## 4 Summary  
Periodic density functional theory (PDFT) calculations have been indispensable to bridge the gaps between observable properties at the condensed phase and the electronic structure of the periodic system. They led to fundamental understanding and tuning of the solid-state behavior of many functional materials and interfaces. In this review, a collection of PDFT simulations of porphyrins in nanostructures and on surfaces were presented. Porphyrins are important compounds used for many have numerous biological and technological applications. While many reviews of porphyrins and their derivatives are available in the literature, a review of periodic porphyrin structures has never been reported to our knowledge. We organized the review based on applications of PDFT simulations to understand specific structural, conformational, adsorption, electronic, magnetic, charge transfer properties, and reactivity of porphyrins on surfaces. The typical properties calculated using PDFT simulations include optimized geometries, binding energetics, density of states, band structure, spin switching and magnetization, charge transport, STM images (local electronic structure), reaction intermediates in catalytic reactions, etc. Hence, this review should be of great interest for the porphyrin research community and to the broader audience performing PDFT simulations. In our survey of periodic simulations on porphyrins with DFT, plane wave pseudopotential basis sets were the predominant choice rather than Gaussian type orbital basis sets. Most of the early simulations were performed with the bottom two rungs of the \"Jacob's ladder\" which are the GGA and LDA type functionals. The drawbacks of using these functionals include underestimation of electronic bandgaps and weak dispersion interactions, especially with systems involving organic molecules like porphyrins. LDA overestimates, while GGA underestimates the binding energies in condensed phase systems like transition metal, metal oxides, carbon, and silicon crystals. Both functionals underestimate interactions involving organic molecules like porphyrins. Recently many PDFT studies were performed with dispersion corrected DFT functionals or with empirical dispersion corrections. Inclusion of vdW interactions greatly improved the calculated binding energies of porphyrins leading to data that better matched experiments. It was reported that dispersion interactions are more important for porphyrins on metallic substrates than on non-metal substrates. Within the last decade hybrid functionals like B3 LYP and HSE were used for PDFT simulations of porphyrins. These functionals improved the band gap and geometric optimizations of porphyrin nanostructures and interfaces. Our review of the literature also found that DFT+U is the method of choice for calculations involving magnetically coupled and spin active porphyrin systems. With the improvement of DFT functionals and computing capability more and more expensive calculations were being performed for a fundamental understanding of porphyrin behavior in periodic systems. Like many quantum mechanical calculations, PDFT calculations have limitations with respect to the size of the modeled system and accuracy of the energies obtained from DFT calculations. Additionally, choosing the right DFT functional for modeling a heterogeneous periodic system like porphyrins is challenging and no single PDFT functional is deemed appropriate for all applications. Based on the problem of interest like electronic structure, binding energies, excited state properties, etc., a variety of PDFT functionals were used to study bulkier systems like porphyrins and phthalocyanines. Unlike molecular DFT functionals used for porphyrin based systems [24], the number of PDFT functionals are limited especially for performing time-dependent or excited state systems. In addition, simulations of larger periodic systems [110] with PDFT is computationally expensive, while ab initio molecular dynamics (MD) simulations of larger systems are practically impossible.