# Theoretical Study on the Mechanism for the Formation of Nitro Compounds in Red Oil

Authors: Meng-Ke Tian; Shuang-Ling Tang; Hong-Bin Tang; Xue-Hai Ju
Journal: Journal of Chemistry
 (2020)

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## Abstract

The mechanisms involved in reactions between methane,n-hexane, n-butanol, cyclohexane, and nitric acid were explored by density functional theory calculations. All the calculations in gas phase and n-tributyl phosphate (TBP) solvent were performed at the B3LYP/6–311++G∗∗ and CCSD(T)/6–311++G∗∗ levels of theory. The results showed that TBP has an important effect on the reactions between nitric acid and alkanes or butanol. The reactions were considered as that the radicals (·NO2 and ·NO3 radicals are formed via the HNO3 decomposition under irradiation) initiate the H-atom depletion of the reactants (R), and the produced radicals in red oil combine with ·NO2 radical to form the nitro compounds spontaneously. The rate constants of reactions R + ·NO2 and R + ·NO3 differ substantially, the rate constants of the latter being much larger than those of the former. In the reactions of R + ·NO3, the transition states and products are 20 kJ/mol and 100 kJ/mol or more stable than the reactants, respectively, but the reactions of R + ·NO2 need to overcome energy barriers over 25 kJ/mol. The formations of products mainly depend on the reactions of R + ·NO3. For the same type of alkanes (either chain or cyclic ones), the lower the relative stabilities of carbon-centered radicals are, the more reactive the alkanes are. Cyclohexane is the most competitive species, followed by n-butanol, n-alkanes, and methane which are the least competitive.


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## Body

## 1. Introduction

The uranium fuel assembly unloaded from the nuclear reactor is called spent fuel. Some organic solvents liken-tributyl phosphate (TBP) and diluents, such as paraffin and cyclohexane, are used to recycle uranium from the spent fuel by the application of the Plutonium Uranium Extraction process [1–6]. The so-called “red oil” was found following several accidents occurring when organic materials inadvertently get into the equipment and overheat with uranyl nitrate and/or nitric acid at uranium processing facilities. However, only some organic compounds can react with uranyl nitrate and/or nitric acid, forming the red oil [3, 7–10]. Since more accidents have happened due to the formation and violent decomposition of red oil [4, 8–10], there was a dawning realization that the formation and decomposition of red oil have become a risk. The safety problem of red oil appealed researchers’ attention, and more researchers worldwide started to carry out investigations with the hope of realizing the safe operating conditions.At present, many investigations have been performed to discuss the formation and decomposition of red oil experimentally. In some accidents, the thermal decomposition of TBP was considered of triggering the thermal release reactions in the nuclear fuel reprocessing plant [3, 9]. And in some other accidents, the cause of the intense exothermic process was thought to be the oxidation of nitric acid in red oil [1, 3, 9–11]. Therefore, researchers studied the degradation of TBP or the thermal reaction between TBP and nitric acid. Smitha et al. reported the reaction of TBP with nitric acid at different acid concentrations [12–15]; the influences of diluents on the reactions and the behaviors of heat emission were also studied previously [5, 16–23]. Nazin et al. reported thermal explosions in mixtures of TBP with nitric acid [14, 24]. And Gordon et al. studied the decomposition of red oil by simulating these accidents conditions experimentally [1, 7]. Kumar et al. also reported the thermal decomposition of red oil with nitric acid [25]. Some works were also performed under radiations [26–28].However, there are majority of investigations concerned with red oil experimentally, which only focus on the degradation of TBP or TBP/HNO3 system, as well as the factors that influence these reactions. The nitrogen-containing organic materials are the most undesirable waste tank components in the “red oil” accidents, since they are energetic species in their own right [3, 7]. However, there are limited investigations about them. Therefore, we performed quantum chemical computations to study the formation of nitro compounds when methane (CH4), n-hexane (n-C6H14), n-butanol (n-C4H9OH), and cyclohexane (c-C6H12) are mixed with nitric acid (HNO3) in TBP as solvent. The whole reactions taking place among these components are as the following:(1)CH4+HNO3⟶CH3NO2+H2O(2a)n−C6H14+HNO3⟶CH3CH25NO2+H2O(2b)n−C6H14+HNO3⟶CH3CHNO2CH23CH3+H2O(2c)n−C6H14+HNO3⟶CH3CH2CHNO2CH22CH3+H2O(3)n−C4H9OH+HNO3⟶n−C4H9ONO2+H2O(4)c−C6H12+HNO3⟶c−C6H11NO2+H2OThe reaction mechanisms of these reactions are discussed in the following sections, and we hope to forecast the feasible reactions in the red oil system consisting of more complex components and to provide guidance for the safety problem.


## 2. Computational Methods

All of the geometrical structures including reactants, transition states, and products involved in red oil were optimized at the B3LYP/6-311++G∗∗ level of theory. It has been proved that the B3LYP method can provide relative accurate geometries for both inorganic and organic systems [29, 30]. To verify the correct connections among the transition states, corresponding reactants, and products, the intrinsic reaction coordinates (IRC) were determined at the same level. In order to get more accurate relative energies, single point energies (SPE) of reactants, transition states, and products were calculated at the CCSD(T)/6-311+G∗∗ level based on the optimized geometries at the B3LYP/6-311++G∗∗ level. The single point energies were used for the discussions unless otherwise stated. All the calculations were performed with the Gaussian 09 set of programs.The rate constants of all the pathways were obtained by using the Eyring expression:(5)k=kBThP0RT1−neΔS≠/R−ΔH≠/RT.in whichkB refers to the Boltzmann constant of 1.38064 × 10−23 J·K−1, h refers to the Planck constant of 6.6260696 × 10−34 J·s, T is the temperature, n is the sum of computation coefficient for all reactants, P0 is the pressure of 1.0 × 105 Pa, R is molar gas constant of 8.314 J·mol−1·K−1, and ∆S≠ and ∆H≠ are the entropy differences and enthalpy differences between the transition states and corresponding reactants, respectively.


## 3. Results and Discussion

Observing the reactions (1) to (4) listed above, it is easily found that the nitro compounds are produced through the nitro-substitution. However, alkanes or butanol cannot react with nitric acids directly, so an active species is needed to trigger the C-H bond cleavage and then react with nitric acids. It was pointed out above that the red oil system is under γ-ray irradiation. Therefore, it was associated that HNO3 can decompose into nitrogen dioxide radical (·NO2) and nitrogen trioxide radical (·NO3) under irradiation, which initiate the subsequent reactions. Thus the reactions are divided into three steps. In the following sections, we only discussed the results obtained in the gas phase unless explicitly stated.


### 3.1. Formation of Nitrogen Dioxide Radical (NO2) and Nitrogen Trioxide Radical (·NO3)

As depicted in Figure1, where R, P, and TS denote the reactant, product, and the transition state, respectively, Pathn represents the reaction pathway, and the initial step is the generation of ·NO2 and·NO3 radicals. There are three possible generation pathways: (i) the rupture of N-O(H) bond of HNO3 leads to ·OH and ·NO2 radicals (Path 1); then the OH radical reacts with HNO3 leading to H2O and NO3 radical (Path 12a) or H2O2 and ·NO2 radical (Path 12b); (ii) the protonated HNO3, after dehydration, reacts with NO3− ion leading to the·NO2 and ·NO3 radicals (Path 2, Path 13); (iii) the dehydration reaction between HNO3 molecules and leads to ·NO2 and ·NO3 radicals and H2O molecule (Path 3, Path 13). Clearly, all the pathways to form radicals occur via bond cleavage under γ-ray irradiation. It should be pointed out that HNO3 is ionized into H+ and NO3− ions in the red oil system, which result in HNO3 molecule protonation firstly, and then protonated HNO3 reacts with NO3− ion via Path 2 and Path 13. Besides, we failed to obtain the transition state of N2O⋯NO2, but it is well known that N2O5 is a highly reactive species, so its dissociation energy at the B3LYP/6–311++G∗∗ level is used for the following discussions.Figure 1
Generation of radicals in the dissociation of HNO3.For the present red oil system, the structures of transition states are depicted in Figure2. The activation free energies of transition states TS1, TS12a, TS12b, TS2, and TS3 are 284.03 kJ/mol, 29.94 kJ/mol, 104.51 kJ/mol, 239.21 kJ/mol, and 166.78 kJ/mol, respectively. Though the activation energies are high, they can be overcome easily under γ-ray irradiation. The energies of the products are 190.32 kJ/mol, 84.95 kJ/mol, and 35.17 kJ/mol higher than corresponding reactants for Path 1, Path 2, and Path 3, respectively. Surely, Path 3 ⟶ Path 12 is the most feasible pathway, forming the ·NO2 or ·NO3 radicals. The results can be understood from transition states listed in Figure 2 (TS1, TS2, and TS3). The original N-O bond changes from 1.416 Å in HNO3 to 1.588 Å in TS1 and 1.565 Å in TS2, while the N-O bond is 1.949 Å in TS3. The N-O bond lengths indicate the N-O bond interaction is weak in TS3, but the interactions are strong in TS1 and TS2, while the O-H bond interaction in TS3 (1.355 Å) is slightly weaker than that of TS2 (O-H bonds lengths are 1.276 Å and 1.274 Å). Therefore, it is easier for TS3 to form radicals.Figure 2
Optimized structures of transition states at the B3LYP/6-311++G∗∗ level in gas phase. Bond lengths are in Angstroms and angles in degrees. The optimized geometrical structures in TBP solvent are similar. (a) TS1. (b) TS2. (c) TS3. (d) TS12a. (e) TS12b. (f) TS4. (g) TS5. (h) TS6a. (i) TS6b. (j) TS6c. (k) TS7a. (l) TS7b. (m) TS7c. (n) TS8. (o) TS9. (p) TS10.
(a)(b)(c)(d)(e)(f)(g)(h)(i)(j)(k)(l)(m)(n)(o)(p)


### 3.2. Attacks of Radicals to Alkanes or Butanol

The second step (Figure3) is the attack of ·NO2 or ·NO3 radical on the alkanes or butanol, which leads to direct intermolecular H-shift from carbon or oxygen atom to ·NO2 or ·NO3 radical. All of the reactions can be written as follows:(6)R+NO2NO3⟶R+HNO2HNO3where R represents reactants (alkanes or butanol). When the ·NO2 radical attacks the hydrogen atom of OH or CH, the isomer products cis-HONO, trans-HONO, and HNO2 can be formed. The activation energies of the reactions R + ·NO2 are listed in Table 1, in which the symbols a, b, and c mean the products HNO2 in different geometrical structures, respectively. The reaction pathways b and c are more competitive than Path a. Meanwhile, Pathb plays a slightly more important role than Pathc. Though the activation energies of these three pathways differ greatly, the reaction mechanisms are similar. There is only the oxygen atom acting as an attacking atom in the ·NO3 radical. From the viewpoints expressed above, we mainly discussed the reactions of ·NO2 radical in Pathb or ·NO3 radical reacting with alkanes or butanol.Figure 3
H-depletion by radicals.Table 1
Activation free energies (in kJ/mol) of reactions between ·NO2 radical and alkanes or butanol in different pathways∗.
ReactantsΔGa≠ΔGb≠ΔGc≠R4172.94151.92165.91R6a161.77140.93144.20R6b148.81128.72127.67R6c150.20129.26130.14R8147.08129.92141.41R1060.0137.8339.46∗Subscripts a, b, and c in ∆G≠ denote the products of trans-HONO, cis-HONO, and HNO2, respectively.The reaction mechanisms between ·NO2 radical and alkanes or butanol can be described as follows. The reactions of R + ·NO2 occur via the formation of van der Waals complexes firstly. ·NO2 radical attaches to H-atom of alkanes or butanol via hydrogen bond interaction in these van der Waals complexes. Then, H-atom transfers from alkanes or butanol to ·NO2 radical through the transition states TSn leading to other van der Waals complexes. In these van der Waals complexes, there is a hydrogen bond interaction between HNO2 molecule and the alkane or butanol radical. At last, the HNO2 molecule and alkane or butanol radical formed via the van der Waals’ force weaken. The reaction mechanisms of R + ·NO3 are a bit different from those of reactions R + ·NO2. The ·NO3 radical attacks H-atom of alkanes or butanol leading to transition states TSn directly, then producing HNO3 and a radical.The geometrical structures of transition states (TS4 ∼ TS10) are shown in Figure 2 and the activation energies, enthalpies, and free energies (∆E≠, ∆H≠ and ∆G≠) of these transition states are listed in Table 2. However, we failed to get the transition state of reaction c-C6H12 + ·NO3 at B3LYP/6-311++G∗∗ level. Thus, the transition state of c−C6H11⋯H⋯O3 is not listed here. It is found that the relative energies of reactions R + ·NO2 are higher than those of reactions R + ·NO3, which can be explained by the changes of C-H or O-H bond lengths in transition states. The O-H bond lengths in transition states RṄO2 are shorter than those in transition states RṄO3. On the contrary, the H-C bond lengths in transition states RṄO2 are longer than those in transition states RṄO3.Table 2
Activation energies, enthalpies, and free energies (∆E≠, ∆H≠, and ∆G≠ in kJ/mol) of transition states at B3LYP/6-311++G∗∗ level of theory in the gas phase.
Transition states∆E≠∆H≠∆G≠TS4124.77122.34151.92TS549.1145.7680.78TS6a103.07102.93140.93TS6b88.8788.88128.73TS6c89.5589.66129.26TS7a24.4123.4366.52TS7b10.389.0754.67TS7c10.188.8555.13TS890.6189.45129.92TS9−0.13−2.7246.25TS101.656.4037.83


### 3.3. Formation of Nitro Compounds

These radicals formed from the above steps combine with each other and form nitro compounds spontaneously (Figure4, where the symbol L means the last reaction between radicals to generate the nitro product). For the reactions n-C6H14 + HNO3, it has the isomer products CH3(CH2)5NO2, CH3CH(NO2)(CH2)3CH3, and CH3CH2CH(NO2)(CH2)2CH3.Figure 4
Formation of nitro compounds.Single point energies in the gas phase (Table3) calculated at the CCSD (T)/6-311++G∗∗ level show that the products of these reactions are 129.2 kJ/mol, 145.3 kJ/mol, 154.5 kJ/mol, 153.6 kJ/mol, 238.70 kJ/mol, and 17.2 kJ/mol more stable than corresponding reactants, respectively, for reactions (1) to (4).Table 3
Single point energies (in a.u.) of reactants and products of the whole reactions.
Reactants or productsSingle point energiesGas phaseTBP solventHNO3−280.353196−280.358935CH4−40.406259−40.406399n-C6H14−236.470822−236.471107n-C4H9OH−233.122168−233.126748c-C6H12−235.231335−235.231583H2O−76.286534−76.293025CH3NO2−244.516677−244.523768CH3(CH2)5NO2−440.590342−440.596577CH3CH(NO2)(CH2)3CH3−440.596533−440.602475CH3CH2CH(NO2)(CH2)2CH3−440.597671−440.603322n-C4H9ONO2−437.199490−437.204375c-C6H11NO2−439.392001−439.397493


### 3.4. Energies along the Reaction Pathways and Rate Constants

According to the discussions above, the differences among the mechanisms of reactionsR + ·NO2/·NO3 are the second step. We mainly discussed the energies and rate constants in the second step in this section. Figure 5 provides the single point energies along the reaction pathways, where the symbols Min and Mln represent van der Waals complexes, and the energies of reactants are set to zero for reference. As seen from these figures, the products of reactions R + ·NO3 are more stable than the corresponding reactants, and the stability of the products in the reactions R + ·NO3 is in the order P9 > P7b > P7c > P7a > P5. However, the energy barriers of transition states RṄO3 are less than ‒15 kJ/mol. The energies of products in reactions R + ·NO2 are higher than those of corresponding reactants, except for reaction c-C6H12 + ·NO2. The energy barriers of the products increase as follows: P8 (27.24), P6b (38.54), P6c (38.87), P6a (47.93), and P4 (57.70). Meanwhile, the energy barriers of transition states RṄO2 are over 100 kJ/mol, which are difficult to overcome at room temperature, expect for TS10 (22.92 kJ/mol). Therefore, the reactions R + ·NO3 are more competitive than reactions R + ·NO2 and all the reactions R + ·NO3 are kinetically feasible.Figure 5
The relative energy along the reaction pathways at CCSD (T)/6-311++G∗∗//B3LYP/6-311++G∗∗ level.The rate constants (K) of the reactions to form transition states at 298 K are listed in Table 4. It shows that TBP contributes to the reactions. The rate constants of the dissociation of N2O5 are 1.14 × 1010 K s−1 and 5.38 × 109 K s−1 in gas phase and TBP solvent, respectively. Surely, N2O5 can decompose easily at room temperature. The rate constants of the reactions to form transition states from 300 K to 500 K are shown in Figure 6. There is a linear relationship between ln (K) and 1/T. As can be seen in Figure 6(a), though the rate constant of TS1 or TS2 increases more than that of TS3 with increasing temperature, the rate constants of TS3 are higher than the others at the temperature from 300 K to 500 K. Hence, Path 3 ⟶ Path 12 plays the main role for the formations of ·NO2 and ·NO3 radicals. This is consistent with the conclusion in Section 3.2. Comparing the rate constants of transition states RṄO2 and RṄO3 in Figure 6(b), it can be seen that the rate constants differ greatly between them, and the attacking of alkanes or butanol by ·NO3 radical plays the dominant role, so we only discussed the rate constants of transition states RṄO3. Here we only show the rate constants of transition state c−C6H11⋯H⋯NO2 in Figure 6(b) because we failed to get the transition state c−C6H11⋯H⋯NO2 (TS11). The rate constants of TS11 are much higher than that of c−C6H11⋯H⋯NO2 according to the rate constants trends. It could predict that the rate constants of TS11 are more than 1.22 × 103 mol‒1·L·s‒1 above 298 K. As a result, the rate constants of these transition states increase as TS11, TS9, TS7c, TS7b, TS7a, and TS5. The product c-C6H11NO2 is the most competitive among the products. Because the rate constants of reactions n-C6H14 + ·NO3 are in the order of TS7c ≈ TS7b > TS7a, the competitions of CH3CH(NO2)(CH2)3CH3 and CH3CH2CH(NO2)(CH2)2CH3 are close to each other, and both of them are less competitive than c-C6H11NO2 and n-C4H9ONO2. The product CH3(CH2)5NO2 is only more competitive than CH3NO2, and the competition of CH3NO2 is negligible. The cyclic alkanes are the easiest to form nitro compound, followed by n-butanol, and n-alkanes are the least reactive to form the nitro compounds. That is consistent with the previous studies [1, 3, 7, 14]. It can be also found that the long n-alkanes are easier to react with nitric acid to form the nitro compound than those of the short ones.Table 4
The rate constantsK (TS1, TS2 in K s‒1 and the others in mol−1·L·s−1) of reactions involved in the red oil system at 298 K in the gas phase or TBP solvent.
Transition statesRate constantsGas phaseTBP solventTS11.07 × 10−371.52 × 10−35TS27.65 × 10−304.19 × 10−27TS39.28 × 10−198.23 × 10−15TS43.71 × 10−162.43 × 10−15TS51.08 × 10−36.46 × 10−2TS6a3.13 × 10−143.13 × 10−14TS6b6.58 × 10−125.41 × 10−11TS6c3.48 × 10−122.87 × 10−11TS7a0.349.08TS7b40.657.47 × 102TS7c33.771.35 × 103TS82.66 × 10−121.32 × 10−12TS91.21 × 1031.70 × 104TS103.63 × 1045.58 × 105Figure 6
Rate constants of radical (·NO2 or ·NO3) formations (a) and reactions between radicals and alkanes or butanol (b) in gas phase at B3LYP/6-311++G∗∗ level.
(a)(b)


### 3.5. Relative Stabilities of Carbon-Centered Radicals and Reactivities of the Alkanes

For the carbon-centered radicals, their relative stabilities (E) were obtained by using the expression [31](7)E=ΔH0+∑​ΔH1+∑n−22ΔHn22.4−2,where ΔH is the energy contribution of a group to the relative stability. The number 0 represents the center C-atom (C0) of a radical that an H-atom is depleted. Number 1 is the C-atom attached to the C0-atom directly, and the other numbers n are the n’th C-atom attached to the C0-atom. The energy contributions of the groups and relative stabilities of carbon-centered radicals are represented in Tables 5 and 6.Table 5
Energy contribution of a group to the relative stability of a radical in kJ/mol [31].
GroupEnergy contributionĊH331.32−ĊH235.82−CH2-−4.93−ĊH-37.45CH3-−10.20——Table 6
Relative stabilities of carbon-centered radicals in kJ/mol.
Carbon-centered radicalRelative stabilityActivation energyĊH3 (·R4)31.32124.77ĊH2 (CH2)4CH3 (·R6a)23.84103.07CH3ĊH (CH2)3CH3 (·R6b)16.1788.87CH3CH2ĊH (CH2)2CH3 (·R6c)16.2889.55(·R10)19.201.65∗R represents carbon-centered radical.As can be seen in Table6, the relative stabilities of carbon-centered radicals are in the order of ·R6b ≈ ·R6c < ·R10 < ·R6a < ·R4. In our calculations, the reactivities between alkanes and nitric acid decrease by the order of Path 10 > Path 6c > Path 6b > Path 6a > Path 4. It is worth noting that the competitions for the formation of CH3CH (NO2)(CH2)3CH3 and CH3CH2CH(NO2)(CH2)2CH3 are similar. In general, the lower the relative stabilities of carbon-centered radicals, the more competitive the reactions between nitric acid and alkanes. The exception is the ·R10 radicals.The relative stability of carbon-centered radical depends on the energy contributions of groups in the radical. The energy contributions of groups are related to their structures and relative positions to the C0-atom. As a result, for the chain and cyclic alkanes with the same number of C-atoms, the relative stabilities of their corresponding carbon-centered radicals may differ slightly. However, the competitions of reactions depend on their activation energies. Comparing the activation energies for the formation of ·R6 and ·R10 radicals (Table 6), their activation energies differ greatly. Though there are small differences of relative stabilities between chain and cyclic carbon-centered radicals, there are still large differences in their reactivities. Therefore, the reactivities of the same type of alkanes (either chain or cyclic alkanes) reacting with nitric acid can be speculated by comparing the relative stabilities of carbon-centered radicals. The lower the relative stabilities of carbon-centered radicals are, the more reactive the alkanes are. However, the reactivities of different type of alkanes cannot be determined by the relative stabilities of their corresponding radicals.


## 3.1. Formation of Nitrogen Dioxide Radical (NO2) and Nitrogen Trioxide Radical (·NO3)

As depicted in Figure1, where R, P, and TS denote the reactant, product, and the transition state, respectively, Pathn represents the reaction pathway, and the initial step is the generation of ·NO2 and·NO3 radicals. There are three possible generation pathways: (i) the rupture of N-O(H) bond of HNO3 leads to ·OH and ·NO2 radicals (Path 1); then the OH radical reacts with HNO3 leading to H2O and NO3 radical (Path 12a) or H2O2 and ·NO2 radical (Path 12b); (ii) the protonated HNO3, after dehydration, reacts with NO3− ion leading to the·NO2 and ·NO3 radicals (Path 2, Path 13); (iii) the dehydration reaction between HNO3 molecules and leads to ·NO2 and ·NO3 radicals and H2O molecule (Path 3, Path 13). Clearly, all the pathways to form radicals occur via bond cleavage under γ-ray irradiation. It should be pointed out that HNO3 is ionized into H+ and NO3− ions in the red oil system, which result in HNO3 molecule protonation firstly, and then protonated HNO3 reacts with NO3− ion via Path 2 and Path 13. Besides, we failed to obtain the transition state of N2O⋯NO2, but it is well known that N2O5 is a highly reactive species, so its dissociation energy at the B3LYP/6–311++G∗∗ level is used for the following discussions.Figure 1
Generation of radicals in the dissociation of HNO3.For the present red oil system, the structures of transition states are depicted in Figure2. The activation free energies of transition states TS1, TS12a, TS12b, TS2, and TS3 are 284.03 kJ/mol, 29.94 kJ/mol, 104.51 kJ/mol, 239.21 kJ/mol, and 166.78 kJ/mol, respectively. Though the activation energies are high, they can be overcome easily under γ-ray irradiation. The energies of the products are 190.32 kJ/mol, 84.95 kJ/mol, and 35.17 kJ/mol higher than corresponding reactants for Path 1, Path 2, and Path 3, respectively. Surely, Path 3 ⟶ Path 12 is the most feasible pathway, forming the ·NO2 or ·NO3 radicals. The results can be understood from transition states listed in Figure 2 (TS1, TS2, and TS3). The original N-O bond changes from 1.416 Å in HNO3 to 1.588 Å in TS1 and 1.565 Å in TS2, while the N-O bond is 1.949 Å in TS3. The N-O bond lengths indicate the N-O bond interaction is weak in TS3, but the interactions are strong in TS1 and TS2, while the O-H bond interaction in TS3 (1.355 Å) is slightly weaker than that of TS2 (O-H bonds lengths are 1.276 Å and 1.274 Å). Therefore, it is easier for TS3 to form radicals.Figure 2
Optimized structures of transition states at the B3LYP/6-311++G∗∗ level in gas phase. Bond lengths are in Angstroms and angles in degrees. The optimized geometrical structures in TBP solvent are similar. (a) TS1. (b) TS2. (c) TS3. (d) TS12a. (e) TS12b. (f) TS4. (g) TS5. (h) TS6a. (i) TS6b. (j) TS6c. (k) TS7a. (l) TS7b. (m) TS7c. (n) TS8. (o) TS9. (p) TS10.
(a)(b)(c)(d)(e)(f)(g)(h)(i)(j)(k)(l)(m)(n)(o)(p)


## 3.2. Attacks of Radicals to Alkanes or Butanol

The second step (Figure3) is the attack of ·NO2 or ·NO3 radical on the alkanes or butanol, which leads to direct intermolecular H-shift from carbon or oxygen atom to ·NO2 or ·NO3 radical. All of the reactions can be written as follows:(6)R+NO2NO3⟶R+HNO2HNO3where R represents reactants (alkanes or butanol). When the ·NO2 radical attacks the hydrogen atom of OH or CH, the isomer products cis-HONO, trans-HONO, and HNO2 can be formed. The activation energies of the reactions R + ·NO2 are listed in Table 1, in which the symbols a, b, and c mean the products HNO2 in different geometrical structures, respectively. The reaction pathways b and c are more competitive than Path a. Meanwhile, Pathb plays a slightly more important role than Pathc. Though the activation energies of these three pathways differ greatly, the reaction mechanisms are similar. There is only the oxygen atom acting as an attacking atom in the ·NO3 radical. From the viewpoints expressed above, we mainly discussed the reactions of ·NO2 radical in Pathb or ·NO3 radical reacting with alkanes or butanol.Figure 3
H-depletion by radicals.Table 1
Activation free energies (in kJ/mol) of reactions between ·NO2 radical and alkanes or butanol in different pathways∗.
ReactantsΔGa≠ΔGb≠ΔGc≠R4172.94151.92165.91R6a161.77140.93144.20R6b148.81128.72127.67R6c150.20129.26130.14R8147.08129.92141.41R1060.0137.8339.46∗Subscripts a, b, and c in ∆G≠ denote the products of trans-HONO, cis-HONO, and HNO2, respectively.The reaction mechanisms between ·NO2 radical and alkanes or butanol can be described as follows. The reactions of R + ·NO2 occur via the formation of van der Waals complexes firstly. ·NO2 radical attaches to H-atom of alkanes or butanol via hydrogen bond interaction in these van der Waals complexes. Then, H-atom transfers from alkanes or butanol to ·NO2 radical through the transition states TSn leading to other van der Waals complexes. In these van der Waals complexes, there is a hydrogen bond interaction between HNO2 molecule and the alkane or butanol radical. At last, the HNO2 molecule and alkane or butanol radical formed via the van der Waals’ force weaken. The reaction mechanisms of R + ·NO3 are a bit different from those of reactions R + ·NO2. The ·NO3 radical attacks H-atom of alkanes or butanol leading to transition states TSn directly, then producing HNO3 and a radical.The geometrical structures of transition states (TS4 ∼ TS10) are shown in Figure 2 and the activation energies, enthalpies, and free energies (∆E≠, ∆H≠ and ∆G≠) of these transition states are listed in Table 2. However, we failed to get the transition state of reaction c-C6H12 + ·NO3 at B3LYP/6-311++G∗∗ level. Thus, the transition state of c−C6H11⋯H⋯O3 is not listed here. It is found that the relative energies of reactions R + ·NO2 are higher than those of reactions R + ·NO3, which can be explained by the changes of C-H or O-H bond lengths in transition states. The O-H bond lengths in transition states RṄO2 are shorter than those in transition states RṄO3. On the contrary, the H-C bond lengths in transition states RṄO2 are longer than those in transition states RṄO3.Table 2
Activation energies, enthalpies, and free energies (∆E≠, ∆H≠, and ∆G≠ in kJ/mol) of transition states at B3LYP/6-311++G∗∗ level of theory in the gas phase.
Transition states∆E≠∆H≠∆G≠TS4124.77122.34151.92TS549.1145.7680.78TS6a103.07102.93140.93TS6b88.8788.88128.73TS6c89.5589.66129.26TS7a24.4123.4366.52TS7b10.389.0754.67TS7c10.188.8555.13TS890.6189.45129.92TS9−0.13−2.7246.25TS101.656.4037.83


## 3.3. Formation of Nitro Compounds

These radicals formed from the above steps combine with each other and form nitro compounds spontaneously (Figure4, where the symbol L means the last reaction between radicals to generate the nitro product). For the reactions n-C6H14 + HNO3, it has the isomer products CH3(CH2)5NO2, CH3CH(NO2)(CH2)3CH3, and CH3CH2CH(NO2)(CH2)2CH3.Figure 4
Formation of nitro compounds.Single point energies in the gas phase (Table3) calculated at the CCSD (T)/6-311++G∗∗ level show that the products of these reactions are 129.2 kJ/mol, 145.3 kJ/mol, 154.5 kJ/mol, 153.6 kJ/mol, 238.70 kJ/mol, and 17.2 kJ/mol more stable than corresponding reactants, respectively, for reactions (1) to (4).Table 3
Single point energies (in a.u.) of reactants and products of the whole reactions.
Reactants or productsSingle point energiesGas phaseTBP solventHNO3−280.353196−280.358935CH4−40.406259−40.406399n-C6H14−236.470822−236.471107n-C4H9OH−233.122168−233.126748c-C6H12−235.231335−235.231583H2O−76.286534−76.293025CH3NO2−244.516677−244.523768CH3(CH2)5NO2−440.590342−440.596577CH3CH(NO2)(CH2)3CH3−440.596533−440.602475CH3CH2CH(NO2)(CH2)2CH3−440.597671−440.603322n-C4H9ONO2−437.199490−437.204375c-C6H11NO2−439.392001−439.397493


## 3.4. Energies along the Reaction Pathways and Rate Constants

According to the discussions above, the differences among the mechanisms of reactionsR + ·NO2/·NO3 are the second step. We mainly discussed the energies and rate constants in the second step in this section. Figure 5 provides the single point energies along the reaction pathways, where the symbols Min and Mln represent van der Waals complexes, and the energies of reactants are set to zero for reference. As seen from these figures, the products of reactions R + ·NO3 are more stable than the corresponding reactants, and the stability of the products in the reactions R + ·NO3 is in the order P9 > P7b > P7c > P7a > P5. However, the energy barriers of transition states RṄO3 are less than ‒15 kJ/mol. The energies of products in reactions R + ·NO2 are higher than those of corresponding reactants, except for reaction c-C6H12 + ·NO2. The energy barriers of the products increase as follows: P8 (27.24), P6b (38.54), P6c (38.87), P6a (47.93), and P4 (57.70). Meanwhile, the energy barriers of transition states RṄO2 are over 100 kJ/mol, which are difficult to overcome at room temperature, expect for TS10 (22.92 kJ/mol). Therefore, the reactions R + ·NO3 are more competitive than reactions R + ·NO2 and all the reactions R + ·NO3 are kinetically feasible.Figure 5
The relative energy along the reaction pathways at CCSD (T)/6-311++G∗∗//B3LYP/6-311++G∗∗ level.The rate constants (K) of the reactions to form transition states at 298 K are listed in Table 4. It shows that TBP contributes to the reactions. The rate constants of the dissociation of N2O5 are 1.14 × 1010 K s−1 and 5.38 × 109 K s−1 in gas phase and TBP solvent, respectively. Surely, N2O5 can decompose easily at room temperature. The rate constants of the reactions to form transition states from 300 K to 500 K are shown in Figure 6. There is a linear relationship between ln (K) and 1/T. As can be seen in Figure 6(a), though the rate constant of TS1 or TS2 increases more than that of TS3 with increasing temperature, the rate constants of TS3 are higher than the others at the temperature from 300 K to 500 K. Hence, Path 3 ⟶ Path 12 plays the main role for the formations of ·NO2 and ·NO3 radicals. This is consistent with the conclusion in Section 3.2. Comparing the rate constants of transition states RṄO2 and RṄO3 in Figure 6(b), it can be seen that the rate constants differ greatly between them, and the attacking of alkanes or butanol by ·NO3 radical plays the dominant role, so we only discussed the rate constants of transition states RṄO3. Here we only show the rate constants of transition state c−C6H11⋯H⋯NO2 in Figure 6(b) because we failed to get the transition state c−C6H11⋯H⋯NO2 (TS11). The rate constants of TS11 are much higher than that of c−C6H11⋯H⋯NO2 according to the rate constants trends. It could predict that the rate constants of TS11 are more than 1.22 × 103 mol‒1·L·s‒1 above 298 K. As a result, the rate constants of these transition states increase as TS11, TS9, TS7c, TS7b, TS7a, and TS5. The product c-C6H11NO2 is the most competitive among the products. Because the rate constants of reactions n-C6H14 + ·NO3 are in the order of TS7c ≈ TS7b > TS7a, the competitions of CH3CH(NO2)(CH2)3CH3 and CH3CH2CH(NO2)(CH2)2CH3 are close to each other, and both of them are less competitive than c-C6H11NO2 and n-C4H9ONO2. The product CH3(CH2)5NO2 is only more competitive than CH3NO2, and the competition of CH3NO2 is negligible. The cyclic alkanes are the easiest to form nitro compound, followed by n-butanol, and n-alkanes are the least reactive to form the nitro compounds. That is consistent with the previous studies [1, 3, 7, 14]. It can be also found that the long n-alkanes are easier to react with nitric acid to form the nitro compound than those of the short ones.Table 4
The rate constantsK (TS1, TS2 in K s‒1 and the others in mol−1·L·s−1) of reactions involved in the red oil system at 298 K in the gas phase or TBP solvent.
Transition statesRate constantsGas phaseTBP solventTS11.07 × 10−371.52 × 10−35TS27.65 × 10−304.19 × 10−27TS39.28 × 10−198.23 × 10−15TS43.71 × 10−162.43 × 10−15TS51.08 × 10−36.46 × 10−2TS6a3.13 × 10−143.13 × 10−14TS6b6.58 × 10−125.41 × 10−11TS6c3.48 × 10−122.87 × 10−11TS7a0.349.08TS7b40.657.47 × 102TS7c33.771.35 × 103TS82.66 × 10−121.32 × 10−12TS91.21 × 1031.70 × 104TS103.63 × 1045.58 × 105Figure 6
Rate constants of radical (·NO2 or ·NO3) formations (a) and reactions between radicals and alkanes or butanol (b) in gas phase at B3LYP/6-311++G∗∗ level.
(a)(b)


## 3.5. Relative Stabilities of Carbon-Centered Radicals and Reactivities of the Alkanes

For the carbon-centered radicals, their relative stabilities (E) were obtained by using the expression [31](7)E=ΔH0+∑​ΔH1+∑n−22ΔHn22.4−2,where ΔH is the energy contribution of a group to the relative stability. The number 0 represents the center C-atom (C0) of a radical that an H-atom is depleted. Number 1 is the C-atom attached to the C0-atom directly, and the other numbers n are the n’th C-atom attached to the C0-atom. The energy contributions of the groups and relative stabilities of carbon-centered radicals are represented in Tables 5 and 6.Table 5
Energy contribution of a group to the relative stability of a radical in kJ/mol [31].
GroupEnergy contributionĊH331.32−ĊH235.82−CH2-−4.93−ĊH-37.45CH3-−10.20——Table 6
Relative stabilities of carbon-centered radicals in kJ/mol.
Carbon-centered radicalRelative stabilityActivation energyĊH3 (·R4)31.32124.77ĊH2 (CH2)4CH3 (·R6a)23.84103.07CH3ĊH (CH2)3CH3 (·R6b)16.1788.87CH3CH2ĊH (CH2)2CH3 (·R6c)16.2889.55(·R10)19.201.65∗R represents carbon-centered radical.As can be seen in Table6, the relative stabilities of carbon-centered radicals are in the order of ·R6b ≈ ·R6c < ·R10 < ·R6a < ·R4. In our calculations, the reactivities between alkanes and nitric acid decrease by the order of Path 10 > Path 6c > Path 6b > Path 6a > Path 4. It is worth noting that the competitions for the formation of CH3CH (NO2)(CH2)3CH3 and CH3CH2CH(NO2)(CH2)2CH3 are similar. In general, the lower the relative stabilities of carbon-centered radicals, the more competitive the reactions between nitric acid and alkanes. The exception is the ·R10 radicals.The relative stability of carbon-centered radical depends on the energy contributions of groups in the radical. The energy contributions of groups are related to their structures and relative positions to the C0-atom. As a result, for the chain and cyclic alkanes with the same number of C-atoms, the relative stabilities of their corresponding carbon-centered radicals may differ slightly. However, the competitions of reactions depend on their activation energies. Comparing the activation energies for the formation of ·R6 and ·R10 radicals (Table 6), their activation energies differ greatly. Though there are small differences of relative stabilities between chain and cyclic carbon-centered radicals, there are still large differences in their reactivities. Therefore, the reactivities of the same type of alkanes (either chain or cyclic alkanes) reacting with nitric acid can be speculated by comparing the relative stabilities of carbon-centered radicals. The lower the relative stabilities of carbon-centered radicals are, the more reactive the alkanes are. However, the reactivities of different type of alkanes cannot be determined by the relative stabilities of their corresponding radicals.


## 4. Conclusion

The reactions of nitric acid with some alkanes or butanol in red oil were studied by the quantum mechanics method. All the calculations were performed in TBP solvent and gas phase. The calculated geometrical structures of the transition states showed that the TBP solvent can speed up all the reactions, and the rate constants of reactions provide insight into the formations of red oil components. The reactions are in three steps. The nitrogen dioxide radicals and nitrogen trioxide radicals form firstly, and then these radicals initiate the depletion of H-atom from alkanes or butanol; finally the generated radicals contact with each other and form the products. Though the energy barriers for the formations of·NO2 and ·NO3 radicals are high, they could be overcome easily under γ-ray irradiation. The energy barriers of reactions R + ·NO3 are much lower than those of reactions R + ·NO2, so the reactions R + ·NO3 are more competitive than the reactions R + ·NO2. Among these products, c-C6H11NO2 is more competitive than the others and is the easiest to form. CH3CH(NO2)(CH2)3CH3 and CH3CH2CH(NO2)(CH2)2CH3 are less competitive than c-C6H11NO2 and CH3(CH2)3ONO2. Since the energy barriers and rate constants of the rate-limiting step for the formation of CH3CH(NO2)(CH2)3CH3 and CH3CH2CH(NO2)(CH2)2CH3 are close to each other, the competition of them will depend on the actual experimental environment. Besides, the product CH3(CH2)5NO2 is only more competitive than CH3NO2, and the competition of product CH3NO2 is negligible. The reactivities of the same type of alkanes reacting with nitric acid can be speculated by comparing the relative stabilities of carbon-centered radicals. The lower the relative stabilities of carbon-centered radicals are, the more reactive the alkanes are. However, the reactivities of different type of alkanes cannot be determined by the relative stabilities of their corresponding radicals. In general, long n-alkanes could be easier than the shorter ones to form nitrogen-containing organic materials that play roles in the “red oil” accidents [3, 7] as a uranium recycling medium.



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