## 3 PDFT Simulations of Porphyrins on Surfaces
### Conformational Studies of Non-Meso-Substituted Porphyrins on Substrates
DFT+U [68] technique with PDFT simulations using LDA [97] functionals were used to determine the face-on and side-on interactions of porphins on Au(111) substrate. [PERSON] et al. studied the effect of translation on binding energy for transition-metal (V, Cr, Mn, Fe, Co, Ni) porphins adsorbed on Ag(111) surface using vdW-DF-cx [105]. They concluded that the bridge positions of Ag(111) are favorable for all transition metal porphins. PDFT calculations of not porphyrins but porphyrin-based molecules are also studied in the literature. For example, [PERSON] et al. studied the adsorption of Ni(Salophen) molecule on Au(111) surface using vdW-DFT functionals and determined the adsorption energy to be 2.74 eV which is about 2/3 of the adsorption energy of similar porphyrin [96, 106] molecules on Au(111). [PERSON] et al. studied the adsorption of pyrphyrin molecules on Au(111) [107] and Ag(111) [108] surfaces using various GGA and vdW-GGA functionals. They reported the effect of surface herringbone reconstruction of Au(111) surface on the adsorption dynamics of Co(Pyrphyrin) molecules. It was reported that the dominant contribution to the adsorption energy are dispersion forces, followed by the interaction of the cyano groups with the metal. The monolayer formation and geometrical configuration of the assembly are mainly driven by the molecule/molecule interactions. Surface adsorption of porphyrins as part of a multicomponent mixture were also studied using PDFT simulations. [PERSON] et al. [109], reported the competitive adsorption of CoOEP and coronene molecules as a function of concentration at the 1-phenyloctane/Au(111) solution solid interface using  
Figure 7: PDFT simulated bias-dependent STM images of Cobalt Octaethylporphyrins (OEP) on Au(111) and HOPG surfaces. Reproduced from reference [96] published by the PCCP Owner Societies. STM. In this work, it was reported that CoOEP prefers to bind to the substrate unto a molar ratio of more than 55:1 coroneneCoOEP. At 55:1 ratio, only coronene molecules are seen on the Au(111) surface with STM. Using PDFT simulations of coronene, CoOEP, and coroneneCoOEP models, that authors reported that the strong preference of CoOEP binding to Au(111) is that CoOEP has about \(\sim\)1.8 times larger binding energy than coronene on Au(111). vdW-DF functionals with PAW pseudopotential basis sets were used to determine the adsorption energetics. Additionally, they report that the 1-1 coronene:CoOEP (A in Figure 8) structure is stable between 22:1 to 45:1 molar ratios because the ethyl groups of the CoOEP molecule trap the coronenes on to the Au(111) surface until further changes in the molar ratios. Additionally, the authors used PDFT calculations to determine the interfacial charge distribution (B in Figure 8) and potential energy surfaces for adsorption of CoOEP and coronene molecules on Au(111) surface and used these energies to determine the vibrational frequencies for molecular desorption. It is important to note that coronene molecules exhibit cooperativity and coverage dependency [110] when desorbing from Au(111) substrates.