## 3 PDFT Simulations of Porphyrins on Surfaces
### Conformational Studies of Non-Meso-Substituted Porphyrins on Substrates  
Porphyrins without the meso substituents lack the structural flexibility of meso-substituted porphyrins [70]. Octaethylporphyrins (OEP) are some of the commonly studied non-meso-substituted porphyrins on substrates [71] using STM. [PERSON] et al. [95] studied the adsorption of CoOEP on Ag(110) surface and reported that CoOEP molecule bind to Ag(110) with a tilt angle of 15\({}^{\circ}\) with respect to the substrate due to strong hybridization of the adlayer with the Ag substrate which the authors confirm by PDFT simulations using GGA-PBE [45] functional. [PERSON] et al. studied the adsorption of PtOEP molecule on bare Au(111) and on NaCl/Au(111) surfaces using STM and PDFT with GGA-PBE [45] functional and reported that the top of the valence band has a downward shift in NaCl/Au(111) substrate relative to Au(111). In either of these studies, the adsorption energy of OEP molecules on these substrates has not been reported. A first comprehensive study of OEP on substrates using PDFT simulations was reported by [PERSON] et al. [96]. It was reported that using standard GGA [45] and LDA [97] functionals would significantly underestimate the adsorption energies of porphyrins on substrates compared to calculations using van der Waals corrected DFT methods like vdW-DF [43; 48] or DFT-D3 [53; 85]. The binding energies of CoOEP on Au(111) with GGA functional was reported to be \(-0.31\) eV, while the value is \(-4.34\) eV with vdW-DF functional. On HOPG the binding energies are \(-1.18\) and \(-2.42\) eV with LDA and vdW-DF functionals respectively. These results indicate that traditional LDA and GGA functionals significantly underestimate dispersion energies with metallic substrates but to a lesser degree with carbon supports. The authors also report the interfacial charge redistribution, DOS and work function changes upon adsorption of CoOEP on substrates. They also reported the first PDFT simulated bias dependent STM images (Figure 7) of OEP molecules on Au(111) and HOPG which matches with experimental observations. The advantage of using dispersion DFT methods on OEPs is further corroborated by [PERSON] et al. [98], who reported that RhIII(OEP)(CI) molecule would not have bound to the basal plane of HOPG if not for dispersion corrected DFT functional. Iron based haem(b) porphyrin has tetraethyl and tetramethyl substituents in the non-meso positions. [PERSON] et al. [99], studied the adsorption of haem(b) porphyrin on Si(111):H substrate using GGA-PW91 [59] functional and determined the STM images using Tersoff-Hamann approach [100]. The binding energy was estimated to be only 0.42 eV which is likely significantly underestimated because they did not include dispersion interactions in their functional. Non-substituted porphins (P) are also studied extensively using PDFT simulations. [PERSON] et al. [101], used PDFT simulations with GGA-PW91 [59] and vdW-DF [43, 48] functionals to determine the surface configurations of H\({}_{2}\)P molecule on Cu(110) surface and the respective adatom interactions were reported. A similar study was performed by [PERSON] et al. [102], using vdW-DF method who reported that H\({}_{2}\)P is chemisorbed to the surface, caused by electron donation into down-shifted and nearly degenerate unoccupied porph \(\pi\)-orbitals accompanied with electron back-donation from molecular \(\pi\)-orbitals. [PERSON] et al. [103], reported the electronic and spin structure of FeP on Pt(111) surface using multiple vdW-DF [43, 48] and functionals with added Hubbard U term. They report that vdW-DF-optPBE and vdW-DF-optB88 functionals found the same binding site to be the most stable and yielded binding energies that were within \(\sim\)20% of each other, whereas vdW-DF-revPBE functional were substantially weaker. One of the earlier PDFT studies of porphing adsorption was done by [PERSON] et al. [104] using MnP and PdP porphins on Au(111).