogen-bridged transition-metal linear-chain compound, ${\mathrm{Pt}}_2$ ${\mathrm{Br}}_6$ ${\left(\mathrm{N}{\mathrm{H}}_3\right)}_4$, modifies the electronic structure to reduce it to an effective one-dimensional system. The dimerization and opening of the band gap is then understood on the basis of a conventional two-band Su-Schrieffer-Heeger model for isolated chains. Despite the strong $\mathrm{pd}\sigma$ coupling between the $\mathrm{Pt} d_{{3z}^2-r^2}$ and $\mathrm{Br} p_z$ orbitals along the chains, the system will not dimerize in the absence of the ligand structure.