Global picture of isomerization and dissociation of CN₂O₂: new metastable isomers

Abstract

Molecules containing carbon (C), nitrogen (N) and oxygen (O) atoms have received considerable attention due to their great relevance in astrophysical, atmospheric and high-energy-density material (HEDM) realms. Greatly differing from most studies that mainly center on the low-lying isomers, study of C, N and O systems appeals for the additional consideration of high-energy species. Thus, understanding the thermodynamic and kinetic stability of diversified isomers is of vital importance to assess their role in these processes. In this work, we investigated a pentatomic CN₂O₂ system, the isomeric study of which was initiated 20 years ago and up to now its three isomers OCNNO, CNNO₂ and NCNO₂ have been experimentally characterized. Based on our global search strategies for both isomers and transition states, we constructed hitherto the most comprehensive potential energy surface of CN₂O₂, covering 15 new isomers and 29 new transition states. The ring-containing isomers, i.e., 14, 22 and 29, were shown to possess considerable rate-determining Gibbs free energy barriers with respect to the radical–radical (P3 NCO + NO, P6 ³NCN + ³O₂ or P10 ³NNC + ³O₂) and lowest-energy product (P1 CO₂ + N₂) at the (U)CCSD(T)/CBS level. Thus, they are expected to be experimentally observable. After the experimentally known OCNNO, CNNO₂ and NCNO₂, the presently found three isomers 14, 22 and 29 warmly welcome future laboratory investigations. In addition, for CNNO₂ 09, we located a previously unreported transition state, which provides a new viewpoint on its kinetic stability.

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1. Introduction

Carbon (C), nitrogen (N) and oxygen (O) are key elements both on Earth and in space. They can form diversified organic or inorganic species that are important intermediates during atmospheric and interplanetary processes. Detailed isomerism and decomposition knowledge of the involved C, N, O-containing molecules is thus very useful for assessment of their relevance in these processes. On the other hand, C, N and O can form simple yet very stable molecules with sp-hybridized multiple bonding, e.g., CO, N₂ and CO₂, with bond energies of 256.5, 225.4 and 382.3 kcal mol⁻¹, respectively, whereas their corresponding single bond energies are 85.6 and 40.0 kcal mol⁻¹.¹ This feature has made C, N, O very attractive building elements in designing the so-called “high-energy density material (HEDM)” molecules, which upon decomposition to the stable products, i.e., N₂, CO₂, CO with a big amount of energy can be released.

Due to the importance in diverse fields, molecules comprising the three elements (C, N, and O) have been extensively explored either in theory or in experiment.^2–27 However, successful characterization of such species in laboratory have still been very limited. The possible obstacles should be (1) absence of the promising research targets, and (2) the difficulty in finding suitable synthetic precursors due to the exotic nature (i.e., most structures are high energy and would easily cause explosion). Fortunately, the modern computational chemistry has played increasing roles in resolving the first problem. By exploring the structures and stability (intrinsic and intermolecular) of various [C_x, N_y, O_z] isomers, chemists can usually tell which isomer deserves to be studied or not, or which isomer is of little likelihood to be observed. Such information should be very useful for synthetic chemists since costing limited time on a sound target is always economic. Nice examples include diazirinone CN₂O-A and nitryl cyanide CN₂O₂-A (see Scheme 1), both of which were initially predicted by computations and about 17 years later verified by experiments.^5,6,9,23,24

Scheme 1 The reported isomers of [C, N₂, O] and [C, N₂, O₂] in literatures.

We have very recently developed a global search strategy for both isomers and transition states of molecular systems, which aims to provide a very comprehensive potential energy surface (PES) for diverse necessities. In this work, we report its application on a penatomic molecule [C, N₂, O₂] system, whose isomerism was studied about 20 years ago.^6,9 We constructed up to present the most extensive PES of CN₂O₂. Besides reproducing the previously studied one complex, 17 isomers and 31 transition states, our PES covers 15 new isomers and 29 new transition states. In addition to the experimentally known isomers CN₂O₂-A, CN₂O₂-B, and CN₂O₂-C (see Scheme 1), the new PES led us to predict three novel viable ring-containing isomers, i.e., 14, 22 and 29, each of which have the considerable rate-determining barriers at the (U)CCSD(T)/CBS level. For the experimentally known CNNO₂ 09, we found a new transition state that should provide a renewed view on its kinetic stability.

2. Computational methods

2.1 Structural search strategy for isomers and transition states

To construct a comprehensive potential-energy surface (PES) covering various isomeric and decomposition pathways, it's indispensable to obtain isomers and transition states as many as possible. The flow chart for constructing CN₂O₂ PES is shown in Scheme 2. The isomeric search was realized via our locally developed “grid-based isomeric search strategy”, which has proven very effective to help generating diverse structures including the global minimum point for small to medium-sized systems.²⁸ The B3LYP/3-21G search was first carried out, followed by the B3LYP/6-31G(d) recalculation for geometries and frequencies on distinct structures. In addition, we have developed an automatic strategy that could help fast and comprehensively find transition states.²⁹ For the target CN₂O₂ molecule, there are two kinds of transition states, both interconversion and fragmentation. For the first type transition states, we applied the “QST2” algorithm. In a typical QST2 calculation, elements in both isomers need to have the same atomic sequence. However, for isomers that are generated in global search and their atoms do not correspond to each other, we have to carefully adjust the sequential number of each atom within isomer. This is quite tedious especially for a number of isomeric pairs. For the second type transition states, we let the computer to automatically consider the fragmentation with extrusion of relatively stable fragments such as N₂, CO₂, NO and so on. Note that the large scale search for transition states between isomers would sometimes lead to the decomposition transition states. While transition state search is always challenging, we expect that such a hybrid strategy could help us find transition states as many as possible. The nature of each transition state structure was checked by the frequency calculations (at the same level) used in optimization (a transition state has only one imaginary frequency). The connection of each transition state was determined by the intrinsic reaction coordinate (IRC) calculations.³⁰

Scheme 2 The strategy for constructing CN₂O₂ potential energy surface.

2.2 Electronic structure energy calculations

The geometries and frequencies of each isomeric and transition state structure in singlet state were refined at the B3LYP/aug-cc-pVTZ optimization level followed by the CCSD(T)/aug-cc-pVTZ single-point energy calculations. The main singlet isomers and transition states were subjected to the CCSD(T)/aug-cc-pVQZ single-point energy calculations and CBS extrapolation.³¹ For all the obtained singlet isomers, we carried out the “stability” analysis of the wavefunction at the B3LYP/6-31G(d) level. If an isomer is “unstable”, we used the “broken-symmetry” method for the refined geometry optimization and single-point energy calculation.³² All the calculations were carried out with the GAUSSIAN03 (ref. 33a) and GAUSSIAN09 (ref. 33b) program packages.

For the energetics of key structures, we applied a modified version of CASPT2 (Complete Active Space with Second-order Perturbation Theory, developed by Celani and Werner,³⁴ referred to as ‘RS2C’ in Molpro), which accounts for dynamic correlation, using the CASSCF wave functions as references in the RS2C calculation, active spaces including 16 electrons and 13 active orbitals, namely CASPT2(16e,13o). The CASPT2 calculations were made without symmetry constraints on the wavefunction and carried out with the Molpro 2010 (ref. 35) program package.

3. Results and discussion

The energy and relative energy of isomers, transition states, decomposition products to P1 at the B3LYP/aug-cc-pVTZ + ZPVE CCSD(T)/aug-cc-pVTZ//B3LYP/aug-cc-pVTZ + ZPVE and CCSD(T)/aug-cc-pVTZ//B3LYP/aug-cc-pVTZ + GFE levels were shown in the Tables 1, 2 and 3, respectively. Note that the symbols “+ZPVE” and “+GFE” were used for the zero-point vibrational energy (ZPVE) correction and the Gibbs free energy (GFE) correction, respectively. In the present work, the GFE values were associated with the standard condition, i.e., temperature is 298.150 Kelvin and pressure is 1.00000 atm. The structures of CN₂O₂ isomers are shown in Scheme 3. Cartesian coordinates, energy and lowest frequency of all the considered isomers and transition states can be found in the ESI (SI1 and SI2†). The comprehensive potential energy surface of CN₂O₂ is shown in Fig. 1, based on the CCSD(T)/aug-cc-pVTZ//B3LYP/aug-cc-pVTZ + GFE energies. Note that the isomers and transition states with “u” indicate that they are performed with “broken-symmetry” method.³² For simplicity, the total energy of the products CO₂ and N₂ is set to be zero as reference. For ease of discussion, we only list the isomers and transition states relevant to 14, 22 and 29 in Fig. 2. The high-level calculations of main competitive isomerization pathways of 14, 22 and 29 are collected in Table 4. Note that unless specified, the following discussions are based on the Gibbs free energies corrected CCSD(T)/aug-cc-pVTZ//B3LYP/aug-cc-pVTZ single-point energy.

Table 1 The energy and relative energy of CN₂O₂ isomers to P1 (CO₂ + N₂) at the B3LYP/aug-cc-pVTZ level with inclusion of ZPVE correction, CCSD(T)/aug-cc-pVTZ//B3LYP/aug-cc-pVTZ level with inclusion of ZPVE correction and with Gibbs free energy correction. For concise, “AVTZ” and “AVQZ” are denoted for “aug-cc-pVTZ” and “aug-cc-pVQZ”, respectively

Isomers	B3(AVTZ) + ZPVE (a.u.)	RE (kcal mol^−1)	SP(AVTZ) + ZPVE (a.u.)	RE (kcal mol^−1)	SP(AVTZ) + GFE (a.u.)	RE (kcal mol^−1)
01	−298.054147	102.0	−297.5290574	109.5	−297.5567864	116.7
02	−298.047306	106.3	−297.5234721	113.0	−297.5519051	119.7
03	−298.030635	116.8	−297.5199457	115.2	−297.5467917	122.9
04	−298.021708	122.4	−297.5023993	126.3	−297.5303723	133.3
05	−298.020094	123.4	−297.4998182	127.9	−297.5278612	134.8
06	−297.986086	144.7	−297.4693048	147.0	−297.4965738	154.5
07	−297.988805	143.0	−297.4622678	151.4	−297.4917088	157.5
08	−297.949907	167.4	−297.4225379	176.4	−297.4501279	183.6
09	−297.94109	173.0	−297.4214629	177.0	−297.4500369	183.7
10	−297.936069	176.1	−297.4172773	179.7	−297.4451493	186.7
11	−297.931664	178.9	−297.4116656	183.2	−297.4397766	190.1
12	−297.919846	186.3	−297.4070408	186.1	−297.4341028	193.7
13	−297.91447	189.7	−297.4071216	186.0	−297.4335986	194.0
14	−297.913821	190.1	−297.4062288	186.6	−297.4330208	194.3
15	−297.913592	190.2	−297.4048519	187.5	−297.4326859	194.5
16	−297.910153	192.4	−297.4019661	189.3	−297.4317111	195.2
17	−297.900834	198.2	−297.3859067	199.4	−297.4132117	206.8
18	−297.897324	200.4	−297.3812452	202.3	−297.4083372	209.8
uL1	−297.904759	195.8	−297.3717207	208.3	−297.4032677	213.0
19	−297.894352	202.3	−297.3700767	209.3	−297.3993637	215.5
20	−297.88998	205.0	−297.368442	210.3	−297.395602	217.8
u21	−297.885358	207.9	−297.366762	211.4	−297.392639	219.7
22	−297.875816	213.9	−297.3654243	212.2	−297.3925703	219.7
23	−297.864732	220.9	−297.3399851	228.2	−297.3669611	235.8
24	−297.860692	223.4	−297.3386707	229.0	−297.3661417	236.3
25	−297.853936	227.7	−297.3382542	229.3	−297.3658962	236.5
26	−297.847845	231.5	−297.3350357	231.3	−297.3649687	237.0
u27	−297.863123	221.9	−297.3329303	232.6	−297.3607383	239.7
28	−297.847086	232.0	−297.3307853	233.9	−297.3580663	241.4
29	−297.830208	242.6	−297.3188541	241.4	−297.3462981	248.8
30	−297.7424	297.7	−297.2430254	289.0	−297.2694544	297.0
31	−297.740295	299.0	−297.222485	301.9	−297.250141	309.1
32	−297.712826	316.2	−297.2113642	308.9	−297.2378492	316.8

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Table 2 The energy and relative energy of CN₂O₂ transition states to P1 (CO₂ + N₂) at the B3LYP/aug-cc-pVTZ level with inclusion of ZPVE correction, CCSD(T)/aug-cc-pVTZ//B3LYP/aug-cc-pVTZ level with inclusion of ZPVE correction and with Gibbs free energy correction. For concise, “AVTZ” and “AVQZ” are denoted for “aug-cc-pVTZ” and “aug-cc-pVQZ”, respectively

TSs	B3(AVTZ) + ZPVE (a.u.)	RE (kcal mol^−1)	SP(AVTZ) + ZPVE (a.u.)	RE (kcal mol^−1)	SP(AVTZ) + GFE (a.u.)	RE (kcal mol^−1)
a The topomeric forms of 08 are not listed in PES but in SI2.†
ts01/02	−298.045519	107.4	−297.5219222	114.0	−297.5492292	121.4
ts03/P1	−298.031282	116.4	−297.5195416	115.5	−297.5461446	123.4
ts02/03	−298.017494	125	−297.5016698	126.7	−297.5283608	134.5
ts04/05	−298.011543	128.8	−297.4923139	132.6	−297.5199559	139.8
ts02/P2	−298.008457	130.7	−297.4877493	135.5	−297.5157103	142.5
ts01/05	−298.007081	131.6	−297.4850535	137.1	−297.5124495	144.5
ts01/07	−297.985744	145	−297.4605825	152.5	−297.4887755	159.4
ts01/P2	−297.975001	151.7	−297.4493664	159.5	−297.4764404	167.1
ts01/P4	−297.949902	167.4	−297.4382686	166.5	−297.4667876	173.2
ts12/P3	−297.920068	186.2	−297.4038333	188.1	−297.4305543	195.9
ts04/10	−297.917268	187.9	−297.4041609	187.9	−297.4304909	195.9
ts01/15	−297.913552	190.3	−297.4026658	188.8	−297.4301268	196.2
ts10/11	−297.920225	186.1	−297.4015921	189.5	−297.4293521	196.6
ts08/08^a	−297.935651	176.4	−297.4024652	189.0	−297.4292532	196.7
ts15/16	−297.908406	193.5	−297.3989044	191.2	−297.4260644	198.7
1-uts13/P1	−297.900473	198.5	−297.3971805	192.3	−297.4237435	200.2
ts06/09	−297.915282	189.2	−297.3930043	194.9	−297.4202313	202.4
ts12/16	−297.901095	198.1	−297.3895949	197.0	−297.4165549	204.7
ts08/11	−297.907297	194.2	−297.3848706	200.0	−297.4124136	207.3
ts05/06	−297.901678	197.7	−297.3851160	199.9	−297.412422	207.3
1-uts01/14	−297.887675	206.5	−297.3901634	206.2	−297.4019544	213.8
ts12/14	−297.888037	206.3	−297.3750301	206.2	−297.4015961	214.1
ts16/21	−297.846176	232.5	−297.3732073	207.3	−297.3998253	215.2
ts01/09	−297.886567	207.2	−297.3717622	208.2	−297.3990172	215.7
ts20/P1	−297.890666	204.6	−297.3705111	209.0	−297.3979011	216.4
ts11/19	−297.892366	203.5	−297.3676326	210.8	−297.3957896	217.7
ts08/L1	−297.882507	209.7	−297.3594521	216.0	−297.3889251	222.0
ts08/15	−297.884127	208.7	−297.3605757	215.3	−297.3881257	222.5
2-ts13/P1	−297.86778	219	−297.3603760	215.4	−297.387228	223.1
2-ts01/14	−297.8667	219.7	−297.3716116	217.6	−297.3839016	225.2
ts14/P4	−297.870283	217.4	−297.3533869	219.8	−297.3807539	227.1
ts14/P1	−297.863369	221.7	−297.3540405	219.4	−297.3808835	227.1
ts08/16	−297.871989	216.3	−297.3483385	222.9	−297.3756935	230.3
ts17/P3	−297.858264	224.9	−297.3426760	226.5	−297.369327	234.3
ts08/17	−297.853795	227.8	−297.3422946	226.7	−297.3684606	234.9
ts02/25	−297.85286	228.3	−297.3392072	228.7	−297.3659232	236.4
ts11/26	−297.847035	232	−297.3353634	231.1	−297.3641744	237.5
ts17/P6	−297.870679	217.2	−297.3347392	231.5	−297.3628292	238.4
uts06/22	−297.852706	228.4	−297.3488285	231.3	−297.3629875	238.8
ts18/22	−297.835564	239.2	−297.3328865	232.6	−297.3601975	240.0
ts18/P6	−297.869776	217.7	−297.331627	233.4	−297.359644	240.4
ts13/24	−297.845785	232.8	−297.3299731	234.5	−297.3567531	242.2
ts17/22	−297.830701	242.2	−297.3295360	234.7	−297.356736	242.2
uts27/P8	−297.862916	222	−297.3287498	235.2	−297.3566748	242.2
ts17/18	−297.83949	236.7	−297.3176143	242.2	−297.3448003	249.7
uts28/P10	−297.847991	231.4	−297.3160832	243.2	−297.3442162	250.1
ts23/P8	−297.839435	236.8	−297.3156450	243.4	−297.343159	250.7
1-ts25/29	−297.782175	272.7	−297.2909349	259.0	−297.3182789	266.3
1-ts28/29	−297.795646	264.2	−297.2894133	259.9	−297.3169383	267.2
uts09/29	−297.80562	258	−297.2865597	261.7	−297.3144117	268.8
1-ts22/29	−297.777762	275.5	−297.2677147	273.5	−297.2953067	280.8
ts08/P6	−297.766969	282.2	−297.2664989	274.3	−297.2932849	282.0
ts02/29	−297.76347	284.4	−297.2529290	282.8	−297.279542	290.6
ts13/30	−297.742716	297.5	−297.2579355	289.0	−297.2691775	297.2
2-ts22/29	−297.741011	298.5	−297.2416527	299.2	−297.2536417	306.9
2-ts28/29	−297.738615	300	−297.2363483	302.5	−297.2483183	310.2
ts31/P3	−297.733389	303.3	−297.2321516	304.9	−297.2452716	312.2
2-ts25/29	−297.731033	304.8	−297.2272537	308.2	−297.2393027	315.9
ts32/P8	−297.704528	321.4	−297.2145292	315.2	−297.2286342	322.6
ts08/32	−297.706773	320	−297.2155115	314.9	−297.2282015	322.9

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Table 3 The energy and relative energy of decomposition products to P1 (CO₂ + N₂) at the B3LYP/aug-cc-pVTZ level with inclusion of ZPVE correction, CCSD(T)/aug-cc-pVTZ//B3LYP/aug-cc-pVTZ level with inclusion of ZPVE correction and with Gibbs free energy correction. For concise, “AVTZ” and “AVQZ” are denoted for “aug-cc-pVTZ” and “aug-cc-pVQZ”, respectively

Products	B3(AVTZ) + ZPVE (a.u.)	RE (kcal mol^−1)	SP(AVTZ) + ZPVE (a.u.)	RE (kcal mol^−1)	SP(AVTZ) + GFE (a.u.)	RE (kcal mol^−1)
P1:CO2 + N2	−298.216738	0.0	−297.7036027	0.0	−297.7427197	0.0
P2:^1NNO + CO	−298.08066	85.4	−297.5581084	91.3	−297.5985224	90.5
P3:NCO + NO	−297.998516	136.9	−297.4736023	144.3	−297.5155833	142.5
P4:c-^1NNO + CO	−297.972684	153.1	−297.4598074	153.0	−297.5020054	151.1
P5:^1COO + N2	−297.956742	163.2	−297.4426592	163.7	−297.4828662	163.1
P6:^3NCN + ^3O2	−297.865818	220.2	−297.3871418	198.6	−297.4278338	197.6
P7:^1NON + CO	−297.896453	201.0	−297.3823147	201.6	−297.4227407	200.8
P8:^2CN + ^2NO2	−297.893737	202.7	−297.3739819	206.8	−297.4176549	204.0
P9:^2CNO + NO	−297.900427	198.5	−297.3760993	205.5	−297.4127913	207.0
P10:^3NNC + ^3O2	−297.865818	220.2	−297.3407606	227.7	−297.3830766	225.7

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Scheme 3 The geometric structures of CN₂O₂ isomers.

Fig. 1 The comprehensive potential energy surface of CN₂O₂ which is based on the CCSD(T)/aug-cc-pVTZ//B3LYP/aug-cc-pVTZ + GFE energies.

Fig. 2 Schematic decomposition and isomerization pathways of stable isomers 14, 22 and 29 in singlet which is based on the CCSD(T)/aug-cc-pVTZ//B3LYP/aug-cc-pVTZ + GFE energies.

Table 4 The main competitive isomerization pathways of 14, 22 and 29 in singlet. For concise, “AVTZ” and “AVQZ” are denoted for “aug-cc-pVTZ” and “aug-cc-pVQZ”, respectively

	T1Diag	<S^2>	CCSD(T)/AVTZ//B3LYP/AVTZ	CCSD(T)/AVQZ//B3LYP/AVTZ	CCSD(T)/CBS//B3LYP/AVTZ	CASPT2/AVTZ//B3LYP/AVTZ
14	0.017	0	0.0	0.0	0.0	0.0
1-uts01/14 (to P1 (CO2 + N2))	0.039	0.640732	19.5	19.7	19.8	19.2
ts12/14 (to P3 (NCO + NO))	0.038	0	19.8	19.8	19.8	20.2
22	0.016	0	0.0	0.0	0.0	0.0
uts06/22 (to P8 (CN + NO2))	0.106	0.854292	19.1	18.9	19.2	12.6
ts17/22 (to P6 (^3NCN + ^3O2))	0.089	0	22.5	23.1	23.5	24.0
ts18/22 (to P6 (^3NCN + ^3O2))	0.079	0	20.3	20.9	21.3	20.4
29	0.017	0	0.0	0.0	0.0	0.0
uts09/29 (to P8 (CN + NO2))	0.060	0.875304	20.0	20.4	20.6	14.2
1-ts25/29 (to P1 (CO2 + N2))	0.115	0	17.5	18.8	19.7	25.3
1-ts28/29 (to P10 (^3NNC + ^3O2))	0.049	0	18.4	18.9	19.3	18.3

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Prior to the discussion, it's desirable to show two basic “stability” terms of an isomer, i.e., thermodynamic stability and kinetic stability. The former is simply based on the isomer's relative energy (better in form of the Gibbs free energy energy). The high-energy isomer is apt to undergo the conversion to the lower-energy one in thermodynamics. The higher the relative energy, the lower thermodynamic stability an isomer has. By contrast, the “kinetic stability” is usually determined by the barrier height of the most feasible process of an isomer. The larger the barrier height, the higher kinetic stability an isomer possesses under certain conditions. It has been suggested that “activation energy of approximately 15 kcal mol⁻¹ is needed to ensure a half-life of a day at room temperature”.³⁶ This value is used in this work to evaluate the likeliness for the observation (at least at the spectroscopic level) of an energy-rich isomer. Surely, for the use of HEDM, the rate-determining barrier of more than 30 kcal mol⁻¹ (in form of Gibbs free energy) is preferable if the isomer has a very large energy release upon fragmentation.³⁷

3.1 Overview of the CN₂O₂ potential energy surface

Ever since the study of the CN₂O₂ system was initiated 20 years ago, it has been explored with much interest from various aspects of interest both theoretically and experimentally.^{2–6,8,9,12,14,18–20,26} For example, the CN₂O₂ isomers are important intermediates in the reactions between CN and NO₂,^3,6,18,20 NCN and O₂ (ref. 19 and 26) and CNO and NO.^2,12,14 In addition, due to the rather large energy release with respect to the stable product N₂ + CO₂, some CN₂O₂ isomers have been proposed as potential high-energy density materials.^4,5,8,9 Up to now, one weakly bound complex L1 and a total of 17 CN₂O₂ isomers (all in singlet state) have been reported, i.e., 01, 02, 03, 04, 05, 06, 08, 09, 10, 11, 13, 15, 16, 17, 18, 24, 32. All of them are covered in the comprehensive potential energy surface of CN₂O₂ (see Fig. 1) obtained via our global isomeric search strategy. Moreover, we located 15 new singlet isomers (07, 12, 14, 19, 20, 21, 22, 23, 25, 26, 27, 28, 29, 30, 31), of which 14, 22 and 29 possess considerable kinetic stability that will be discussed in detail below.

The transition states are very important to connect the intermediate isomers or fragments. They provide a detailed kinetic picture for the associated isomers. Based on our global transition state search strategy, we reproduced all the previously reported 31 singlet TSs. In addition, we located 29 new singlet TSs. Of particular note, ts06/09 is a new transition state for an experimentally characterized isomer CNNO₂ 09, and will re-determine the kinetic stability of 09. For simplicity, in the following parts, we mainly discuss the key or new structures related to the CN₂O₂ PES.

Usually, there is only one transition state connecting two species. It is of great interest to find out that for CN₂O₂, the interconversion between the isomeric pairs (01, 14), (22, 29) and (25, 29) each involve two transition states (see Scheme 4). The general difference in the latter two isomeric pairs is that one TS is structurally looser (lower-energy) than the other. For (01, 14), the two TSs mainly differ in the dihedral angle of the O-atom that is associated with the ring opening/closure. The detailed IRC curves can be found in SI3.†

Scheme 4 The involved transition states of interconversion between the isomeric pairs (01, 14), (22, 29) and (25, 29).

3.2 New transition state for isomer CNNO₂ 09

CNNO₂ 09 is the isocyano counterpart of NCNO₂ and has been previously studied both experimentally⁷ and computationally.¹⁹ For its kinetic stability, we located three singlet TSs, i.e., ts01/09 (32.0 kcal mol⁻¹), ts06/09 (18.7 kcal mol⁻¹) and ts09/29 (85.1 kcal mol⁻¹). The three TSs are associated with the 1, 2-CN transfer, CN ↔ NC exchange, and ring-closure of NO₂, respectively. The first TS has been reported previously.¹⁹ The latter two were newly found in this work. The energy of the direct C–N cleavage to P8 CN + NO₂ is 20.3 kcal mol⁻¹. Notably, among all the possible evolution pathways, the CN ↔ NC exchange via ts06/09 is the most feasible, and is thus the rate-determining step for determining the kinetic stability of 09. With ts06/09, the barrier height of 09 was determined to be 18.7 kcal mol⁻¹ at the CCSD(T)/aug-cc-pvtz//B3LYP/aug-cc-pVTZ with Gibbs free energy correction. It is worth mentioning that the new ts06/09 has important implications. In the previous studies,¹⁹ ts01/09 is the only evolution transition state for 09. Since ts01/09 lies 11.7 kcal mol⁻¹ higher than the direct C–N fission product P8 CN + NO₂, the most favorable channel of 09 was reported to be the direct decomposition to P8 CN + NO₂ rather than to the low-lying isomer ONNCO 01. The considerable rate-determining Gibbs free energy barrier 18.7 kcal mol⁻¹ indicates that the branched isomer CNNO₂ 09 would be experimentally viable. In fact, it has been characterized via the spectroscopic techniques.⁷

3.3 Isomers 14, 22 and 29

The singlet isomers 14, 22 and 29 were found in the present work for the first time. Isomer 14 is butterfly-shaped structure consisting with a N–N cross bond. Except the exocyclic C=O bond, all the bonds within 14 are single bonding, which contributes to its high-energy feature (194.3 kcal mol⁻¹ above P1). 14 can be structurally viewed as a product of the O-addition to the N=N bond of diazirinone CN₂O-A. Turned from the sp²-hybridization to sp³-hybridization, the two N-atoms become pyramidal each with one lone pair of electrons. The main competition channels of 14 are as follows:

Path 14-1: 14 → 12 → P3 (NCO + NO) (19.8 kcal mol⁻¹);

Path 14-2: 14 → 01 → 02 → 03 → P1 (CO₂ + N₂) (19.8 kcal mol⁻¹).

Note that the value in parenthesis is the overall barrier height (the energy difference between the reactant isomer and the highest-energy transition state) of the given pathway. With the radical–radical product P3, the energy release of Path 14-1 (48.2 kcal mol⁻¹) is much less than that (194.3 kcal mol⁻¹) of Path 14-2. Note that 12 was also a newly located isomer in this work and contains the singlet diradical character. Unfortunately, its kinetic stability is very low, i.e., 2.6 kcal mol⁻¹, with respect to the ring-opening to P3. Kinetically, both Path 14-1 and Path 14-2 are highly competitive with almost equal barrier heights 19.8 kcal mol⁻¹ at the CCSD(T)/CBS level with the Gibbs free energy correction. The large value 19.8 kcal mol⁻¹ well suggests its high viability for experimental detection. In comparison to CN₂O-A, the O-addition converts the N=N bond to N–N bond, which considerably increases the energy release, i.e., 99.6 kcal mol⁻¹ for CN₂O-A⁵ and 194.3 kcal mol⁻¹ for 14. The cost of such energy-gaining is that the rate-determining barrier height is decreased from 27 kcal mol⁻¹ for CN₂O-A to 19.8 kcal mol⁻¹ for 14.

22 and 29 can be seen as the cyano and isocyano-substituted oxaziridines (RNO₂), both of which possess the same moiety c-NO₂. The main competition channels of 22 and 29 can be described as follows:

Path 22-1: 22 → 06 → P8 (CN + NO₂) (19.2 kcal mol⁻¹);

Path 22-2: 22 → 18 → P6 (³NCN + ³O₂) (21.3 kcal mol⁻¹);

Path 22-3: 22 → 17 → P6 (³NCN + ³O₂) (23.5 kcal mol⁻¹);

Path 29-1: 29 → 25 → 02 → 03 → P1 (CO₂ + N₂) (19.7 kcal mol⁻¹);

Path 29-2: 29 → 28 → P10 (³NNC + ³O₂) (19.3 kcal mol⁻¹);

Path 29-3: 29 → 09 → 06 → P8 (CN + NO₂) (20.6 kcal mol⁻¹).

The isomers 22 and 29 both have three competitive channels involving the decomposition to the lower-energy (P3 (NCO + NO)) and high-energy radical–radical product (P6, P10). The most kinetically favored channel of 22 is Path 22-1 with the rate-determining barrier 19.2 kcal mol⁻¹ at the CCSD(T)/CBS level with Gibbs free energy correction. At the CCSD(T)/CBS level, dissociation to P10 is slightly more favorable with the rate-determining barrier 19.3 kcal mol⁻¹. Clearly, both 22 and 29 isomers are expected to be kinetically stable and viable in experiment. Of particular interest, the Gibbs free energy calculations showed that for all the three newly located isomers, the thermodynamically most favored P1 is in fact less competitive than the radical–radical products.

3.4 Possible synthetic routes to 14, 22 and 29

By means of the structural comparison, 14 can be obtained via the O-addition to the N=N bond of diazirinone CN₂O-A that was characterized in 2011.²³ The isomers 22 and 29 belong to the family of dioxiranes (XO₂) that are important intermediates in photochemical and thermal reactions.³⁸ Many such dioxiranes have been experimentally characterized.³⁸ An approach to the generation of XO₂ is often based on the reaction of an oxidant with mono-, di-, or trivalent (neutral) centers, such as nitrenes, silylenes, phosphines, sulfides, selenides, and so on. Oxidants that have been used in the generation of these high-energy XO₂ dioxiranes include lowest excited singlet state oxygen (¹O₂), ground state triplet oxygen (³O₂), ozone (O₃), superoxide ion (O₂˙⁻), and hydrogen peroxide. This will provide the possibility for the synthesis of isomers 22 and 29. To assist their future laboratory characterization, the vibrational frequencies, rotational constants and dipole moments are provided in Table 5.

Table 5 The key spectroscopic parameters including wave numbers M_wav (cm⁻¹), rotational constants R (GHz) and dipole moment D (Debye) of 14, 22 and 29 at the B3LYP/aug-cc-pVTZ level

	Mwav (cm^−1)	R (GHz)	D (Debye)
14	184.0221, 508.1086, 668.2793, 673.5074, 755.5372, 883.4728, 956.2877, 1113.6246, 2003.2457	18.38810, 5.08526, 4.75150	0.0829
22	232.8269, 243.2824, 596.8890, 599.3739, 747.4999, 808.6776, 952.6085, 1161.5485, 2327.1165	20.49199, 3.98262, 3.71273	1.3492
29	160.5204, 195.5691, 532.1401, 560.6040, 713.7855, 825.4605, 908.7385, 1140.4474, 2131.7311	21.05931, 4.24523, 3.91255	1.0235

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Further, we computed the diagnostic values (T1Diag) for the three new isomers and associated key transition states at the CCSD/aug-cc-pVTZ level. Clearly, as listed in Table 4, the isomers 14, 22 and 29 all have the T1Diag values smaller than 0.02, a recommended threshold by Lee.³⁹ Yet, the T1Diag values of the associated transition states are far larger than 0.02, indicating a need for the energy calculation based on the multi-reference wavefunctions (Table 4). Interestingly, at the CASPT2(16e,13o)/aug-cc-pVTZ//(U)B3LYP/aug-cc-pVTZ level with GFE correction, the predicted barrier heights of 14 are very similar to those at the CCSD(T)/CBS level, both around 20 kcal mol⁻¹. Yet, for 22, the O–O cleavage barrier is to some degree decreased from 19.2 (at CCSD(T)/CBS) to 12.6 kcal mol⁻¹ (at CASPT2), while the barriers of the other paths are little changed. For 29, CASPT2 induces contrastive effect on the two ring-opening processes of the c-NO₂ moiety. The O–O cleavage barrier is decreased from 20.6 (at CCSD(T)/CBS) to 14.2 kcal mol⁻¹ (at CASPT2), whereas the N–O cleavage barrier to isomer 25 is increased from 19.7 (at CCSD(T)/CBS) to 25.3 kcal mol⁻¹ (at CASPT2). It seems that the nondynamic calculations have great influence on the c-NO₂ ring-opening kinetics.

Despite the very “small” size and the 20 year isomeric research history of CN₂O₂, the present PES study still newly find 15 isomers (3 are kinetically stable) and 29 transition states, almost one times the reported species, i.e., 17 isomers and 31 transition states. This surely merits from the application of our global search strategy for both isomers and transition states. The successfulness of our strategy depends on the operation of isomeric optimization (“grid” method²⁸) and the transition state search (QST2 and fragmentation²⁹) by trying all possible combinative possibilities. It is worthy of note that an effective global reaction route mapping (GRRM) program has been recently developed by Morokuma et al.⁴⁰ Basing on the anharmonic downward distortion following (ADDF) and artificial force induced reaction (AFIR) methods, the program can automatically follow reaction pathways starting from local minima toward transition structures (TSs) and dissociation channels and then constructs a global potential energy surface (PES). The GRRM strategies have been applied to a variety of chemical systems ranging from thermal- and photochemical-reactions in small systems to organometallic- and enzymecatalysis, on the basis of quantum chemical calculations.⁴⁰ Formally, our strategy follows “all isomers → all transition states”, while GRRM follows the sequential “isomer/product → transition state → isomer → …”. It is our belief that for constructing the isomerization/fragmentation potential energy surface of simple systems, the GRRM and ours could generate very similar reaction pictures.

Due to the great relevance of C, N, O-containing systems in combustion, in space as well as the interest in molecular HEDMs, the presently constructed comprehensive isomerization and fragmentation picture should provide a useful base for further understanding of the chemistry of various processes. Especially, the kinetic behavior of various isomers at the Gibbs free energy level could help establish the kinetic model of relevant isomers or reactions. Notably, previous studies on the kinetic stability of [C, N₂, O₂] isomers have all neglected the influence of Gibbs free energies (GFE), which are yet very important for some key processes. We are currently investigating the kinetic properties of some important radical–radical reactions, e.g., CN + NO₂, NCO/CNO + NO, based on the present PES by means of the master equation rate constant calculations.

4. Conclusions

Based on our global search strategies for both isomers and transition states, the hitherto most comprehensive potential energy surface of CN₂O₂, covering 15 new isomers and 29 new transition states, was constructed. For the experimentally known CNNO₂ 09, we newly found that a direct –CN ↔ NC conversion to NCNO₂ 06 followed by the subsequent sequential dissociation to P8 CN + NO₂ is its rate-determining step. Besides, three newly located isomers 14, 22 and 29 each possess the considerable rate-determining Gibbs free energy barriers at the (U)CCSD(T)/CBS level. They are expected to be experimentally observable. In addition to the experimentally known OCNNO, CNNO₂ and NCNO₂ species, the presently found three isomers 14, 22 and 29 should enrich the CN₂O₂ family and warmly welcome future laboratory investigations. Besides, the potential energy surface constructed at the Gibbs free energy level could provide a useful base for understanding the kinetic behavior of various chemical processes.

Acknowledgements

This work was funded by the National Natural Science Foundation of China (No. 21273093, 21473069, 21073074). The reviewers' invaluable comments and suggestions are greatly acknowledged.

References

1. (a) T. L. Cottrell, The Strengths of Chemical Bonds, 2nd edn, Butterwoth, London, 1958; (b) B. deB. Darwent, National Standard Reference Data Series, National Bureau of Standards, no. 31, Washington, 1970; (c) S. W. Benson, J. Chem. Educ., 1965, 42, 502.
2. G. A. McGibbon, C. A. Kingsmill, J. K. Terlouw and P. C. Burgers, Int. J. Mass Spectrom. Ion Processes, 1992, 121, R11.
3. M. Lin, Y. He and C. Melius, J. Phys. Chem., 1993, 97, 9124.
4. J. Park and J. F. Hershberger, J. Chem. Phys., 1993, 99, 3488.
5. A. A. Korkin, P. von Ragué Schleyer and R. J. Boyd, Chem. Phys. Lett., 1994, 227, 312.
6. A. Averyanov, Y. G. Khait and Y. V. Puzanov, J. Mol. Struct., 1996, 367, 87.
7. T. M. Klapötke, G. McIntyre and A. Schulz, J. Chem. Soc., Dalton Trans., 1996, 3237.
8. T. M. Klapötke and A. Schulz, Inorg. Chem., 1996, 35, 7897.
9. (a) A. A. Korkin, J. Leszczynski and R. J. Bartlett, J. Phys. Chem., 1996, 100, 19840; (b) F. F. He, S. M. Gao, G. de Petris, M. Rosi and Y. H. Ding, J. Phys. Chem. A, 2016 DOI:10.1021/acs.jpca.5b12275.
10. A. A. Korkin, A. Lowrey, J. Leszczynski, D. B. Lempert and R. J. Bartlett, J. Phys. Chem. A, 1997, 101, 2709.
11. G. Maier, H. P. Reisenauer, J. Eckwert, M. Naumann and M. De Marco, Angew. Chem., Int. Ed., 1997, 36, 1707.
12. J. Bylykbashi and E. Lewars, J. Mol. Struct., 1999, 469, 77.
13. R. Zhu and M. Lin, J. Phys. Chem. A, 2000, 104, 10807.
14. S. Dua and J. H. Bowie, J. Phys. Chem. A, 2003, 107, 76.
15. R. Prasad, J. Chem. Phys., 2004, 120, 10089.
16. C. S. Jamieson, A. M. Mebel and R. I. Kaiser, Phys. Chem. Chem. Phys., 2005, 7, 4089.
17. Y. J. Wu and Y. P. Lee, J. Chem. Phys., 2005, 123, 174301.
18. X. Zeng, M. Ge, Z. Sun and D. Wang, Inorg. Chem., 2005, 44, 9283.
19. J. X. Zhang, Z. S. Li, J. Y. Liu and C. C. Sun, J. Phys. Chem. A, 2005, 109, 10307.
20. R. Zhu and M.-C. Lin, Int. J. Chem. Kinet., 2005, 37, 593.
21. W. Feng and J. F. Hershberger, J. Phys. Chem. A, 2009, 113, 3523.
22. P. R. Schreiner, H. P. Reisenauer, E. Mátyus, A. G. Császár, A. Siddiqi, A. C. Simmonett and W. D. Allen, Phys. Chem. Chem. Phys., 2009, 11, 10385.
23. X. Zeng, H. Beckers, H. Willner and J. F. Stanton, Angew. Chem., Int. Ed., 2011, 50, 1720.
24. M. Rahm, G. Bélanger-Chabot, R. Haiges and K. O. Christe, Angew. Chem., Int. Ed., 2014, 53, 6893.
25. F. F. He, X. Y. Zhang and Y. H. Ding, RSC Adv., 2015, 5, 46648.
26. R. Zhu and M. Lin, J. Phys. Chem. A, 2007, 111, 6766.
27. N. Faßheber and G. Friedrichs, Int. J. Chem. Kinet., 2015, 47, 586.
28. (a) C. B. Shao and Y. H. Ding, Grid-Based Comprenhensive Isomeric Search Algorithm, Jilin University, Changchun, China, 2010; (b) Z. H. Cui, M. Contreras, Y. H. Ding and G. Merino, J. Am. Chem. Soc., 2011, 133, 13228; (c) S. M. Gao and Y. H. Ding, RSC Adv., 2012, 2, 11764; (d) X. Y. Tang, Z. H. Cui, C. B. Shao and Y. H. Ding, Int. J. Quantum Chem., 2012, 112, 1299; (e) S. M. Gao and Y. H. Ding, RSC Adv., 2012, 2, 11764; (f) C. Guo, Z. H. Cui and Y. H. Ding, Struct. Chem., 2013, 24, 263; (g) C. Guo, Z. H. Cui and Y. H. Ding, Int. J. Quantum Chem., 2013, 113, 2213; (h) C. Guo, C. Wang and Y. H. Ding, Struct. Chem., 2014, 25, 1023; (i) X. Y. Zhang and Y. H. Ding, Comput. Theor. Chem., 2014, 1048, 18; (j) X. Y. Zhang and Y. H. Ding, RSC Adv., 2015, 5, 27134.
29. Yi-hong Ding, A comprehensive transition-state search strategy, Jilin University, Changchun, 2015.
30. K. Fukui, Acc. Chem. Res., 1981, 14, 363.
31. A. Halkier, T. Helgaker, P. Jørgensen, W. Klopper, H. Koch, J. Olsen and A. K. Wilson, Chem. Phys. Lett., 1998, 286, 243.
32. (a) L. Noodleman, J. Chem. Phys., 1981, 74, 5737; (b) L. Noodleman and E. R. Davidson, Chem. Phys., 1986, 109, 131; (c) A. Ovchinnikov and J. K. Labanowski, Phys. Rev. A, 1996, 53, 3946; (d) C. Adamo, V. Barone, A. Bencini, F. Totti and I. Ciofini, Inorg. Chem., 1999, 38, 1996.
33. (a) 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, O. Farkas, J. B. Foresman, J. V. Ortiz, J. Cioslowski and D. J. Fox, Gaussian 03, Revision D.02, Gaussian, Inc., Wallingford, CT, 2009; (b) 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. Kita, H. Nakai, M. Klene, X. Li, J. E. Knox, H. P. Hratchian, J. B. Cro, 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. Dannenbe, 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 09, Revision D.01, Gaussian, Inc., Wallingford, CT, 2004.
34. P. Celani and H.-J. Werner, J. Chem. Phys., 2000, 112, 5546.
35. H. J. Werner, P. J. Knowles, G. Knizia, F. R. Manby and M. Schütz, Molpro: A General Purpose Quantum Chemical Program Package, WIREs Computational Molecular Science, 2012, 2, 242.
36. R. Hoffmann, P. v. R. Schleyer and H. F. Schaefer, Angew. Chem. Int. Ed., 2008, 47, 7164.
37. M. Rahm and T. Brinck, Chem.–Eur. J., 2010, 16, 6590.
38. N. Sawwan and A. Greer, Chem. Rev., 2007, 107, 3247.
39. T. J. Lee and P. R. Taylor, Int. J. Quantum Chem., 1989, 36, 199.
40. S. Maeda, K. Ohno and K. Morokuma, Phys. Chem. Chem. Phys., 2013, 15, 3683.

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Footnote

† Electronic supplementary information (ESI) available. See DOI: 10.1039/c5ra27576h

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