## 3 PDFT Simulations of Porphyrins on Surfaces
### Porphyrin Molecular Junctions  
Porphyrins and substituted porphyrins were widely studied in single molecule junctions [14]. These junctions typically involve a molecule covalently linking two electrodes. PDFT studies were used to understand the binding and charge transport properties of the molecule and electrodes in the junction. [PERSON] et al. [141] performed one of the early studies of the covalently bound Pd porphyrin to gold electrode. They studied the side on (hydrogens of one pyrrole) interactions of Pd porphyrin on Au(111) using the LDA functional. Although this initial model is not a full Pd porphyrin molecular junction (because only one gold electrode was used), the simulation was helpful to gain atomic level understanding of rectifying behavior and charging effects associated with molecular conduction via single-electron tunneling. Another study with the same Pd porphyrin in a one sided junction with Al(111) electrode was performed by [PERSON] et al. [142], with both LDA-PW [59] and GGA-PBE [45] functionals. The energy level alignments, binding energy, and DOS were calculated, and it was reported that PdP/Al(111) interaction is weak yet rectifying. PDFT study of a complete junction involving a porphyrin sandwiched between two gold electrodes was conducted by [PERSON] et al. [143]. A nonequilibrium Green's functions (NEGF) [113] approach with PDFT was used to determine the electron transport properties of the porphyrin molecular junction. The porphyrin molecule is linked to the gold electrodes through two (5,15)-meso-diphenyl substituents. In addition, the role of electron donating and withdrawing substituent (at the 10-meso position) on the electron transport properties was determined. The authors report a negative differential resistance behavior from PDFT calculations which is a critical property for many molecular electronics applications. In another PDFT study, [PERSON] et al. [144] studied high efficiency switching in porphyrin ethyne benzene/gold molecular junction using GGA-PBE functional. The electron transport properties from PDFT simulations indicated that ethyne-bridged phenyl porphyrin molecules are good candidates for molecular switching devices. The rotation of the phenyl substituent allows for high and low currents due to change in orbital overlaps upon rotation. Additionally, placing amino and nitro substituents caused high ON/OFF current ratios with larger substituent effect when entire porphyrin molecule is in a co-planar geometry than in perpendicular configuration. [PERSON] et al. [145], developed an optimally-tuned range-separated hybrid (OT-RSH) functional [146] using DFT+\(\Sigma\) method [147; 148] and NEGF [113] approach for accurate description of molecular conduction in junctions. The effect of central metal (M = 2H, Ni, Co, Cu) of porphyrins in the molecular conductance between two gold electrodes was studied using PDFT simulations. It was reported that changing the central metal can change the conductance by nearly a factor of 2. [PERSON] et al. [149], studied magnetic and charge transport properties of a metal (M = H2, Cr, Mn Fe, Co) porphyrin array (PA\({}_{\infty}\)) connected through thiol groups to two gold electrodes. PDFT simulations with GGA-PBE functional and NEGF formalism was used to determine the conductance and band structure of metal porphyrin junction. It was reported that CrP\({}_{\infty}\) exhibits half-metallic behavior originating from the high spin state of Cr which causes spin asymmetry of the conduction band in CrP\({}_{\infty}\). Additionally, it was reported that spin-filtering ability occurs with an array size of 2, Cr-PA\({}_{2}\). [PERSON] et al. [150] studied the effect of the length of the substituent side chain in oligo porphyrin molecular wires on the long-range electron tunneling and conductance properties in molecular junction. Three oligo-porphyrins with oligomer length of 1, 2, 3 were sandwiched between gold electrodes and, PDFT simulations and scattering theory were used to study the molecular conductance.