## 3 PDFT Simulations of Porphyrins on Surfaces
### Conformational Studies of Meso-Substituted Porphyrins on Substrates
The mechanism and energetics for the surface transmetalation reaction was determined using PDFT calculations with GGA-PBE [45] functional and DFT-D3 [53; 85] van der Waals (vdW) corrections. They also report that while identical transmetalation in TPyP molecules were observed, they are not prevalent as in TPP molecules. The reason for this is attributed to peripheral pyridyl groups offering additional coordination sites for the metals, thus suppressing the metal exchange. [PERSON] et al. [86], used PDFT studies with GGA-PBE [45] with DFT-D3 [53; 85] and vdW-DF [43; 48] functionals to understand the adsorption and coupling of Cl\({}_{4}\)TPP molecules on Cu(111). Using DFT, they reported two coupling reaction pathways: direct dechlorination and Cu adatom-mediated Ullmann coupling. The latter is barrierless, whereas the former faces a barrier of about 0.9 eV for inverted Cl\({}_{4}\)TPP on Cu(111). Adatoms of Au(111) also interact with H\({}_{2}\)TPP [87] forming different surface electronic structures. These observations were confirmed by simulated STM images from PDFT calculations of H\({}_{2}\)TPP on Au(111) in various configurations. Tetraphenyl porphyrins on non-metallic substrates have also been studied using PDFT simulations. [PERSON] et al. [88], studied the self-assembly of H\({}_{2}\)TPP, CoTPP, and NiTPP molecules on HOPG (highly ordered pyrolytic graphite) surface using STM. It was reported that these TPP molecules only adsorb  
Figure 6: Typical confirmations of meso-substituted tetraphenyl porphyrins on a surface. Reprinted with permission from reference [74] Copyright 2017 American Chemical Society. at surface defects due to weak pi-pi or vdW interactions between TPPs and HOPG. PDFT calculations were performed to understand the TPP adsorption at the step edges and defects of HOPG. Simulations with PW91 [59] LDA functional showed that the electronic structure is modified significantly at the surface defects and edges of HOPG causing the adsorption and nucleation TPP molecules. TPP molecules on SiC(110) substrate were studied by [PERSON] et al. [89] using PDFT with GGA-PBE [45]. The sensitization of SiC(110) substrate based on the adsorbed components of a TPP like pyrrole group, phenyl group, and the whole TPP molecule was studied. It was reported that none of these molecules changes the polarity of the SiC(110) substrate even with dispersion interactions. [PERSON] et al. [90], and [PERSON] et al. [91], studied the adsorption if Cu-5,10,15,20-tetrakis(3,5-ditert-butyl-phenyl) porphyrin (Cu-TBPP) on Si(111) and boron-defect Si(111)-B surfaces respectively using PDFT simulation and in both cases the CuTBPP confirmations on the substrate were determined. All the PDFT studies of meso-substituted porphyrins listed above involve aromatic substituents in the meso positions. PDFT studies of meso-substituted porphyrins with tetra-alkyl groups were also reported in the literature. [PERSON] et al. [92] studied the adsorption of tetranonadecyl (C\({}_{19}\)H\({}_{39}\)) porphyrin on HOPG using STM and DFT. While the structural optimization was carried with molecular DFT, the authors used to determine the STM structure with PDFT simulations with GGA-PW91 [59] functional. Due to long alkyl chains in the molecule, ONIOM [93] method with quantum mechanical simulations on the porphyrin macrocycle and molecular mechanics simulations on alkyl substituents was used to determine the optimized geometries. The STM simulation of the optimized structure matched with STM experiments. In a later study, [PERSON] et al. [94], studied the adsorption of tetra-alkyl porphyrins with alkyl chain lengths (C\({}_{\rm n}\)H\({}_{2n+1}\) with n = 6-28) on HOPG using multiple computational methods. It was reported that molecular QM/MM calculations and PDFT calculations with PBE-D3 method predicted similar properties for the chain-length dependence of monolayer formation and polymorphism.