Comparison of DFT Methods for the Investigation of the Reduction Mechanisms of Aromatic Nitro-and Nitroso Compounds

The main goal of this paper is to find an adequate level of theory for the computational investigation of the reduction mechanisms of aromatic nitroand nitroso compounds. To this end, five standard reduction potentials of nitroand nitrosobenzene in three different solvents and four pKa values of species involved in the mechanism were compared with the values calculated at different DFT and CBS-X levels of theory. Out of fourteen tested functionals, five showed good linear correlation between calculated and experimental ΔrG° values. However, at all explored levels of theory, the calculated ΔrG° values systematically deviate from the experimental ones, indicating the necessity of better description of solvation effects for charged species, possibly via a cluster-continuum approach.


INTRODUCTION
ITROBENZENE and its derivatives have an important role in chemical and pharmaceutical industry.An estimated 95 % of produced nitrobenzene undergoes reduction into aniline during the manufacture of dyes, pesticides, explosives and pharmaceuticals [1] Since both nitrobenzene and its reduction intermediates are much more toxic than the amine product, [2,3] a detailed understanding of the reduction mechanism is of great environmental importance.
The main goal of this paper is to find a level of theory that can be used for not just the first elementary step of the reduction -a single electron transfer to nitrobenzene molecule -but also for the full computational investigation of this and similar reaction mechanisms.Our intention is to identify all possible participating species and viable N Scheme 1. Reduction mechanism of nitrobenzene.

COMPUTATIONAL METHODS
The available experimental data pertinent to these reactions are standard reduction potentials obtained by cyclic voltammetry.[17] However, the advent of new DFT methods and solvation models has warranted an increase in both the accuracy and the affordability of such a calculations.The common approach is based on the calculation of standard Gibbs energies of both the oxidized and the reduced species, i.e. the electron affinity, and its comparison against a reference reaction.The Faraday's Law allows conversion of standard Gibbs energies to electrode potentials and vice versa: No consensus regarding the best computational method for modeling standard reduction potentials exists.For the reduction of aromatic nitro compounds, several different functionals were used, with basis sets ranging from 6-31G(d) to aug-cc-pVTZ.Leszczynski et al. calculated reduction potentials of nitrobenzenes against standard hydrogen electrode (SHE) as a reference and reported a MUE of 0.07 V (1.8 kcal / mol) at mPWB1K/aug-cc-pVTZ level of theory using the PCM solvation model. [18]A similar method was employed by Zhu and Wang for the modeling of various quinones in acetonitrile and DMSO. [19]A standard deviation from experimental data of 0.1 V (2.5 kcal / mol) was achieved with the B3LYP/aug-cc-pVDZ model.
To find the DFT level of theory capable of modeling wider range of species included in the target mechanism, we decided to test various functionals against existing experimental data.22][23][24][25][26][27] Standard reduction potentials measured relative to saturated calomel (SCE) or Ag | AgCl reference electrodes were converted to standard reduction potentials relative to SHE by adding to them 0.2444 or 0.197 V, respectively.To convert standard potentials reported relative to SHE to standard Gibbs energies, the absolute value of E°(SHE) of 4.281 V recommended by Isse and Gennaro [28] was used.
In the model reactions set we also included four protonation/deprotonation equilibria of species known to take part in the mechanism (reactions VII-X, Table 1).The experimental pKa values of PhNO2H • , PhNOH • , PhNOH + and PhNH3 + were converted to the corresponding ΔrG° values using the formula In order to compute standard Gibbs energies of examined species by a DFT approach, we performed their solution-phase geometry optimizations and vibrational frequency calculations using SMD continuum method.SMD was chosen because of its high reliability for thermochemical data and near-universal applicability for various combinations of solutes, solvents and levels of theory. [29]ble 1.Model reactions used in this paper, with corresponding experimental standard reduction potentials (E°) or pKa values and standard reaction Gibbs energies (in kcal / mol) calculated from experimental data using formulas (1) or (2).To minimize the negative influence of small frequencies to thermodynamic data, molecular partition functions were calculated using the quasiharmonic oscillator approximation. [30]All calculations were performed using Gaussian09, Revision D.01. [31]heoretical standard reaction Gibbs energies for the reduction reactions relative to the SHE were calculated by the formula where G°calc(R,s) and G°calc(O,s) are theoretical standard Gibbs energies of reduced and oxidized reagent in solvent s, n number of exchanged electrons, and ΔredG°abs(SHE) standard reaction Gibbs energy equivalent to the absolute value of E°(SHE).Theoretical standard reaction Gibbs energies for the deprotonation equilibria were calculated by the formula where G°exp(H + ,aq) is the experimental value of the standard Gibbs energy of proton in water (-270.3kcal/mol), [32] also used for the calculation of standard reaction Gibbs energy of the nitrosobenzene to phenylhydroxyamine reduction (reaction VI, Table 1).

RESULTS AND DISCUSSION
Fourteen commonly used functionals were tested.Some of them were chosen because they have been previously used for the similar calculations, some because of our good experience with them, and the rest because of their increasing popularity. [33]Møller-Plesset calculations were also performed, but due to the excessive spin contaminations for the radical species, the approach was dropped from further considerations.We also examined the influence of increasing basis sets size to the results, finally settling with the Pople's 6-311+G(2df,2p).While smaller basis sets gave noticeably inferior results, larger Dunning's augmented correlation consistent basis sets (up to aug-cc-pVQZ) gave marginally better results, at a significant expense of the calculation efficiency.The DFT results were compared against the results of two efficient composite methods for computing accurate energies, CBS-QB3 and CBS-APNO.Required standard solvation Gibbs energies (ΔsolG°) of participating species were calculated at M06-2X/6-311+ G(2df,2p)-SMD level of theory.
In Table 2 are given differences between calculated and experimental standard reaction Gibbs (ΔΔrG°) energies for the model reactions arranged in such a way that the charged species appear on the right-hand side of the corresponding chemical equation.
However, both DFT and CBS-X energy differences are systematically lower than the experimental ones.The average value of the constant term for all of the regression lines is 5 ± 1 kcal / mol.Taking in mind that the charged species appear on the right-hand side of the equations, these results probably indicate the inadequacy of continuum approach to reproduce charged species solvation in polar solvents.
In conclusion, for the preliminary investigation of nitrobenzene to aniline reduction mechanism we suggest the use of B98, M11L, PBE0 or ωB97X-D functionals, 6-311+G(2df,2p) basis set and SMD continuum solvation method.For final results it is essential to include better description of solvation of charged species, possibly via a cluster-continuum approach.Both avenues are currently being explored in our laboratory.