A theoretical study of the activation of nitromethane under applied electric fields

Abstract

C–N activation is the key step of nitromethane (NM) decomposition. The energy landscape of C–N rupture under applied electric fields with various directions and strengths were first studied by using CCSD and CCSD(T) calculations. When the field is applied in the C → N direction, the activation energy barrier (E_a) increases under a weak field, but decreases when the field is strong enough. When the field is applied in the C ← N direction, E_a decreases with the field strength. The E_a may vanish when the field is strong enough. The applied field perpendicular to the C–N bond has little effect on E_a. The reactivity of NM under the fields was analyzed with local softness, and the variation of E_a with the direction and strength of the applied field was rationalized with electron density change on the C–N bond driven by the field. Our studies provide useful information for the process, transportation and storage of energetic materials in presence of electric fields.

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1. Introduction

A molecule may have new physical and chemical properties under an applied electric field. The field can cause electron or charge transfer^1–3 within a molecule or between molecules.⁴ Meanwhile, the electron redistribution, electronic energy level shift, as well as the changes in molecular structure driven by the field may lead to bond rupture,⁵ conformational transformation and isomerization processes in some cases.^6–8 Knowledge about the structure and property variation under an external field is important for the manufacture, storage and application of materials which are made of molecules. For example, electric fields were applied to analyze the surface elemental composition of materials using an atom probe tomography method,⁹ to control the H₂ uptake or release in nitrogen doped graphene,¹⁰ to adjust the molecular cooperativity of molecular clusters,¹¹ to enhance the wetting of apolar nanopores in nanoporous materials for absorbing more ions and water from electrolyte bath,¹² and to change the reactivity and aromaticity of nucleobases.¹³

In recent years many theoretical and experimental studies have been conducted to understand the effect of external electric fields on molecular structures and properties, and the applied fields have become a powerful tool for discovering new physical and chemical phenomena, and developing new materials.^14–31 The quantum-mechanical theory of field-induced chemistry was firstly developed by Kreuzer et al.,²¹ and have been used to address the kinetics of insulator and semiconductor clusters under electrostatic field.^22–25 The variations of cluster geometries, HOMO–LUMO gaps, and fragmentation paths with external field were studied with density functional theory (DFT) calculations. Hirao et al.²⁶ have found that the reaction rate, mechanism, and selectivity of nonheme iron(IV)-oxo species toward alkanes were impacted by an external electric field. Schirmer and Grimme²⁷ have assessed the accuracy of different functionals in DFT calculations for the hydrogen dissociation reaction in an electric field, and found the dissociation changes from bi-radical to zwitterionic under large strengths (F > 0.06 a.u.). Zhang et al.²⁸ suggested to use a negative electric field to facilitate the interaction of O₂ with Au-doped graphene substrate, and vice versa. In addition, Song et al.²⁹ employed DFT to study the adsorption and desorption of hydrogen on a Ca-decorated silicene in an external electric field. Rokob et al.³⁰ studied the heterolytic cleavage of H₂ polarized by a stronger field in the cavity of reactive intermediates. Park et al.³¹ investigated the electronic properties of bilayer graphene in different stackings under external electric fields. Fried et al.³² studied the electric field generated by the active sites of enzyme ketosteroid isomerase and its effect on the C=O bond activation using vibrational Stark effect spectroscopy, addressing a strong correlation between the magnitude of the electric field and the enzyme's catalytic rate.

Nitromethane (NM, CH₃NO₂) is one of the simplest organic nitro compound and also a momentous energetic material. Used as fuel, rocket propellant and raw material for preparing other high energy explosives, NM has low corrosive, fine security and stability and extensive practicability. In addition, NM is widely applied in various industrial processes, such as a monopropellant, a solvent for chemical processing and analysis, and a high-performance fuel additive for internal combustion engines and pulsed detonation engines.^33–36 Many theoretical and experimental studies^37–58 have focused on NM, for instance, its decomposition and isomerization,^37–46 explosion,^36,47 assembling,^48–50 interaction with carbon nanotubes,^51–53 as well as its behaviors under complex environment.^54–58

As one of important weak blasting explosives, the stability of CH₃NO₂ in the process of storage, transport and application are very important for safety. It is often exposed to environments with various external fields, such as an electric field. The existence of external electric field will definitely have influence on the stability of NM. Understanding to the NM activity under an external field is useful for its storage, transport and application. However, the behaviors of NM under electric fields have scarcely been studied. Recently, Ren et al.⁵⁹ employed DFT-B3LYP and MP2 methods to obtain the structure, vibration frequencies, and chemical descriptors of NM under different electric field strengths. In this work, we studied the C–N bond activation in presence of external fields with various strengths using ab initio calculations, and analyzed how the fields affect the C–N dissociation and its activation barrier. Although the chemical kinetics of NM decomposition has been extensively studied, to our knowledge, its activation under an electric field has not been investigated theoretically.

Since Wodtke et al.⁶⁰ reported the first experimental study of NM decomposition mechanism in 1986, many computational studies^37–46 have been conducted to predict its reaction kinetics. Hu et al.³⁷ used a G2MP2 method to calculate the potential energy surface (PES) of C–N bond dissociation, and predicted an energy barrier of 61.9 kcal mol⁻¹. Nguyen et al.³⁸ reported an activation energy of 60.2 kcal mol⁻¹ for the C–N cleavage. Zhu et al.⁴⁰ studied the influence of pressure on the NM decomposition mechanism using CCSD(T) and CASPT3(8,8) method. Wang et al.⁴⁴ compared the energy barrier of C–N bond homolytic cleavage of isolated NM and NM confined inside a single-walled carbon nanotube. However, the kinetics of NM under external electric field has not been addressed computationally.

The energy release of energetic materials is related to the bond dissociation in molecules.^61–63 The bond dissociation of NM may occurs at either C–N or N–O bond.^37–46 It remains an open question which process is preferred in NM decomposition. We focus on the C–N bond cleavage in this work, and leave the isomerization process for future study. The dependence of the chemical reactivity of molecular NM, and its C–N bond activation on the strength and direction of applied electric field were studied in order to provide information for the NM processing and application under complex environment.

2. Computational methods

Fig. 1 gives the schematic structure of NM and its C–N rupture reactions. A methyl radical and nitrogen dioxide are formed in the homolytic path I, while in the heterolytic path II and III, a cation and an anion are formed. To obtain the potential energy surface of C–N rupture under an external field, we scanned the C–N bond from 1.4 Å to 4.0 Å in step of 0.1 Å. CCSD^64,65 method with 6-311++G(d,p) basis set was used in the structure scanning. The C atom was fixed at the origin and the N atom on the x axis, as shown in Fig. 1. The external field was applied in the +x, −x or +y direction with various strengths. In the structure scanning all atoms but C and N were relaxed. The energy of relaxed structures was further calculated with CCSD(T)/6-311++G(d,p)^66,67 in a single point calculation. For all the structures both the singlet and triplet states were optimized. The electric field strength was set to 0.00, 0.01, 0.02, 0.03, 0.04, and 0.05 a.u. (1 a.u. = 5.1422 × 10¹¹ V m⁻¹), respectively. All the calculations were carried out using Gaussian program.⁶⁸ The reactivity of NM was analyzed both in qualitative and quantitative ways. In the qualitative way, the variation of Fukui function with the external field was analyzed. The Fukui function is defined as^69–72where μ is chemical potential and ρ(r) is electron density. f(r) can be approximately computed with^73–75

f⁺(A) = [q_A(N) − q_A(N + 1)] (2)

f⁻(A) = [q_A(N − 1) − q_A(N)] (3)

where q_A(N + 1), q_A(N) and q_A(N − 1) are net charge at atom A evaluated with natural bond orbital (NBO) analysis when the molecule has (N + 1), (N), (N − 1) electrons at fixed geometry. f⁺ and f⁻ represent the electrophilic or nucleophilic reactivity of active region,^70–76 respectively. In the quantitative way the energy barriers of C–N rupture were obtained from their potential energy surfaces (PES).

Fig. 1 The homolytic (I) and heterolytic (II and III) C–N ruptures in CH₃NO₂.

3. Result and discussion

3.1 Reactivity descriptors under external electric fields

The condensed Fukui functions of NM were evaluated at the CCSD(T)/6-311++G(d,p) level (see ESI†). The Fukui function contains relative information about nucleophilic or electrophilic reactivity at different sites in a given molecule. To compare the Fukui functions under different external fields, the local softness should be used, which was introduced by Yang and Parr⁶⁹ and computed with⁷¹

s(r) = Sf(r) (4)

where S is total softness, f(r) is Fukui function. S is estimated wit⁷¹where EA and IP are vertical electron affinity and ionization potential, respectively. s⁺ and s⁻ represent electrophilic and nucleophilic local character,^71,77 respectively, which measure the ability of accepting or donating electrons. The greater the s⁺ or s⁻ value, the stronger the electrophilicity or nucleophilicity. Fig. 2 shows both s⁺ and s⁻ of NM under external fields. In absence of external fields, O is the active site to donate an electron, while H is the active site to accept an electron. When an external field is applied, O remains active to donate an electron in regardless of the field directions, while the active site to accept an electron is dependent on the field direction, C under a field in the +x direction and O under a field in the −x direction. It is demonstrated qualitatively that the reactivity of NM under an external field may be different from that without a field.

Fig. 2 Local softness at atom C, H, N, O in nitromethane under electric fields either in the +x or −x direction.

Both the homolytic and heterolytic reactions of NM have been reported. The homolytic reaction of NM usually occurs in thermal decomposition,⁷⁸ while the heterolytic reaction in photochemical process.⁷⁹ The homolytic and heterolytic reactions have their products in different spin multiplicities. Path I is a homolytic reaction in which the electron pair shared by the C–N bond are equally distributed to the methyl and nitrogen dioxide fragments, leaving the system in triplet state. Path II and III are heterolytic reactions in which the electron pair shared by the C–N bond move to the nitrogen dioxide or the methyl fragment, leaving the system in singlet state. It is then possible that a singlet–triplet crossing caused by the C–N rupture. In this kind of reactions, a spin crossing can be noted and a lower energy path would be chosen. The spin crossing point has to be found to obtain the barrier energy for the C–N rupture.

In the absence of external fields, the PES of C–N rupture is presented in Fig. 3a, the total energy of NM increases when the C–N distance varies from its equilibrium point, approaching to a constant for r_C–N > 2.93 Å. The energy of its triplet state decreases with r_C–N and crosses with curve of singlet state at r_C–N = 3.37 Å where a jump from singlet to triplet state then occurs in the process of C–N rupture. The corresponding activation energy (E_a) is 60.97 kcal mol⁻¹, which is in good agreement with the previous studies (61.9 kcal mol⁻¹ (ref. 37) and 60.2 kcal mol⁻¹ (ref. 38)).

Fig. 3 Energy landscapes of NM under electric fields in the +x direction. The field strength is 0.00 (a), 0.01 (b), 0.02 (c), and 0.03 a.u. (d).

3.2 Effect of electric fields in the C → N direction

The energy landscapes of NM under an electric field of 0.01, 0.02, and 0.03 a.u. in the +x direction are presented in Fig. 3b–d, respectively. The geometric parameters of NM for singlet at the equilibrium C–N bondlengths under different field strengths are given in the ESI.† The energy increases sharply when r_C–N becomes small from its stationary point for all cases. For F_x = 0.01 a.u., the energy increases fast at beginning when r_C–N increases, and the increase becomes slow at large r_C–N. The singlet and triplet states meet at r_C–N = 3.50 Å with E_a = 69.99 kcal mol⁻¹. This is therefore a homolytic reaction. When F_x = 0.02 a.u., the energy of singlet state increases, while the energy of triplet state decreases. Both approach constant values, 76.71 and 77.86 kcal mol⁻¹. The two curves do not meet and therefore E_a = 76.71 kcal mol⁻¹. When F_x = 0.03 a.u., a wide gap about 37.63 kcal mol⁻¹ lies between the singlet and triplet states. The E_a corresponds to the maximum energy (48.22 kcal mol⁻¹) for the singlet state. Therefore, the C–N rupture is a heterolytic reaction when F_x > 0.02 a.u. Furthermore, population analysis indicates that the products are cationic CH₃ and anionic NO₂. The reaction then proceeds via path II.

The E_a values under F_x = 0.01 and 0.02 a.u. are higher than that without an external field, but decreases remarkably when F_x = 0.03 a.u. The E_a variation can be interpreted with the energy shift of NM caused by the external fields. Fig. 4 compares the energy landscape of NM in singlet state. The energy of NM decreases when an electric field is applied in the +x direction. Since the methyl and nitro groups are positive and negative in net charge, respectively. NM has a dipole moment along the +x direction. Its energy is computed as

E(F_x) = E⁰ − p_xF_x (6)

where E⁰ is the NM energy in absence of external field, p_x is the permanent dipole moment component. The second term is negative when the field is positive. The higher-order terms, for example, the polarizability term, have smaller contribution than the second term even if the strongest field in this study (0.05 a.u.) is applied. The total energy of NM therefore decreases under an electric field in the +x direction. However, the decreases are different for various C–N distances. The decreases are small at small r_C–N and become big when r_C–N increases. Moreover, the decreases become big under strong fields. As a result, the energy increases caused by C–N rupture decrease with the field strength, as shown in Fig. 4. The activation energy of NM in singlet state first increases for F_x = 0.00, 0.01 and 0.02 a.u. and then drops rapidly for F_x = 0.03, 0.04 and 0.05 a.u. The energy barriers for F_x = 0.00 and 0.01 a.u. are further lowered by the energy cross of corresponding triplet states. That is why the E_a value without an applied field is lower than those of F_x = 0.01 and 0.02 a.u., but higher than that of F_x ≥ 0.03 a.u.

Fig. 4 The energy landscapes of nitromethane in singlet state under electric fields in the x direction.

3.3 Effect of electric fields in the C ← N direction

Fig. 5 shows the energy landscapes of NM under an electric field with strength of 0.01, 0.02, 0.03 a.u. in the −x direction. The energy variation without an applied field is also given in Fig. 5a for ease of comparison. The energy of NM in singlet state increases rapidly for all these four cases when the C–N distance (r_C–N) is apart from its stationary point and approaches a constant value at large r_C–N. The energy in triplet state decreases with r_C–N, and meets with the curve for the singlet state, indicating a hemolytic rupture under these conditions. Increasing with the field strength, the energy barriers are evaluated as 53.17, 45.76, and 40.19 kcal mol⁻¹ for F_x = 0.01, 0.02 and 0.03 a.u., respectively.

Fig. 5 Energy landscapes of NM under electric fields in the −x direction. The field strength is 0.00 (a), 0.01 (b), 0.02 (c), and 0.03 a.u. (d).

The energy variations with C–N distance and external field strength shown in Fig. 5 are different from those in Fig. 3 in which the fields are applied in an opposite direction. The activation energy of NM under an electric field can be higher or lower than that of free molecule when the field is applied in the +x direction, but is always reduced when the applied field is in the −x direction. Moreover, the energy barrier decreases with the field strength. This can be interpreted qualitatively with the charge separation in NM. NM is a polar molecule in which the electron-rich nitro and the electron-deficient methyl are bridged via the C–N bond. The electron cloud on NO₂ is more polarizable than that on CH₃. Under a field in the +x direction (C → N), electrons on NO₂ tend to move toward C, making a higher electron density between C and N atoms and in consequence a stronger C–N bond. As a result, the activation energy increases. When the applied field is in the −x direction, electrons on the C–N bond tend to move toward NO₂, making a lower density between C and N and in consequence a weaker C–N bond. As a result, the activation energy decreases. When the electric field is very strong, however, the electron cloud distorts in the whole molecule. The directional electron transfer driven by the external field, either toward NO₂ or CH₃, leads to lower electron density between C and N atoms and a weaker C–N bond. Therefore, the activation energy of NM is small when the applied field is strong enough, regardless of its direction.

Alternatively, the field-dependent activation energy can be understood with an electric dipole model by considering NM as a charge-separated dipole. When the dipole of NM, which originates at positive pole and ends at negative pole, is parallel to the external field, the distance between two poles is compressed by field-induced charge transfer. Therefore, the C–N bond is strengthened by the applied field and its activation energy increases. On the other hand, the two poles are stretched by the field when the dipole of NM is antiparallel to the external field. The C–N bond then has lower activation energy. This trend is in agreement with previous prediction on the energies, geometries, and vibrational Stark shifts of diatomic molecules in external fields.⁸⁰

The decrease in activation energy under a field in the −x direction is clearly depicted in Fig. 6. The energy landscapes of NM in singlet state are compared by removing the spin crossing effect from the corresponding triplet state. With increasing field strength, the energy barrier decreases remarkably. The total energy has a peak when the field strength is lower than 0.04 a.u., but the peak lowers down with the field strength. When the field strength reaches 0.05 a.u., the energy barrier almost vanishes, indicating that the C–N rupture occurs spontaneously under this field.

Fig. 6 The energy landscapes of nitromethane in singlet state under electric fields in the −x direction.

3.4 Effect of electric fields perpendicular to the C–N bond

The PES of C–N rupture under an electric field perpendicular to the C–N bond is presented in Fig. 7 and S2 in ESI.† In this case, the field was applied in the +y direction. Similar energy variations were noted for different field strengths when the C–N distance (r_C–N) increases. The energy increases when r_C–N, deviates from its equilibrium bondlength. The increase becomes slow when r_C–N > 2.5 Å. The curves under different field strengths have similar shapes with a shift between each other. Moreover, the shifts are almost unchanged at different r_C–N distances, indicating that the influence of an applied field is similar to the NM during the C–N rupture. Furthermore, we computed the energy of NM in triplet state under F_y = 0.01–0.03 a.u. The three curves are similar with each other, and with the curve for F_y = 0.00 a.u. It is apparent the field in the +y direction has rather limited influence on the C–N rupture. The curves for the singlet and triplet states meet at similar r_C–N, implying a homolytic C–N rupture under all these three field strengths. The corresponding energy barriers are 60.97, 61.11, 60.88 and 60.64 kcal mol⁻¹ for F_y = 0.00, 0.01, 0.02 and 0.03 a.u., respectively, which are subjected to very small changes when the field is applied or the field strength is changed. In a word, the applied electric field perpendicular to the C–N bond has little effect on the C–N rupture.

Fig. 7 The energy landscapes of nitromethane in singlet state under electric fields in the +y direction.

Finally, it should be pointed out that our calculations are a model study of the field effect on the chemical reactivity of NM. The applied field is static and uniform, in contrast to the real situation that the field strength and direction are time-dependent. In other words, our calculations provide some critical clips of NM in a frequency-dependent field if the continuous variation of NM is considered as a film.

4. Conclusions

The energy landscapes of C–N rupture in NM were studied with ab initio calculations in presence of external electric fields. The molecular structures with various C–N distances were optimized with CCSD/6-311++G(d,p), followed by single point calculations at the CCSD(T)/6-311++G(d,p) level. While the C–N bond was put on the x-axis, the electric field was applied in the +x, −x, or +y direction. The active sites in NM were compared with their local softness, which vary with the field direction and strength. Moreover, the energy variation with C–N distance is dependent on the direction and strength of applied field.

When the field is applied in the C → N direction, the C–N bond activation energy increases when F_x ≤ 0.02 a.u., but decreases when F_x = 0.03 a.u. A spin-state switching was predicted for the singlet and triplet states under weak field of F_x < 0.02 a.u., while the energy of triplet state is always higher than that singlet state during C–N rupture under F_x ≥ 0.02 a.u. When the field is applied in the C ← N direction, the activation energy decreases. Moreover, the activation energy may vanish if the applied field is strong enough. When the field is applied in the direction perpendicular to the C–N bond, it has little impact on the activation energy for F_y = 0.01–0.05 a.u. The variations of energy landscapes and activation energy barriers are related to molecular polarization that is distinguished by the C–N bond. The C–N bond is strengthened when a C → N field is applied, and weakened under a field in an opposite direction. As the C–N bond rupture is the key step of NM decomposition, we revealed an important phenomenon of its activation energy variation under external electric field. It is evident that the field has considerable effect on C–N activation and has to be taken into account in the process, transportation and storage of NM energetic materials.

Acknowledgements

The authors thank financial support from the National Natural Science Foundation of China (No. 21373140) and supported by National High Technology Research and Development Program of China (No. 2015AA034202). Part of calculations was carried out at the State Key Laboratory of Physical Chemistry of Solid Surfaces, Xiamen University and National Supercomputing Center in Shenzhen, China. All authors thank the reviewers for helpful comments.

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Footnote

† Electronic supplementary information (ESI) available. See DOI: 10.1039/c6ra00724d

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