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A conceptual dft study of the chemical reactivity of magnesium octaethylporphyrin (MgOEP) as predicted by the Minnesota family of density functionals |

Juan Frau 1. Departament de Química, Universitat de les Illes Balears, Palma de Mallorca, Illes Balears 07122, Spain Recebido em 05/10/2016 Endereço para correspondência
*e-mail: daniel.glossman@cimav.edu.mx RESUMO
The Minnesota family of density functionals has been assessed for the calculation of the molecular structure and electronic properties of a Mg(II)-porphyrin, namely Magnesium Octaethylporphyrin (MgOEP). Several global descriptors arising from Conceptual DFT have been calculated through a ΔSCF procedure, and by means of the HOMO and LUMO frontier orbitals. On the basis of the obtained Conceptual DFT indices, a series of descriptors have been devised in order to verify the fulfillment of the "Koopmans' theorem in DFT" procedure. It is shown that the density functionals that verify this approximation with a certain degree of accuracy are only those denoted as range-separated hybrids (RSH), while the usual GGA-hybrids and the local density functionals fail completely. Palavras-chave: Computational Chemistry; Molecular Modeling; Magnesium octaethylporphyrin (MgOEP); Conceptual DFT; Chemical Reactivity Theory
Porphyrins are large macrocyclic compounds with strong absorbance and fluorescence characteristics. They have been applied in a wide variety of detection approaches due to the sensitivity of those characteristics to their immediate environment. Conceptual Density Functional Theory (DFT) or Chemical Reactivity Theory (as it is also known) is a powerful tool for the prediction, analysis and interpretation of the outcome of chemical reactions. Following the pioneering work of Parr and others, In order to obtain quantitative values of the Conceptual DFT Descriptors, it is necessary to resort to the Kohn-Sham theory through calculations of the molecular density, the energy of the system, and the orbital energies, in particular, those related to the frontier orbitals, that is, the HOMO and LUMO. The usual way to proceed implies as a first step the choice of a model chemistry for the study of the molecular system or chemical reaction of interest. There is a plethora of information in the literature about how to choose this model chemistry and one generally follows the experience of previous researchers and his/her own work. Although the foundations of DFT have established that a universal density functional must exist, and that all the properties of the system can be obtained through calculations with this functional, in practice one needs to resort to some of the approximate density functionals that have been developed during the last thirty years. Due to the fact that these are approximate functionals (that is, not a universal functional), many of them are good for predicting some properties and others are good for another properties. Sometimes, you can find density functionals that are excellent for describing the properties of a given molecular system with a particular functional group, but it is necessary to resort to other density functionals for a different functional group that you want to include in the molecular system under study. When one is dealing with the study of the chemical reactivity, that is, a process that involve the transference of electrons, it is usual to perform calculations not only of the ground state, but also for open systems like the radical cation and radical anion. These systems are often difficult to converge giving trustworthy results, especially if diffuse functions must be included in the basis set. This means that the goodness of a given density functional can be estimated by checking how well it follows the "Koopmans' theorem in DFT" that makes it behave closer to the exact density functional, and this will be crucial for a good calculation of the Conceptual DFT descriptors that predict and explain the chemical reactivity of molecular systems. However, the γ tuning procedure for the RSH density functionals is system dependent and that implies that different density functionals are going to be used for the calculation of the descriptors for the different molecular systems. Thus, it will be interesting to study other RSH density functionals where the γ parameter is fixed by constructions, although other parameters have been fitted to reproduce some molecular properties. In particular, we are going to consider several density functionals that have shown great accuracy across a broad spectrum of databases in chemistry and physics. The aim of this work is to conduct a comparative study of the performance of the latest Minnesota family of density functionals for the description of the chemical reactivity of a Mg(II)-porphyrin, namely magnesium octaethylporphyrin (MgOEP), whose molecular structure is shown in Figure 1.
Figure 1. Molecular structure of magnesium octaethylporphyrin (MgOEP)
Within the conceptual framework of DFT, where χ is the electronegativity. The global hardness η can be seen as the resistance to charge transfer: Using a finite difference approximation and Koopmans' theorem, where ε The electrophilicity index ω has been defined as: The electrodonating (ω It follows that a larger ω that is, the electroaccepting power relative to the electrodonating power.
All computational studies were performed with the Gaussian 09 For the calculation of the molecular structure and properties of the studied systems, we have chosen several density functionals from the Minnesota density functionals family, which consistently provide satisfactory results for several structural and thermodynamic properties:
The molecular structures of MgOEP was pre-optimized by starting with the readily available MOL structure, and finding the most stable conformer by means of the Avogadro 1.2.0 program The HOMO and LUMO orbital energies (in eV), global electronegativity χ, total hardness η, global electrophilicity ω, electrodonating power (ω
The ionization potentials I and electron affinities A (in eV), global electronegativity χ, total hardness η, global electrophilicity ω, electrodonating power (ω
Inspired from previous works on this subject, The first three descriptors are related to the simplest fulfillment of the Koopmans' theorem by relating ε Next, we consider four other descriptors that analyze how well the studied density functionals are useful for the prediction of the electronegativity χ, the global hardness η and the global electrophilicity ω, and for a combination of these Conceptual DFT descriptors, just considering the energies of the HOMO and LUMO or the vertical I and A: where D1 stands for the first group of Conceptual DFT descriptors. Finally, we designed other four descriptors to verify the goodness of the studied density functionals for the prediction of the electroaccepting power ω where D2 stands for the first group of Conceptual DFT descriptors. The results of the calculations of J
As can be seen from Tables 1 and 2, and the results presented in Table 3, the "Koopmans' theorem in DFT" holds with great accuracy for the MN12SX and N12SX density functionals, which are a range-separated hybrid meta-NGA and a range-separated hybrid NGA density functionals, respectively. Indeed, the values of J The usual GGA (SOGGA11) and hybrid-GGA (SOGGA11X) presented greater deviations in the results and were therefore less adequate for the fulfillment of the "Koopmans' theorem in DFT" procedure, and the same conclusion is valid for the local functionals M11L, MN12L and N12, as well as for the M11 density functional. An important fact is that although the range-separated hybrid NGA and range-separated hybrid meta-NGA density functionals can be useful for the calculation of the Conceptual DFT descriptors, it is not the same for the range-separated hybrid GGA (M11) density functional. An inspection of Tables 1 and 2 shows that this is due to the fact that this functional describes inadequately the energy of the LUMO.
From the whole of the results presented in this contribution it has been clearly demonstrated that the chemical reactivity of the MgOEP molecule can be predicted by using DFT-based reactivity descriptors such as the electronegativity, global hardness, global electrophilicity, electrodonating and electroaccepting powers, and net electrophilicity. The Minnesota family of density functionals (M11, M11L, MN12L, MN12SX, N12, N12SX, SOGGA11 and SOGGA11X) have been tested for the fulfillment of the "Koopmans' theorem in DFT" by comparison of the HOMO- and LUMO- derived values with those obtained through a ΔSCF procedure. It has been shown that the range-separated hybrid meta-NGA density functional (MN12SX) and the range-separated hybrid NGA density functional (N12SX) are the best for the accomplishment of this objective. One of the possible explanations for this behavior lies on the fact they are screened-exchange hybrid density functionals. The approach considered in these density functionals uses a finite amount of HF exchange at short-range, but none in the long-range limit, in order to cut the computational cost of non-local exchange integrals for extended systems. Therefore, they are a good alternative to those density functionals whose behavior have been tuned through a gap-fitting procedure and a good prospect for their usefulness in the description of the chemical reactivity of porphyrin molecular systems of larger sizes.
This work has been partially supported by CIMAV, SC and Consejo Nacional de Ciencia y Tecnología (CONACYT, Mexico) through Grant 219566/2014 for Basic Science Research and Grant 265217/2016 for a Foreign Sabbatical Leave. Daniel Glossman-Mitnik conducted this work while a Sabbatical Fellow at the University of the Balearic Islands from which support is gratefully acknowledged. This work was cofunded by the Ministerio de Economía y Competitividad (MINECO) and the European Fund for Regional Development (FEDER) (CTQ2014-55835-R).
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