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:
N2extrusion 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—N2bond 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−1in hydrazoic acid to 43.3 cm−1in 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 reactionsIntroduction
T
hermal decomposition of azide compounds (XN3) is attractive for several reasons. For example, azides play significant roles in organic reactions such as heterocycle syntheses [1]. More-over, nowadays, there is a renewed interest in the mechanistic aspects of such reactions because of theCorrespondence to:J. F. Arenas; J. Soto.
Contract grant sponsor: Dirección General de Investigación Científica y Técnica.
Contract grant number: PB96-0697.
potential use of these compounds as high-energy storage sources and as precursors for the prepara-tion of electronic materials [2].
Pyrolysis of methyl azide was studied by O’Dell and Darwent (OD) [3] and more recently by Bock and Dammel (BD) [4a]. The final products observed are N2, H2, and HCN. Additionally BD were able to detect methyleneimine. The most remarkable dif-ference between both experiments is the conversion degree of the starting material. The experiments of BD were conducted to total conversion, while OD carried out the thermolysis to conversions less than 1%.
Thermal decomposition of ethyl azide in the gas phase under reduced pressure in a quartz tube filled with quartz wool has been studied by BD [4b]. The final products arecis/transethanimines, HCN, NH3, acetilene, and CH4. When the reactor is filled with four times the original amount of quartz wool in or-der to increase the contact time, the decomposition starts at lower temperature, yielding N2, H2, and acetonitrile.
On the other hand, experiments [5 – 7] and theo-retical studies [8, 9] agree that pyrolysis of hydrazoic acid gives nitrene in both the singlet and triplet state. Two mechanisms are proposed for such a de-composition: One is a spin-allowed path yielding the singlet nitrene; the other is a spin-forbidden re-action, which gives the most stable triplet nitrene. However, for aliphatic azides, it is currently ac-cepted that nitrogen elimination is concurrent with 1,2-H shift; therefore, the nitrene should not be ex-pected as an intermediate in the mechanism of the decomposition [4]. The only experimental work, which proposes the nitrene as an intermediate in the thermal decomposition of such molecules, is the study carried out by OD [3] on methyl azide 30 years ago. The mechanism and the main con-clusions obtained by OD have been corroborated recently by ourselves performing high-quality ab initio calculations [10, 11], that is, the first step in the decomposition of aliphatic azides is the nitrogen extrusion.
The goal of the present work is to show that nitrene formation is a general process in the pyrol-ysis of organic azides, being the rate-limiting step of the global reaction. Therefore, we have carried out the theoretical study of the N2 extrusion for three azides: hydrazoic acid (HN3), methyl azide (CH3N3), and ethyl azide (CH3CH2N3) with the aim of giving a unified and consistent picture of the de-composition mechanism of this class of compounds.
Computational Details
All the calculations have been performed at the multiconfigurational self-consistent field (MC-SCF) level, in order to describe singlet and triplet states in a balanced way, provided that we are going to deal with spin-forbidden reactions involving a crossing between the singlet and triplet potential energy sur-faces (PES). On the other hand, MC-SCF methods have been shown to be suitable to describe properly bond breaking.
Geometry optimizations have been performed at the complete active space SCF (CASSCF) level of theory in conjunction with the standard 6-31G∗ basis [12] and a modified version of the corre-lation-consistent double-zeta basis of Dunning (cc-pVDZ) [13]. For this type of calculations, we have used the MC-SCF program released in GAUSSIAN 98 [14].
In order to correct the energetics for dy-namic electron correlation, we have used the sec-ond-order multireference perturbation algorithm (CASPT2) [15] using the MOLCAS 4.1 quantum chemistry software [16]. Thus, single point en-ergy calculations on the CAS/cc-pVDZ optimized geometries have been performed with two different basis sets: the cc-pVTZ basis of Dunning [13] and the generally contracted basis sets of atomic nat-ural orbital (ANO-L) type [17]. The primitive set of the ANO-L basis C,N(14s9p4d)/H(8s) was con-tracted according to the scheme C,N[4s3p1d]/H[2s]. The smallest active space to obtain correct re-sults is composed of 10 electrons occupying 8 or-bitals [11, 18]. Thus, all the CASSCF calculations have been performed with such an active space. These orbitals represent in the dissociation region twoπ(N—N), twoπ∗(N—N), one nitrogen 2pπ, the X—N3bonding and antibonding orbitals, and theσ N3—N2bond (see Fig. 1 for atom labels).
The localization of the minima, transition states, intersystem crossing minima, and mapping of the intrinsic reaction coordinates (IRC) [19] have been performed in the space of Cartesian coordinates; therefore, the results are independent of any specific choice of internal coordinates.
All the computations of the crossing sur-faces have been performed with state-average or-bitals [20], ensuring a balanced description of both states at the intersection geometries without impos-ing symmetry conditions on the wave function and avoiding symmetry breaking [21].
The optimizations of the minimum energy points on the singlet-triplet crossing surfaces (ISCs), where both states have the same energy, were carried out with the algorithm developed by Ragazos et al. [22] as implemented in G98. Thus, in the seam of cross-ing between the two surfaces, the energy is mini-mized along a (3N−7)-dimensional hyperline (Nis the number of atoms). On the other hand, the energy is not minimized and the degeneracy will be lifted along the direction of the gradient difference, corre-sponding this direction to motion from the initial to final state.
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/S0intersystem crossing for nitrogen
extrusion from hydrazoic acid, the arrows on the structure correspond to the direction of the gradient difference vector; (h) ISC2,T1/S0intersystem crossing for nitrogen extrusion from methyl azide, the gradient difference vector is shown as
in (g); (i) ISC3,T1/S0intersystem crossing for nitrogen extrusion from ethyl azide, the gradient difference vector is
shown as in (g).
The stationary points (minima and transition states) have been characterized by their CAS-SCF/cc-pVDZ analytic harmonic vibrational fre-quencies computed by diagonalizing the mass-weighted Cartesian force constant matrix, i.e., the Hessian matrix H. In turn, these frequencies have been used in the respective zero-point energy (ZPE) corrections. On the other hand, frequen-cies for ZPE corrections to ISCs must be calcu-lated in a different manner. Since the gradient at the geometry of the ISC is not zero in the full 3N−6 coordinate space, it is meaningless, a con-ventional frequency calculation by diagonalizing the Hessian matrix. However, for those 3N − 7 degrees of freedom, which preserve the degener-acy, and for which the gradient is zero, frequencies
and normal modes can be calculated byproject-ing the seven zero frequency directions, i.e., the three translations, the three rotations, and the gra-dient difference vector, out of H [23, 24], as given by Eq. (1):
HP =(1−P)H(1−P), (1)
where H is the 3N × 3N Hessian matrix, HP is the projected force constant matrix, and P is the projector, a 3N × 3N matrix, which is built from the unit vector that points along the mass-weighted gradient difference obtained di-rectly in the optimization process, and the six 3N -dimensional infinitesimal rotation and translation vectors obtained according to expressions given in Ref. [25].
Results and Discussion
In this section, the main features of the singlet and triplet surfaces related to the thermal produc-tion of the nitrene intermediate from azides will be stressed. The energetic data for all the critical points under discussion are collected in Table I, the geo-metrical parameters in Table II, and the optimized structures for such points are displayed in Figure 1, respectively.
In labeling the critical points, minima, transition states, and intersystem crossings are denoted by Mβ, TSβ, and ISCβ, respectively; whereβis a
num-ber that runs from 1 to 3, i.e., 1 for hydrazoic acid, 2 for methyl azide, and 3 for ethyl azide.
The most important geometrical parameters of the system investigated are collected in Table II. Ad-ditionally, we show the available experimental para-meters of hydrazoic acid [26] and methyl azide [27] together with the results obtained at the density functional theory (DFT) and second-order Møller– Plesset (MP2) levels of theory, respectively. Gener-ally speaking, the overall agreement between the calculated and experimental values is very good, the CASSCF and MP2 values being closer to the experimental ones than the corresponding DFT pre-dictions are. The most remarkable differences be-tween the DFT and CASSCF methods lie in the
TABLE I
Energetics for the potential energy surfaces related to N2extrusion 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/S0intersystem crossing [Fig. 1(g)] −163.97698 −164.33465 10.9 45.5
−163.98525 −164.42314
M2, methyl azide [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/S0intersystem 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/S0intersystem crossing [Fig. 1(i)] −242.06386 −242.69476 49.1 42.6
−242.07893 −242.86522
aCAS(10, 8) energy in hartrees. bCASPT2 energy in hartrees. cCAS/cc-pVDZ ZPE in kcal/mol.
dCASPT2/ANO-L+ZPE relative energy in kcal/mol. eActivation energy in kcal/mol.
fIn italic, cc-pVTZ values.
gMean value between the calculated barrier heights for the spin-forbidden and spin-allowed processes in Ref. [7]. hRef. [9].
TABLE II
Relevant geometrical parameters for the critical points related to the thermal decomposition of the studied azides.a
Geometry N1–N2b N2–N3 N3–X N1–N2–N3c 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/S0intersystem crossing [Fig. 1(d)] 1.107 1.794 1.024 149.7 94.57
M2, methyl azide [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/S0intersystem 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/S0intersystem crossing [Fig. 1(f)] 1.109 1.790 1.451 145.5 108.1
aCAS(10,8)/cc-pVDZ.
bInternuclear distances are given in Å. cAngles in degrees.
dIn 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 (—N3backbone) with deviations as large as 0.02 Å.
It is described in the literature [28, 29] that me-thodologies—such as Møller–Plesset perturbation theory and DFT—that are based on single-reference wave functions overestimateπ conjugation giving larger interatomic distances for the atoms involved in theπsystem. However, the opposite effect is ob-served for the DFT values of the three azides. The computed DFT interatomic distances of the —N3 moiety are the shortest ones among the three meth-ods.
The global topological features of the potential energy surfaces for the three azides are essentially the same; therefore we shall discuss all of them to-gether. We have found two critical points in the region dominated by the ground-state minimum [M1–M3, Figs. 1(a)–1(c)]. One of them is a transi-tion state [TS1–TS3, Figs. 1(d)–1(f)], and the other is an intersystem crossing minimum [ISC1–ISC3, Figs. 1(g)–1(i)]. The energy difference between these two points and the minimum on the singlet sur-face is approximately the same for the three azides, ranging from 48 kcal/mol in HN3 to 43 kcal/mol
in CH3CH2N3. The directions of the transition and gradient difference vectors are plotted together with each of the respective figures. Both vectors are al-most parallel, and their directions correspond to the stretching of the N2—N3 internuclear distance. As-suming that the bond being broken (N2—N3) is the reaction coordinate, it must be noted that such a distance increases from the ISCs to the TSs, which means that the reactive molecule sees the intersys-tem crossing before the transition state.
On the other hand, the spin-orbit coupling mag-nitudes (HSO
IJ ) have been calculated at the geome-tries of the lowest energy crossing points (Table III) by using the method of Koseki et al. [30].
In accordance with the Landau–Zenner mo-del [31 – 33], the efficiency of the intersystem cross-ing depends on the magnitude of the spin-orbit coupling, on the difference between the gradients of the singlet and triplet states, and on the nuclear ve-locities as the system approaches to the intersection region. Thus, provided that the computed spin-orbit coupling is not very small, the gradients for the S0 and T1 states are similar, and the velocity near the intersection point must be slow because such a point
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/S0intersystem crossing [Fig. 1(d)] 43.3 43.9
ISC2,T1/S0intersystem crossing [Fig. 1(e)] 42.5 43.7
ISC3,T1/S0intersystem crossing [Fig. 1(f)] 42.5 43.3
aBasis set.
is very close to a transition state; this process must be favored in the pyrolysis of aliphatic azides.
In order to verify the reliability of our calcula-tions, we have computed the IRCs (Fig. 2) starting at the two critical points found on the PESs of hy-drazoic acid; the corresponding IRCs for methyl and ethyl azide have been published elsewhere [10, 11]. It can be seen in Figure 1 that such critical points connect nicely the reactive molecule with the
prod-ucts. Although the CASSCF calculations predict the spin-forbidden reaction as exothermic [Fig. 2(b)], the computed energies at the CASPT2 level re-veal that such reactions are slightly endothermic (Table I). The energies of the forbidden reactions have been computed on the supermolecule by elon-gating the N2—N3 distance about 6 Å, while the remaining coordinates keep their values at the min-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.
point, the geometries of the two fragments to be formed, nitrene and molecular nitrogen, are close to their respective equilibrium values [9 – 11].
Conclusions
It is shown that two reaction paths exist for the nitrene production from aliphatic azides. One channel is a spin-forbidden mechanism, while the other is allowed by the selection rules for spin con-servation. The barrier heights of both pathways are almost isoenergetic in the three studied azides, agreeing quite well with the experimental activa-tion energies. Whether the process is spin-allowed or spin-forbidden cannot be unambiguously estab-lished only on the basis of these calculations. It has been previously demonstrated that both reactions are equally probable for hydrazoic acid [5 – 7], and it has been demonstrated as well that the minimum energy point on the intersection of two surfaces represents a key bottleneck along the minimum en-ergy path, playing the role of the transition state for the forbidden reaction [33, 34]. Consequently, we have to accept that methyl and ethyl azide will decompose through both channels and any other mechanism should be neglected [11].
ACKNOWLEDGMENTS
This research has been supported by the Di-rección General de Investigación Científica y Téc-nica (DGICYT; Grant PB96-0697). The authors thank D. R. Larrosa for the technical support in running the calculations and SCAI (University of Málaga) for use of an Origin 2000 SGI computer.
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