How Do Aromatic Nitro Compounds React with Nucleophiles? Theoretical Description Using Aromaticity, Nucleophilicity and Electrophilicity Indices

In this study, we present a complete description of the addition of a model nucleophile to the nitroaromatic ring in positions occupied either by hydrogen (the first step of the SNAr-H reaction) or a leaving group (SNAr-X reaction) using theoretical parameters including aromaticity (HOMA), electrophilicity and nucleophilicity indices. It was shown both experimentally and by our calculations, including kinetic isotope effect modeling, that the addition of a nucleophile to the electron-deficient aromatic ring is the rate limiting step of both SNAr-X and SNAr-H reactions when the fast transformation of σH-adduct into the products is possible due to the specific reaction conditions, so this is the most important step of the entire reaction. The results described in this paper are helpful for better understanding of the subtle factors controlling the reaction direction and rate.


S1. Geometry preparation details.
In the main text of this work we present the theoretical results obtained using Gaussian 09 package 1 . The geometries were created using GaussView 5.0. The optimization of equilibrium and transition state structures has been performed using PBE1PBE hybrid functional 2 with 6-31+G(d) basis set and the energy in each single point has been recalculated using the much more accurate basis set 6-311+G(2d,p). No geometry restrictions have been applied. The thermal and ZPE correction has been used in the calculations. Frequency analysis has been performed to find the proper ground state (no imaginary frequencies) and transition state (one imaginary frequency) structures. In the case when more than one transition state or stationary structure has been found the statistical contribution of energy and electron density (Hirschfeld electron density population, shown on Fig. 4 in the main text) has been calculated using standard Boltzmann equation. For each type of aromatic ring, the transition state structure with the lowest energy has been taken for further IRC calculations that were performed to present the reaction profiles showing the smooth connection between the substrates and intermediates or product structures. The HOMA indices 3 and Fukui functions 4 computed based on Hirschfeld population analysis were performed on selected points along the IRC routes. The computational strategy was adopted based on work published by R. Ormazá bal-Toledo et al. 5,6 The gas-phase calculation has been performed to consider electron effects that control the reaction directions. No solvation model has been used in the calculations to show pure electronic interactions in the molecular systems. The synthetic experiments are performed in nonpolar solvents 7 , which is why the reproduction of solvent effects in the presented case are less important. The solute-solvent interactions, especially hydrogen bond formation, is minimized and does not affect the overall shape of the potential energy surface. 8 The electron density population for each step of reaction paths has been calculated using Hirschfeld 9 method .

S2. Nucleophilicity and electrophilicity indexes calculation details.
The global nucleophilicity index has been calculated using equation proposed by Jaramillo et al. 10 : The global electrophilic index has been described and argued by Parr et al. 11 as below: The chemical potential 12 is defined as and chemical hardness 13

= −
,where IE is the ionization energy defined as energetic change for the electron removal reaction. That means the IE is a energy needed to move an electron from the molecular system to infinity, namely: The second part of the equation determining the chemical hardness parameter is the electron affinity , which is a negative value of the energy needed to attach an electron from environment to the molecular system. Which is defined as: ,where, ∆ is the Gibbs energy of N-electron molecular system, ∆ +1 is the Gibbs energy of molecular system with additional single electron charge and ∆ −1 is the Gibbs energy with single electron-deficient system. For the calculations of the global electrophilicity and nucleophilicity of the systems, ∆ has been calculated using equation: where ∆ is a sum of Gibbs energies of nitrobenzene ∆ and nucleophile ∆ − .
Local indices of nucleophilicity and electrophilicity have been calculated using equations 5

S6. The interatomic distances changes between substrates and σ X -adducts structures in in [Å].
S6a. The changes of interatomic distancec between substrate and σ H adducts.
Addition into ortho position relative to the nitro group: X=tBu, TS1