## 3 PDFT Simulations of Porphyrins on Surfaces
### Ligand-Perphyrin Reactions on Surfaces  
Central metals in metalloporphyrins can react with many axial ligands [152] forming porphyrin-ligand complexes. These ligands can be mono or bi-axial leading to pentavalent and hexavalent complexes. When metalloporphyrins bind to solid surfaces, the surface may act like an axial ligand in the fifth coordination site [153; 154; 155]. In this section we present a collection of PDFT studies on coordination of ligands to metalloporphyrins that are adsorbed to surfaces. Coordination of gaseous molecules like CO [156], NO [155], O\({}_{2}\)[157], etc. to porphyrins on surfaces were studied by various experimental techniques. PDFT simulations were used to understand the binding mechanism of these ligands to substrate bound porphyrins. [PERSON] et al. [106], used PDFT simulations with vdW-DF [43; 48] functional to understand the binding mechanism of imidazole (Im) ligand to Ni-octaethylporphyrin (NiOEP) bound on HOPG surface. Using STM, solution-spectroscopy, and molecular DFT calculations the authors reported that Im ligand does not bind to NiOEP in solution or in gas-phase but does bind when NiOEP is on the HOPG surface. The reactivity of imidazole toward NiOEP adsorbed on HOPG is attributed to charge donation from the graphite stabilizing the Im-Ni bond (Figure 10). This charge transfer pathway is supported by molecular and periodic modeling calculations which indicate that the Im ligand behaves as a \(\pi\)-acceptor. DFT calculations also show that the nickel ion in the Im-NiOEP/HOPG complex is in a singlet ground state. This is surprising because the gas phase Im-NiOEP complex is found to be stable in a triplet ground state. Integrated charge transfer data (Figure 10) from PDFT also showed that HOPG donates the charge to Imidazole ligand via the NiOEP macrocycle, which indicates that the porphyrin molecule only acts as a charge mediator. Binding of gaseous molecules to substrate bound porphyrins using PDFT were carried with tetraphenyl-porphyrins and tape porphyrins. [PERSON] et al. [155], reported the'surface trans effect' of NO axial coordination to Co-porphyrin on Ag(111). GGA-PBE [45] functional with dispersion corrections was used to model the NO/CoP/Ag(111) surface and the corresponding structural and energetics were determined. They reported that competition effects, like the trans effect, play a central role and lead to a mutual interference of the two axial ligands, NO and Ag, and their bonds to the  
Figure 10: From left to right, charge density difference mappings for positive (colored in brown) and negative (colored in pink) charges for NiOEP/HOPG (A and B) and Im-NiOEP/HOPG (C and D) systems respectively. The images in the top row (**A1–D1**) represent side-view (along the a-axis) and the bottom row (**A2–D2**) represent top-view (along c-axis). Element colors are carbon—gray, nitrogen—blue, nickel—yellow (not visible). Hydrogens are masked for clarity. In the cross-section (**A1–D1**, top row) the rainbow colors (blue to red) indicate charge with blue being highly negative and red being highly positive. Reproduced from reference [106] published by the PCCP Owner Societies. metal center. [PERSON] et al. [158], used PDFT simulations with DFT+U approach [68] and showed that surface magnetization of porphyrin/ferromagnetic surfaces can be tuned via the choice of axial ligands. NO (S = 1/2) and NH\({}_{3}\) (S = 0) ligands were used to coordinate with FeTPP and MnTPP porphyrins on Ni and Co ferromagnetic surfaces. PDFT simulations revealed that they reported that the structural trans effect on the surface rules the molecular spin state, as well as the sign and strength of the exchange interaction with the substrate. In another study, [PERSON] et al. [159] compared DFT+U approach and semi-local DFT simulations with GGA-PBE [45] functional using O\({}_{2}\) coordination with CoTPP/Au(111) interface. They reported that semi-local DFT simulations can optimize a structure but DFT+U approach is better for charge and spin predictions in the system.