The chemical bonding, electronic structure, and optical properties of the experimentally available metal-organic framework IRMOF-14 and its metal-substituted analogues M-IRMOF-14 (M = Zn, Cd, Be, Mg, Ca, Sr, Ba), which contain a pyrene-2,7-dicarboxylate linker group, have been systematically investigated using DFT calculations. The unit cell volume and atomic positions were optimized with the Perdew-Burke-Ernzerhof (PBE) functional and showed good agreement between experimental and theoretical equilibrium structural parameters for Zn-IRMOF-14. The calculated bulk moduli indicate that the whole M-IRMOF-14 series are soft materials. The estimated band gap from DOS calculations for the M-IRMOF-14 series is ca. 2.5 eV, essentially independent of the metal ion and indicative of nonmetallic character. The band gap value is distinctly different from those calculated previously for the M-IRMOF-1 (benzene-1,4-dicarboxylate linker; ca. 3.5 eV) and M-IRMOF-10 (biphenyl-4,4'-dicarboxylate linker; ca. 3.0 eV) series and this confirms that the identity of the linker is a key parameter to control band gaps in an isoreticular series of main-group MOFs. In view of potential uses of MOFs in organic semiconducting devices such as field-effect transistors, solar cells, and organic light-emitting devices, the linear optical properties of these materials were also investigated. Comparisons are made with the M-IRMOF-1 and M-IRMOF-10 series.