A corrected benzene nitration three-step mechanism derived by DFT calculation and MO theory European Journal of Chemistry 14 (1) (2023) 39-52 European Journal of Chemistry ISSN 2153-2249 (Print) / ISSN 2153-2257 (Online) – Copyright © 2023 The Authors – Atlanta Publishing House LLC – Printed in the USA. This work is published and licensed by Atlanta Publishing House LLC – CC BY NC – Some Rights Reserved. https://dx.doi.org/10.5155/eurjchem.14.1.39-52.2340 European Journal of Chemistry View Journal Online View Article Online A corrected benzene nitration three-step mechanism derived by DFT calculation and MO theory Hongchang Shi * Department of Chemistry, Tsinghua University, Beijing 100084, China * Corresponding author at: Department of Chemistry, Tsinghua University, Beijing 100084, China. e-mail: shihc@mail.tsinghua.edu.cn (H. Shi). 10.5155/eurjchem.14.1.39-52.2340 Received: 24 August 2022 Received in revised form: 26 September 2022 Accepted: 02 November 2022 Published online: 31 March 2023 Printed: 31 March 2023 Density-functional theory (DFT) calculations at the LC-wHPBE/6-311++G(d,p) level found that the textbook three-step nitration mechanism of benzene in mixed acids was seriously wrong. Step 1 of generating nitronium ion (NO2+) is not spontaneous, the NO2+ is generated by Lewis collision, and needs to overcome a barrier Ea = 18 or 22 kcal/mol in mixed acid or in nitric acid. Obtaining the Ea of the Lewis collision by quantum chemical calculations is a highlight of the study. The reaction system (NO2+ + H2O) + HSO4⎺ or + NO3⎺ or + nH2O (n ≥ 1) can make NO2+ spontaneously change to HNO3 through a poly(≥3)-molecular acidification. Sulfuric acid can greatly reduce [H2O] and increase [NO2+]. Therefore, the nitration rate in mixed acid is much faster than that in nitric acid. Step 2, C6H6 + NO2+, is an electrophilic addition, follows the transition state theory, and needs to overcome a low barrier, ΔE* = 7 kcal/mol. The product of Step 2 is the σ-complex C6H6-NO2+. The essence of the electrophilic addition is the transfer of HOMO-1 electrons of C6H6 to LUMO of NO2+. Step 3 is a spontaneous Lewis acid-base neutralization without any barrier, and generates the target product nitrobenzene C6H5NO2. NO2+ and σ-complex are the two active intermediates in nitration. The benzene nitration rate control step is not Step 2 of generating σ-complex, but is Step 1 to generate NO2+. The DFT calculation obtains the barriers Ea and ΔE*, the reaction heats ΔHσ and ΔHp of each step of the nitration, resulting in the total nitration reaction heat ΔH = -35 kcal/mol. It is consistent with the experimental ΔH = -34 kcal/mol. Based on the results, a corrected benzene nitration three-step mechanism proposed. Nitration σ-Complex LC-wHPBE Mixed acid Nitronium ion DFT calculation Cite this: Eur. J. Chem. 2023, 14(1), 39-52 Journal website: www.eurjchem.com 1. Introduction The nitration of benzene in mixed acid is an important reaction in the electrophilic substitution of aromatics, and thus it is always an indispensable content in the authoritative general or advanced organic chemistry textbooks [1-6]. Benzene reacts slowly with hot concentrated nitric acid to yield nitrobenzene, but if the reaction is carried out by benzene with a hot mixture (usually 1:2-4) of concentrated nitric acid and sulfuric acid, then it is much faster as the following Equation (1). In nitration, sulfuric acid is not consumed, but it greatly accelerates the reaction. Over a hundred years, the nitration reaction mechanism has been extensively investigated. In 1904, Euler [7] suggested that the nitronium ion (NO2+) is the nitrating agent. The classic aromatic nitration mechanism finally was established through subsequent large number of studies from many chemists [8- 20], which took about half a century. Among them, the contribution of the Ingold group [12-20] to the mechanism is the largest. In organic chemistry textbooks [1-6], the classic nitration mechanism is shown as Scheme 1. Step 1 (Scheme 1) is the hydroxyl oxygen of HNO3 being protonated by H2SO4 in the mixed acid to generate NO2+, and is a chemical equilibrium without any barrier. However, Step 1 means that HNO3 reacts with two H2SO4 molecules, and it is able to generate another positive ion H3O+ and another negative ion HSO4⎺. However, there is a key question without answer: is the left → right spontaneous or need to overcome a barrier for the generation of NO2+? If there is a barrier, is it how high? As early as 1945, Ingold [21] had raised the question; Forming NO2+ may be ‘unimolecular’ or ‘bimolecular’, according as the heterolysis of the nitric acid molecule to yield the NO2+ is rate-determining step or not? But in 1950, Ingold, based on the N2O5-H2O freezing point diagram, concluded that the NO2+ ion is generated by an automatic proton transfer and an ion self-dissociation of the 2 HNO3 (Equation (2)) [13,16]. In March’s advanced organic textbook [5], the HNO3 + 2H2SO4 and HNO3 + HNO3 are even considered as an acid-base reaction. Apparently, he also thinks that the formation of NO2+ is achieved by automatic or spontaneous proton transfer to form O2N-OH2+, then dissociated into NO2+. Therefore, the generation of NO2+ in Step 1 (Scheme 1) has always considered as a spontaneous process without barrier. But the nitration is carried out at 50-60 °C, there must be a barrier, and thus the barrier is judged to appear in Steps 2 and 3 in Scheme 1. In organic chemistry textbooks, Step 2 marks by the adjective, slow, showing that Step 2 is the rate-controlling step. In Step 3, the σ-complex transfers the H proton of benzene ring to HSO4⎺ or H2O, it is considered as also need to overcome a barrier, but its barrier is lower than that of Step 2, thus mark by the ABSTRACT RESEARCH ARTICLE KEYWORDS https://dx.doi.org/10.5155/eurjchem.14.1.39-52.2340 https://www.eurjchem.com/ https://dx.doi.org/10.5155/eurjchem.14.1.39-52.2340 mailto:shihc@mail.tsinghua.edu.cn http://www.eurjchem.com/ https://crossmark.crossref.org/dialog/?doi=10.5155/eurjchem.14.1.39-52.2340&domain=pdf&date_stamp=2023-03-31 40 Hongchang Shi / European Journal of Chemistry 14 (1) (2023) 39-52 2023 – European Journal of Chemistry – CC BY NC – DOI: 10.5155/eurjchem.14.1.39-52.2340 Scheme 1. The popular textbook three-step nitration mechanism of benzene in mixed acid. (1) 2 HNO3 → O2N-OH2+ + NO3⎺ → O2N+ + H2O + NO3⎺ (2) adjective, fast. Many textbooks often give a potential energy curve with two barriers, and the barrier of Step 2 is higher than that of Step 3, which again shows that Step 2 is the rate- controlling step (Scheme 1). However, NO2+ is a high-potential cation. Isn’t there any barrier to be overcome for forming such an ion? In 1978, Sheats and Strachan [22] performed a kinetic study on the nitration mechanism of toluene in mixed acids. By using a stopped-flow spectrometer, they obtained the kinetic parameters of toluene nitration in 77.3 or 78.45 wt % sulfuric acid (Nitric acid: sulfuric acid ≈ 1:3.4 or 1:3.6) and the activation energy of forming NO2+ was obtained by kinetic calculation, Ea = 18.3±4.0 kcal/mol. The Ea of the reverse reaction is 10.5 or 12.0±4.0 kcal/mol. The Ea of CH3-C6H5 + NO2+ generating σ-complex is 5.9±0.1 and 6.3±0.5 kcal/mol, respectively. The results indicate that the rate control step of the nitration in mixed acids is not Step 2 in Scheme 1, but is Step 1 of generating NO2+. The barrier data of toluene nitration in mixed acid is the only experimental one in the literature so far. However, their method cannot determine which one of the two steps of forming NO2+ and σ-complex follows the transition state theory and which one follows the Lewis collision theory. Last over 30 years, many groups have made quantum chemistry study on the aromatic nitration mechanism [23-33], but no one paid attention to how the nitronium ion NO2+ be formed, and all focus on the “rate-controlling step”, Step 2 in Scheme 1. These ab-initio or DFT calculation studies on the C6H6 + NO2+ mechanism have yielded great results. The results confirmed that the C6H6 + NO2+ reaction follows the transition state theory and the product is an σ-complex (arylium ion). A recent research of Brinck group [33] is representative. They get by DFT calculation at M06-2x/6-311G(d,p) level that the addition barrier of forming the σ-complex of benzene is low, 3.1 kcal/mol (H2O as solvent), and the reaction heat is -13.0 kcal/mole. The nitration mechanism given in Scheme 1 is a three-step process, NO2+ and the σ-complex are two active intermediates, and these contents are correct. However, the DFT calculations show that the rate-controlling step of the benzene nitration is not Step 2 of generating σ-complex, but is Step 1 of generating NO2+. Step 3 of generating the target product is a spontaneous Lewis acid-base neutralization without any barrier. 2. Computational methods and frontier orbital theory The DFT computation was carried out with Gaussian 16, Revision B.01 program [34] and DFT methods. LC-wHPBE [35] is a recommended version of the long-range corrected ωPBE functional. In 2014, Galano [36] found that LC-wHPBE was the best among 18 functional for kinetic calculations of radical reactions by using 6-311++G(d,p) basis set and experimental data as reference; and found that the second best functional is M06-2x [37]. One of our recent research on the solvolysis mechanism [38] of t-butyl chloride or bromide shows that the LC-wHPBE also is a suitable functional. Considering that benzene is a large conjugate molecule, the hydroxyl group of H2O is a key active group, and negative ions (HSO4⎺, NO3⎺) appear in the nitration, the DFT calculation also uses the 6- 311++G(d,p) basis set. Kenichi Fukui’s frontier orbital theory (FO) [39-41] is the most widely used molecular orbital theory (MO) to demonst- rate the electron transfer process of many organic reactions. In the frontier orbital theory (FO), the bonding three-principles [42] are the basic conditions for chemical bonding, of which symmetry matching is the most critical. In order to show the electron transfer process in nitration, many structures are attached with their HOMO and LUMO images. However, for organic reactions, especially poly-molecular reactions, the frontier MOs are diverse. The HOMO-1 or LUMO+1 or other MOs are also often frontier MOs. The solvent of the nitration reaction is a mixture of containing strong polar HNO3, H2SO4, H2O and product C6H5NO2. Nitration is carried out in such a solvent, and thus the solvent effect must be included in the DFT calculation. However, the Gaussian program cannot calculate the solvent effect of the two strong acids. In order to estimate the solvent effect of the nitration, HCONH2 (ε = 108.9) is used as solvents to perform the simulation calculation. HCONH2 was chosen because it has the highest polarity (H2SO4 ε ≌ 100), and it had already been used in a study [32] of the benzene nitration mechanism performed by DFT calculation. The Tomasi’s polarizable continuum model IEFPCM [43-46] is used to calculate the solvent effects. In the study, the energies obtained by the DFT calculation all have included the zero-point correction and the thermal correction to the Gibbs free energy, which allows the calculation to obtain the Ea and ΔE*, reaction heat ΔHσ and ΔHp of the three Hongchang Shi / European Journal of Chemistry 14 (1) (2023) 39-52 41 2023 – European Journal of Chemistry – CC BY NC – DOI: 10.5155/eurjchem.14.1.39-52.2340 Scheme 2. Generating NO2+ and H3O+ by HNO3 + 2H2SO4 in the textbook mechanism. (a) H2SO4 ⇋ HSO4⎺ + H+ (b) HO-NO2 + H+ ⇋ H2O+-NO2 (3) (4) steps at default 298.15 K, and enables the data obtained from the DFT calculation to be compared with the experimental data. 3. Results and discussions 3.1. Generation of NO2+ in textbook mechanism is a wrong description For the nitration of benzene, the electrophile NO2+ must first be generated, as shown in Step 1 in Scheme 1. Step 1 is a reaction between one nitric acid and two sulfuric acid molecules. The product is 1 NO2+, 1 H3O+, and 2 HSO4⎺. How did the NO2+ and H3O+ formed? Some textbooks [1,4] already explain: Step 1 in Scheme 1 is a three-step reaction as shown in Scheme 2. Step 1 in Scheme 2 generates a key active intermediate through the automatic proton transfer to HNO3, σ- complex H2O+-NO2. Step 2 in Scheme 2 is the formation of NO2+ by a spontaneous dissociation of the σ-complex. Finally, another product H2O from Step 2 in Scheme 2 is protonated by the second H2SO4 molecule to form H3O+ in Step 3 (Scheme 2). However, the study shows that the three Steps 1-3 in Scheme 2 all are wrong. First, the σ-complex H2O+-NO2 cannot be formed in mixed acid. Second, here H2O cannot also be protonated by H2SO4 to H3O+ because the H2SO4 molecule is not in water but is in mixed acid. Note that, in some textbooks [1,3], Step 1 in Scheme 1 is HNO3 + H2SO4 ⇋ NO2+ + H2O + HSO4-, so only Steps 1 and 2 in Scheme 2 exist. Of course, these two steps are also wrong. The DFT calculation shows that HNO3 and H2SO4 or 2HNO3 cannot react spontaneously to form σ-complex H2O+-NO2. Then, how is the H2O+-NO2 in the textbooks formed? Apparently, it is a classic acid-base neutralization process [5], HNO3 + H2SO4 is through the reaction in Equation (3). However, in mixed acid, there is no such H2SO4 automatic dissociation to form the free H+, because the O-H bond in the H2SO4 or HNO3 molecule is an σ-bond with high strength, so there is no automatic protonation either. The 1 is the optimized initial structural of H2SO4 (Figure 1) and 2 is the optimized product structure after H2SO4 being dissociated (Figure 1). From 1 and 2 (Figure 1), the dissociation energy is ΔE = E1* – E1 = 0.235030 a.u. = 147.4 kcal/mol. Also using ab-initio MP2 to perform this calculation, the ΔE = 0.237408 a.u. = 148.9 kcal/mol. It has a high dissociation energy, indicating that it is impossible to generate free H+ ion by automatic dissociation of H2SO4 in mixed acid. The dissociation of H2SO4 in Equation (3a) does not exist in mixed acid. The 3 is an initial structural setting of σ-complex H2O+-NO2 after HNO3 is protonated by H+ (Figure 1) and 4 is the optimized structure of 3 (Figure 1). The 4 shows that the σ-bond of H2O+- NO2 has been broken, that is, the H2O+-NO2 become to H2O and NO2+ after optimization. A stable σ-complex will definitely exist in its optimized structure (Ex. C6H6-NO2+ behind). The above results show that there is no free H+, also no σ-complex H2O+- NO2 in the mixed acid. The formation of NO2+ does not occur through the dissociation of H2O+-NO2, but rather through another pathway. If the hydroxyl oxygen protonation of HNO3 can form the H2O+-NO2, then H2O + NO2+ can also form the σ-complex, but why cannot the two form the σ-complex? The 5 and 6 is an optimized structure of NO2+ + H2O with HOMO and LUMO images and energy E′ (Figure 1). This is an Opt = Modredundant calculation with freezing coordinates (H2O···NO2+ = 2.000 Å). The nature of generating σ-complex by NO2+ and H2O is the transfer of HOMO electrons of H2O to LUMO of NO2+. According to the “+*” and “-*” in the HOMO of 5 and the “-*” in the LUMO of 6, the symmetry of the two frontier MOs non-match (Figure 1). At the same time, the energy of internuclear repulsion increases N···O approaches each other. The energy E’ of the systems 5 or 6 is 6.6 kcal/mole higher than the E1 of 4. If the σ- complex is set to H2O···NO2+ = 1.5 Å, the DFT calculation gives that its energy rises by 24.7 kcal/mol. These show that electron transfer HOMO → LUMO cannot occur, and therefore, even though H2SO4 can automatically form H+ (Equation 3a), protonation (HNO3 + H+) cannot also form the σ-complex H2O- NO2+. Therefore, in the generation of NO2+, the σ-complex intermediate H2O+-NO2 does not exist in the mixed acid, that is, the two chemical equilibriums 1 and 2 in Scheme 2 are wrong. The following needs to continue to examine the Step 3 in Scheme 2. If the H2SO4 molecule is in water, the proton of its - OH group can easily be transferred to a H2O molecule. However, the DFT calculation shows that the generation of H3O+ in water also is not a simple bimolecular reaction of H2SO4 + H2O. It is a poly-(n ≥ 4) molecular proton-transfer process. In Figure 2, the system 1 is the optimized initial structure of one H2SO4 molecule and three H2O molecules, and system 2 is the optimized product structure. It can be seen from 2 (Figure 2), H3O+ spontaneously formed and released reaction heat ΔH = Ep – E1 = -0.018454 a.u. = -11.6 kcal/mol. If the number of water molecules is increased, the bond length of the H3O+ will be shorter and the reaction heat released will increase. Therefore, H2SO4 tends to form H3O+ in water. The protonation of H2O is a spontaneous poly-molecular (H2SO4 + nH2O, n ≥ 3) proton transfer. The generation of H3O+ can be expressed as Equation (4). Note that it is not a chemical equilibrium. 42 Hongchang Shi / European Journal of Chemistry 14 (1) (2023) 39-52 2023 – European Journal of Chemistry – CC BY NC – DOI: 10.5155/eurjchem.14.1.39-52.2340 H2SO4 Optimized initial structure E1= -700.002134 a.u. H+ + HSO4⎺ Optimized product structure after H2SO4 proton dissociation E1*= -699.767104 a.u. 1 2 O2N-OH2+ An σ-complex structure setting from HNO3 hydroxyl oxygen protonation NO2+ + H2O Optimized structure of 3 E1 = -281.154120 a.u. 3 4 HOMO NO2+ + H2O An optimized setting structure EHOMO = -0.506407 a.u. E′= -281.143602 a.u. LUMO NO2+ + H2O An optimized setting structure ELOMO = -0.073079 a.u. E′= -281.143602 a.u. 5 6 Figure 1. 1 is the optimized structure of H2SO4. 2 is the optimized product structure after H2SO4 proton dissociation. 3 is an initial structure setting of HNO3 hydroxyl oxygen protonation; 4 is an optimized structure of 3 and energy E1. 5 and 6 are an optimized structure setting of NO2+ + H2O with HOMO and LUMO images and energy E′. The solvent is HCONH2. In 2, -O⎺···H+ = 3.500 AÅ ; In 5 and 6, H2O···NO2+ = 2.000 AÅ , the Chem3D orbital iso-contour = 0.05. H2SO4 + 3H2O Optimized initial structure setting E1 = -929.160929 a.u. HSO4− + H3O+ + 2H2O Optimized product structure Ep = -929.179383 a.u. 1 2 H2SO4 + H2O Optimized initial structure E1 = -776.397913 a.u. HSO4− + H3O+ Optimized product structure after Lewis collision Ep = -776.354076 a.u. 3 4 Figure 2. The systems 1 and 2 are the formation of H3O+ in water by H2SO4 + 3H2O. The systems 3 and 4 are H2SO4 and H2O in mixed acid by Lewis collision to generate H3O+. The systems 1 and 2, H2O as solvent. The systems 3 and 4, HCONH2 as solvent. The atom coordinates of structures 1-4 see the Supplementary material, S1. 3.500 H+ HSO4 - H+ + 1.370 129.0 2.452 NO2 + H2O 177.0 + 2.000 NO2 + H2O + 161.9 ** 2.000 NO2 + H2O + + + 161.9 * H 3.200 H2SO4 H2O H2O H2O 1 2 3 1.897 1.896 H 1.568 HSO4 - H3O+ H2O H2O 2 3 1.034 1.0111.454 1.558 + H 1.521 H2SO4 H2O 1.024 Lewis collision HSO4 - H3O+ + 0.978 0.976 3.200 + H HSO - H O+ Hongchang Shi / European Journal of Chemistry 14 (1) (2023) 39-52 43 2023 – European Journal of Chemistry – CC BY NC – DOI: 10.5155/eurjchem.14.1.39-52.2340 H2SO4 HSO4 - H2O H3O++ + Spontaneous Ea 27 kcal/mol Lewis collision Lewis acid-base neutralization (5) Even in water, if H2SO4 molecules only interact with one or two H2O molecules, they cannot spontaneously form H3O+. Fortunately, H2O molecules are everywhere in water. The state of H2SO4 in mixed acid is completely different from that of water. The 3 in Scheme 2 gives a chemical equilibrium for the formation of H3O+, but the authors [1,4,5] do not take into account that the H2SO4 molecule is in mixed acid and is not in water. For the nitration in mixed acid, usually HNO3:H2SO4 = 1:2-4. If the ratio is 1:2, and the nitric acid is with 30% water, it is easy to calculate that ten H2SO4 molecules in the mixed acid can only get eight H2O molecules to complex with them, that is, on average, one H2SO4 molecule cannot get one H2O molecule to complex. This makes the formed NO2+ difficult to be acidified by H2O molecules, which increases the lifetime of NO2+. Therefore, NO2+ is easy to survive in mixed acid. A potential energy surface scan (PES) calculation can show that in mixed acid the NO2+ and H3O+ can only be generated by a Lewis collision between H2SO4 and H2O molecules. The 3 is the optimized complex structure of H2SO4 + H2O (Figure 2). The distance between the hydroxyl H of H2SO4 and the O of H2O is 1.521 Å, and thus it is a strong complex. The 4 is the product structure after the Lewis collision. It is an Opt = Modredundant calculation under freezing coordinates (HOSO3⎺···H3O+ = 3.200 Å), because there is no the stable product structure of H3O+ + HSO4⎺. From Figure 2, the 3 and 4, Ea = Ep – E1 = 0.043837 a.u. = 27.4 kcal/mol, is a high barrier. The chemical Equilibrium (3) in Scheme 2 can be expressed as Equation (5). Left → right in Equation (5), H2SO4 and H2O become into products H3O+ + HSO4⎺ is through a Lewis collision. It needs to overcome a high barrier 27.4 kcal/mol, which indicates that it is difficult to form H3O+. The reverse process right → left is a spontaneous bimolecular Lewis acid-base neutralization, indicating that once H3O+ formed, no matter where it is around HSO4⎺, these two will immediately change back to H2SO4 and H2O, and release the same energy, -27.4 kcal/mole. This shows that the number of H3O+ in mixed acids is actually zero because it is not a stable intermediate, that is, the chemical equilibrium Step 3 in Scheme 2 does not exist in mixed acid. Therefore, the Step 1 is wrong in Scheme 1. As you will see below, NO2+ from Lewis collision is different from the H3O+: it is a stable active intermediate in mixed acid. 3.2. Generating active intermediate NO2+ by Lewis collision The study shows that the generation of NO2+ is not through the formation and dissociation of the fictitious σ-complex H2O+- NO2 (Scheme 2, Steps 1 and 2). NO2+ is directly generated by the Lewis collision between a HNO3 and a H2SO4 or between 2HNO3 molecules, but it needs to overcome the highest-barrier in the three-step nitration. Generating NO2+ by Lewis collision needs to meet three conditions. First, the collision products must be good leaving groups. The generation of NO2+ in mixed acid can consider as a HNO3 and a H2SO4 molecule collide to form a NO2+, a H2O and a HSO4⎺. These three products are good leaving groups in mixed acid or strong polar solvents. Second, the generation of NO2+ is through Lewis collision, which does not follow the transition state theory, and thus there is no transition state (TS) barrier in the collision path. A potential energy surface scan calculation shows that there is no transition state barrier along the collision path of forming NO2. Figure 3 is the optimized initial structure with the collision path (red dotted line) between HNO3 and H2SO4. This is the most direct and reasonable Lewis collision path. The distance between the H atom of H2SO4 and the oxygen of the -OH group of HNO3 is 1.870 Å. The optimization result also shows that HNO3 cannot be automatically protonated by H2SO4 to form water and NO2+. If the H···OH length is ≦1.015 Å, it will bond to form H2O. Therefore, the interval of the scan is 1.870-1.015 Å. Figure 4 shows the energy curve of the potential energy surface scan (PES). The energy keeps rising with the approach of the distance between the H atom of H2SO4 and the -OH of HNO3, the energy is the highest at when it reaches 1.015 Å, and is higher 22.0 kcal/mole than that at 1.870 Å. This proves that there is no transition state barrier in the path of Lewis collision. Third, the opt calculation of the product system must show that the NO2+ from Lewis collision is a stable active intermediate, which ensures that NO2+ has a measurable concentration in solution. The barrier get by Lewis collision called activation energy Ea. Note that if a reaction follows the transition state theory, its barrier is called as the activation barrier, labeled as ΔE*. The Ea calculation only requires the energies of optimized initial structure and optimized product structure before and after collision of HNO3 and H2SO4, but without having to consider how the collision proceeds [38]. The initial structure of the two molecules with the lowest energy before collision is generally easy to determine. However, the product structure after collision is often difficult to do because there are many different product configurations after collision, which needs to find the product system that NO2+ is a stable intermediate. The 1 is the optimized initial structure and the energy E1 of HNO3 + H2SO4 before collision (Figure 5); 2 is the optimized product structure and energy E1* after collision (Figure 5). For the optimized product 2, here H2O and HSO4⎺ are on both sides of NO2+, and NO2+ has good linearity, ∠ON+O = 176.7°. This is an Opt calculation, the three are a stable product system, that is, the NO2+ is an independent and stable active intermediate. Of course, ∠ON+O ≠ 180° showing that there is a weak electrostatic interaction between the three, but this is normal in solution. The energy E1* of product 2 is higher than the energy E1 of initial structure 1 (Figure 5). The elevated energy is the Ea of forming NO2+, Ea = E1* - E1 = 0.028058 a.u. = 17.6 kcal/mol, is not high, but in the three-step nitration of benzene, the barrier is the highest. The barrier obtained by the DFT calculation is consistent with Sheats’ experimental Ea of toluene 18.3±4 kcal/mol [22]. Note that the structure of Figure 3 cannot be used for the initial structure, because the bimolecular system does not have the lowest energy; it is 2.8 kcal/mole higher than that of 1 (Figure 5). The calculation of Ea must use the 1 initial structure with the lowest energy (Figure 5). Based on the barrier and the stability of NO2+, [NO2+] is high at 50-60 °C, that is, NO2+ is a measurably stable intermediate. Therefore, the Lewis collision reaction in Figure 5 can be expressed as Equation (6), a chemical equilibrium. Left → right shows that a H2SO4 and a HNO3 molecule become to products NO2+ + H2O + HSO4⎺ through a Lewis collision, which makes a bimolecular system becomes a tri- molecular one, later will prove that right → left is NO2+ to be acidified back to HNO3 and H2SO4, which is a spontaneous tri- molecular electrophilic substitution, NO2+ is the electrophile, and thus there is no reverse barrier in the equilibrium. 44 Hongchang Shi / European Journal of Chemistry 14 (1) (2023) 39-52 2023 – European Journal of Chemistry – CC BY NC – DOI: 10.5155/eurjchem.14.1.39-52.2340 HNO3 + H2SO4 An optimized initial structure with a Lewis collision path E1 = -980.777551 a.u. Figure 3. An optimized structure of H2SO4 and HNO3 with a Lewis collision path (red dotted line). Figure 4. The potential energy surface scan curve along the collision path R (HO3SOH···O(H)NO2). HNO3 + H2SO4 Optimized initial structure E1 = -980.780930 a.u. NO2+ + H2O + HSO4− Optimized product structure after an effective collision E1* = -980.752872 1 2 Figure 5. Generating NO2+ by Lewis collision of HNO3 and H2SO4 in mixed acid. 1 is the optimized initial structure and energy E1; 2 is the optimized product structure and energy E1* after an effective collision obtained by DFT calculation at the LC-wHPBE/6-311++G(d,p) level. The solvent is HCONH2. The atom coordinate tables of structures 1 and 2 are presented in the Supplementary material, S2. NO2 + +HO-NO2 HO-SO3H+ Spontaneous Ea Lewis collision Tri-molecular acidification H2O + HSO4 - (6) However, although the reverse reaction is spontaneous, the ternary molecule system in Figure 5, 2 takes quite a long time to form an effective tri-molecular acidification system, which gives NO2+ a considerable lifetime, that is, it can form a measurable [NO2+] in the H2SO4 + HNO3 solution. Therefore, Equation (6) is a good chemical equilibrium. Generating NO2+ in nitric acid also occurs through the Lewis collision between two HNO3 molecules. The 1 is the optimized initial structure and energy E1 of 2HNO3 before collision (Figure 6), 2 is the optimized product structure and energy E1* after collision (Figure 6). The optimized product structure 2 also is a stable opt structure, but different from the collision product structure between HNO3 and H2SO4 (Figures 5), the products H2O and NO3- are on the same side of NO2+ and are close to each other. Due to such a configuration, the three are easy to form a tri-molecular acidification system (See Section 3.3, Figure 7, 5). The ∠ON+O = 173.2°, showing that the NO2+ linearity is worse than that in mixed acid. Therefore, the stability of NO2+ in nitric acid is not as good as in mixed acid. From Figure 6, the 1 and 2, Ea = E1* - E1 = 0.034431 a.u. = 21.6 kcal/mol, showing that the collision between the 2 HNO3 needs to overcome a much higher barrier Ea than the HNO3 + H2SO4 in mixed acid. The Lewis collision reaction in Figure 6 can be expressed as Equation (7). HNO3 H2SO4 1.870H H Lewis collision 0 5 10 15 20 25 0.8 1.0 1.2 1.4 1.6 1.8 2.0 E (k ca l/m ol ) R (Å) HNO3 1.826 H2SO4 1.673 H H H H2O 3.523 NO2 + HSO4 - 2.545 176.7 Hongchang Shi / European Journal of Chemistry 14 (1) (2023) 39-52 45 2023 – European Journal of Chemistry – CC BY NC – DOI: 10.5155/eurjchem.14.1.39-52.2340 HNO3 + HNO3 Optimized initial structure E1 = -561.563639 a.u. NO2+ + H2O + NO3− Optimized product structure after an effective collision E1* = -561.529208 a.u. 1 2 Figure 6. Generating NO2+ by Lewis collision between two HNO3 molecules: 1 is the optimized initial structure and energy E1 of 2 HNO3 before collision; 2 is optimized product structure and energy E1* after collision. The solvent is HCONH2. The atom coordinate tables of structures 1 and 2 are presented in the Supplementary material, S3. NO2 + +HO-NO2 HONO2+ Spontaneous Ea Lewis collision Tri-molecular acidification H2O + NO3 - (7) Equation (7) also is a chemical equilibrium [47], the left → right shows that the two HNO3 molecules become into the product NO2+ + H2O + NO3⎺ through a Lewis collision, and that makes the bimolecular system becomes a tri-molecular one, but the Ea is much higher than in mixed acid. The right → left is the NO2+ to be acidified into 2 HNO3, which is a spontaneous tri- molecular electrophilic substitution. Due to the fact that NO2+ is not an adequate stable ion in nitric acid, the rate at which NO2+ is acidified is much faster than in mixed acid. Therefore, the [NO2+] is much lower than that in mixed acid. Although Equation (7) is a chemical equilibrium, it is not a good one. The Ea of generating NO2+ is 21.6 kcal/mol, which is 4 kcal/mol higher than in mixed acid. This is a big increase for reaction barrier. Ingold [15,16] referred to the generation of NO2+ in nitric acid as an automatic “self-dissociation” of 2HNO3 molecules. However, the “self-dissociation” is not only incorrect, but also needs to overcome a barrier much higher than in mixed acid. 3.3. Acidification of NO2+ is a spontaneous poly(≥3)- molecular electrophilic substitution The DFT calculation found that the nitronium ion NO2+ is easily acidified back to the HNO3 molecule. The system in mixed acid is a tri-molecular one NO2+ + H2O + HSO4⎺ (Equation (6), right → left). A similar tri-molecular system NO2+ + H2O + NO3⎺ (Equation (7), right → left) also exists in pure nitric acid. For the benzene nitration in nitric acid, the acidification system NO2+ + nH2O (n ≥ 2) also exists because there are large amount of water in nitric acid. The acidification is a spontaneous poly(≥3)- molecular electrophilic substitution. NO2+ ion is the electrophile. The HSO4⎺ or NO3⎺ or H2O is the proton acceptor. It is generally believed that NO2+ is acidified through a two- step reaction: NO2+ + H2O → O2N-OH2+ + H2O → HONO2 + H3O+, but the two-step acidification is incorrect. As mentioned above (Section 3.1), the NO2+ and one H2O molecule cannot form the σ-complex (Figure 1, 3-6). 1 shows an initial tri-molecular structure setting of NO2+ + H2O + HSO4⎺ (Figure 7), 2 is the optimized structure of 1, the optimization generates a HNO3 and a H2SO4 molecule (Figure 7). In the tri-molecular acidification, NO2+ combines with the H2O at the same time the HSO4⎺ ion accepted a proton H+ of the H2O, and thus a H2SO4 and a HNO3 are formed. 1 → 2 is the reverse reaction in Equation (6). The electrophilic substitution process for acidification of NO2+ is also the transfer of frontier MO electrons of H2O to LUMO of NO2+. NO2+ and HSO4⎺ are acidified to HNO3 and H2SO4 in one step. The products 3 and 4 are the optimized structure of the setting 1 with HOMO-3 and LUMO images and energy E’ (Figure 7). This also is an Opt = Modredundant calculation under freezing coordinates (H2O···NO2+ = 2.661 Å). Since HSO4- is a negative ion, the HOMO, HOMO-1 and HOMO-2 are all on it, so the frontier MOs of the optimized tri-molecular system are the HOMO-3 on H2O and LUMO on NO2+. The orbital symmetry of HOMO-3 (+*) and LUMO (+*) matches, and thus the electron transfer HOMO-3 → LUMO can proceed. Similarly, 5 is an initial tri-molecular structure setting of NO2+ + H2O + NO3-, 6 is the optimized structure of 5, showing that the optimization spontaneously generates two HNO3 molecules (Figure 7). The electron transfer process of the tri-molecular acidification of NO2+ + H2O + NO3 is similar to NO2+ + H2O + HSO4⎺ (Figure 7, 3 and 4) in mixed acid. However, in nitric acid, there is 30-35% water. NO2+ + nH2O (n ≥ 2) is also easy to come back HNO3. NO2+ + 2H2O also is a tri-molecular electrophilic substitu- tion and follows transition state theory, it is not a spontaneous reaction. This is because HSO4⎺, NO3⎺ are strong Lewis alkali, but H2O is weak one. 1 and 2 are the optimized initial structure with HOMO and LUMO and energy E1 (Figure 8). The orbital symmetry of the HOMO (p orbital “+*”, “-*” of H2O 1, Figure 8) and the LUMO (p orbital “+*”, “-*” of the N atom) in NO2+ is compatible. Therefore, the HOMO electrons of H2O 1 (Figure 8) can be transferred to the LUMO of NO2+. The 3 is the transition state TS structure with HOMO-1 image, here a small amount of HOMO electrons has transferred to the two oxygen atoms of NO2+ (see inside curly brackets) (Figure 8). Note that this is a tri-molecular reaction; the pair of HOMO electrons of H2O (Figure 8) in 1 is not always in the HOMO orbital of thr reaction system during the electron transfer process. In the TS, the frontier MO electron of H2O 1 (Figure 8) is now in the HOMO-1 (HOMO is not given here). From 1 and 3, ΔE* = 0.009029 a.u. = 5.7 kcal/mol (Figure 8). The barrier is low, so the electron transfer is similar to be a spontaneous process. 4 is the optimized product structure with HOMO image of the tri-molecular acidification (Figure 8). The H2O 1 in Figure 8 has completed the electron transfer and HNO3 has been generated. At the same time, the H2O 2 (Figure 8) molecule accepts the proton of H2O 1, the H3O+ ion has been generated, and thus the tri-molecular electrophilic substitution is completed. H2O 2.482 NO2 + 1.760 NO3 - 173.2 2.435 + 46 Hongchang Shi / European Journal of Chemistry 14 (1) (2023) 39-52 2023 – European Journal of Chemistry – CC BY NC – DOI: 10.5155/eurjchem.14.1.39-52.2340 NO2+ + H2O + HSO4− An initial structure setting HNO3 + H2SO4 Optimized structure of 3 1 2 HOMO-3 NO2+ + H2O + HSO4− Optimized structure of 1 EHOMO = -0.446721 a.u. E′ = -980.749470 a.u. LUMO NO2+ + H2O + HSO4− Optimized structure of 1 ELUMO = -0.069409 a.u. E′ = -980.749470 a.u. 3 4 NO2+ + H2O + NO3− An initial structure setting HNO3 + HNO3 Optimized product structure of 5 Ep = -561.562751 a.u. 5 6 Figure 7. Products 1 and 5 are an initial tri-molecular structure setting of NO2+ + H2O + HSO4- and NO2++ H2O + NO3-. Products 2 and 6 are the optimized product structures of 1 and 5. Products 3 and 4 are the optimized initial structure setting of 1 with HOMO-3 and LUMO images and energy E’ under freezing coordinates H2O···NO2+ = 2.661 AÅ . The solvent is HCONH2. Chem3D Orbital iso-contour = 0.05. The DFT calculation shows that if the acidification of NO2+ is carried out under the action of 2-5H2O molecules, it needs to overcome a barrier of 1-6 kcal/mol. The barriers are very low, and thus they are an approximately spontaneous reaction. The study found that if NO2+ is to spontaneously complete the acidification by water, at least six H2O molecules must participate in the reaction. The 1 is an initial structure setting of NO2+ + 6H2O, a seven molecular reaction system (Figure 9). The product 2 is the optimized product structure of 1 (Figure 9). The acidification of NO2+ in Figure 9 is a spontaneous seven- molecular electrophilic substitution [38]. The products are HNO3 and H3O+. The four H2O molecules, H2O and H2O 4-6 played a catalytic role in the reaction. Of course, such a sponta- neous seven-molecular acidification is completely impossible in mixed acids. It is estimated that even in nitric acid, the chance of occurrence also is extremely small. In mixed acid, although [H2O] is greatly reduced, there is a content of ~10%. The tri-molecular acidification (Figure 7, 1→2) is spontaneous and fast, and thus the benzene nitration often maintains at 50-60 °C and under effective stirring. This can increase [NO2+], and enables that once NO2+ is formed, benzene molecules can be nitrated immediately. Nitric acid contains 30-35% water, which is very high. The molecular weight of HNO3 is 3.5 times that of H2O, that is, the mole amount of H2O in nitric acid is about 1.5 times that of HNO3. Therefore, in nitric acid, there is not only an acidification path of NO2+ + H2O + NO3⎺, but also NO2+ can be quickly acidified by water, and therefore [NO2+] in nitric acid is extremely low. It is inevitable that the nitration of benzene is difficult to perform in nitric acid. 3.4. Generating σ-complex intermediate by electrophilic addition of C6H6 and NO2+ The DFT calculation shows that the electrophilic addition of NO2+ and C6H6 generate an σ-complex intermediate, it follows the transition state theory, and need to overcome a low activation barrier ΔE*. NO2+ is the electrophile. 1 and 2 show the optimized initial structure with HOMO and HOMO-1 of C6H6 and energy E1 (Figure 10). The HOMO and HOMO-1 are two degenerate orbitals. The orbital energy difference of HOMO and HOMO-1 is ΔEHH-1 = 0.03 eV, is very small, and thus HOMO-1 is also a frontier MO (Figure 10). 3 is the optimized initial struc- ture with LUMO image of NO2+ (Figure 10). Note that the LUMO and LUMO+1 of NO2+ both are approximately the degenerate HNO3 H2SO4 1.876 H H H 2.661 NO2 + H2O + 178.9 HSO4 - 1.772 * 2.661 NO2 + H2O LUMO + + + 1.772 HSO4 - * 2.629 H2O NO2 + NO3 - 2.183 HNO3 1.913 HNO3 Hongchang Shi / European Journal of Chemistry 14 (1) (2023) 39-52 47 2023 – European Journal of Chemistry – CC BY NC – DOI: 10.5155/eurjchem.14.1.39-52.2340 HOMO NO2+ + H2O + H2O Optimized initial structure E1 = -357.541810 a.u. LUMO NO2+ + H2O + H2O Optimized initial structure E1 = -357.541810 a.u. 1 2 HOMO-1 TS NO2+ + H2O + H2O E1* = -357.532781 a.u. HOMO HNO3 + H3O+ Optimized product structure Ep = -357.541639 a.u. 3 4 Figure 8. The systems 1 and 2 are the optimized initial structure with HOMO and LUMO images, and Energy E1 of NO2+ + 2H2O system. 3 is the transition state TS with HOMO -1 and energy E1*, 4 is the optimized product structure with HOMO images and energy Ep. Chem3D, Orbital iso-contour = 0.05. The solvent is HCONH2. The coordinate tables of structures 1-4 see Supplementary material, S4. NO2+ + H2O + 2H2O + 3H2O An initial structure setting HNO3 + H3O+ + 4H2O Optimized product structure of 1 1 2 Figure 9. The acidification of NO2+ + 6H2O is a spontaneous seven-molecular electrophilic substitution. 1 is the initial structure setting of the seven-molecular system. 2 is the optimized product structures of 1. orbitals (ΔELL+1 = 0.01 eV). Therefore, LUMO+1 is also a frontier MO. However, the LUMO+1 and the HOMO or HOMO-1 do not match, so the optimized initial structure with the LUMO+1 image is not shown. The C6H6 + NO2+ is an electrophilic addition between both. The essence of the addition is the transfer of HOMO-1 electrons of C6H6 in 2 to the LUMO orbital of NO2+ in 3 (Figure 10). From 2 and 3, the orbital symmetry of the HOMO-1 (+*, -*) of C6H6 and the LUMO (+*, -*) of NO2+ matches (Figure 10). Therefore, the HOMO-1 electrons of C6H6 can transfer to the LUMO of NO2+. 4 is the transition state (TS) structure with the HOMO image and the energy E1* (Figure 10). The C···NO2+ distance is 2.261 Å (Figure 10). The transfer of HOMO electrons of C6H6 in TS to the LUMO of NO2+ does not appear. This is the inevitable result of the symmetry mismatch between 1 and 3. 5 is the TS structure with HOMO-1 image. In the TS, many HOMO-1 electrons of C6H6 have transferred to the C- - NO2+ region (see inside blue braces). This is also the inevitable result of the symmetry match between 2 and 3. 4 and 5 indicate that the symmetry matching between two frontier MOs is a necessary condition for the realization of electron transfer. It can be seen from Figure 10 2, 3 and 5, the frontier MOs electron- transfer of the electrophilic addition is HOMO-1 2 → LUMO 3. From the initial structure energy E1 and the energy E1* of TS, the activity barrier of NO2+ and C6H6 electrophilic addition ΔE1* = E1 – E1* = 0.010975 a.u = 6.7 kcal/mol (Figure 10). The barrier (HCONH2 as solvent) is consistent with Sheats’s [22] two barriers 5.9±0.1 and 6.3±0.5 kcal/mol of the generated toluene σ-complex. 1.774 2.398 H2O 175.5 H2O + 2 1 NO2 + * ** 2.398 NO2 + H2O H2O + 2 1 + + +* * 1.774 1.701 2.800 174.0 H2O + 1 NO2 + H2O 2 H2O 3 H2O 4 H2O 5 H2O 61.713 1.849 1.871 1.849 1.392 H2O 2 H2O 5 H2O 6 1.795 1.676 1.538 + HNO3 H3O+ H2O 1.369 4 1.347 48 Hongchang Shi / European Journal of Chemistry 14 (1) (2023) 39-52 2023 – European Journal of Chemistry – CC BY NC – DOI: 10.5155/eurjchem.14.1.39-52.2340 Table 1. The optimized initial energy EI, the TS energy E1*, the optimized σ-complex energy Eσ, activation barrier ΔE*, reverse barrier ΔEr* and the reaction heat ΔHσ of generating σ-complex in HCONH2 obtained by DFT calculation at the LC-wHPBE, M06-2x, M05-2x/6-311++G(d,p) level. DFT method E1 (a.u.) E1* (a.u.) Eσ (a.u.) ΔE* ΔEr* ΔHσ (kcal/mol) LC-wHPBE -436.701413 -436.690750 -436.717861 6.7 17.0 -10.3 M06-2x -436.820069 -436.815555 -436.838644 2.8 14.5 -11.7 M05-2x -436.937376 -436.935834 -436.959364 1.1 14.8 -13.8 HOMO C6H6 + NO2+ Optimized initial structure EHOMO = -0.378236 a.u. E1 = -436.701413 a.u. HOMO-1 C6H6 + NO2+ Optimized initial structure EHOMO-1 = -0.379370 a.u. E1 = -436.701413 a.u. 1 2 LUMO C6H6 + NO2+ Optimized initial structure ELUMO= -0.078832 a.u. E1 = -436.7011413 a.u. TS, HOMO C6H6 + NO2+ Optimized initial structure EHOMO= -0.410595 a.u. E1 = -436.690750 a.u. 3 4 TS, HOMO-1 C6H6 + NO2+ EHOMO-1 = -0.413096 a.u. E1 = -436.690750 a.u. HOMO-1 σ-Complex C6H6-NO2+ Optimized product structure Eσ = -436.717861 a.u. 5 6 Figure 10. The 1, 2 and 3 are the optimized initial structure with HOMO, HOMO-1 and LUMO, and system energy E1; 4 and 5 are the transition state TS structure with HOMO, HOMO-1 images and energy E1*. 6 is an optimized product structure with HOMO-1 and energy Eσ. Orbital iso-contour = 0.04. The bond distance is in AÅ . Angle is in degree. The solvent is HCONH2. The atom coordinate tables of structures 1-6 see the Supplementary material, S5. It is reasonable that toluene has a lower barrier of gene- rating σ-complex than benzene, because toluene has a higher reactivity than benzene. The 6 is the optimized product structure with the HOMO-1 image and energy Eσ (Figure 10). The σ-complex of C6H6 + NO2+ has been generated. The σ-C-NO2+ bond is 1.517 Å. At this time, almost all HOMO-1 electrons have transferred to the σ-C-NO2 area. This further shows that the essence of the electrophilic addition is the transfer of HOMO-1 electrons of C6H6 to LUMO of NO2+. From 2 and 6, the reaction heat is ΔHσ = Eσ – E1 = - 0.016448 a.u. = -10.3 kcal/mol, showing that the σ-complex is a stable intermediate (Figure 10). Since the electrophilic addition of NO2+ + C6H6 follows the transition state theory, there is an inverse barrier ΔEr* for the addition. C6H6 3.288 O O NO2 + N 3.282 C6H6 3.288 NO2 + N 3.282 + * * C6H6 3.288 NO2 + N 3.282 + ** C6H6 NO2 + N 2.261 + 148.6 C6H6 NO2 + N 2.261 + 148.6 C6H6 NO2 + NO2 + H 1.517 1.116 126.5 Hongchang Shi / European Journal of Chemistry 14 (1) (2023) 39-52 49 2023 – European Journal of Chemistry – CC BY NC – DOI: 10.5155/eurjchem.14.1.39-52.2340 Table 2. The optimized initial structure energy E1, optimized product structure energy Ep, and released reaction heat ΔHp of generating final products of σ-C6H6- NO2+ + HSO4⎺ or + NO3⎺ or + H2O in HCONH2. Reaction E1 (a.u.) Ep (a.u.) ΔHp (kcal/mol) 1 → 2 σ-C6H6-NO2+ + HSO4⎺ → C6H5NO2 + H2SO4 (Figure 11) -1136.310969 -1136.380100 -43.4 3 → 4 σ-C6H6-NO2+ + NO3⎺ → C6H5NO2 + HNO3 (Figure 11) -717.088022 -717.167531 -49.9 5 → 6 σ-C6H6-NO2+ + H2O → C6H5NO2 + H3O+ (Figure 11) -513.105180 -513.140748 -22.3 Table 3. Ea, ΔHσ, and ΔHp (here take the integer according to rounding after the decimal point) and total reaction heat ΔH of benzene nitration obtained by DFT calculation at the LC-wHPBE/6-311++G(d,p) level. HCONH2 as solvent. Nitration solvent Ea ΔHσ ΔHp ΔH (kcal/mole) Mixed acid 18 -10 -43 -35 Nitric acid 22 -10 -50 -38 From 5 and 6, ΔEr* = 0.027111 a.u. = 17.0 kcal/mol (Figure 10). Sheats [22] gave the reverse activation energy of toluene generating NO2+ to be 10.5 or 12.0±4.0 kcal/mol. The barrier is consistent with the inverse barrier 17.0 kcal/mol for C6H6 + NO2+. This is because Sheats’s detection method cannot deter- mine whether the reaction follows the transition state theory or is through Lewis collision, so he cannot determine the reverse barrier should attribute to the ΔEr* of toluene generating σ- complex. Table 1 lists the activation barriers ΔE* and the reaction heat ΔHσ of the forming σ-complex obtained by the DFT calculation at the LC-wHPBE/6-311++G(d,p) level. The barrier is consistent with the experimental data [22]. The reaction heat ΔHσ from the DFT calculation are -10.3 kcal/mol, showing that the σ-complex is a stable intermediate. The ΔHσ is closer to the experimental value (-7.4 kcal/mol) than that (-13.0 kcal/mol) of Brinck group [33]. Table 1 also presents the results of the DFT calculation at the M06-2x and M05-2x/6-311++G(d,p) level [48]. Clearly, the barriers ΔE* of generating σ-complex of C6H6 + NO2+ are much lower than those obtained by LC-wHPBE, but the released reaction heats ΔHσ are much larger than those obtained by LC- wHPBE. These ΔE*, ΔEr*, and ΔHσ data are greatly deviated from the experimental results [22]. Especially the results of M05-2x are the worst. Furthermore, if the old functional B3LYP or B3P86 or B3PW91 is used in the DFT calculation, the C6H6 + NO2+ addition is spontaneous without any barrier, the result is highly inconsistent with the experiment [22]. Therefore, these old functionals are more than not suitable for the study of the mechanism of benzene nitration. In fact, the LC-wHPBE functional is the best for mechanism research [36]. 3.5. Last Step 3 of benzene nitration is a spontaneous Lewis acid-alkali neutralization The DFT calculations found that the σ-complex C6H6-NO2+ can complete the last Step 3 (Scheme 1) with the HSO4⎺ or NO3⎺ ions or the H2O molecule through a spontaneous Lewis acid- base neutralization, and release a lot of heat. That is, Step 3 in Scheme 1 of generating product nitrobenzene is a spontaneous reaction and does not need to overcome any barrier. The 1, 3, and 5 show the optimized initial structures of σ- C6H6-NO2+ + HSO4⎺ or + NO3⎺ or + H2O (Figure 11). The HSO4⎺ or NO3⎺ or H2O definitely is on the side of σ-C6H6-NO2+, which can ensure that it is a stable initial structure. There is considerable electrostatic interaction between the positive and negative two ions. It is important to include the energy of the interaction between the two ions to correctly calculate the reaction heat of Step 3 (Scheme 1). The 2, 4 and 6 show the optimized product structures of σ-C6H6-NO2 + + HSO4⎺ or + NO3⎺ or + H2O (Figure 11). The product nitrobenzene C6H5 -NO2 + H2SO4 or + HNO3 or + H3O+ all generated, showing that the nitration reaction has ended. The optimized initial system energies EI, optimized product energy Ep, and released reaction heat ΔHp of 1 → 2, 3 → 4 and 5 → 6 (Figure 11) are listed in Table 2. From Table 2, the 1 → 2 and 3 → 4 are a strongly exothermic reaction, the heats are -43.4 and -49.9 kcal/mole (Figure 11). The reason for releasing so much heat is that the σ-C6H6-NO2+ is a strong Lewis acid, HSO4- or NO3- is a strong Lewis base, and therefore 1 → 2 and 3 → 4 are a strong acid-base neutralization. The 5 → 6, ΔHp is -22.3 kcal/mol (Figure 11). The heat released is much less than that of 1 → 2 and 3 → 4, which is because H2O is a neutral molecule, a weak Lewis base. The reaction product is C6H5NO2 + H3O+. The occurrence of 5 → 6 in mixed acids is negligible because even a trace amount of H3O+ is generated, it will immediately will immediately acid-base neutralize with HSO4⎺ to form H2SO4. However, in nitric acid there will be a considerable amount of occurrence of 5 → 6 because nitric acid contains 30-35% water. Of course, the H3O+ will also be neutralized by NO3- soon. The total nitration reaction is C6H6 + HNO3 → C6H5-NO2 + H2O, which is a strongly exothermic reaction. The experimental reaction heat of benzene nitration in mixed acid is ΔH = -34 kcal/mol (-142 kJ/mol) [49]. According to the results above, the total nitration reaction heat ΔH released by the three steps in mixed acid or nitric acid is expressed as Equation (8), ΔH = Ea + ΔHσ + ΔHp (8) The Ea, ΔHσ, ΔHp and ΔH data of nitration in mixed acid and in nitric acid are given in Table 3. The released nitration reaction heat in mixed acid is ΔH = - 35 kcal/mol, which is good consistent with the experimental reaction heat ΔH = -34 kcal/mol. We have not found the experimental reaction heat ΔH of benzene nitration in nitric acid, and thus lack a comparison with its experimental data. If there is no the experimental result in nitric acid so far, the DFT calculation result can regard as a prediction for the reaction heat ΔH. 3.6. A corrected benzene nitration three-step mechanism Based on the above calculation results, the classic nitration mechanism in mixed acid is corrected as following Scheme 3. The Ea, ΔHσ, and ΔHp values (Table 3, Scheme 3) are from the DFT calculation results of benzene nitration in HCONH2 with the highest polarity (ε = 108.9; H2SO4 ε ≌ 100). Step 1 shows the formation of nitronium ions NO2+ by Lewis collision of HNO3 and H2SO4 in mixed acid and the collision needs to overcome a barrier Ea = 18 kcal/mol. The study also shows how to calculate its activation energy Ea for Lewis collision reaction (see Section 3.2). Step 2 is the electrophilic addition of C6H6 + NO2+, NO2+ is the electrophile (Scheme 3). The addition follows the transition state theory and needs to overcome a low barrier ΔE* = 7 kcal/mol. The product is an σ-complex C6H6-NO2+. The activation barrier ΔE* of the generating σ-complex also is consistent with Sheats’s that obtained by stopped flow spectrometer [22]. Generating σ-complex is an exothermic reaction, ΔHσ = -10 kcal/mol. Therefore, the σ-complex is a stable intermediate, which agrees with the experimental facts [23]. 50 Hongchang Shi / European Journal of Chemistry 14 (1) (2023) 39-52 2023 – European Journal of Chemistry – CC BY NC – DOI: 10.5155/eurjchem.14.1.39-52.2340 C6H6-NO2+ + HSO4⎺ Optimized initial structure E1 = -1136.310969 a.u. C6H5-NO2 + H2SO4 Optimized product structure Ep = -1136.379747 a.u. 1 2 C6H6-NO2+ + NO3⎺ Optimized initial structure E1 = -717.088022 a.u. C6H5-NO2 + HNO3 Optimized product structure Ep = -717.167531 a.u. 3 4 C6H6-NO2+ + H2O Optimized initial structure E1 = -513.105180 a.u. C6H5-NO2 + H3O+ Optimized product structure Ep = -513.140748 a.u. 5 6 Figure 11. Systems 1, 3 and 5 are the optimized initial structure of σ-C6H6-NO2+ + HSO4- or + NO3- or + H2O. Systems 2, 4, and 6 are the optimized product structure. The solvent is HCONH2. The bond distance is in AÅ . Angle is in degree. The atom coordinate tables of 1-6 are given in the Supplementary material, S6. Scheme 3. A corrected three-step mechanism of benzene nitration in mixed acid (HNO3 + H2SO4) obtained by DFT calculation at the LC-wHPBE/6-311++G(d,p) level. 2.455 1.115 H 2.103 HSO4 - 126.4 C6H6 NO2 + + H 1.472 C6H5NO2 2.433 H H2SO4 H 124.3 1.515 C6H6 NO2 + 2.223 H + NO - NO3 - 126.3 C H NO + + 2.322 1.115 1.471 C6H5NO22.771 H HNO3 124.0 2.690 1.515 1.116 H 2.682 H2O 126.4 C6H6 NO2 + + 2.283 1.473 C6H5NO2 2.137 H H3O+ 124.2 Hongchang Shi / European Journal of Chemistry 14 (1) (2023) 39-52 51 2023 – European Journal of Chemistry – CC BY NC – DOI: 10.5155/eurjchem.14.1.39-52.2340 The DFT calculation found that the nature of the electrophilic addition of the generated σ-complex is the transfer of the HOMO-1 electrons of C6H6 to the LUMO of NO2+. The inverse barrier ΔEr* = 17 kcal/mol is much higher than the addition barrier ΔE* = 7 kcal/mol, and thus Step 2 is not a chemical equilibrium, is a one-way reaction (Scheme 3). Step 3 is a spontaneous Lewis acid-base neutralization, and is a strongly exothermic reaction ΔHp = -43 kcal/mol, and thus it also is a one-way reaction (Scheme 3). The results of the DFT calculation indicate that the rate control step of benzene nitration is not step 2 of generating σ-complex, but is Step 1 of generating NO2+ (Scheme 3). Quantum chemistry calculations can obtain the barrier or reaction heat of each step, but it is impossible to get these data using classical research methods. Chemical kinetic study [15] shows that benzene nitration exhibits second-order kinetics in sulfuric acid, V = k×[C6H6]×[HNO3]. Step 1 in Scheme 3 shows that the [NO2+] is proportional to [HNO3], and the probability of forming σ-complex is proportional to the reaction probability between C6H6 and NO2+, that is, the rate proportional to [C6H6] and [HNO3], which is consistent with the second-order kinetics. In nitric acid, V = k×[C6H6], because [HNO3] = constant. Therefore, the corrected mechanism in Scheme 3 is consistent with the experimental result [15,16]. In kinetic study of nitration reaction, often by comparing deuterated, tritiated aromatic nitration rate to determine whether the C-H bond of σ-complex is broken in rate- controlling step. Melander’s experiment [50] shows that there is no isotopic effect in the nitration of most aromatic compounds including benzene. The nitration of benzene is a three-step reaction, and the first step is a rate-controlling step. Steps 2 and 3 determine whether there is an isotope effect in the nitration (Scheme 3). Step 2 generates the σ-complex, which needs to overcome a barrier (7 kcal/mole), which is a slow (K1) step. Step 3 is to remove the proton, it is a spontaneous Lewis acid-base neutralization, so it is a very fast (K2) step. Hence K1 � K2, which is consistent with the Melander’s experimental result. The textbook mechanism in Scheme 1 is qualitatively consistent with the experiment, because step 2 and step 3 both need to overcome the barriers, and the rate of step 2 is slow, that of step 3 is fast. However, no one knows how high the two barriers are. Therefore, there is a lack of quantitative comparison on these two barriers. For Step 3 of the nitration mechanism, some textbooks use HSO4⎺ as the proton acceptor [1,2], but the others [3,4] use H2O as the acceptor. Which one is right, or which one is better? The DFT calculation shows that the correct choice should be HSO4⎺ in mixed acid. 4. Conclusions The study shows that in organic chemistry textbooks the benzene nitration mechanism is a three-step reaction, and NO2+ and σ-complex C6H6NO2+are the two active intermediates of benzene nitration, which are correct. However, no correct answers are given as to how to generate these two active intermediates and how to complete these three nitration steps. Step 1 of generating NO2+ is not a spontaneous reaction. Its generation occurs through Lewis collision and must overcome an no-high barrier Ea = 18 kcal/mol, but the NO2+ can return to HNO3 through a spontaneous poly(≥3)-molecular acidification. Step 2 is the electrophilic addition of NO2+ + C6H6. The product is an σ-complex. The addition follows the transition state theory and needs to overcome a much lower barrier ΔE1* = 7 kcal/mol than Step 1 of generating NO2+. The essence of electrophilic addition is the transfer of HOMO-1 electrons of C6H6 to LUMO of NO2+. Step 3 is a spontaneous Lewis acid-base neutralization, generates the target product nitrobenzene, and releases a lot of heat ΔHp = -43 kcal/mol. The final step does not need to overcome any barrier. Therefore, the rate-controlling step of the benzene nitration is not Step 2 of generating σ-complex, but is step 1 of generating NO2+ The DFT calculation obtains the total nitration reaction heat ΔH = -35 kcal/mol. It is consistent with the experimental ΔH = -34 kcal/mol, indicating that the corrected benzene nitration three-step mechanism has been experimentally confirmed. Acknowledgement I am grateful to Professor Guoshi Wu, Institute of Physical Chemistry, Tsinghua University, for his effective support in quantum chemistry calculation. Supporting information The atom coordinate tables of reaction structures in Figures. S1, Structures 1-4 in Figure 2; S2, Structures 1 and 2 in Figure 5; S3, Structures 1 and 2 in Figure 6; S4, Structures 1-4 in Figure 8; S5, Structures 1-6 in Figure 10; S6, Structures 1-6 in Figure 11. Disclosure statement Conflict of interest: The author declares that he has no conflict of interest. Ethical approval: All ethical guidelines have been adhered. CRediT authorship contribution statement Conceptualization, Methodology, Formal Analysis, Investigation, Data Curation, Writing - Original Draft, Writing - Review and Editing, Visualization, Project Administration: Hongchang Shi. The selection of topic, literature search, DFT calculation, data sorting, structure diagram production, and paper writing were all done by the author. ORCID and Email Hongchang Shi shihc@mail.tsinghua.edu.cn https://orcid.org/0000-0001-7505-4976 References [1]. Graham Solomons, T. W. Organic Chemistry; 6th ed.; John Wiley and Sons (WIE): Brisbane, QLD, Australia, 1995. [2]. Carey, F. A. Organic Chemistry; 2nd ed.; McGraw-Hill: New York, NY, 1992. [3]. Vollhardt, K. P. C.; Schore, N. Organic Chemistry; 2nd ed.; W.H. Freeman: New York, NY, 1993. [4]. Xing Q. Y.; Pei W. W.; Xu R.; Pei Q. J. Foundation of Organic Chemistry, Third Edition (Chinese); Higher Education Press: Beijing, China, 2005. [5]. Smith, M. B.; March, J. March’s advanced organic chemistry: Reactions, mechanisms, and structure; 7th ed.; Wiley-Blackwell: Hoboken, NJ, 2012. [6]. Carey, F. A.; Sundberg, R. J. Advanced organic chemistry: Part A: Structure and mechanisms; 5th ed.; Springer: New York, NY, 2007. [7]. Euler, H. Zur Kenntniss der aliphatischen Amine. Justus Liebigs Ann. Chem. 1904, 330, 280–291. [8]. Westheimer, F. H.; Kharasch, M. S. The kinetics of nitration of aromatic Nitro compounds in sulfuric acid. J. Am. Chem. Soc. 1946, 68, 1871– 1876. [9]. Bennett, G. M.; Brand, J. C. D.; Williams, G. 188. Nitration in sulphuric acid. Part I. The nature of the nitrating agent in nitric–sulphuric acid mixtures. J. Chem. Soc. 1946, 869–875. [10]. Olah, G. A. Aromatic substitution. XXVIII. Mechanism of electrophilic aromatic substitutions. Acc. Chem. Res. 1971, 4, 240–248. [11]. Ridd, J. H. Mechanism of aromatic nitration. Acc. Chem. Res. 1971, 4, 248–253. [12]. Hughes, E. D.; Ingold, C. K.; Reed, R. I. Kinetics of aromatic nitration: The nitronium ion. Nature 1946, 158, 448–449. [13]. Hughes, E. D.; Ingold, C. K.; Reed, R. I. 493. Kinetics and mechanism of aromatic nitration. Part II. Nitration by the nitronium ion, NO2 +, derived from nitric acid. J. Chem. Soc. 1950, 2400–2440. [14]. Gold, V.; Hughes, E. D.; Ingold, C. K.; Williams, G. H. 495. Kinetics and mechanism of aromatic nitration. Part IV. Nitration by dinitrogen pentoxide in aprotic solvents. J. Chem. Soc. 1950, 2452–2466. [15]. Gold, V.; Hughes, E. D.; Ingold, C. K. 496. Kinetics and mechanism of aromatic nitration. Part V. Nitration by acyl nitrates, particularly by benzoyl nitrate. J. Chem. Soc. 1950, 2467–2473. mailto:shihc@mail.tsinghua.edu.cn https://orcid.org/0000-0001-7505-4976 52 Hongchang Shi / European Journal of Chemistry 14 (1) (2023) 39-52 2023 – European Journal of Chemistry – CC BY NC – DOI: 10.5155/eurjchem.14.1.39-52.2340 [16]. Gillespie, R. J.; Hughes, E. D.; Ingold, C. K. 504. Cryoscopic measurements in nitric acid. Part I. The solutes dinitrogen pentoxide and water. The self-dissociation of nitric acid. J. Chem. Soc. 1950, 2552–2558. [17]. Ingold, C. K.; Millen, D. J.; Poole, H. G. 506. Vibrational spectra of ionic forms of oxides and oxy-acids of nitrogen. Part I. Raman-spectral evidence of the ionisation of nitric acid by perchloric, sulphuric, and selenic acids. Spectroscopic identification of the nitronium ion, NO2 +. J. Chem. Soc. 1950, 2576–2589. [18]. Ingold, C. K.; Millen, D. J. 510. Vibrational spectra of ionic forms of oxides and oxy-acids of nitrogen. Part V. Raman spectral evidence of the ionisation of dinitrogen pentoxide in nitric acid, and of the constitution of anhydrous nitric acid. J. Chem. Soc. 1950, 2612–2619. [19]. Bunton, C. A.; Hughes, E. D.; Ingold, C. K.; Jacobs, D. I. H.; Jones, M. H.; Minkoff, G. J.; Reed, R. I. 512. Kinetics and mechanism of aromatic nitration. Part VI. The nitration of phenols and phenolic ethers: the concomitant dealkylation of phenolic ethers. The role of nitrous acid. J. Chem. Soc. 1950, 2628–2656. [20]. Ingold, C. K. Structure and mechanism in organic chemistry; 2nd ed.; HarperCollins Distribution Services: Glasgow, Scotland, 1970. [21]. Benford, G. A.; Bunton, C. A.; Halbertstadt, E. S.; Hughes, E. D.; Ingold, C. K.; Minkoff, G. J.; Reed, R. I. Univalent electron transfers in aromatic nitration? Nature 1945, 156, 688–688. [22]. Sheats, G. F.; Strachan, A. N. Rates and activation energies of nitronium ion formation and reaction in the nitration of toluene in ∼78% sulphuric acid. Can. J. Chem. 1978, 56, 1280–1283. [23]. Politzer, P.; Jayasuriya, K.; Sjoberg, P.; Laurence, P. R. Properties of some possible intermediate stages in the nitration of benzene and toluene. J. Am. Chem. Soc. 1985, 107, 1174–1177. [24]. Olah, G. A.; Malhotra, R.; Narang, S. C. Nitration: Methods and mechanisms; Wiley-Interscience: Newy York, 1989. [25]. Cardoso, S. P.; Carneiro, J. W. de M. Nitração aromática: substituição eletrofílica ou reação com transferência de elétrons? Quim. Nova 2001, 24, 381–389. [26]. Gwaltney, S. R.; Rosokha, S. V.; Head-Gordon, M.; Kochi, J. K. Charge- transfer mechanism for electrophilic aromatic nitration and nitrosation via the convergence of (ab initio) molecular-orbital and Marcus-Hush theories with experiments. J. Am. Chem. Soc. 2003, 125, 3273–3283. [27]. Esteves, P. M.; De M Carneiro, J. W.; Cardoso, S. P.; Barbosa, A. G. H.; Laali, K. K.; Rasul, G.; Prakash, G. K. S.; Olah, G. A. Unified mechanistic concept of electrophilic aromatic nitration: convergence of computational results and experimental data. J. Am. Chem. Soc. 2003, 125, 4836–4849. [28]. Nieves-Quinones, Y.; Singleton, D. A. Dynamics and the regiochemistry of nitration of toluene. J. Am. Chem. Soc. 2016, 138, 15167–15176. [29]. Peluso, A.; Del Re, G. On the occurrence of an electron-transfer step in aromatic nitration. J. Phys. Chem. 1996, 100, 5303–5309. [30]. Chen, L.; Xiao, H.; Xiao, J.; Gong, X. DFT study on nitration mechanism of benzene with nitronium ion. J. Phys. Chem. A 2003, 107, 11440– 11444. [31]. Parker, V. D.; Kar, T.; Bethell, D. The polar mechanism for the nitration of benzene with nitronium ion: ab initio structures of intermediates and transition states. J. Org. Chem. 2013, 78, 9522–9525. [32]. Koleva, G.; Galabov, B.; Hadjieva, B.; Schaefer, H. F., 3rd; Schleyer, P. von R. An experimentally established key intermediate in benzene nitration with mixed acid. Angew. Chem. Int. Ed Engl. 2015, 54, 14123– 14127. [33]. Liljenberg, M.; Stenlid, J. H.; Brinck, T. Mechanism and regioselectivity of electrophilic aromatic nitration in solution: the validity of the transition state approach. J. Mol. Model. 2017, 24, 15. [34]. Frisch, M. J.; Trucks, G. W.; Schlegel, H. B.; Scuseria, G. E.; Robb, M. A.; Cheeseman, J. R.; Montgomery, J. A.; Vreven, T.; Kudin, K. N.; Burant, J. C.; Millam, J. M.; Iyengar, S. S.; Tomasi, J.; Barone, V.; Mennucci, B.; Cossi, M.; Scalmani, G.; Rega, N.; Petersson, G. A.; Nakatsuji, H.; Hada, M.; Ehara, M.; Toyota, K.; Fukuda, R.; Hasegawa, J.; Ishida, M.; Nakajima, T.; Honda, Y.; Kitao, O.; Nakai, H.; Klene, M.; Li, X.; Knox, J. E.; Hratchian, H. P.; Cross, J. B.; Adamo, C.; Jaramillo, J.; Gomperts, R.; Stratmann, R. E.; Yazyev, O.; Austin, A. J.; Cammi, R.; Pomelli, C.; Ochterski, J. W.; Ayala, P. Y.; Morokuma, K.; Voth, G. A.; Salvador, P.; Dannenberg, J. J.; Zakrzewski, V. G.; Dapprich, S.; Daniels, A. D.; Strain, M. C.; Farkas, O.; Malick, D. K.; Rabuck, A. D.; Raghavachari, K; Foresman, J. B.; Ortiz, J. V.; Cui, Q.; Baboul, A. G.; Clifford, S.; Cioslowski, J.; Stefanov, B. B.; Liu, G.; Liashenko, A.; Piskorz, P.; Komaromi, I.; Martin, R. L.; Fox, D. J.; Keith, T.; Al-Laham, M. A.; Peng, C. Y.; Nanayakkara, A.; Challacombe, M.; Gill, P. M. W.; Johnson, B.; Chen, W.; Wong, M. W.; Gonzalez, C.; Pople, J. A. Gaussian 16, revision B0.1., Gaussian, Inc., Wallingford CT, 2004. [35]. Henderson, T. M.; Izmaylov, A. F.; Scalmani, G.; Scuseria, G. E. Can short-range hybrids describe long-range-dependent properties? J. Chem. Phys. 2009, 131, 044108. [36]. Galano, A.; Alvarez-Idaboy, J. R. Kinetics of radical-molecule reactions in aqueous solution: a benchmark study of the performance of density functional methods. J. Comput. Chem. 2014, 35, 2019–2026. [37]. Zhao, Y.; Truhlar, D. G. The M06 suite of density functionals for main group thermochemistry, thermochemical kinetics, noncovalent interactions, excited states, and transition elements: two new functionals and systematic testing of four M06-class functionals and 12 other functionals. Theor. Chem. Acc. 2008, 120, 215–241. [38]. Shi, H. A solvent-catalyzed four-molecular two-path solvolysis mechanism of t-butyl chloride or bromide in water or alcohol derived by density functional theory calculation and confirmed by high- resolution electrospray ionization-mass spectrometry. React. Kinet. Mech. Catal. 2020, 129, 583–612. [39]. Fukui, K.; Yonezawa, T.; Shingu, H. A molecular orbital theory of reactivity in aromatic hydrocarbons. J. Chem. Phys. 1952, 20, 722–725. [40]. Fukui, K.; Yonezawa, T.; Nagata, C.; Shingu, H. Molecular orbital theory of orientation in aromatic, heteroaromatic, and other conjugated molecules. J. Chem. Phys. 1954, 22, 1433–1442. [41]. Fukui, K. Frontier orbitals and reaction paths: Selected papers of Kenichi Fukui: Selected papers of Kenichi Fukui; Fukui, K., Ed.; World Scientific Publishing: Singapore, Singapore, 1997. [42]. Coulson, C. A. Coulson 's Valence; 3rd ed.; Oxford University Press: London, England, 1979. [43]. Barone, V.; Cossi, M.; Tomasi, J. Geometry optimization of molecular structures in solution by the polarizable continuum model. J. Comput. Chem. 1998, 19, 404–417. [44]. Barone, V.; Cossi, M. Quantum calculation of molecular energies and energy gradients in solution by a conductor solvent model. J. Phys. Chem. A 1998, 102, 1995–2001. [45]. Cancès, E.; Mennucci, B.; Tomasi, J. Analytical derivatives for geometry optimization in solvation continuum models. II. Numerical applications. J. Chem. Phys. 1998, 109, 260–266. [46]. Tomasi, J.; Mennucci, B.; Cammi, R. Quantum mechanical continuum solvation models. Chem. Rev. 2005, 105, 2999–3093. [47]. Belson, D. J.; Strachan, A. N. Aromatic nitration in aqueous nitric acid. J Chem Soc Perkin Trans 2 1989, 15–19. [48]. Zhao, Y.; Schultz, N. E.; Truhlar, D. G. Design of density functionals by combining the method of constraint satisfaction with parametrization for thermochemistry, thermochemical kinetics, and noncovalent interactions. J. Chem. Theory Comput. 2006, 2, 364–382. [49]. Zhou, X.; He, C.; Zhang, Z.; Cao, C. Experimental investigation on nitration of benzene at different molar ratio of sulfuric acid and nitric acid, J. Qinghai Univ. 2010, 2010 (4), 12-15. [50]. Winkler, F. J. Reaction rates of isotopic molecules. VonL. Melander und W. H. saunders, Jr. Wiley, New York 1980. XIV, 391 S., geb. £ 16.30. Angew. Chem. Weinheim Bergstr. Ger. 1981, 93, 220–220. Copyright © 2023 by Authors. This work is published and licensed by Atlanta Publishing House LLC, Atlanta, GA, USA. The full terms of this license are available at http://www.eurjchem.com/index.php/eurjchem/pages/view/terms and incorporate the Creative Commons Attribution-Non Commercial (CC BY NC) (International, v4.0) License (http://creativecommons.org/licenses/by-nc/4.0). By accessing the work, you hereby accept the Terms. This is an open access article distributed under the terms and conditions of the CC BY NC License, which permits unrestricted non-commercial use, distribution, and reproduction in any medium, provided the original work is properly cited without any further permission from Atlanta Publishing House LLC (European Journal of Chemistry). No use, distribution, or reproduction is permitted which does not comply with these terms. Permissions for commercial use of this work beyond the scope of the License (http://www.eurjchem.com/index.php/eurjchem/pages/view/terms) are administered by Atlanta Publishing House LLC (European Journal of Chemistry). http://www.eurjchem.com/index.php/eurjchem/pages/view/terms http://creativecommons.org/licenses/by-nc/4.0 http://www.eurjchem.com/index.php/eurjchem/pages/view/terms 1. Introduction 2. Computational methods and frontier orbital theory 3. Results and discussions 3.1. Generation of NO2+ in textbook mechanism is a wrong description 3.2. Generating active intermediate NO2+ by Lewis collision 3.3. Acidification of NO2+ is a spontaneous poly(≥3)-molecular electrophilic substitution 3.4. Generating σ-complex intermediate by electrophilic addition of C6H6 and NO2+ 3.5. Last Step 3 of benzene nitration is a spontaneous Lewis acid-alkali neutralization 3.6. A corrected benzene nitration three-step mechanism Supporting information Disclosure statement CRediT authorship contribution statement ORCID and Email References PrintField10: PrintField11: PrintField12: PrintField13: PrintField14: PrintField15: PrintField16: PrintField17: PrintField18: PrintField19: PrintField110: PrintField111: PrintField112: PrintField113: PrintField20: PrintField21: PrintField22: PrintField23: PrintField24: PrintField25: PrintField26: PrintField27: PrintField28: PrintField29: PrintField210: PrintField211: PrintField212: PrintField213: