Nitrenes As Intermediates in the Thermal Decomposition of Aliphatic Azides

Nitrenes as Intermediates in the Thermal Decomposition of Aliphatic Azides

J. F. ARENAS, J. I. MARCOS, J. C. OTERO, I. L. TOCÓN, J. SOTO Department of Physical Chemistry, Faculty of Sciences, University of Málaga, E-29071-Málaga, Spain

Received 4 September 2000; revised 28 December 2000; accepted 20 February 2001

ABSTRACT: N2 extrusion from hydrazoic acid, methyl azide, and ethyl azide to yield the corresponding nitrene has been studied with high-level ab initio calculations. Geometry optimizations of stationary points and surfaces crossing seams were carried out with the complete active space self-consistent ﬁeld (CASSCF) method, and their energies were reevaluated with the second-order multireference perturbation (CASPT2) theory and corrected by the zero-point energy (ZPE). The analytic harmonic frequencies calculated at the CASSCF level have been used in the ZPE corrections. The decomposition reaction is a competitive mechanism between a spin-allowed and a spin-forbidden channel, giving the nitrene either in the singlet or triplet states. The energy barrier height for XN—N2 bond ﬁssion is approximately the same in both channels for each azide, respectively. The spin-orbit (HSO) interactions were determined at the minimum energy point on the seam − of crossing between the singlet and triplet surfaces, the value ranges from 43.9 cm 1 in − hydrazoic acid to 43.3 cm 1 in ethyl azide. c 2001 John Wiley & Sons, Inc. Int J Quantum Chem 84: 241–248, 2001

Key words: ab initio calculations; azides; nitrenes; intersystem crossings; forbidden reactions

potential use of these compounds as high-energy Introduction storage sources and as precursors for the prepara- tion of electronic materials [2]. hermal decomposition of azide compounds Pyrolysis of methyl azide was studied by O’Dell T (XN3) is attractive for several reasons. For and Darwent (OD) [3] and more recently by Bock example, azides play significant roles in organic and Dammel (BD) [4a]. The final products observed reactions such as heterocycle syntheses [1]. More- are N2,H2, and HCN. Additionally BD were able over, nowadays, there is a renewed interest in the to detect methyleneimine. The most remarkable dif- mechanistic aspects of such reactions because of the ference between both experiments is the conversion degree of the starting material. The experiments Correspondence to: J.F.Arenas;J.Soto. of BD were conducted to total conversion, while Contract grant sponsor: Dirección General de Investigación Científica y Técnica. OD carried out the thermolysis to conversions less Contract grant number: PB96-0697. than 1%.

International Journal of Quantum Chemistry, Vol. 84, 241–248 (2001) c 2001 John Wiley & Sons, Inc. ARENAS ET AL.

Thermal decomposition of ethyl azide in the gas Geometry optimizations have been performed phase under reduced pressure in a quartz tube filled at the complete active space SCF (CASSCF) level with quartz wool has been studied by BD [4b]. The of theory in conjunction with the standard 6-31G∗ final products are cis/trans ethanimines, HCN, NH3, basis [12] and a modified version of the corre- acetilene, and CH4. When the reactor is filled with lation-consistent double-zeta basis of Dunning (cc- four times the original amount of quartz wool in or- pVDZ) [13]. For this type of calculations, we have der to increase the contact time, the decomposition used the MC-SCF program released in GAUSSIAN starts at lower temperature, yielding N2,H2,and 98 [14]. acetonitrile. In order to correct the energetics for dy- On the other hand, experiments [5 – 7] and theo- namic electron correlation, we have used the sec- retical studies [8, 9] agree that pyrolysis of hydrazoic ond-order multireference perturbation algorithm acid gives nitrene in both the singlet and triplet (CASPT2) [15] using the MOLCAS 4.1 quantum state. Two mechanisms are proposed for such a de- chemistry software [16]. Thus, single point en- composition: One is a spin-allowed path yielding ergy calculations on the CAS/cc-pVDZ optimized the singlet nitrene; the other is a spin-forbidden re- geometries have been performed with two different action, which gives the most stable triplet nitrene. basis sets: the cc-pVTZ basis of Dunning [13] and However, for aliphatic azides, it is currently ac- the generally contracted basis sets of atomic nat- cepted that nitrogen elimination is concurrent with ural orbital (ANO-L) type [17]. The primitive set 1,2-H shift; therefore, the nitrene should not be ex- of the ANO-L basis C,N(14s9p4d)/H(8s)wascon- pected as an intermediate in the mechanism of the tracted according to the scheme C,N[4s3p1d]/H[2s]. decomposition [4]. The only experimental work, The smallest active space to obtain correct re- which proposes the nitrene as an intermediate in sults is composed of 10 electrons occupying 8 or- the thermal decomposition of such molecules, is bitals [11, 18]. Thus, all the CASSCF calculations the study carried out by OD [3] on methyl azide havebeenperformedwithsuchanactivespace. 30 years ago. The mechanism and the main con- These orbitals represent in the dissociation region ∗ clusions obtained by OD have been corroborated two π (N—N), two π (N—N), one nitrogen 2pπ ,the recently by ourselves performing high-quality ab X—N3 bonding and antibonding orbitals, and the σ initio calculations [10, 11], that is, the first step in N3—N2 bond (see Fig. 1 for atom labels). the decomposition of aliphatic azides is the nitrogen The localization of the minima, transition states, extrusion. intersystem crossing minima, and mapping of the The goal of the present work is to show that intrinsic reaction coordinates (IRC) [19] have been nitrene formation is a general process in the pyrol- performed in the space of Cartesian coordinates; ysis of organic azides, being the rate-limiting step therefore, the results are independent of any specific of the global reaction. Therefore, we have carried choice of internal coordinates. out the theoretical study of the N2 extrusion for All the computations of the crossing sur- three azides: hydrazoic acid (HN3), methyl azide faces have been performed with state-average or- (CH3N3), and ethyl azide (CH3CH2N3)withtheaim bitals [20], ensuring a balanced description of both of giving a unified and consistent picture of the de- states at the intersection geometries without impos- composition mechanism of this class of compounds. ing symmetry conditions on the wave function and avoiding symmetry breaking [21]. The optimizations of the minimum energy points Computational Details on the singlet-triplet crossing surfaces (ISCs), where both states have the same energy, were carried out All the calculations have been performed at the with the algorithm developed by Ragazos et al. [22] multiconfigurational self-consistent field (MC-SCF) as implemented in G98. Thus, in the seam of cross- level, in order to describe singlet and triplet states in ing between the two surfaces, the energy is mini- a balanced way, provided that we are going to deal mized along a (3N − 7)-dimensional hyperline (N is with spin-forbidden reactions involving a crossing the number of atoms). On the other hand, the energy between the singlet and triplet potential energy sur- is not minimized and the degeneracy will be lifted faces (PES). On the other hand, MC-SCF methods along the direction of the gradient difference, corre- have been shown to be suitable to describe properly sponding this direction to motion from the initial to bond breaking. final state.

242 VOL. 84, NO. 2 NITRENES AS INTERMEDIATES

FIGURE 1. Optimized structures at the CAS(10, 8)/cc-pVDZ level on the singlet and triplet surfaces: (a) ground-state hydrazoic acid; (b) ground-state methyl azide; (c) ground-state ethyl azide; (d) TS1, transition state for nitrogen extrusion from hydrazoic acid, the arrows on the structure correspond to the transition vector; (e) TS2, transition state for nitrogen extrusion from methyl azide, the transition vector is shown as in (d); (f) TS3, transition state for nitrogen extrusion from ethyl azide, the transition vector is shown as in (d); (g) ISC1, T1/S0 intersystem crossing for nitrogen extrusion from hydrazoic acid, the arrows on the structure correspond to the direction of the gradient difference vector; (h) ISC2, T1/S0 intersystem crossing for nitrogen extrusion from methyl azide, the gradient difference vector is shown as in (g); (i) ISC3, T1/S0 intersystem crossing for nitrogen extrusion from ethyl azide, the gradient difference vector is shownasin(g).

The stationary points (minima and transition and normal modes can be calculated byproject- states) have been characterized by their CAS- ing the seven zero frequency directions, i.e., the SCF/cc-pVDZ analytic harmonic vibrational fre- three translations, the three rotations, and the gra- quencies computed by diagonalizing the mass- dient difference vector, out of H [23, 24], as given weighted Cartesian force constant matrix, i.e., the by Eq. (1): Hessian matrix H. In turn, these frequencies have HP = (1 − P)H(1 − P), (1) been used in the respective zero-point energy (ZPE) corrections. On the other hand, frequen- where H is the 3N × 3N Hessian matrix, HP cies for ZPE corrections to ISCs must be calcu- is the projected force constant matrix, and P lated in a different manner. Since the gradient at is the projector, a 3N × 3N matrix, which is the geometry of the ISC is not zero in the full built from the unit vector that points along the 3N − 6 coordinate space, it is meaningless, a con- mass-weighted gradient difference obtained di- ventional frequency calculation by diagonalizing rectly in the optimization process, and the six 3N- the Hessian matrix. However, for those 3N − 7 dimensional inﬁnitesimal rotation and translation degrees of freedom, which preserve the degener- vectors obtained according to expressions given in acy, and for which the gradient is zero, frequencies Ref. [25].

INTERNATIONAL JOURNAL OF QUANTUM CHEMISTRY 243 ARENAS ET AL.

ber that runs from 1 to 3, i.e., 1 for hydrazoic acid, Results and Discussion 2 for methyl azide, and 3 for ethyl azide. The most important geometrical parameters of the system investigated are collected in Table II. Ad- In this section, the main features of the singlet ditionally, we show the available experimental para- and triplet surfaces related to the thermal produc- meters of hydrazoic acid [26] and methyl azide [27] tion of the nitrene intermediate from azides will be together with the results obtained at the density stressed. The energetic data for all the critical points functional theory (DFT) and second-order Møller– under discussion are collected in Table I, the geo- Plesset (MP2) levels of theory, respectively. Gener- metrical parameters in Table II, and the optimized ally speaking, the overall agreement between the structures for such points are displayed in Figure 1, calculated and experimental values is very good, respectively. the CASSCF and MP2 values being closer to the In labeling the critical points, minima, transition experimental ones than the corresponding DFT pre- states, and intersystem crossings are denoted by dictions are. The most remarkable differences be- Mβ,TSβ,andISCβ, respectively; where β is a num- tween the DFT and CASSCF methods lie in the

TABLE I Energetics for the potential energy surfaces related to N2 extrusion of azides.

Geometry CASa CASPT2b ZPEc Ed AEe

M1, hydrazoic acid [Fig. 1(a)]f −164.03609 −164.41189 13.9 0.0 45.9g −164.04569 −164.50535 Vertical excitation (11A–13A) −163.85984 −164.25206 Dissociation products (13A) −164.05192 −164.39432 TS1, transition state [Fig. 1(d)] −163.97478 −164.32476 10.6 51.4 −163.98272 −164.42104 ISC1, T1/S0 intersystem crossing [Fig. 1(g)] −163.97698 −164.33465 10.9 45.5 −163.98525 −164.42314 M2,methylazide[Fig.1(b)] −203.07425 −203.58452 33.2 40.5h −203.08512 −203.71662 Vertical excitation (11A–13A) −202.90429 −203.43529 Dissociation products (13A) −203.09872 −203.57754 TS2, transition state [Fig. 1(e)] −203.02121 −203.51291 30.2 41.9 −203.03126 −203.64098 ISC2, T1/S0 intersystem crossing [Fig. 1(h)] −203.01945 −203.51286 29.8 41.6 −203.02957 −203.64077 M3, ethyl azide [Fig. 1(c)] −242.12109 −242.76759 52.2 0.0 40.1i −242.13676 −242.94175 Vertical excitation (11A–13A) −241.95072 −242.61812 Dissociation products (13A) −242.14291 −242.75809 TS3, transition state [Fig. 1(f)] −242.06616 −242.69421 49.3 43.1 −242.08110 −242.86471 ISC3, T1/S0 intersystem crossing [Fig. 1(i)] −242.06386 −242.69476 49.1 42.6 −242.07893 −242.86522

a CAS(10, 8) energy in hartrees. b CASPT2 energy in hartrees. c CAS/cc-pVDZ ZPE in kcal/mol. d CASPT2/ANO-L + ZPE relative energy in kcal/mol. e Activation energy in kcal/mol. f In italic, cc-pVTZ values. g Mean value between the calculated barrier heights for the spin-forbidden and spin-allowed processes in Ref. [7]. h Ref. [9]. i Ref. [35].

244 VOL. 84, NO. 2 NITRENES AS INTERMEDIATES

TABLE II Relevant geometrical parameters for the critical points related to the thermal decomposition of the studied azides.a

b c Geometry N1–N2 N2–N3 N3–X N1–N2–N3 N2–N3–X

M1, hydrazoic acid [Fig. 1(a)]d 1.130 1.255 1.010 170.3 108.5 1.134 1.243 1.015 171.3 108.8 (1.126) (1.235) (1.017) (171.9) (110.4) [1.146] [1.242] [1.018] [171.5] [109.5] TS1, transition state [Fig. 1(d)] 1.100 2.009 1.025 163.8 89.7 ISC1, T1/S0 intersystem crossing [Fig. 1(d)] 1.107 1.794 1.024 149.7 94.57 M2,methylazide[Fig.1(b)]d 1.134 1.245 1.464 171.7 115.1 1.137 1.231 1.483 173.1 113.9 (1.131) (1.226) (1.472) (173.5) (116.0) [1.150] [1.234] [1.472] [173.2] [114.5] TS2, transition state [Fig. 1(e)] 1.102 1.815 1.431 159.1 104.5 ISC2, T1/S0 intersystem crossing [Fig. 1(e)] 1.109 1.793 1.442 146.5 107.6 M3, ethyl azide [Fig. 1(c)] 1.134 1.244 1.472 172.1 115.2 (1.131) (1.225) (1.482) (174.0) (116.0) [1.151] [1.234] [1.481] [173.7] [114.5] TS3, transition state [Fig. 1(f)] 1.102 1.829 1.438 160.0 104.3 ISC3, T1/S0 intersystem crossing [Fig. 1(f)] 1.109 1.790 1.451 145.5 108.1

a CAS(10,8)/cc-pVDZ. b Internuclear distances are given in Å. c Angles in degrees. d In bold, experimental values from Ref. [26] for hydrazoic acid, and from Ref. [27] for methyl azide; in brackets, B3-LYP/cc-pVTZ parameters; in squared brackets, MP2/cc-pVTZ parameters.

regions of high delocalization (—N3 backbone) with in CH3CH2N3. The directions of the transition and deviations as large as 0.02 Å. gradient difference vectors are plotted together with It is described in the literature [28, 29] that me- each of the respective ﬁgures. Both vectors are al- thodologies—such as Møller–Plesset perturbation most parallel, and their directions correspond to the theory and DFT—that are based on single-reference stretching of the N2—N3 internuclear distance. As- wave functions overestimate π conjugation giving suming that the bond being broken (N2—N3)isthe larger interatomic distances for the atoms involved reaction coordinate, it must be noted that such a in the π system. However, the opposite effect is ob- distance increases from the ISCs to the TSs, which served for the DFT values of the three azides. The means that the reactive molecule sees the intersys- computed DFT interatomic distances of the —N3 tem crossing before the transition state. moiety are the shortest ones among the three meth- On the other hand, the spin-orbit coupling mag- SO ods. nitudes (HIJ ) have been calculated at the geome- The global topological features of the potential tries of the lowest energy crossing points (Table III) energy surfaces for the three azides are essentially by using the method of Koseki et al. [30]. the same; therefore we shall discuss all of them to- In accordance with the Landau–Zenner mo- gether. We have found two critical points in the del [31 – 33], the efﬁciency of the intersystem cross- region dominated by the ground-state minimum ing depends on the magnitude of the spin-orbit [M1–M3, Figs. 1(a)–1(c)]. One of them is a transi- coupling, on the difference between the gradients of tion state [TS1–TS3, Figs. 1(d)–1(f)], and the other the singlet and triplet states, and on the nuclear ve- is an intersystem crossing minimum [ISC1–ISC3, locities as the system approaches to the intersection Figs. 1(g)–1(i)]. The energy difference between these region. Thus, provided that the computed spin-orbit two points and the minimum on the singlet sur- coupling is not very small, the gradients for the S0 face is approximately the same for the three azides, and T1 states are similar, and the velocity near the ranging from 48 kcal/mol in HN3 to 43 kcal/mol intersection point must be slow because such a point

INTERNATIONAL JOURNAL OF QUANTUM CHEMISTRY 245 ARENAS ET AL.

TABLE III Magnitude of the spin-orbit coupling (in cm−1) evaluated at the lowest energy point in the seam of crossing between the singlet and triplet surfaces.

6-31G∗a cc-pVDZa

ISC1, T1/S0 intersystem crossing [Fig. 1(d)] 43.3 43.9 ISC2, T1/S0 intersystem crossing [Fig. 1(e)] 42.5 43.7 ISC3, T1/S0 intersystem crossing [Fig. 1(f)] 42.5 43.3

a Basis set. is very close to a transition state; this process must ucts. Although the CASSCF calculations predict the be favored in the pyrolysis of aliphatic azides. spin-forbidden reaction as exothermic [Fig. 2(b)], In order to verify the reliability of our calcula- the computed energies at the CASPT2 level re- tions, we have computed the IRCs (Fig. 2) starting veal that such reactions are slightly endothermic at the two critical points found on the PESs of hy- (Table I). The energies of the forbidden reactions drazoic acid; the corresponding IRCs for methyl and have been computed on the supermolecule by elon- ethyl azide have been published elsewhere [10, 11]. gating the N2—N3 distance about 6 Å, while the It can be seen in Figure 1 that such critical points remaining coordinates keep their values at the min- connect nicely the reactive molecule with the prod- imum energy crossing point, given that at such a

FIGURE 2. CAS(10,8)/6-31G∗ IRC plots for hydrazoic acid starting (a) at the transition state TS1; (b) at the minimum energy crossing point ISC1.

246 VOL. 84, NO. 2 NITRENES AS INTERMEDIATES point, the geometries of the two fragments to be 7.Foy,B.R.;Casassa,M.P.;Stephenson,J.C.;King,D.S. formed, nitrene and molecular nitrogen, are close to J Chem Phys 1989, 90, 7037. their respective equilibrium values [9 – 11]. 8. Alexander, M. H.; Werner, H.-J.; Dagdigian, P. J. J Chem Phys 1988, 89, 1388. 9. Alexander, M. H.; Werner, H.-J.; Hemmer, T.; Knowles, P. J. Conclusions J Chem Phys 1990, 93, 3037. 10. Arenas, J. F.; Marcos, J. I.; Otero, J. C.; Sánchez-Gálvez, A.; Soto, J. J Chem Phys 1999, 111, 551. It is shown that two reaction paths exist for 11. Arenas, J. F.; Marcos, J. I.; López-Tocón, I.; Otero, J. C.; Soto, the nitrene production from aliphatic azides. One J. J Chem Phys 2000, 113, 2282. channel is a spin-forbidden mechanism, while the 12. (a) Ditchfield, R.; Hehre, W. J.; Pople, J. A. J Chem Phys 1971, other is allowed by the selection rules for spin con- 54, 724. (b) Hehre, W. J.; Ditchfield, R.; Pople, J. A. Ibid. 1972, servation. The barrier heights of both pathways 56, 2257. (c) Hariharan, P. C.; Pople, J. A. Theor Chim Acta are almost isoenergetic in the three studied azides, 1973, 28, 213. agreeing quite well with the experimental activa- 13. Dunning, Jr., T. H. J Chem Phys 1989, 90, 1007. tion energies. Whether the process is spin-allowed 14. Frisch, M. J.; Trucks, G. W.; Schlegel, H. B.; Scuseria, G. B.; or spin-forbidden cannot be unambiguously estab- Robb,M.A.;Cheeseman,J.R.;Zakrzewski,V.G.;Mont- lished only on the basis of these calculations. It has gomery,Jr.,J.A.;Stratmann,R.E.;Burant,J.C.;Dapprich, S.; Millam, J. M.; Daniels, A. D.; Kudin, K. N.; Strain, M. C.; been previously demonstrated that both reactions Farkas, O.; Tomasi, J.; Barone, V.;Cossi, M.; Cammi, R.; Men- are equally probable for hydrazoic acid [5 – 7], and nucci, B.; Pomelli, C.; Adamo, C.; Clifford, S.; Ochterski, J.; it has been demonstrated as well that the minimum Petersson,G.A.;Ayala,P.Y.;Cui,Q.;Morokuma,K.;Mal- energy point on the intersection of two surfaces ick, D. K.; Rabuck, A. D.; Raghavachari, K.; Foresman, J. B.; represents a key bottleneck along the minimum en- Cioslowski, J.; Ortiz, J. V.; Baboul, A. G.; Stefanov, B. B.; Liu, G.; Liashenko, A.; Piskorz, P.; Komaromi, I.; Gomperts, R.; ergy path, playing the role of the transition state Martin,R.L.;Fox,D.J.;Keith,T.;Al-Laham,M.A.;Peng, for the forbidden reaction [33, 34]. Consequently, C. Y.; Nanayakkara, A.; Gonzales, C.; Challacombe, M.; Gill, we have to accept that methyl and ethyl azide will P.M.W.;Johnson,B.;Chen,W.;Wong,M.W.;Anders,J.L.; decompose through both channels and any other Gonzales, C.; Head-Gordon, M.; Replogle, E. S.; Pople, J. A. mechanism should be neglected [11]. Gaussian 98 Revision A.7; Gaussian: Pittsburgh, 1998. 15. (a) Andersson, K.; Malmqvist, P.-Å; Roos, B. O. J Chem Phys ACKNOWLEDGMENTS 1992, 96, 1218. (b) Andersson, K.; Malmqvist, P.-Å; Roos, B. O. J Phys Chem 1990, 94, 5483. This research has been supported by the Di- 16.Andersson,K.;Blomberg,M.R.A.;Fülscher,M.P.;Karl- stöm,G.;Lindh,R.;Malmqvist,P.-Å;Neogrády,P.;Olsen, rección General de Investigación Científica y Téc- J.;Roos,B.O.;Sadlej,A.J.;Schütz,M.;Seijo,L.;Serrano- nica (DGICYT; Grant PB96-0697). The authors thank Andrés, L.; Siegbahn, P. E. M.; Widmark, P.-O. MOLCAS D. R. 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