Theoretical study of nitrogen-rich CN₃⁻ anion and related salts M⁺[CN₃]⁻ (M = Li, Na, K)

Abstract

Hetero-doped nitrogen-rich compounds are of great interest for potential use in high energy density materials (HEDM) fields. In this paper, we report in detail the structures and stabilities of a tetra-atomic cluster CN₃⁻, which is isoelectronic to the well-known N₄. A series of higher-level energetic calculations were carried out at the CCSD(T)/6-311+G(d)//B3LYP/6-311+G(d), CASPT2(12,12)/6-311+G(d)//CASSCF (12,12)/6-311+G(d) and CASPT2(12,12)/aug-cc-pVTZ//CASSCF(12,12)/aug-cc-pVTZ levels. The kinetic stability of CN₃⁻ was evaluated for the first time by studying the dissociation, isomerization and intersystem crossing barriers, as well as the Born–Oppenheimer molecular dynamic (BOMD) simulations. We found that the ground state isomer, i.e., chain-like triplet NCNN⁻(C_s), and a higher-energy isomer, i.e., tetrahedral-like singlet CN₃⁻(C_3v), are both kinetically stable, even when the intersystem crossing (ISC) is included. Therefore, the two isomers, ³NCNN⁻ and ¹CN₃⁻ (C_3v), could be observable in future laboratory studies. By comparison with the isoelectronic N₄ system, we conclude that the carbon-doping for XN₃ (X = N to C⁻) greatly enhances the kinetic stability of the chain-like triplet and the tetrahedral-like singlet structures. Finally, for more practical use, our studies on the related salts M⁺[CN₃]⁻ (M = Li, Na, K) showed that both the chain-like ³NCNN⁻ and tetrahedral-like ¹CN₃⁻ could act as promising building blocks for novel HEDMs.

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1. Introduction

Polynitrogen compounds are promising highly energetic materials with high energy densities that are environmentally benign. The decomposition of these materials would ideally produce only the environmentally safe dinitrogen. In the last 30 years, theoretical calculations have evaluated the structures and stabilities of numerous isomers for hypothetical N_n molecules with n ranging from 3 to 60.^1–4 Although all calculations have shown their high potential energies with respect to molecular nitrogen, only selected isomers⁵ exhibit a unique property that makes them high energy density material (HEDM) candidates, i.e., sufficient energy barriers against dissociation to allow a relatively long lifetime. The reason is that nitrogen atoms have electron lone pairs repelling each other, which makes their single bonds much weaker than, for example, a carbon–carbon single bond. That also explains why, in more than 200 years of research since the discovery of N₂, only a handful of nitrogen allotropes, like N₃⁺, N₃, N₃⁻, N₄⁺, N₅⁺ and N₅⁻,^6–10 have been experimentally observed.

The tetra-atomic all-nitrogen species, i.e., N₄, has long been the subject of a large number of studies.^{1o,2i–x,3a–c,11–14} Theoretical investigations have consistently shown that the spin-allowed dissociation barrier of the high-energy tetrahedral N₄ (T_d) to 2N₂ is around 60 kcal mol⁻¹.^2s,t Yet it has also been theoretically pointed out that the intersystem crossing would significantly reduce the kinetic stability of N₄ (T_d) to 28 kcal mol⁻¹,^2u which is still very considerable to stabilize N₄ (T_d). Thus, N₄ (T_d) has been long considered as one of the most powerful HEDM candidates. Unfortunately, up to now, the spectroscopic evidence for N₄ (T_d) is inconclusive due to the large difference between the theoretical and experimental ¹⁵N isotopic shifts.^11b–11f In a 2002 experimental study, the open-chain N₄ (³A′′) isomer was detected with a lifetime exceeding 1 μs based on neutralization–reionization mass spectrometry.^{11g,11h,13–14} The subsequent theoretical studies showed that although such a triplet chain-like structure is thermodynamically unstable with an exothermicity 22.7 kcal mol⁻¹ to ³N₂ + ¹N₂ , it needs to overcome a considerable barrier of 13.1 kcal mol⁻¹, which sufficiently allows its experimental accessibility.

Hetero-doped nitrogen-rich compounds have been another recent hot topic.^15–24 Compared to all-nitrogen species, hetero-doped nitrogen-rich clusters could be even more promising in synthesis. On one hand, suitable doping could reduce the strong repulsion between the neighboring N-lone pairs to increase the kinetic stability. On the other hand, such doping might help find appropriate synthetic precursors. Up to now, a series of nitrogen-rich compounds have been synthesized experimentally. For example, CN⁻, CN₂²⁻,¹⁷ C₂N₃⁻,¹⁸ C₂N₅⁻,²⁰ C₂N₆⁻,²¹ C₂N₈²⁻,²² C₂N₁₀²⁻,²³ C₄N₁₂²⁻,²⁴ CN₇⁻¹⁶ and ON₃⁺²⁵ have been experimentally known species, while many of the corresponding pure nitrogen species remain unknown. In light of the improvement of the hetero-doping strategy on the experimental accessibility of nitrogen-rich clusters, chemists have devoted much time to the understanding of the structures and stabilities of diversely doped nitrogen-rich compounds.¹⁵

In the present work, we are interested in a nitrogen-rich tetra-atomic cluster, CN₃⁻. It is isoelectronic to the well-known all-nitrogen N₄. Bearing one negative charge, CN₃⁻ might act as a useful building block with the presence of cationic counterions, if it is intrinsically stable in kinetics. To the best of our knowledge, the structures and energetics of the CN₃⁻ isomers have been considered recently at a relatively low B3LYP/6-311+G(d)//B3LYP/6-311+G(d) level.²⁶ Yet, the intrinsic kinetic stability of these isomers is unclear, which is vital for assessing their experimental accessibility²⁷ and their potential as a HEDM building block. In addition, in view of the potential multireference character of CN₃⁻ isomers, precise multireference methods should be more appropriate for predicting the structures and stabilities of the related isomers of CN₃⁻.

In this paper, we investigated the structures and stabilities of CN₃⁻ at the CCSD(T)/6-311+G(d)//B3LYP/6-311+G(d), CASPT2(12,12)/6-311+G(d)//CASSCF(12,12)/6-311+G(d) and CASPT2(12,12)/aug-cc-pVTZ//CASSCF(12,12)/aug-cc-pVTZ) levels. To illustrate the kinetic stability of each CN₃⁻ isomer by evaluating the dissociation barriers and isomerization barriers, both singlet and triplet potential energy surfaces of CN₃⁻ were established at various precise levels. Both the spin-allowed and spin-forbidden potential energy surface calculations, as well as the Born–Oppenheimer molecular dynamics studies indicate that two distinct structures, i.e., chain-like ³NCNN⁻ and tetrahedral-like ¹CN₃⁻ (C_3v), have good kinetic stability and have great possibility to be obtained in experiment. Finally, the stabilities of the salts M⁺[CN₃]⁻ (M = Li, Na, K) were investigated at the CCSD(T)/6-311+G(d)//B3LYP/6-311+G(d) level, which leads us to conclude that the two isomers of the CN₃⁻ molecule could be promising building blocks in assembled nitrogen-rich clusters.

2. Computational methods

All of the calculations were carried out using the Gaussian03,²⁸ Gaussian09²⁹ and Molpro 2008³⁰ program packages. The optimized geometries and harmonic frequencies of minimum isomers and transition states were initially calculated using the B3LYP method^31a–d with 6-311+G(d)^32a–j basis sets. To check the connection of each transition state, the intrinsic reaction coordinate (IRC) calculations were carried out using the same theoretical methodology that was employed in the geometry optimization. Single-point calculations for all isomers and transition states were performed at the CCSD(T)/6-311+G(d)//B3LYP/6-311+G(d) level.^33–35 The simulations conducted in this study use Born–Oppenheimer molecular dynamics (BOMD), as implemented within the Gaussian series of electronic structure codes.^36a–d These simulations utilize the B3LYP hybrid density functional with double-ζ polarized-diffused 6-31G(d) basis, as suggested from previous studies on similar systems.^36e–i In light of the potential multireference character, all isomers and a portion of important transition state structures were re-optimized using the multi-configurational CASSCF method,^38–40 in conjunction with the 6-311+G(d) and aug-cc-pVTZ^37b,c basis set. A correct characterization of the CN₃⁻ potential energy surface requires that all isomers and transition states are treated equivalently. The active space in the CASSCF calculations was selected to fulfill this requirement, and included all molecular orbitals arising from the valence atomic carbon and nitrogen p-orbital. As a result, 12 electrons were distributed over 12 active orbitals, namely, CAS(12,12). The 8 inner orbitals were inactive and held doubly occupied in the CASSCF wave function.

The harmonic vibrational frequencies were also obtained at the CASSCF(12,12)/6-311+G(d) and aug-cc-pVTZ level. To get more reliable relative energies, we further applied a modified version of CASPT2 (Complete Active Space with Second-order Perturbation Theory, developed by Celani and Werner,^41a referred to as “RS2C” in Molpro), which accounts for dynamic correlation, using the CASSCF wavefunctions as references in the RS2C calculation. The two singlet–triplet PES conical intersection points were located by performing CASSCF(8,8)/6-311+G(d) and CASSCF(12,12)/6-311+G(d) calculations, respectively, using the Molpro 2008 program. Spin–orbit coupling (SOC) calculations were performed at the CASSCF(8,8)/6-311+G(d) level with the CASSCF wave function and Pauli–Breit Hamiltonian, including rigorous one and two-electron terms.^41b–d

3. Results and discussions

We have performed a global isomeric search for CN₃⁻ in both the singlet and triplet electronic states using the grid-based comprehensive isomeric search⁴² strategies at the B3LYP/6-311+G(d) level. 8 CN₃⁻ minimum isomers (3 for singlet and 5 for triplet) (^sm) and 10 interconversion transition states (5 for singlet and 5 for triplet) (^sTSm/n) were obtained at the CCSD(T)/6-311+G(d)//B3LYP/6-311+G(d). Note that the top left corner number s denotes the electronic state (1 for singlet and 3 for triplet) of the isomers or transition states. The optimized structures of all of the singlet and triplet CN₃⁻ species calculated using the B3LYP/6-311+G(d), CASSCF(12,12)/6-311+G(d) and CASSCF(12,12)/aug-cc-pVTZ methods are illustrated in Fig. 1. For comparison, the geometrical parameters obtained at the three levels are given in the notations. The energetic properties of CN₃⁻ species are listed in Table S1, ESI†. Finally, the schematic potential energy surfaces (PESs) showing the isomerization and dissociation of CN₃⁻ are presented in Fig. 2 (for triplet) and Fig. 3 (for singlet).

Fig. 1 Optimized structures of isomers and interconversion transition states at the B3LYP/6-311+G(d) level. Parameters in italic are at the CASSCF(12,12)/6-311+G(d) level and parameters in bold are at the CASSCF(12,12)/aug-cc-pVTZ. The symmetry of Ts1/P1 is C1 at the CASSCF(12,12)/aug-cc-pVTZ level, while at the B3LYP/6-311+G(d) and CASSCF(12,12)/6-311+G(d) levels, both are in Cs symmetry. Bond lengths are in angstroms and angles in degrees.

Fig. 2 The schematic potential-energy surface of triplet CN₃⁻ at the CCSD(T)/6-311+G(d)//B3LYP/6-311+G(d) level. The relative values in parentheses are at the CASPT2 (12,12)/6-311+G(d)//CASSCF(12,12)/6-311+G(d) level, the values in brackets are at the CASPT2(12,12)/aug-cc-pVTZ//CASSCF(12,12)/aug-cc-pVTZ level.

Fig. 3 The schematic potential-energy surface of singlet CN₃⁻ at the CCSD(T)/6-311+G(d)//B3LYP/6-311+G(d) level. The relative values in parentheses are at the CASPT2 (12,12)/6-311+G(d)//CASSCF(12,12)/6-311+G(d) level, the values in brackets are at the CASPT2(12,12)/aug-cc-pVTZ//CASSCF(12,12)/aug-cc-pVTZ level.

3.1 Structures and energetics of CN₃⁻ isomers

The eight isomers are of the chain-like, three membered, four membered ring, tetrahedral-like forms, as shown in Fig. 1. As indicated in Table 1S, ESI†, CCSD(T)/6-311+G(d)//B3LYP/6-311+G(d), CASPT2(12,12)/6-311+G(d)//CASSCF/(12,12)/6-311+G(d) and CASPT2(12,12)/aug-cc-pVTZ//CASSCF(12,12)/aug-cc-pVTZ used in this paper all predict ³1 to be the ground state with the C_s symmetry. The structure of chain-like ³1 can be described as resonating between the valence structures [·N2≡C1–N3=N4·]⁻ and [·N2=C1=N3–N4·]⁻, which is consistent with the calculated Wiberg bond index (WBI) and bond distances, i.e.,WBI_{N2–C1, C1–N3, N3–N4} = 2.544, 1.331, 1.427 and R_{N2–C1, C1–N3, N3–N4} = 1.182, 1.301, 1.292 Å. Like the ground state of N₄ of C_s symmetry, NCNN ³1 also has two sets of delocalized π-orbitals on internal C–N bonding and has two sets of localized π-orbitals within N–C and N–N. As a result, the shorter inner C–N bond (1.301 Å), compared to the typical C–N single bond value 1.465 Å in H₃CNH₂, is due to the delocalized π-orbitals at the B3LYP/6-311+G(d) level. The N–N distance lies in between the typical N=N double bond in HNNH (1.236 Å in cis and 1.238 Å in trans form) and N–N single bond in H₂NNH₂ (1.482 Å).

The structure of tetrahedral-like ¹6 (C_3v) is very similar to the analogue N₄ with T_d symmetry. As shown in Fig. 1, for ¹6, the distance between the carbon atom and the three nitrogen atoms is 1.489 Å at the B3LYP/6-311+G(d) level; a little longer than the typical C–N single bond in H₃CNH₂ (1.465 Å) at the same level. The distance between N–N bond is 1.469 Å, which is a little shorter than the typical N–N single bond in H₂NNH₂ (1.482 Å). As shown in Fig. 1, geometrical parameters obtained using B3LYP method are close to those obtained at the CASSCF(12,12)/6-311+G(d) and CASSCF(12,12)/aug-cc-pVTZ level. Besides, the basis set between 6-311+G(d) and aug-cc-pVTZ have very little influence on the geometrical parameters of CN₃⁻ isomers. Usually, CASSCF overestimates the equilibrium distances. Yet luckily, this might be different here due to the rather large active space. The ground state of the chain-like ³NCNN⁻ is mainly characterized by the open-shell electronic configuration. In the construction of CASSCF wave functions, the active spaces, including 12 electrons in 8a′ (9a′–16a′) and 4a′′ (1a′′–4a′′) orbitals, have been selected. The calculated value of the CI vector is 0.96 around the equilibrium position. The construction of the CASSCF wave function for the tetrahedral-like ¹6 includes 12 electrons in 8a′ (7a′–14a′) and 4a′′ (3a′′–6a′′) orbitals. The corresponding CI vector is 0.94 at the equilibrium position, which demonstrates that the multi-reference description is warranted.

As is well known, the high dissociation barrier of tetrahedral N₄ originates from its inherent orbital nature. The decomposition route to 2N₂ is prohibited by the orbital symmetry rule, which means that a lot more energy should be required for the reaction.^2s,r For CN₃⁻ (C_3v), its configuration from CASSCF calculations in C_s symmetry is:

¹A′: 1a′1a′′2a′3a′4a′2a′′5a′6a′7a′3a′′8a′9a′10a′4a′′.

This clearly differs from the configuration of ¹CN⁻+N₂, i.e., ¹A′: 1a′2a′3a′4a′5a′6a′7a′8a′9a′10a′1a′′11a′2a′′12a′.

The configuration of the associated spin-allowed dissociation transition state, i.e., ¹A′: 1a′1a′′2a′3a′4a′5a′2a′′6a′7a′8a′3a′′9a′4a′′10a′, is the mixing of the reactant (CN₃⁻ (C_3v)) and the product (¹CN⁻+N₂). Thus, the dissociation from 1 to ¹CN⁻+N₂ is an orbital symmetry forbidden process.

3.2 Stability of ground state ³CN₃⁻ (C_s)

The schematic potential energy surface (PES) of the triplet CN₃⁻ system is depicted in Fig. 2. Different from the potential energy surfaces of N₄, the dissociation of the ground state ³1 is found to be an endothermic process with reaction energy of 87.4 kcal mol⁻¹. This clearly contrasts with the exothermic fragmentation of ³NNNN→ ³N₂ + ¹N₂. Thus, the hetero-doping of N by C⁻ can increase the thermodynamic stability of NXNN.

NCNN ³1 → ³CN⁻ + ¹N₂ (a)

This process corresponds to a simple bond cleavage without a transition structure.

As shown in Fig. 2, the remaining three isomers, i.e., ³2, ³3 and ³8, on the triplet potential energy surface each have a small energy barrier towards the isomerization to the ground isomer, i.e., less than 5 kcal mol⁻¹ at CCSD(T)/6-311+G(d)//B3LYP/6-311+G(d) level. Thus, they could be viewed as kinetically unstable. For the higher-energy branched isomer ³7, we did not locate any transition state connecting it. Yet, our BOMD calculations (see Fig. 4) showed that ³7 should also be kinetically unstable with its lifetime being less than 0.2 ps.

Fig. 4 BOMD simulation of 7 CN₃⁻(Cs) at 300 K at the B3LYP/6-31G(d) level. Potential energy (in au) versus time (in fs).

It’s of interest to inspect the singlet dissociation products ¹CN⁻ + ¹N₂, which have lower energies than the triplet 1 (i.e., −74.3 kcal mol⁻¹ at the CCSD(T)/6-311+G(d)//B3LYP/6-311+G(d) level). To reach the singlet product, a crossing and spin inversion process needs to take place in the reaction pathway. Spin inversion is a nonadiabatic process and we need to inspect a crossing seam on the singlet and triplet PESs to determine the mechanism of intersystem crossing (ISC).

We first carried out point-wise calculations for both the ¹A′ and ³A′′ surfaces of NCNN⁻ in C_s symmetry at a series of the R(C1–N3) bond values (a set of partial geometry optimization calculations at the fixed R(C1–N3) values). We found that at the R(C1–N3) value of 1.451 Å, the ¹A′ and ³A′′ reaction systems have equal CASSCF(8,8)/6-311+G(d) energy values of −201.8019 a.u. Thus, at this point of geometry, we performed CASSCF(8,8)/6-311+G(d) conical intersection calculations. The conical intersection region of the reaction system from ³NCNN⁻ to ³CN⁻+N₂ was located at the following crossing point geometry (see Table S3, ESI†) and energy at the conical intersection was −201.7769 a.u. at the CASPT2(8,8)/6-311+G(d)//CASSCF(8,8)/6-311+G(d) level (the energy difference between the singlet and triplet states being 0.43 × 10⁻⁷ kcal mol⁻¹). At the same level, the energy of NCNN (³A˝) was calculated to be −201.8097 a.u., which is lower than the energy at the conical intersection of 20.6 kcal mol⁻¹. Therefore, the reaction system will access a relatively lower energy pathway by changing its spin multiplicity via the minimum energy crossing point (MECP). However, the kind of mechanism (non-adiabatic or adiabatic) involved will depend on the magnitude of the transition probability. Among the factors that affect the magnitude of the transition probability is the spin–orbit coupling (SOC) interaction between the two states. Therefore, the strength of SOC is the key to understanding the mechanism. Although the crossing has an energy of 20.6 kcal mol⁻¹ relative to that of ³NCNN⁻, the corresponding SOC constant is comparatively small (23.9 cm⁻¹). Thus, ISC at chain-like geometries seems unlikely because of the small SOC involved. The situation of ³NCNN⁻ contrasts sharply with that of NNNN (³A′′), the ground isomer of N₄, for which 1) the fragmentation is exothermic by 22.7 kcal mol⁻¹, 2) there is a fragmentation barrier of 13.1 kcal mol⁻¹ and 3) there is no ISC. Thus, we can say that in comparison to NNNN (³A′′), the stability of ³NCNN⁻ is much increased.

The Born–Oppenheimer molecular dynamic (BOMD)^36a–d calculations at the B3LYP/6-31G(d) level further supported the good stability of the chain-like CN₃⁻. As shown in Fig. 5, we recorded a movie of the MD simulation at 300 K. The simulation indicates that NCNN⁻ (³A′′) could keep the original structure well for at least 100 ps, sufficiently allowing for future spectroscopic detection. Thus, we conclude that NCNN⁻ (C_s) should be considered as thermally stable.

Fig. 5 The BOMD simulation of ground state 1 CN₃⁻(Cs) at 300 K at the B3LYP/6-31G(d) level. Potential energy (in au) versus time (in fs).

3.3 Stability of ¹CN₃⁻ (C_3v)

The schematic potential energy surface (PES) of the singlet CN₃⁻ system is depicted in Fig. 3. The corresponding total energies and relative energies are also listed in Table S1, ESI†. Isomer 6 can release a large amount of heat of 136.8 kcal mol⁻¹ when the fragmentation is considered (¹CN⁻+N₂). Such a large heat is indicative of the potential of tetrahedral-like 6 as a HEDM candidate, if it is kinetically stable. As shown in Fig. 3, isomer 6 can convert to a four-membered ring isomer 5 by breaking one N–N bond via the transition state ¹Ts5/6. This process needs to overcome a high barrier of 45.0 kcal mol⁻¹ at the CASPT2(12,12)/6-311+G(d)//CASSCF(12,12)/6-311+G(d) level. Alternatively, isomer 6 can directly dissociate to the fragments ¹CN⁻+N₂via a concerted transition state ¹Ts6/P₁ by breaking two N–N bonds at the same time. The corresponding barrier is 38.6 kcal mol⁻¹ at this level. Thus, the fragmentation is the rate-determining step of the tetrahedral-like isomer 6 on the singlet PES. At our highest CASPT2(12,12)/aug-cc-pVTZ//CASSCF(12,12)/aug-cc-pVTZ level, the dissociation barrier is increased to be as considerable as 42.2 kcal mol⁻¹. Such a value should sufficiently stabilize CN₃⁻ (C_3v).

The BOMD calculations at the B3LYP/6-31G(d) level further supported the good kinetic stability of the tetrahedral-like CN₃⁻. As shown in Fig. 6, we recorded a movie of the MD simulation at 300 K. The simulation indicates that CN₃⁻ (C_3v) could keep the original structure well for at least 25 ps, sufficiently allowing for future spectroscopic detection. Thus, we conclude that CN₃⁻ (C_3v) should be considered as kinetically stable.

Fig. 6 BOMD simulation of 6 CN₃⁻(C_3v) at 300 K at the B3LYP/6-31G(d) level. Potential energy (in a.u.) versus time (in fs).

It’s of interest to inspect whether the tetrahedral-like isomer 6 can undergo the intersystem crossing like N₄. To our surprise, different from the potential energy surfaces of N₄, the triplet dissociation products ³CN⁻ + ¹N₂ have higher energies than the singlet 6 (i.e., 4.2 kcal mol⁻¹ at the CCSD(T)/6-311+G(d)//B3LYP/6-311+G(d) level). We carried out point-wise calculations for both the ¹A′ and ³A′′ surfaces of CN₃⁻ in C_3v symmetry at a series of ∠(N2–C1–N4) and ∠(N2–C1–N3) values (two sets of partial geometry optimization calculations at the fixed angle ∠(N2–C1–N4)). The result showed that for CN₃⁻ (C_3v), the singlet–triplet crossing point is very close to the singlet transition state. Thus, for exploring the ¹A′–³A′′ conical intersection, we performed CASSCF(12,12)/6-311+G(d) conical intersection calculations and the CASSCF(12,12)/6-311+G(d) Ts6/P1 geometry was taken as a starting geometry. The conical intersection region of the reaction system from ¹CN₃⁻ to ¹CN⁻+N₂ was located at the following CN₃⁻ geometry (see Table S4, ESI†) and the energy at the conical intersection was −201.643024 a.u. at the CASPT2(12,12)/6-311+G(d)//CASSCF(12,12)/6-311+G(d) level (the energy difference between the singlet and triplet states is 0.4 × 10⁻⁷ a.u.). At the same level, the energy of Ts6/P1 (1A′) was calculated to be −201.645160 a.u., which is lower than the CASPT2(12,12)/6-311+G(d)//CASSCF(12,12)/6-311+G(d) energy at the conical intersection 1.3 kcal mol⁻¹. The ∠(N2–C1–N4) and ∠(N2–C1–N3) angle values in the CASSCF(12,12)/6-311+G(d) geometry of Ts6/P1 (1A′) are 87.3° and 90.0°, respectively, which are both a little larger than the value of 80.2 in the geometry for the conical intersection. Hence, we conclude that the conical intersection of CN₃⁻ PES occurs before Ts6/P1 (1A′), but away from the singlet minimum energy path. As a result, the singlet–triplet intersystem crossing (6→P2³CN⁻+N₂) does not influence the kinetic stability of isomer 6. We performed CASSCF(8,8)/6-311+G(d) calculations for the ¹A′–³A′′ spin–orbital coupling constant at the conical intersection geometry and the obtained spin–orbital coupling constant values 18.5 cm⁻¹ (very small). Since the energy of Ts6/P1 is lower than that of the ¹A′–³A′′ conical intersection and the spin–orbit coupling between the ¹A′ and ³A′′ states (at the conical intersection geometry) is rather small, there is little possibility for a process from ¹A′ PES to ³A′′ PES via an intersystem transition. We concluded that the intersection between ¹A′ and ³A′′ PESs does not cause a predissociation of CN₃⁻ into the product ³CN⁻+¹N₂.

It's of interest to compare with the well-known N₄ (T_d), for which the intersystem crossing can significantly (by half) reduce the dissociation barrier to 28 kcal mol⁻¹. Thus, though the spin-allowed barrier of CN₃⁻ (C_3v) (around 42 kcal mol⁻¹) is much smaller than that (around 60 kcal mol^−12s,t) of N₄ (T_d), the overall kinetic stability (42 kcal mol⁻¹) of the former is much larger than that (28 kcal mol⁻¹) of the latter when the intersystem crossing is included. So the singlet–triplet intersystem crossing does not have an effect on the dissociation stability of isomer 6. Overall, we can say that due to the C-doping, the kinetic stability of the tetrahedral-like structure CN₃⁻ is raised relative to N₄.

3.4 Stability of M⁺[CN₃]⁻ (M = Li, Na, K)

The good kinetic stability and the anionic nature give us hope that two isomers of CN₃⁻ could serve as a promising building block for complexes. To test this hypothesis, we studied the salt-like complexes M⁺[CN₃]⁻ (X = Li, Na, K) following the “assembly” strategy⁴³ at the B3LYP/6-311+G(d) level, which allows the M-atom to position at various directions of the designated isomer. The located isomeric structures of M = Li, Na and K and their relative energies are all illustrated in Fig. 7, 8 and 9, respectively. It can be seen that with presence of three types of counterions, the triplet NCNN⁻ skeleton can still persist as the global minima. Moreover, the decomposition of the triplet complexed NCNN⁻ is still an endothermic process, though the endothermicity becomes less than that of the naked NCNN⁻. Thus, the triplet NCNN⁻ has good stability with the presence of counterions.

Fig. 7 Optimized structures of Li⁺[CN₃]⁻ at the B3LYP/6-311+G(d) level. The values in parentheses (kcal mol⁻¹) are the relative energies calculated at the CCSD(T)/6-311+G(d)//B3LYP/6-311+G(d)+ZPVE level.

Fig. 8 Optimized structures of Na⁺[CN₃]⁻ at the B3LYP/6-311+G(d) level. The values in parentheses (kcal mol⁻¹) are the relative energies calculated at the CCSD(T)/6-311+G(d)//B3LYP/6-311+G(d)+ZPVE level.

Fig. 9 Optimized structures of K⁺[CN₃]⁻ at the B3LYP/6-311+G(d) level. The values in parentheses (kcal mol⁻¹) are the relative energies calculated at the CCSD(T)/6-311+G(d)//B3LYP/6-311+G(d)+ZPVE level.

For the tetrahedral-like CN₃⁻, we focus on its fragmentation and isomerization stability with the counterion-complexation, whose channels are presented in Fig. 10, 11 and 12. It can be found that various isomeric forms can be formed when the counterions attach to the tetrahedra with close energies. Besides, they could easily undergo the interconversion to each other via the appropriate M⁺-migration (for example see Fig. 10 with M = Li). Taking Li⁺[CN₃]⁻ as an example (see Fig. 10), at the CCSD(T)/6-311+G(d)//B3LYP/6-311+G(d)+ZPVE level, the conversion from the tetrahedral-like structure to the four-membered ring structure (¹Li-15→¹Li-13) and to the fragments (¹Li-18→¹LiCN + N₂ and ¹Li-20→¹LiCN + N₂) have to consume high barriers. The associated barriers are as considerable as 33.5, 35.6 and 36.8 kcal mol⁻¹. Clearly, the salt-like form M⁺[CN₃]⁻ (M = Li) has good kinetic stability. The main features of the PESs of Na⁺[CN₃]⁻ (Fig. 11) and K⁺[CN₃]⁻ (Fig. 12) are similar to that of Li⁺[CN₃]⁻. The Na⁺ and K⁺ can easily migrate around the CN₃⁻ (C_3v) moiety. The lowest fragmentation barrier is 32.7 kcal mol⁻¹ and 35.4 kcal mol⁻¹, respectively.

Fig. 10 The schematic potential-energy surface of singlet Li⁺[CN₃]⁻ at the CCSD(T)/6-311+G(d)//B3LYP/6-311+G(d)+ZPVE level. The relative values are at the CCSD(T)/6-311+G(d)//B3LYP/6-311+G(d)+ZPVE level.

Fig. 11 The schematic potential-energy surface of singlet Na⁺[CN₃]⁻ at the CCSD(T)/6-311+G(d)//B3LYP/6-311+G(d) +ZPVE level. The relative values are at the CCSD(T)/6-311+G(d)//B3LYP/6-311+G(d)+ZPVE level.

Fig. 12 The schematic potential-energy surface of singlet K⁺[CN₃]⁻ at the CCSD(T)/6-311+G(d)//B3LYP/6-311+G(d)+ZPVE level. The relative values are at the CCSD(T)/6-311+G(d)//B3LYP/6-311+G(d)+ZPVE level.

Conclusions

At various levels, including the CCSD(T)/6-311+G(d)//B3LYP/6-311+G(d), CASPT2(12,12)/6-311+G(d)//CASSCF(12,12)/6-311+G(d) and CASPT2(12,12)/aug- cc-pVTZ//CASSCF(12,12)/aug-cc-pVTZ, we for the first time theoretically investigate the structures and stability of a tetra-atom molecule CN₃⁻ which is isoelectronic to the well-known N₄. Our results showed that two isomers ³NCNN⁻ and ¹CN₃⁻ (C_3v) have great possibility to be obtained in experiment. Besides the global minimum ³NCNN⁻, the tetrahedral-like isomer of CN₃⁻ (C_3v) has very high barriers, both for dissociation and isomerization. Although the spin-allowed barrier (around 42 kcal mol⁻¹) of CN₃⁻ (C_3v) is much lower than that of N₄ (around 60), the overall kinetic stability (around 42 kcal mol⁻¹) is greatly improved when the intersystem crossing is included. Similar to the case of the CN₃⁻ unit, the rate-determining step of the salt-like M⁺[CN₃]⁻ is associated with the fragmentation to MCN+N₂. The corresponding barriers are 33.5, 32.7 and 35.4 kcal mol⁻¹ for M = Li, Na and K, respectively. These large values show that the CN₃⁻-based salts are kinetically very stable. Future laboratory studies on the tetra-atom CN₃⁻ are greatly desired.

Acknowledgements

This work was funded by the National Key Basic Research and Development Program of China under Grant No. 2010CB327701, the National Natural Science Foundation of China (No. 20773054, 60977024, 21073074), Doctor Foundation by the Ministry of Education (20070183028), Excellent Young Teacher Foundation of Ministry of Education of China, Excellent Young People Foundation of Jilin Province (20050103) and Program for New Century Excellent Talents in University (NCET).

References

1. (a) T. W. Archibald and J. R. Sabin, J. Chem. Phys., 1971, 55, 1821; (b) J. M. Dyke, N. B. H. Jonathan, A. E. Lewis and A. Morris, Mol. Phys., 1982, 47, 1231; (c) J. N. Murrell, O. Novaro, S. Castillo and V. Saunders, Chem. Phys. Lett., 1982, 90, 421; (d) C. Petrongolo, J. Mol. Struct., 1988, 175, 215; (e) J. M. L. Martin, J. P. Francois and R. Gijbels, J. Chem. Phys., 1989, 90, 6469; (f) D. Yu, A. Rauk and D. A. Armstrong, J. Phys. Chem., 1992, 96, 6031; (g) P. Zhang, K. Morokuma and A. M. Wodtke, J. Chem. Phys., 2005, 122, 014106; (h) D. Babikov, P. Zhang and K. Morokuma, J. Chem. Phys., 2004, 121, 6743; (i) M. Bittererova, H. Ostmark and T. Brinck, J. Chem. Phys., 2002, 116, 9740; (j) R. Prasad, J. Chem. Phys., 2003, 119, 9549; (k) M. J. Pellerite, R. L. Jackson and J. I. Brauman, J. Phys. Chem., 1981, 85, 1624; (l) D. Babikov, V. A. Mozhayskiy and A. I. Krylov, J. Chem. Phys., 2006, 125, 084306; (m) V. A. Mozhayskiy, D. Babikov and A. I. Krylov, J. Chem. Phys., 2006, 124, 224309; (n) Z. L. Cai, Y. F. Wang and H. M. Xiao, Chem. Phys., 1992, 164, 377; (o) T. J. Venanzi and J. M. Schulman, Mol. Phys., 1975, 30, 281; (p) J. S. Wright, J. Am. Chem. Soc., 1974, 96, 4753; (q) R. Tarroni and P. Tosi, Chem. Phys. Lett., 2004, 389, 274; (r) Y. G. Byun, S. Saebo and C. U. Pittman, J. Am. Chem. Soc., 1991, 113, 3689.
2. (a) F. M. Bickelhaupt, R. Hoffmann and R. D. Levine, J. Phys. Chem. A, 1997, 101, 8255; (b) S. C. Decastro and H. F. Schaefer, J. Chem. Phys., 1981, 74, 550; (c) L. B. Knight, K. D. Johannessen, D. C. Cobranchi, E. A. Earl, D. Feller and E. R. Davidson, J. Chem. Phys., 1987, 87, 885; (d) S. Williams, R. A. Dressler and Y. H. Chiu, J. Chem. Phys., 1999, 111, 9634; (e) D. C. Conway, J. Chem. Phys., 1975, 63, 2219; (f) J. H. Langenberg, I. B. Bucur and P. Archirel, Chem. Phys., 1997, 221, 225; (g) C. Leonard, P. Rosmus, S. Carter and N. C. Handy, J. Phys. Chem. A, 1999, 103, 1846; (h) I. Carmichael, J. Phys. Chem., 1994, 98, 5044; (i) M. F. Guest, I. H. Hillier and V. R. Saunders, J. Chem. Soc., Faraday Trans. 2, 1972, 68, 2070; (j) G. Trinquier, J. P. Malrieu and J. P. Daudey, Chem. Phys. Lett., 1981, 80, 552; (k) S. Elbel, J. Kudnig, M. Grodzicki and H. Lempka, Chem. Phys. Lett., 1984, 109, 312; (l) A. Y. Shibaev and Y. V. Puzanov, J. Struct. Chem., 1986, 27, 472; (m) M. N. Glukhovtsev, B. Y. Simkin and V. I. Minkin, J. Struct. Chem., 1987, 28, 483; (n) B. Y. Simkin, M. N. Glukhovtsev and V. I. Minkin, Zh. Org. Khim., 1988, 24, 24; (o) J. M. Seminario and P. Politzer, Chem. Phys. Lett., 1989, 159, 27; (p) M. M. Francl and J. P. Chesick, J. Phys. Chem., 1990, 94, 526; (q) T. J. Lee and J. E. Rice, J. Chem. Phys., 1991, 94, 1215; (r) W. J. Lauderdale, J. F. Stanton and R. J. Bartlett, J. Phys. Chem., 1992, 96, 1173; (s) K. M. Dunn and K. Morokuma, J. Chem. Phys., 1995, 102, 4904; (t) A. A. Korkin, A. Balkova, R. J. Bartlett, R. J. Boyd and P. V. Schleyer, J. Phys. Chem., 1996, 100, 5702; (u) D. R. Yarkony, J. Am. Chem. Soc., 1992, 114, 5406; (v) M. N. Glukhovtsev and P. V. Schleyer, Int. J. Quantum Chem., 1993, 46, 119; (w) M. N. Glukhovtsev and S. Laiter, J. Phys. Chem., 1996, 100, 1569; (x) M. Bittererova, T. Brinck and H. Ostmark, J. Phys. Chem. A, 2000, 104, 11999.
3. (a) M. T. Nguyen, T. L. Nguyen, A. M. Mebel and R. Flammang, J. Phys. Chem. A, 2003, 107, 5452; (b) M. Bittererova, H. Ostmark and T. Brinck, Chem. Phys. Lett., 2001, 347, 220; (c) S. Evangelisti, Int. J. Quantum Chem., 2004, 96, 598; (d) M. T. Nguyen and T. K. Ha, Chem. Phys. Lett., 2000, 317, 135; (e) X. Wang, H. R. Hu, A. M. Tian, N. B. Wong, S. H. Chien and W. K. Li, Chem. Phys. Lett., 2000, 329, 483; (f) M. T. Nguyen and T. K. Ha, Chem. Phys. Lett., 2001, 335, 311; (g) M. R. Manaa, Chem. Phys. Lett., 2000, 331, 262; (h) M. T. Nguyen, M. A. Mc Ginn and A. F. Hegarty, Polyhedron, 1985, 4, 1721; (i) M. T. Nguyen, M. Sana and G. Leroy, J. Can. Chem. (Rev. Can. Chim.), 1983, 61, 1435; (j) M. T. Nguyen and T. K. Ha, Chem. Ber., 1996, 129, 1157; (k) T. K. Ha, R. Cimiraglia and M. T. Nguyen, Chem. Phys. Lett., 1981, 83, 317; (l) P. Saxe and H. F. Schaefer, J. Am. Chem. Soc., 1983, 105, 1760; (m) H. Huber, T. K. Ha and M. T. Nguyen, J. Mol. Struct.: THEOCHEM, 1983, 14, 351; (n) M. Ramek, J. Mol. Struct.: THEOCHEM, 1984, 18, 391; (o) R. Engelke, J. Phys. Chem., 1989, 93, 5722; (p) R. Engelke, J. Phys. Chem., 1990, 94, 6924; (q) M. T. Nguyen, J. Phys. Chem., 1990, 94, 6923; (r) T. K. Ha and M. T. Nguyen, Chem. Phys. Lett., 1992, 195, 179; (s) R. Engelke, J. Phys. Chem., 1992, 96, 10789; (t) B. M. Gimarc and M. Zhao, Inorg. Chem., 1996, 35, 3289; (u) M. Bittererova, T. Brinck and H. Ostmark, Chem. Phys. Lett., 2001, 340, 597.
4. (a) M. Tobita and R. J. Bartlett, J. Phys. Chem. A, 2001, 105, 4107; (b) M. N. Glukhovtsev and P. V. Schleyer, Chem. Phys. Lett., 1992, 198, 547; (c) T. M. Klapotke, J. Mol. Struct.: THEOCHEM, 2000, 499, 99; (d) L. Gagliardi, S. Evangelisti, V. Barone and B. O. Roos, Chem. Phys. Lett., 2000, 320, 518; (e) L. J. Wang, P. Warburton and P. G. Mezey, J. Phys. Chem. A, 2002, 106, 2748; (f) Q. S. Li and Y. D. Liu, J. Phys. Chem. A, 2002, 106, 9538; (g) H. H. Michels, J. A. Montgomery, K. O. Christe and D. A. Dixon, J. Phys. Chem., 1995, 99, 187; (h) C. K. Law, W. K. Li, X. Wang, A. Tian and N. B. Wong, J. Mol. Struct.: THEOCHEM, 2002, 617, 121; (i) Y. D. Liu, J. F. Zhao and Q. S. Li, Theor. Chem. Acc., 2002, 107, 140; (j) J. F. Zhao and Q. S. Li, Chem. Phys. Lett., 2003, 368, 12; (k) Q. S. Li, X. Hu and W. Xu, Chem. Phys. Lett., 1998, 287, 94; (l) X. Wang, Y. Ren, M. B. Shuai, N. B. Wong, W. K. Li and A. M. Tian, J. Mol. Struct.: THEOCHEM, 2001, 538, 145; (m) X. Wang, A. M. Tian, N. B. Wong, C. K. Law and W. K. Li, Chem. Phys. Lett., 2001, 338, 367; (n) R. Engelke and J. R. Stine, J. Phys. Chem., 1990, 94, 5689; (o) M. W. Schmidt, M. S. Gordon and J. A. Boatz, Int. J. Quantum Chem., 2000, 76, 434.
5. M. N. Glukhovtsev, H. J. Jiao and P. V. Schleyer, Inorg. Chem., 1996, 35, 7124.
6. (a) T. Curtius, Berichte, 1890, 23, 3023; (b) B. A. Thrush, Proc. R. Soc. London, Ser. A, 1956, 235, 143; (c) A. E. Douglas and W. J. Jones, Can. J. Phys., 1965, 43, 2216; (d) M. Winnewisser and R. L. Cook, J. Chem. Phys., 1964, 41, 999; (e) C. R. Brazier, P. F. Bernath, J. B. Burkholder and C. J. Howard, J. Chem. Phys., 1988, 89, 1762.
7. (a) F. Carnovale, J. B. Peel and R. G. Rothwell, J. Chem. Phys., 1988, 88, 642; (b) K. Norwood, G. Luo and C. Y. Ng, J. Chem. Phys., 1989, 91, 849; (c) V. Aquilanti, M. Bartolomei, D. Cappelletti, E. Carmona-Novillo and F. Pirani, Phys. Chem. Chem. Phys., 2001, 3, 3891; (d) V. Aquilanti, M. Bartolomei, D. Cappelletti, E. Carmona-Novillo and F. J. Pirani, Chem. Phys., 2002, 117, 615; (e) L. B. Knight, K. D. Johannessen, D. C. Cobranchi, E. A. Earl, D. Feller and E. R. Davidson, J. Chem. Phys., 1987, 87, 885; (f) S. Williams, R. A. Dressler and Y. H. Chiu, J. Chem. Phys., 1999, 111, 9634; (g) I. Carmichael, J. Phys. Chem., 1994, 98, 5044; (h) M. Saporoschenko, Phys. Rev., 1958, 111, 1550; (i) W. E. Thompson and M. E. Jacox, J. Chem. Phys., 1990, 93, 3856; (j) T. Ruchti, T. Speck, J. P. Connelly, E. J. Bieske, H. Linnartz and J. P. Maier, J. Chem. Phys., 1996, 105, 2591; (k) H. Bohringer, F. Arnold, D. Smith and N. G. Adams, Int. J. Mass Spectrom. Ion Phys., 1983, 52, 25; (l) L. G. McKnight, K. B. McAfee and D. P. Sipler, Phys. Rev., 1967, 164, 62; (m) M. Whitaker, M. A. Biondi and R. Johnsen, Phys. Rev. A, 1981, 24, 743; (n) M. F. Jarrold, A. J. Illies and M. T. Bowers, J. Chem. Phys., 1984, 81, 214; (o) T. F. Magnera, D. E. David and J. Michl, Chem. Phys. Lett., 1986, 123, 327; (p) G. P. Smith and L. C. Lee, J. Chem. Phys., 1978, 69, 5393; (q) S. C. Ostrander and J. C. Weisshaar, Chem. Phys. Lett., 1986, 129, 220.
8. (a) R. Huisgen, Angew. Chem., 1956, 68, 705; (b) J. D. Wallis and J. D. Dunitz, J. Chem. Soc., Chem. Commun., 1983, 910; (c) R. N. Butlers, S. Collier and A. F. M. Fleming, J. Chem. Soc., Perkin Trans. 2, 1996, 801; (d) R. N. Butler, A. Fox, S. Collier and L. A. Burke, J. Chem. Soc., Perkin Trans. 2, 1998, 2243; (e) M. Witanowski, L. Stefaniak, H. Januszewski, K. Bahadur and G. A. Webb, J. Cryst. Mol. Struct., 1975, 5, 137; (f) R. Muller, J. D. Wallis and W. Vonphilipsborn, Angew. Chem., Int. Ed., 1985, 24, 513; (g) P. Carlqvist, H. Ostmark and T. Brinck, J. Phys. Chem. A, 2004, 108, 7463.
9. (a) K. O. Christe, D. A. Dixon, D. McLemore, W. W. Wilson, J. A. Sheehy and J. A. Boatz, J. Fluorine Chem., 2000, 101, 151; (b) K. O. Christe, X. Z. Zhang, J. A. Sheehy and R. Bau, J. Am. Chem. Soc., 2001, 123, 6338; (c) R. Haiges, S. Schneider, T. Schroer and K. O. Christe, Angew. Chem., Int. Ed., 2004, 43, 4919; (d) K. O. Christe, W. W. Wilson, J. A. Sheehy and J. A. Boatz, Angew. Chem., Int. Ed., 1999, 38, 2004.
10. P. C. Samartzis and A. M. Wodtke, Int. Rev. Phys. Chem., 2006, 25, 527.
11. (a) J. P. Zheng, J. Waluk, J. Spanget-Larsen, D. M. Blake and J. G. Radziszewski, Chem. Phys. Lett., 2000, 328, 227; (b) T. J. Lee and J. M. L. Martin, Chem. Phys. Lett., 2002, 357, 319; (c) S. A. Perera and R. J. Bartlett, Chem. Phys. Lett., 1999, 314, 381; (d) M. Bittererova, T. Brinck and H. Ostmark, Chem. Phys. Lett., 2001, 340, 597; (e) H. Ostmark, O. Launila, S. Wallin and R. Tryman, J. Raman Spectrosc., 2001, 32, 195; (f) T. J. Lee and C. E. Dateo, Chem. Phys. Lett., 2001, 345, 295; (g) F. Cacace, Chem. – Eur. J., 2002, 8, 3839; (h) F. Cacace, G. de Petris and A. Troiani, Science, 2002, 295, 480.
12. M. T. Nguyen, T. L. Nguyen, A. M. Mebel and R. Flammang, J. Phys. Chem. A, 2003, 107, 5452.
13. E. E. Rennie and P. M. Mayer, J. Chem. Phys., 2004, 120, 10561.
14. J. Barber, D. E. Hof, C. A. Meserole and D. J. Funk, J. Phys. Chem. A, 2006, 110, 3853.
15. (a) X. L. Zhu, X. H. Lu and X. Feng, Spectrochim. Acta, Part A, 2007, 67, 756; (b) A. Hammerl and T. M. Klapotke, Inorg. Chem., 2002, 41, 906; (c) L. J. Wang, M. Z. Zgierski and P. G. Mezey, J. Phys. Chem. A, 2003, 107, 2080; (d) L. J. Wang and M. Z. Zgierski, J. Phys. Chem. A, 2004, 108, 4679; (e) Q. S. Li and L. P. Cheng, J. Phys. Chem. A, 2003, 107, 5561; (f) K. J. Wilson, S. A. Perera and R. J. Bartlett, J. Phys. Chem. A, 2001, 105, 7693; (g) G. Chaban, D. R. Yarkony and M. S. Gordon, J. Chem. Phys., 1995, 103, 7983; (h) M-J. Crawford, A. Ellern, K. Karaghiosoff, F. Martin and P. Mayer, Inorg. Chem., 2010, 49, 2674; (i) L. P. Cheng and W. Q. Cao, J. Mol. Model., 2007, 13, 1073; (j) G. H. Zhang, Y. F. Zhao, F. Y. Hao, P. X. Zhang and X. D. Song, Int. J. Quantum Chem., 2009, 109, 226; (k) L. P. Cheng and X. Q. Li, J. Mol. Model., 2006, 12, 805; (l) E. P. F. Lee, J. M. Dyke and R. P. Claridge, J. Phys. Chem. A, 2002, 106, 8680.
16. T. M. Klapötke and J. Stierstorfer, J. Am. Chem. Soc., 2009, 131, 1122.
17. (a) R. Riedel, E. Kroke, A. Greiner, A. O. Gabriel, L. Ruwisch and J. Nicolich, Chem. Mater., 1998, 10, 2964; (b) M. A. Bredig, J. Am. Chem. Soc., 1942, 64, 1730; (c) N. G. Vannerberg, Acta Chem. Scand., 1962, 16, 2263; (d) M. J. Cooper, Acta Crystallogr., 1964, 17, 1452; (e) M. G. Down, M. J. Haley, P. Hubberstey, R. J. Pulham and A. E. Thunder, J. Chem. Soc., Chem. Commun., 1978,(2), 52.
18. (a) B. Jürgens, E. Irran and W. Schnick, J. Solid State Chem., 2001, 157, 241; (b) M. Becker, M. Jansen, A. Lieb, W. Milius and W. Z. Schnick, Z. Anorg. Allg. Chem., 1998, 624, 113.
19. (a) J. R. Witt and D. Britton, Acta Crystallogr., 1971, B27, 1835; (b) L. Jäger, M. Kretschmann and H. Köhler, Z. Anorg. Allg. Chem., 1992, 611, 68; (c) H. Köhler, M. Jeschke and V. I. Nefedov, Z. Anorg. Allg. Chem., 1987, 552, 210; (d) P. Andersen, B. Klewe and E. Thom, Acta Chem. Scand., 1967, 21, 1530.
20. (a) H. P. H. Arp, A. Decken, J. Passmore and D. J. Wood, Inorg. Chem., 2000, 39, 1840; (b) E. J. Graeber and B. Morosin, Acta Crystallogr., 1983, C39, 567.
21. (a) T. M. Klapötke, C. Kuffer, P. Mayer, K. Polborn, A. Schulz and J. J. Weigand, Inorg. Chem., 2005, 44, 5949; (b) W. P. Norris and R. J. Henry, J. Am. Chem. Soc., 1963, 29, 650.
22. (a) R. Reed, V. L. Brady and J. M. Hitner, Proceedings of the 18th International Pyrotechnics Seminar, 1992, 13, 701; (b) Y. Akutsu and M. J. Tamura, J. Energ. Mater., 1993, 11, 205.
23. (a) M. A. Hiskey, D. E. Chavez, D. L. Naud, S. F. Son, H. L. Berghout and C. A. Bolme, Proc. Int. Pyrotech. Semin., 2000, 27, 3; (b) M. A. Hiskey, N. Goldman and J. R. Stine, J. Energ. Mater., 1998, 16, 119.
24. (a) J. Lifschitz, Chem. Ber., 1915, 48, 410; (b) T. Curtius, A. Darapsky and E. Müller, Chem. Ber., 1915, 48, 1614; (c) J. Lifschitz, Chem. Ber., 1916, 49, 489; (d) J. Lifschitz and W. F. Donath, Recl. Tra. Chim. Pays-Bas., 1918, 37, 270.
25. R. Engelke, N. C. Blais and R. K. Sander, J. Phys. Chem. A, 1999, 103, 5611.
26. M. D. Chen, J. W. Liu, L. Dang and Q. E. Zhang, J. Chem. Phys., 2004, 121, 11661.
27. R. Hoffmann, P. R. Schleyer and H. F. Schaefer, Angew. Chem., Int. Ed., 2008, 47, 7164.
28. Gaussian 03, Revision C.02, M. J. Frisch, G. W. Trucks, H. B. Schlegel, G. E. Scuseria, M. A. Robb, J. R. Cheeseman, J. A. Montgomery Jr., T. Vreven, K. N. Kudin, J. C. Burant, J. M. Millam, S. S. Iyengar, J. Tomasi, V. Barone, B. Mennucci, M. Cossi, G. Scalmani, N. Rega, G. A. Petersson, H. Nakatsuji, M. Hada, M. Ehara, K. Toyota, R. Fukuda, J. Hasegawa, M. Ishida, T. Nakajima, Y. Honda, O. Kitao, H. Nakai, M. Klene, X. Li, J. E. Knox, H. P. Hratchian, J. B. Cross, V. Bakken, C. Adamo, J. Jaramillo, R. Gomperts, R. E. Stratmann, O. Yazyev, A. J. Austin, R. Cammi, C. Pomelli, J. W. Ochterski, P. Y. Ayala, K. Morokuma, G. A. Voth, P. Salvador, J. J. Dannenberg, V. G. Zakrzewski, S. Dapprich, A. D. Daniels, M. C. Strain, O. Farkas, D. K. Malick, A. D. Rabuck, K. Raghavachari, J. B. Foresman, J. V. Ortiz, Q. Cui, A. G. Baboul, S. Clifford, J. Cioslowski, B. B. Stefanov, G. Liu, A. Liashenko, P. Piskorz, I. Komaromi, R. L. Martin, D. J. Fox, T. Keith, M. A. Al-Laham, C. Y. Peng, A. Nanayakkara, M. Challacombe, P. M. W. Gill, B. Johnson, W. Chen, M. W. Wong, C. Gonzalez and J. A. Pople, Gaussian, Inc., Wallingford CT, 2004.
29. Gaussian 09, Revision A.1, M. J. Frisch, G. W. Trucks, H. B. Schlegel, G. E. Scuseria, M. A. Robb, J. R. Cheeseman, G. Scalmani, V. Barone, B. Mennucci, G. A. Petersson, H. Nakatsuji, M. Caricato, X. Li, H. P. Hratchian, A. F. Izmaylov, J. Bloino, G. Zheng, J. L. Sonnenberg, M. Hada, M. Ehara, K. Toyota, R. Fukuda, J. Hasegawa, M. Ishida, T. Nakajima, Y. Honda, O. Kitao, H. Nakai, T. Vreven, J. A. Montgomery Jr., J. E. Peralta, F. Ogliaro, M. Bearpark, J. J. Heyd, E. Brothers, K. N. Kudin, V. N. Staroverov, R. Kobayashi, J. Normand, K. Raghavachari, A. Rendell, J. C. Burant, S. S. Iyengar, J. Tomasi, M. Cossi, N. Rega, J. M. Millam, M. Klene, J. E. Knox, J. B. Cross, V. Bakken, C. Adamo, J. Jaramillo, R. Gomperts, R. E. Stratmann, O. Yazyev, A. J. Austin, R. Cammi, C. Pomelli, J. W. Ochterski, R. L. Martin, K. Morokuma, V. G. Zakrzewski, G. A. Voth, P. Salvador, J. J. Dannenberg, S. Dapprich, A. D. Daniels, Ö. Farkas, J. B. Foresman, J. V. Ortiz and J. Cioslowski, D. J. Fox, Gaussian, Inc., Wallingford CT, 2009.
30. MOLPRO, version 2008.1, a package of abinitio programs , Werner, H.-J.; Knowles, P. J.; Lindh, R.; Manby, F. R.; Schütz, M.; Celani, P.; Korona, T.; Mitrushenkov, A.; Rauhut, G.; Adler, T. B.; Amos, R. D.; Bernhardsson, A.; Berning, A.; Cooper, D. L.; Deegan, M. J. O.; Dobbyn, A. J.; Eckert, F.; Goll, E.; Hampel, C.; Hetzer, G.; Hrenar, T.; Knizia, G.; Köppl, C.; Liu, Y.; Lloyd, A. W.; Mata, R. A.; May, A. J.; McNicholas, S. J.; Meyer, W.; Mura, M. E.; Nicklass, A.; Palmieri, P.; Pflüger, K.; Pitzer, R.; Reiher, M.; Schumann, U.; Stoll, H.; Stone, A. J.; Tarroni, R.; Thorsteinsson, T.; Wang, M.; Wolf, A., see http://www.molpro.net.
31. (a) A. D. Becke, J. Chem. Phys., 1993, 98, 5648; (b) P. J. Stephens, F. J. Devlin, C. F. Chabalowski and M. J. Frisch, J. Phys. Chem., 1994, 98, 11623; (c) C. Lee, W. Yang and R. G. Parr, Phys. Rev. B, 1988, 37, 785; (d) S. H. Vosko, L. Wilk and M. Nusair, Can. J. Phys., 1980, 58, 1200.
32. (a) J.-P. Blaudeau, M. P. McGrath, L. A. Curtiss and L. Radom, J. Chem. Phys., 1997, 107, 5016; (b) A. D. McLean and G. S. Chandler, J. Chem. Phys., 1980, 72, 5639; (c) R. Krishnan, J. S. Binkley, R. Seeger and J. A. Pople, J. Chem. Phys., 1980, 72, 650; (d) A. J. H. Wachters, J. Chem. Phys., 1970, 52, 1033; (e) P. J. Hay, J. Chem. Phys., 1977, 66, 4377; (f) K. Raghavachari and G. W. Trucks, J. Chem. Phys., 1989, 91, 1062; (g) M. P. McGrath and L. Radom, J. Chem. Phys., 1991, 94, 511; (h) R. C. Binning Jr. and L. A. Curtiss, J. Comput. Chem., 1990, 11, 1206; (i) T. Clark, J. G. Chandrasekhar, W. Spitznagel and P. v. R. Schleyer, J. Comput. Chem., 1983, 4, 294; (j) M. J. Frisch, J. A. Pople and J. S. Binkley, J. Chem. Phys., 1984, 80, 3265.
33. J. Cizek, Adv. Chem. Phys., 1969, 14, 35.
34. G. D. Purvis and R. J. Bartlett, J. Chem. Phys., 1982, 76, 1910.
35. (a) G. E. Scuseria, C. L. Janssen and H. F. Schaefer III, J. Chem. Phys., 1988, 89, 7382; (b) G. E. Scuseria and H. F. Schaefer III, J. Chem. Phys., 1989, 90, 3700; (c) J. A. Pople, M. Head-Gordon and K. Raghavachari, J. Chem. Phys., 1987, 87, 5968.
36. (a) I. S. Y. Wang and M. Karplus, J. Am. Chem. Soc., 1973, 95, 8160; (b) C. Leforestier, J. Chem. Phys., 1978, 68, 4406; (c) K. Bolton, W. L. Hase and G. H. Peslherbe, Direct Dynamics of ReactiVe Systems; World Scientific: Singapore, 1998; p 143; (d) M. C. Payne, M. P. Teter, D. C. Allan, T. A. Arias and J. D. Joannopoulos, Rev. Mod. Phys., 1992, 64, 1045; (e) S. S. Iyengar, M. K. Petersen, T. J. F. Day, C. J. Burnham, V. E. Teige and G. A. Voth, J. Chem. Phys., 2005, 123, 084309; (f) S. S. Iyengar and M. J. Frisch, J. Chem. Phys., 2004, 121, 5061; (g) S. S. Iyengar, T. J. F. Day and G. A. Voth, Int. J. Mass Spectrom., 2005, 241, 197–204; (h) D. Svozil and P. Jungwirth, J. Phys. Chem. A, 2006, 110, 9194; (i) S. Sadhukhan, D. Munoz, C. Adamo and G. E. Scuseria, Chem. Phys. Lett., 1999, 306, 83.
37. (a) H. Dunning Jr., J. Chem. Phys., 1989, 90, 1007; (b) R. A. Kendall, T. H. Dunning and R. J. Harrison, J. Chem. Phys., 1992, 96, 6796; (c) J. E. Del Bene, J. Phys. Chem., 1993, 97, 107.
38. H. -J. Werner and P. J. Knowles, J. Chem. Phys., 1985, 82, 5053.
39. P. J. Knowles and H. -J. Werner, Chem. Phys. Lett., 1985, 115, 259.
40. B. O. Roos, P. R. Taylor and P. E. M. Siegbahn, Chem. Phys., 1980, 48, 157.
41. (a) P. Celani and H. -J. Werner, J. Chem. Phys., 2000, 112, 5546; (b) D. G. Fedorov and M. S. Gordon, J. Chem. Phys., 2000, 112, 5611; (c) A. Berning, M. Schweizer, H.-J. Werner, P. J. Knowles and P. Palmieri, Mol. Phys., 2000, 98, 1823; (d) D. G. Fedorov, S. Koseki, M. W. Schmidt and M. S. Gordon, Int. Rev. Phys. Chem., 2003, 22, 551.
42. C. B. Shao and Y. H. Ding, Grid-Based Comprenhensive Isomeric Search Algorithm; Jilin University: Changchun, China, 2010.
43. J. Xu and Y.-H. Ding, Assembly code, Jilin University, Changchun, P. R. China, 2011.

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Footnote

† Electronic supplementary information (ESI) available: The total energies (a.u.) and relative energies of singlet and triplet isomers, the transition states and the dissociation products P1, P2, P3, P4 at four levels. The structure parameters and total energies of the conical intersections between singlet and triplet potential energy surfaces. See DOI: 10.1039/c2ra21250a

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