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.