## 2 PDFT Simulations of Porphyrins in Nanostructures
### Porphyrins in Organic Frameworks  
Porphyrins are used to develop many supramolecular frameworks like metal organic (MOF), covalent organic (COF), surface metal organic (SURMOF) frameworks with applications for gas storage/separation, catalysis, drug delivery, photovoltaics, etc. Hence, PDFT calculations of porphyrin organic frameworks have gained importance for understanding their electronic structure to tune their applications. [PERSON] et al. [55], studied the electronic structure of porphyrin-based MOFs (PMOF) with porphyrins connected through phenyl-carboxyl ligands and AlOH species to assess their suitability for the photocatalysis of fuel production reactions using sunlight. They used the rhombohedral primitive cell obtained from the orthorhombic crystal structure of Al-PMOF [56] and replaced the porphyrin core with either hydrogens or various 3d transition metals and performed PDFT calculations of each model. The calculations were performed with GGA-PBE [45] functional starting with optimization of each lattice structure, followed by single point calculations for determination of DOS and band structure with HSE06 functional [46; 47]. A typical crystal structure of the PMOF unit cell is presented in Figure 4a. From PDFT calculations, they reported that the bandgaps for PMOFs are in a favorable range (2.0-2.6 eV) for efficient adsorption of solar light. Furthermore, it was shown that the MOFs' band edges align with the redox potentials (Figure 4b) for water splitting and carbon dioxide reduction with reactions that can occur at neutral pH. This study was followed up with another PDFT study by [PERSON] et al. [4] by modifying the octahedral Aluminum metal center of the lattice structure with Fe\({}^{+3}\) metal to determine the changes in the band structure and electronic properties of PMOFs. It was reported that adding Fe at the porphyrin core slightly raises the valence band edge, while Fe at the octahedral node significantly lowers the conduction band edge. So, iron can be used as a good dopant for band structure alignment in porphyrin-based MOFs.  
PDFT calculations of porphyrin based SURMOFs has been reported by [PERSON] et al. [57; 58], who studied the photophysical properties of Zn(II)porphyrin-based SURMOFs. Using PDFT band structure with PBE functional [45] its was shown that a small dispersion of occupied and unoccupied bands in the \(\Gamma\)-\(Z\) direction [57], which is the porphyrin stacking direction, leads to the formation of a small indirect band gap. In a follow up study [58], the effect of introducing an electron-donati  
Figure 4: Perspective view of the porphyrin-based metal organic framework (MOF) investigated in this study in (**a**) the protonated case, and (**b**) the metal-substituted case. Color code: gray = carbon, white = hydrogen, red = oxygen, blue = nitrogen, magenta = aluminum, green = transition metal. (**c**) Bandgaps and band edge positions of MOFs with respect to the vacuum level, as calculated with the HSE06 functional. Energy levels corresponding to redox potentials of water splitting and carbon dioxide reduction reactions producing methane, methanol, and formic acid at pH = 7 are also shown with dotted lines. Reproduced from reference [55] published by The Royal Society of Chemistry.  
into Zn SURMOFs was studied and PDFT simulations showed that DPA causes a shift in the charge localization pattern in the valence band minimum. This charge shift was attributed to the DPA groups which causes a shift of the optical absorption spectrum and the improved photocurrent generation in Zn SURMOFs. PDFT simulations are also used to study the stability of the porphyrin-COFs upon gas adsorption. [PERSON] et al. used GGA-PW91 [59] and LDA-PZ [60] functionals to study hydrogen storage in H\({}_{2}\)P-COF. The structural stability of COF upon introducing pyridine molecules to bridge the interlayer gaps in porphyrin COFs is studied.