Screening of different interactions in oxo-manganese porphyrin dimers containing axial N-donor ligands: a theoretical study

A theoretical analysis for describing the dimeric assemblies of high-valent manganese(v)-oxo meso-tetraphenylporphyrin (TPP) ([(TPP)MnVO]22+) and meso-tetrakis(pentafluorophenyl)porphyrin (TPFPP) ([(TPFPP)MnVO]22+) in the presence of axial N-donor ligands is presented. Our theoretical results revealed two types interactions in dimers: a sandwich-like interaction between phenyl rings of porphyrin molecules, and a non-bonded T-shape interaction between nitrogen donors attached to Mn centers. The curvature in the geometry of porphyrin in the [(TPP)MnVO]22+/N-donor system is significantly smaller than that of [(TPFPP)MnVO]22+/N-donor system. Moreover, the Mn–N(ax) distances in [(TPFPP)MnVO]22+/N-donor system are shorter than those of [(TPP)MnVO]22+/N-donor system. Also, the donor–acceptor interaction between the imidazoles and the Mn centers are stronger than those of the other ligands in both porphyrins. These results are supported by atoms in molecules (AIM) and natural bond orbital (NBO) analysis.


Introduction
Multiporphyrin arrays have a wide range of potential applications in areas such as light harvesting, nonlinear optics (NLO), organic light-emitting diodes (OLEDs), and photodynamic therapy (PDT). Hence, these systems have been investigated widely. 1-3 A number of porphyrin dimers have been reported as promising viscosity-sensitive molecular rotors, efficient electrocatalytic CO 2 to CO conversion, dimer-sensitized solar cells, as ionophores in chemical sensing of anions and cations. 4-6 p-Conjugated molecules with a small highest occupied molecular orbital-lowest unoccupied molecular orbital (HOMO-LUMO) gap have also been studied with regard to their potential use as molecular wires in molecular-scale electronics and nanotechnological devices. 7 Porphyrin nanoparticles are favorable apparatuses of advanced materials because of the rich photochemistry, stability, and conrmed catalytic activity. 8 In analogy to inorganic and other organic nanoparticles, it is predictable that nanoparticles of porphyrins will have unique photonic properties not accessible by larger-scaled materials having the macrocycle, or by the molecules themselves. 9,10 The promising results obtained in our recent work on the synthesis and catalytic oxidation activity of Mn-porphyrin nanoparticles 11 induced us to investigate a computational density functional theory (DFT) study to describe the effect of diverse agents on the structure and activity of manganese(V)-oxo meso-tetraphenylporphyrin. [12][13][14] Herein, new porphyrinic dimers comprising two distinct oxo-Mn-porphyrin complexes containing nitrogen donors is designed which are linked to each other through phenyl/phenyl as well as axial ligands interactions. The main purpose of this research is a DFT study to investigate the interactions between high-valent manganese(V)-oxo meso-tetraphenyl porphyrin dimer (

Computational methodology
The Gaussian 09W program suite 15 was used for all quantum chemistry computations. The electronic geometries of all systems were fully optimized in their ground states in the gas phase, using the B3LYP/6-31G (d) level of theory [16][17][18] and the relativistic effective core potentials of Mn atom are considered using the LANL2DZ (Los Alamos National Laboratory 2 double z) as extra basis. 19 Approximate distances between the phenyl rings in the complexes investigated have been assessed by introducing 'ghost atoms' in geometric centers of the rings and measurement of the distances between them. The frequency calculations were performed at the same level to verify whether stationary points from geometry optimization calculations were local minima or saddle points. The binding energies were corrected for the basis set superposition error (BSSE) by the Boys-Bernardi counterpoise technique. 20 The procedure for obtaining the adsorption energy is as follows: where X monomers i EðiÞ ! is the sum of electronic energies of the fully optimized geometries of isolated monomers, while E complex denotes the electronic energy of a system studied. It should be mentioned that the adsorption energy encompasses both interaction (E int ) and deformation (E def ) energy contributions, which are both occurred during the adsorption process. Hence, the following equations are applied to calculate these contributions: The natural bond orbital (NBO) analysis 21 is also conducted on optimized geometries with the NBO 3.1 included in Gaussian 09. In order to understand the nature of bonding between the constituent atoms, the topological properties of the complexes have been calculated using the atoms-in-molecules (AIM) approach 22 with MULTIWFN soware. 23  structures shows the existence of sandwich-like interaction between the phenyl rings at the meso-positions (Fig. 1). We found that in the energy minima geometries the distance between sandwiched aromatic rings is about 1.72Å which is about a single C-C bond. The torsion angle between phenyl groups and porphyrin plan is about 93 . The structures were optimized in association with different N-donor ligands (imidazole, pyridine and piperidin). The sandwich-like interaction between phenyl rings of porphyrin molecules as well as a nonbonded T-shape interaction between nitrogen donors attached to Mn centers of porphyrins were identied as the most energetically stable geometries (an example show in Fig. 2 in combination with pyridine with À11 347.7 kcal mol À1 . It means that T-shape interaction between pyridines coordinated to Mn centers of [(TPFPP)

Optimized geometries and energetic
is more favorable than the other derivatives. The adsorption energy encompasses interaction (E int ) and deformation (E def ) energy contributions, both of which occur during the adsorption process. The deformation and interaction energies of these systems were calculated ( /N-donor system, which

Frontier molecular orbital analysis
The energy difference between the highest occupied (HOMO) and the lowest unoccupied ( Thus a hard molecule has a large energy gap, and a so one provides a small gap. According to the data presented in

Atoms-in-molecules (AIM) topological analysis
The quantum theory of ''atoms in molecules'' (QTAIM) 22 was applied in this study to nd critical points (CP) and further to analyze them in terms of electron densities, Laplacians and the total electron energy density H C . The QTAIM topological results are summarized in Table S2 (ESI †). Inspection of the results in Table S2, † shows the relatively high r (ranging from 0.3220-0.3276) and V r BCP 2 (ranging from

Natural bond orbital (NBO) analyses
To nd more exact information about the nature of these systems, further study is devoted to the NBO analysis. 21 The results presented in Table S3 (ESI †) shows second-order perturbation stabilization energies, E (2) , corresponding to charge transfer between nitrogen lone pair of axial ligand and s * MnÀO orbital ðE ð2Þ lpN ðaxÞ /s * MnÀO Þ. The maximum and minimum values of the second-order perturbation stabilization Table 1 The selected geometric parameters (r and q is inÅ and ), torsion angle between the phenyl groups and porphyrin plan (4), adsorption energy (E ads ), interaction (E int ) and deformation (E def

Conclusion
In this study, a sandwich-like interaction between phenyl rings of porphyrin ligands and a T-shape conguration interaction between nitrogen donors attached to Mn centers were described. The geometries, electronic structures, vibrational frequencies and physical properties such as dipole moment, chemical potential, and chemical hardness of [

Conflicts of interest
There are no conicts to declare.