## 1 Introduction  
Porphyrins are tetrapyrlic macrocycles with \(\pi\)-conjugated electronic system that are ubiquitous in nature and have numerous biological and technological applications. For example, porphyrins are found in our body as prosthetic groups in hemeproteins. In plants, porphyrins are important components of chlorophyll which is a pigment playing an essential role in photosynthesis. Porphyrins also have numerous biomedical applications including photoinmunotherapy, photo diagnosis [1], biosensors [2], cancer therapy, etc. Porphyrins also play an important role in organic synthesis of dendrimers [3], metal-organic frameworks (MOFs) [4], biomimetic reactions [5], and as photo-catalysts [6] in numerous oxidation/reduction reactions. Finally, porphyrins act as important components in various technological applications like solar cells [7], chemical sensors [8], optoelectronics [9], spintronics [10], field effect transistors (FETs) [11; 12; 13; 14], and in nanotechnology like single molecule junctions [15], nanowires, nanomotors [10], etc. All the applications listed above are possible only due to the characteristic, yet tunable chemical structure and properties of porphyrins [16]. The backbone of each porphyrin molecule is the porph group which constitutes four pyrrole groups linked with melting (-CH-) bridges, Figure 1a. Each porphine group has 22 \(\pi\) electrons forming a conjugated system. Due to their large pi-conjugation, porphyrins have strong absorption in the UV and visible regions forming colored compounds. In addition, the large \(\pi\)-electron system is responsible for many properties of porphyrins including optical [17; 18], electronic [19], mechanical [20], and chemical [21; 22] properties. Additionally, porphyrins from many coordinate covalent complexes with transition metals (metallopporphyrins) and some non-metals at the center of the porphyrin core. In addition, the peripheral substituents at \(\alpha\), \(\beta\), and meso positions (Figure 1b) can be modified to yield tunable molecular and crystal properties such as solubility, reactivity, conductivity, and photophysics. Metalloporphyrins tend to react with ligands to form numerous (porphyrin)metal-ligand complexes [23] that are also useful for a variety of applications. A broad scan of the literature of theoretical modeling of porphyrins showed that a variety of computational methods were used to study porphyrins and their derivatives. A review by [PERSON] [24] listed these computational methods, which ranged from linear combination of atomic orbitals (LCAO), molecular mechanics, semi-empirical methods, through self-consistent field method (SCF) in the earlier literature, to the modern day methods which include molecular dynamics (MD), density functional theory (DFT) [25], Moller-Plesset perturbation theory (MPn), configuration interaction (CI), coupled cluster (CC), and CASSCF/CASPT2 [26] methods. Among the many computational methods used, recent literature is flooded with DFT calculations of molecular porphyrin and its derivatives primarily to understand their frontier orbital configuration, electron occupancy [27], charge transfer, and excited state properties [25]. The DFT functionals used to study the porphyrin complexes include all the rungs of the \"Jacob's Ladder\" [28] with variable approximations which include local density approximation (LDA), generalized gradient approximations (GGA), meta-GGAs, hybrid, and hybrid-meta GGA functionals [29; 30]. While molecular DFT calculations of porphyrin complexes are prevalent, periodic DFT calculations of porphyrins are relatively limited. Periodic DFT (PDFT) calculations [31] refers to the use of density functional theory to describe the electronic structure of periodic systems. PDFT simulations are performed on lattice structures, surfaces, interfaces, and molecules with a defined unit cell in real and reciprocal spaces (k-space). The reciprocal space is obtained from the Brillouin zone of the unit cell.