Abstract.- MNDO-PM3 level calculations and ab initio calculations at UHF/6-31G* level were performed for neutral molecules (S₀ state), the lowest excited states (T₀ and S₁) and radical anions (D₀ and D₁ states) of p-nitrophenyl, p-acetylphenyl, phenyl azides and 4-azidopyridine and HN₃. Consideration of the nature of the frontier molecular orbitals, changes of bond orders, values of activation barriers shows, that decomposition of azido group facilitates on excitation of azide into the lowest excited states and on formation of radical anion.
Keywords: MNDO-PM3, ab initio, aromatic azide, radical anion, dissociation of azido-group.

• Introduction
• Results

• Molecular orbitals and electron levels
• Geometry and charge distribution
• Energy parameters and electron affinities

• References

• Introduction

The photochemical properties of organic azides have been extensively investigated [1-5], however there are only the restricted number of theoretical publications on this subject. The first excites singlet state S₁ and the lowest triplet state T₀ are the most interesting from the point of view of photochemistry, so these states are examined in the present paper in comparison with the ground state S₀. The electron transfer to azide, as well as an excitation, is known to lead to decomposition of azido-group [6,7], the radical anions of azides being the necessary intermediates in these reactions. Therefore another subjects for discussion in the present paper are the two states of radical anions - D₀ and D₁.
The structures of azides and their radical anions were calculated with full optimization of geometrical parameters using semi-empirical method MNDO-PM3 [8] (program package MOPAC 7.0). Energy parameters were improved by ab initio RHF, UHF methods with basis 6-31G*; correlation energy was calculated using the second and third order of Moller-Plesset perturbation theory (MP2 and MP3); GAUSSIAN-94 code was used [9]. Excited states were calculated using CIS and CASSCF levels of theory in GAUSSIAN-94 and EXCITED and C.I. operators in MOPAC 7.0.
Fig.1 shows the coordinate system used and the structures of aromatic azides investigated: p-nitrophenyl azide (NPA), p-acetylphenyl azide (APA), 4-azidopyridine (AP), phenyl azide (PA), and, for comparison, the simplest azide HN₃.

Fig.1. Structures of azides investigated and the coordinate system used

• Results

• Molecular orbitals and electron levels

Conventionally, we define MO, lying in the plane of aromatic ring, as a sigma-type MO, and that, lying in the perpendicular plane, as a pi-type MO. Fig.2 shows the structures of the frontier MOs: the highest occupied MO (HOMO), the lowest unoccupied MO (LUMO) and the second lowest unoccupied MO (SLUMO) of neutral aromatic azides in the region of azido-group using NPA as an example.

Fig. 2. Frontier orbitals of NPA in the region of azido-group.

In accordance with our definition, HOMO and LUMO are pi-type orbitals, and SLUMO is sigma-type orbital. All three MOs are antibonding on N(2)-N(3) bond, at the same time in the region of N(1)-N(2) bond HOMO is slightly bonding, LUMO is nonbonding, and SLUMO is antibonding.

Fig.3 shows the changes of electron levels of neutral molecules in the series NPA-APA-AP-PA-HN₃. In this series electron level of the sigma-type SLUMO changes slightly, but the level of the pi-type LUMO increases, so that in passing from PA to HN₃ the change of order of these levels is observed.

Fig. 4 shows the filling of electron levels in different states on the example of APA and its radical anion.One can see that the excited states S₁ and T₀ are similar to D₀ state of radical anion on the nature of the highest singly occupied MOs, that are sigma-type MOs. In S₀ and D₁ states the highest occupied MOs are pi-types MOs.

Fig. 3. PM3-calculated changes of electron levels of neutral azides.

Fig. 4. Filling of electron levels in different states of APA and its radical anion (PM3 calculation).

• Geometry and charge distribution

Geometrical parameters are shown in Table 1, and bond orders (Mulliken density populations) and effective atom charges are shown in Table 2. Example of HN₃, PA and NPA molecules shows that geometrical parameters, calculated by PM3 method are in good accordance (within 0.02-0.03 A for bond lengths and 1-5° for valence angles) with more precise ab initio calculations and with experimental data. From Tabl.2 one can see the same tendency of changes of bond orders, density populations and charges in azides investigated for both semi- and non-empirical calculations.
In the neutral azides azido-group has near linear geometry: valence angle NNN = 169-170° , N(2)-N(3) bond length is 1.12-1.13 A (bond order p₂₃ = 2.48-2.55) , N(1)-N(2) bond length is 1.26-1.27 A (bond order p₁₂ = 1.33-1.35) for NPA-APA-AP-PA and 1.25 A (p₁₂ =1.43) for HN₃.
Excitation of electron in aryl azides from highest occupied pi-MO to lowest unoccupied sigma-MO, which is antibonding on N(1)-N(2) bond, results in lengthening of this bond by 0.07-0.10 A in S₁ state. On transition from S₁ to T₀ state the further lengthening takes place, bond order being reduced to p₁₂ =0.88-0.91.
In radical anions (D₀ state) azido-group has trans-bent geometry: valence angle NNN =130-132°, N(2)-N(3) bond length is 1.16-1.18 A (bond order p₂₃ = 2.19-2.24), N(1)-N(2) bond length is 1.36-1.38 A (bond order p₁₂ = 0.92-0.99) for aryl azides and 1.31 A (p₁₂ =1.20) for HN₃. One can see that on the geometrical parameters D₀ state is similar to S₁ state, as a result of similar nature of the singly occupied MOs (sigma-types MOs).
D₁ state differs from D₀ mainly by the values of valence angle NNN and bond length r₁₂. For aryl azides, according to the geometrical parameters, D₁ state is similar to S₀ state, as a result of similar nature of the highest occupied MOs (pi-types MOs).
Thus, analysis of changes of bond orders, N(1)-N(2) bond lengths, and nature of occupied MOs testifies that removal of N₂ molecule from T₀, S₁ and D₀ states will occur easier than from S₀ state.
In all azides under consideration central nitrogen atom N(2) of azido-group is positively charged, and terminal atoms N(1) and N(3) are negatively charged.
Calculations show that in aryl azides about 0.08-0.12 e moves through pi-system from N(1) and N(3) atoms to benzene ring, that results in alteration of charges on carbon atoms in the ring. It is noteworthy that quantity of electron density, which moves to ring through pi-system, decreases in the series NPA-AP-APA-PA.

• Energy parameters and electron affinities

Heats of formation (total energies), the first singlet vertical excitation energies and electron affinities of azides are shown in Table 3. Example HN₃ and PA shows that total energies, calculated on RHF/6-31G*//PM3 and RHF/6-31G*//6-31G* levels differ by 0.0045 and 0.0093 a.u., correspondingly. In all cases PM3 and HF/6-31G* calculated E_v values are in good agreement with experimental ones (within 0.14-0.29 eV for PM3 and 0.03-0.08 eV for HF/6-31G*). The case of NPA is an exception and should be discussed separately.
The example of HN₃ shows, that the electron affinity changes significantly by going from PM3 semi-empirical calculation to ab initio RHF/6-31G*//PM3 level, however it changes only slightly during geometry optimization on the 6-31G* level. By going from RHF to UHF, electron affinity changes by 0.2 eV. Electron correlation on the MP3(FC)/6-31G*//6-31G* level results also in a minor (0.2 eV) change of EA value.
For aromatic azides investigated, RHF/6-31G*//PM3 calculated electron affinities differ from semi-empirical values less than for HN₃ (by 1.7 eV), and by going from RHF to UHF, changes are the same, as in the case of HN₃. Therefore, calculations on the RHF/6-31G*//PM3 level are sufficient for revealing the qualitative picture of electron affinity changes in the set of azides under investigation. Calculation shows that in the series of NPA-APA-AP-PA-HN₃ the electron affinity decreases monotonically (Fig.5), and, as a result, for the last members of the series the formation of radical anions becomes thermodynamically unfavorable.

Fig.5. Changes of electron affinities of azides, calculated by different methods.

Fig.6 shows PM3 and HF/6-31G* level calculated minimal energy path of azido group dissociation for S₀ T₀ and S₁ states of HN₃.

Fig.6.Minimal energy path of azido group dissociation in the ground (S₀) and excited (T₀, S₁) states of HN₃: a) - PM3 calculated; b) calculated at HF/6-31G* level (in accordance with Tab. 3, 4).

Fig.7 shows the relative position of states under discussion and minimal energy paths of azido group dissociation in aryl azides on the example of NPA. Fig.7 demonstrates the principle of calculation of the energy differences (Delta) between different states of azides and radical anions and activation barriers (E_a) for azidogroup dissociation reaction (the value of E_a(S₀-T₀) was approximately estimated as a cross point of two curves). Calculated Delta values for all discussion states of azides are shown in Table 4 and E_a values in Table 5.

Fig.7.Minimal energy paths of azido group dissociation in the ground (S₀) and excited (T₀, S₁) states and in radical anions (D₀ and D₁ states) of NPA. The examples of E_a and Delta calculations are shown.

Difference of the heats of formation (or total molecular energies) in S₀ and T₀ states of HN₃ (Delta(S₀-T₀), Tabl.4) shows that ROHF/6-31G*//6-31G* and ROHF/6-31G*//PM3 calculated values are similar and less than PM3 calculated value by 5 kcal/mol. The MP3(FC)/6-31G*//6-31G* calculated value exceeds PM3 calculated value by 19 kcal/mol.
One can see that values of Delta(S₀-T₀) and Delta(S₀-S₁) change slightly for azides under investigation and lie in region of 29-33 and 35-38 kcal/mol, respectively. More significant change is observed for difference Delta(D₀-D₁), this value is minimal for NPA (18 kcal/mol) and increases (to 25 kcal/mol) in the series NPA-APA-AP.
From Fig.6 one can see, that the semi-empirical and ab initio methods give the qualitatively similar picture of the HN₃ dissociation process. PM3 calculated activation barrier E_a(S₀) coincides with experimental values (52 and 53.6 kcal/mol, respectively, Tabl.5). RHF/6-31G*//6-31G* and RHF/6-31G*//PM3 calculated values of E_a(S₀) are similar and less than PM3 calculated value by 25 kcal/mol, correlation correction makes up 21 kcal/mol.
The value of E_a(S₀-T₀) was estimated as difference of total energies (S₀) of the system at minimal point and at N(1)-N(2) bond length when the total energies in S₀ and T₀ states coincide (Fig.7). PM3 calculated activation barrier E_a(S₀-T₀) agrees with experimental values (32 and 36.2 kcal/mol, respectively, Tabl.5). RHF/6-31G*//6-31G* calculated value is equal to 25 kcal/mol, correlation correction increases this value by 10 kcal/mol.
For excited states (T₀, S₁) PM3-and ab initio calculated activation barriers differ within 2-5 kcal/mol.
Taking into account the above corrections, PM3 method can be used for qualitative estimation of relative reactivity of aromatic azides in different states.
For all azides under consideration activation barrier, both semi- and non-empirical calculated (Fig.6, Fig.7, Tabl.5) is the highest for S₀ state and is comparatively small for excited states (T₀, S₁) and for radical anion (D₀ and D₁ states).
Comparison of E_a values for different azides in different states (Tab.5) shows that the value of activation barrier for every state of azides does not practically depend on the nature of azide and is mainly determined by the nature of azide state.

Thus, the calculations show, that decomposition of azido group facilitates on excitation of azide into the lowest excited states (T₀ or S₁) and on formation of radical anion (D₀ or D₁ state). This conclusion is in full accordance with the known experimental results [1-7].

The work is financially supported by the Russian Foundation for Basic Research (Grant 94-03-08673). Part of ab initio calculations were carried out at the Supercomputer Center (IOC RAS) in connection with RFBR grant 95-07-20201.

Table 1. Geometry of XNNN fragment (X = H, C) in aryl azides and in HN₃.
Return to text

^a) calculated using Huzinaga basis (10s6p1d)_N, (6s2p)_H [10]
^b) see [11]
^c) crystallographic data [12]

Return to text

Table 2. Bond orders (PM3 calculated), Mulliken density populations (RHF/6-31G* calculated) and effective atom charges in XNNN fragment (X = H, C) in aryl azides and HN₃.
Return to text

Return to text

Table 3. Heats of formation (H_f) and total energies (E) of aryl azides and HN₃ (S₀ state) and their radical anions (D₀ state), the first singlet vertical excitation energies (E_v) and electron affinities (EA) .
Return to text

^a) experimental values are given in parenthesis

Return to text

Table 4. Calculated energy differences (Delta) between different states of azides and radical anions (definition see Fig.7).
Return to text

^a) estimated value

Return to text

Table 5. Calculated activation energy (E_a) of azido group dissociation reaction in different states of azides and their radical anions (definition see Fig.7).
Return to text

^a) see [13]
^b) calculated using Huzinaga basis (10s6p1d)_N, (6s2p)_H [10]
^c) estimated value

Return to text

• References

Return to text

1. A.Reiser, H.M.Wagner, in The chemistry of the azido group, Ed. S.Patai, Wiley, New York, 1971, 441.
2. P.A.S.Smith, in Azides and nitrenes, Ed. E.F.V. Scriven, Academic Press, Orlando, 1984, 95.
3. G.B.Schuster, M.S.Platz, Advances in photochemistry, 17 (1992) 69.
4. M.F.Budyka, M.M.Kantor, M.V.Alfimov, Rus.Chem.Rev., (1992) 48.
5. N.P.Gritzan, E.A.Pritchina, Rus.Chem.Rev, 61 (1992) 910
6. W.Abraham, St.Siegert, J.Inf.Rec.Mater., 17 (1989) 379.
7. Y.Zhu, G.B.Schuster, J. Am. Chem. Soc., 115 (1993) 2190.
8. J.J.P.Stewart, J.Comp.Chem., 10 (1989) 221.
9. Gaussian 94, Revision D.1, M. J. Frisch, G. W. Trucks, H. B. Schlegel, P. M. W. Gill, B. G. Johnson, M. A. Robb, J. R. Cheeseman, T. Keith, G. A. Petersson, J. A. Montgomery, K. Raghavachari, M. A. Al-Laham, V. G. Zakrzewski, J. V. Ortiz, J. B. Foresman, J. Cioslowski, B. B. Stefanov, A. Nanayakkara, M. Challacombe, C. Y. Peng, P. Y. Ayala, W. Chen, M. W. Wong, J. L. Andres, E. S. Replogle, R. Gomperts, R. L. Martin, D. J. Fox, J. S. Binkley, D. J. Defrees, J. Baker, J. P. Stewart, M. Head-Gordon, C. Gonzalez, and J. A. Pople, Gaussian, Inc., Pittsburgh PA, 1995.
10. M.H.Alexander, H.-J.Werner, P.J.Dagdigian, J.Chem.Phys., 89 (1988) 1388.
11. B.P.Winnewiser, J.Mol.Spectr., 82 (1980) 220.
12. A.Mugnoli, C.Mariani, M.Simonetta, Acta Cryst., 19 (1965) 367.
13. O.Kajimoto, T.Yamamoto, T.Fueno, J.Phys.Chem., 83 (1979) 429