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

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 ( · NO 2 and · NO 3 radicals are formed via the HNO 3 decomposition under irradiation) initiate the H-atom depletion of the reactants ( R ), and the produced radicals in red oil combine with · NO 2 radical to form the nitro compounds spontaneously. The rate constants of reactions R + · NO 2 and R + · NO 3 diﬀer substantially, the rate constants of the latter being much larger than those of the former. In the reactions of R + · NO 3 , the transition states and products are 20kJ/mol and 100kJ/mol or more stable than the reactants, re-spectively, but the reactions of R + · NO 2 need to overcome energy barriers over 25kJ/mol. The formations of products mainly depend on the reactions of R + · NO 3 . 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.


Introduction
e uranium fuel assembly unloaded from the nuclear reactor is called spent fuel. Some organic solvents like ntributyl 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][2][3][4][5][6]. e 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][8][9][10]. Since more accidents have happened due to the formation and violent decomposition of red oil [4,[8][9][10], there was a dawning realization that the formation and decomposition of red oil have become a risk. e 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][10][11]. erefore, 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][13][14][15]; the influences of diluents on the reactions and the behaviors of heat emission were also studied previously [5,[16][17][18][19][20][21][22][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][27][28].
However, there are majority of investigations concerned with red oil experimentally, which only focus on the degradation of TBP or TBP/HNO 3 system, as well as the factors that influence these reactions. e 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. erefore, we performed quantum chemical computations to study the formation of nitro compounds when methane (CH 4 ), n-hexane (n-C 6 H 14 ), nbutanol (n-C 4 H 9 OH), and cyclohexane (c-C 6 H 12 ) are mixed with nitric acid (HNO 3 ) in TBP as solvent. e whole reactions taking place among these components are as the following: e 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.

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. e single point energies were used for the discussions unless otherwise stated. All the calculations were performed with the Gaussian 09 set of programs. e rate constants of all the pathways were obtained by using the Eyring expression: in which k B 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, P 0 is the pressure of 1.0 × 10 5 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.

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 c-ray irradiation. erefore, it was associated that HNO 3 can decompose into nitrogen dioxide radical (·NO 2 ) and nitrogen trioxide radical (·NO 3 ) under irradiation, which initiate the subsequent reactions. us the reactions are divided into three steps. In the following sections, we only discussed the results obtained in the gas phase unless explicitly stated. Figure 1, where R, P, and TS denote the reactant, product, and the transition state, respectively, Path n represents the reaction pathway, and the initial step is the generation of ·NO 2 and·NO 3 radicals.

Formation of Nitrogen Dioxide Radical (NO 2 ) and Nitrogen Trioxide Radical (·NO 3 ). As depicted in
ere are three possible generation pathways: (i) the rupture of N-O(H) bond of HNO 3 leads to ·OH and ·NO 2 radicals (Path 1); then the OH radical reacts with HNO 3 leading to H 2 O and NO 3 radical (Path 12a) or H 2 O 2 and ·NO 2 radical (Path 12b); (ii) the protonated HNO 3 , after dehydration, reacts with NO 3 − ion leading to the·NO 2 and ·NO 3 radicals (Path 2, Path 13); (iii) the dehydration reaction between HNO 3 molecules and leads to ·NO 2 and ·NO 3 radicals and H 2 O molecule (Path 3, Path 13). Clearly, all the pathways to form radicals occur via bond cleavage under c-ray irradiation. It should be pointed out that HNO 3 is ionized into H + and NO 3 − ions in the red oil system, which result in HNO 3 molecule protonation firstly, and then protonated HNO 3 reacts with NO 3 − ion via Path 2 and Path 13. Besides, we failed to obtain the transition state of N 2 O · · · NO 2 , but it is well known that N 2 O 5 is a highly reactive species, so its dissociation energy at the B3LYP/ 6-311++G * * level is used for the following discussions.
For the present red oil system, the structures of transition states are depicted in Figure 2.
e activation free energies of transition states TS1, TS12a, TS12b, TS2, and  respectively. Surely, Path 3 ⟶ Path 12 is the most feasible pathway, forming the ·NO 2 or ·NO 3 radicals. e results can be understood from transition states listed in Figure 2 Figure 3) is the attack of ·NO 2 or ·NO 3 radical on the alkanes or butanol, which leads to direct intermolecular H-shift from carbon or oxygen atom to ·NO 2 or ·NO 3 radical. All of the reactions can be written as follows: where R represents reactants (alkanes or butanol). When the ·NO 2 radical attacks the hydrogen atom of OH or CH, the isomer products cis-HONO, trans-HONO, and HNO 2 can be formed. e activation energies of the reactions R + ·NO 2 are listed in Table 1, in which the symbols a, b, and c mean the products HNO 2 in different geometrical structures, respectively. e reaction pathways b and c are more competitive than Path a. Meanwhile, Path b plays a slightly more important role than Path c. ough the activation energies of these three pathways differ greatly, the reaction mechanisms are similar. ere is only the oxygen atom acting as an attacking atom in the ·NO 3 radical. From the viewpoints expressed above, we mainly discussed the reactions of ·NO 2 radical in Path b or ·NO 3 radical reacting with alkanes or butanol. e reaction mechanisms between ·NO 2 radical and alkanes or butanol can be described as follows.
e reactions of R + ·NO 2 occur via the formation of van der Waals complexes firstly. ·NO 2 radical attaches to H-atom of alkanes or butanol via hydrogen bond interaction in these van der Waals complexes. en, H-atom transfers from alkanes or butanol to ·NO 2 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 HNO 2 molecule and the alkane or butanol radical. At last, the HNO 2 molecule and alkane or butanol radical formed via the van der Waals' force weaken. e reaction mechanisms of R + ·NO 3 are a bit different from those of reactions R + ·NO 2 . e ·NO 3 radical attacks H-atom of alkanes or butanol leading to transition states TSn directly, then producing HNO 3 and a radical. e 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-C 6 H 12 + ·NO 3 at B3LYP/6-311++G * * level. us, the transition state of c − C 6 H 11 · · · H · · · O 3 is not listed here. It is found that the relative energies of reactions R + ·NO 2 are higher than those of reactions R + ·NO 3 , which can be explained by the changes of C-H or O-H bond lengths in transition states. e O-H bond lengths in transition states RṄO 2 are shorter than those in transition states RṄO 3 . On the contrary, the H-C bond lengths in transition states RṄO 2 are longer than those in transition states RṄO 3 .

Formation of Nitro Compounds.
ese radicals formed from the above steps combine with each other and form nitro compounds spontaneously (Figure 4, where the symbol L means the last reaction between radicals to generate the nitro product). For the reactions n-C 6 H 14 + HNO 3 , it has the isomer products CH 3 (CH 2 ) 5 NO 2 , CH 3 CH(NO 2 ) (CH 2 ) 3 CH 3 , and CH 3 CH 2 CH(NO 2 )(CH 2 ) 2 CH 3 .

Energies along the Reaction Pathways and Rate Constants.
According to the discussions above, the differences among the mechanisms of reactions R + ·NO 2 /·NO 3 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 M i n and M l n 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 + ·NO 3 are more stable than the corresponding reactants, and the stability of the products in the reactions R + ·NO 3 is in the order P9 > P7b > P7c > P7a > P5. However, the energy barriers of transition states RṄO 3 are less than -15 kJ/mol. e energies of products in reactions R + ·NO 2 are higher than those of corresponding reactants, except for reaction c-C 6 H 12 + ·NO 2 . e 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 RṄO 2 are over 100 kJ/mol, which are difficult to overcome at room temperature, expect for TS10 (22.92 kJ/ mol). erefore, the reactions R + ·NO 3 are more competitive than reactions R + ·NO 2 and all the reactions R + ·NO 3 are kinetically feasible. e 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. e rate constants of the dissociation of N 2 O 5 are 1.14 × 10 10 K s −1 and 5.38 × 10 9 K s −1 in gas phase and TBP solvent, respectively. Surely, N 2 O 5 can decompose easily at room temperature. e rate constants of the reactions to form transition states from 300 K to 500 K are shown in Figure 6. ere 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 ·NO 2 and ·NO 3 radicals. is is consistent with the conclusion in Section 3.2. Comparing the rate constants of transition states RṄO 2 and RṄO 3 in Figure 6(b), it can be seen that the rate constants differ greatly between them, and the attacking of alkanes or butanol by ·NO 3 radical plays the dominant role, so we only discussed the rate constants of transition states RṄO 3 . Here we only show the rate constants of transition state c − C 6 H 11 · · · H · · · NO 2 in Figure 6(b) because we failed to get the transition state c− C 6 H 11 · · · H · · · NO 2 (TS11). e rate constants of TS11 are much higher than that of c − C 6 H 11 · · · H · · · NO 2 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. e product c-C 6 H 11 NO 2 is the most competitive among the products. Because the rate constants of reactions n-  Journal of Chemistry C 6 H 14 + ·NO 3 are in the order of TS7c ≈ TS7b > TS7a, the competitions of CH 3 CH(NO 2 )(CH 2 ) 3 CH 3 and CH 3 CH 2 CH(NO 2 )(CH 2 ) 2 CH 3 are close to each other, and both of them are less competitive than c-C 6 H 11 NO 2 and n-C 4 H 9 ONO 2 . e product CH 3 (CH 2 ) 5 NO 2 is only more competitive than CH 3 NO 2 , and the competition of CH 3 NO 2 is negligible. e 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. at 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.

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] E � ΔH 0 + where ΔH is the energy contribution of a group to the relative stability. e number 0 represents the center C-atom (C 0 ) of a radical that an H-atom is depleted. Number 1 is the C-atom attached to the C 0 -atom directly, and the other numbers n are the n'th C-atom attached to the C 0 -atom. e energy contributions of the groups and relative stabilities of carbon-centered radicals are represented in Tables 5 and 6. As can be seen in Table 6, the relative stabilities of carbon-centered radicals are in the order of ·R 6b ≈ ·R 6c < ·R 10 < ·R 6a < ·R 4 . 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 CH 3 CH (NO 2 )(CH 2 ) 3 CH 3 and CH 3 CH 2 CH(NO 2 )(CH 2 ) 2 CH 3 are similar. In general, the lower the relative stabilities of carbon-centered radicals, the more competitive the reactions between nitric acid and alkanes. e exception is the ·R 10 radicals.
e relative stability of carbon-centered radical depends on the energy contributions of groups in the radical. e energy contributions of groups are related to their structures and relative positions to the C 0 -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.
ough there are small differences of relative stabilities between chain and cyclic carbon-centered radicals, there are still large differences in their reactivities. erefore, 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. e 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.

Conclusion
e 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. e 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. e reactions are in three steps. e 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. ough the energy barriers for the formations of ·NO 2 and ·NO 3 radicals are high, they could be overcome easily under c-ray irradiation. e energy barriers of reactions R + ·NO 3 are much lower than those of reactions R + ·NO 2 , so the reactions R + ·NO 3 are more competitive than the reactions R + ·NO 2 . Among these products, c-C 6 H 11 NO 2 is more competitive than the others and is the easiest to form. CH 3 CH(NO 2 )(CH 2 ) 3 CH 3 and CH 3 CH 2 CH(NO 2 )(CH 2 ) 2 CH 3 are less competitive than c-C 6 H 11 NO 2 and CH 3 (CH 2 ) 3 ONO 2 . Since the energy barriers and rate constants of the rate-limiting step for the formation of CH 3 CH(NO 2 )(CH 2 ) 3 CH 3 and CH 3 CH 2 CH(NO 2 )(CH 2 ) 2 CH 3 are close to each other, the competition of them will depend on the actual experimental environment. Besides, the product CH 3 (CH 2 ) 5 NO 2 is only more competitive than CH 3 NO 2 , and the competition of product CH 3 NO 2 is negligible. e reactivities of the same type of alkanes reacting with nitric acid can be speculated by comparing the relative stabilities of carbon-centered radicals. e 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  Figure 6: Rate constants of radical (·NO 2 or ·NO 3 ) formations (a) and reactions between radicals and alkanes or butanol (b) in gas phase at B3LYP/6-311++G * * level.  the shorter ones to form nitrogen-containing organic materials that play roles in the "red oil" accidents [3,7] as a uranium recycling medium.

Data Availability
e data used to support the findings of this study are available from the corresponding author upon request.

Conflicts of Interest
e authors declare that they have no conflicts of interest.