## 3 PDFT Simulations of Porphyrins on Surfaces
### Porphyrins on Oxide Supports  
Porphyrins are widely used as dyes in dye sensitized solar cells where the solar energy trapped by porphyrins is transferred into conductive oxide substrates like TiO\({}_{2}\), ZnO, etc. In this section, we present a collection of PDFT studies involving interactions of porphyrins with oxide supports used in photovoltaic devices and in catalysis.  
[PERSON] et al. [118], used PDFT simulations with GGA-PW91 [59] functionals to study the surface interactions and charge transfer of [COOH-TPP-Zn(II)] porphyrin on TiO\({}_{2}\)(110) surface. Using PDFT simulations they identified the stable binding site for the anchoring group (-COO-) to the TiO\({}_{2}\) surface that facilitates electron injection. Using frontier orbitals and DOS from DFT simulations, the authors report that Zn(II) porphyrin is capable of electron injection into TiO\({}_{2}\), as has been shown from experiments. A similar study was performed by [PERSON] et al. [119], and they used PDFT simulations to study the optical and charge transfer properties of Zn porphyrin adsorbed on the TiO\({}_{2}\) surface. If the TiO\({}_{2}\)(110) surface is hydroxylated, [PERSON] et al. [120], showed that the iminic nitrogens of free base porphyrins (OEP, TPP, and tetra-butyl TPP) capture the hydrogen atoms from the TiO\({}_{2}\)(110) surface. They used x-ray photoelectron spectroscopy (XPS) experiments combined with PDFT simulations using GGA-PBE [45] functional and DFT-D corrections, and showed the favorable energetics and mechanism for hydrogen capture by porphyrins.  
In-situ metalation of TPP using Ni atoms adsorbed on TiO\({}_{2}\)(110) surface was studied by [PERSON] et al. [121] using STM. PDFT simulations were done with the DFT-FIREBALL [122] method. STM images and currents were simulated using Keldysh-Green function formalism. The surface electronic structure from STM experiments matched with the simulated STM images. PDFT simulations [123] are also used to determine the band gap of porphyrin MOFs adsorbed on TiO\({}_{2}\)(110) surface, and it was found that HSE06 functional [47] predicted the bandgap and TiO\({}_{2}\) structure matching the experimental data. [PERSON] et al. [124], studied the effect of asymmetric modification of meso-substituents of TPPs on TiO\({}_{2}\)(110) using PDFT simulations. Experiments have shown that asymmetric modifications can improve the light-harvesting properties and enhance the electron distribution, but the surface adsorbed structure was unknown. In this work, the authors used molecular and PDFT simulations with GGA-PW91 [59] functional to optimize the adsorption geometries of various asymmetric meso-substituted porphyrins on TiO\({}_{2}\) and determine their electronic properties. While TiO\({}_{2}\) is the extensively used oxide support for many PDFT simulations involving porphyrin binding, supports like ZnO [125] and SiO\({}_{2}\)[126] are also studied. In the case of ZnO, the support was used as an alternative for TiO\({}_{2}\) in dye sensitized solarcellsand PDFT calculations were used to understand the charge transfer characteristics. SiO\({}_{2}\)-porphyrin [126] studies are used to determine the binding strength for porphyrins to SiO\({}_{2}\) support for application as a trapping agent in petroleum industry.