THEO CHEM

Journal of Molecular Structure (Theochem) 309 (1994) 45-52

An ab initio study of the azoniaspiro[2,2]pentane cation (aziridineaziridinium ion)

Ana Martineza, Josi Elguero*Ta, Otilia Mob, Manuel YQnezb

aInstituto de Quimica MPdica (CSIC), Juan de la Cierva. 3. 28006 Madrid, Spain

‘Departamento de Quimica Fisica, Universidad Autdnoma de Madrid, Cantoblanco. 28049 Madrid, Spain

(Received 15 November 1993; accepted 4 December 1993)

Abstract

An ab initio 6-31G* study of the azoniaspiro[2.2]pentane cation (aziridineaziridinium ion) was carried out, together with a Bader analysis of the topological characteristics of the electronic charge density, p, its Laplacian, V2p, and the ellipticity. By comparison with the results of the same analysis done on the aziridine and aziridinium cations it appears that, although the title compound behaves as a constrained double-aziridinum cation, it should be a stable and isolable molecule.

1. Introduction

Azoniaspiro[2.2]pentane (4) is an elusive com- pound which has never been isolated. Its existence has been postulated to account for the peak in the mass spectrum at 70 Th (we advocate the use of the thompson, Th, instead of the more conventional m/z units) [1,2]. Nevertheless, it is part of a chain of reactions starting from the double nitrogen mustard 1 and ending in the polymer 6 (Scheme 1).

Compound 1 has been the subject of many studies, both chemical [3-51 and biological [6,7]. Compounds 2 and 3 have been described [8-111 and so have structures related to 5, but these latter have only one aziridinium ring 7 [12]. The quater- nary compounds 8 related to structure 2 are known [ 13,141 and the equilibrium between aziridinium and piperazinium salts, for instance between 8 and 9, is well documented [ 15,161.

* Corresponding author.

Due to our interest in small heterocyclic rings from a theoretical point of view [ 17,181, we decided to carry out a study of compound 4 with the aim of gaining insight into its structure, bond- ing and ring strain.

2. Computational details

Ab initio calculations were carried out with the GAUSSIAN 90 series of computer codes [19]. The geometries of the different species included in this study were optimized at the HF/6-31G* level [20] using gradient techniques.

The harmonic vibrational frequencies were determined by using analytical second-derivative techniques and the results obtained were used to characterize the stationary points of the potential energy surface and to evaluate the zero-point energies, which were scaled using an empirical

0166-1280/94/$07.00 0 1994 Elsevier Science B.V. All rights reserved SSDZ 0166-l 280(94)03644-Z

A. Martinez et al.lJ. Mol. Struct. (Theochem) 309 (1994) 45-52

C +/ H

CICH,CH,NHCH,CH,CI - N Cl-

1 ’ CH&H&I 2

Scheme 1.

factor of 0.89 [21]. The geometry of 4 was refined at the MP2/6-31G* level, as it has been proved that this level of theory provides accurate molecular structures [22].

As far as we know, there is no theoretical information on cation 4, at least at the ab initio level, and thus we considered it of interest to analyse its structure and bonding in terms of the topological characteristics of the electronic charge density (p), its Laplacian (V*p), and the ellipticity (6) of the bonds. These topological analyses are particularly well suited for use in describing bond activation, bond reinforcement and ring strain phenomena. As we have shown recently [23-251 for the particular case of ion-molecule complexes in the gas phase, bond activation can be detected by comparing the Laplacian of the charge densities of the molecular ion and the neutral molecule from which it derives. In fact, Bader and co-workers

[26-291 have demonstrated that the Laplacian of the electronic charge density (V*p) identifies regions of space wherein p is locally concentrated (V*p < 0) or depleted (V*p > 0). Hence, bond activation should be accompanied by a decrease in the absolute value of V*p, while bond reinforce- ment would imply a more negative value of the Laplacian. Therefore, in general, an inspection of the topological characteristics of the Laplacian of the charge density will reveal the most significant charge redistributions undergone by the neutral molecule upon cation association or upon ion- ization. In addition, the existence of a chemical bond implies the existence of a (3,-2) critical point in p, i.e. a point in which p presents two negative curvatures (X,, X2) and a positive one (As), indicating that, at that point, the electronic charge density is minimum along the bond and maximum in the other directions. Usually, the

A. Martinez et al./J. Mol. Struct. (Theochem) 309 (1994) 45-52 47

value of the density and its Laplacian at these points, called “bond critical points”, allows the bonding between two given atoms to be character- ized. In particular, the ratio between the two negative curvatures is a measure of the ellipticity of the bond (defined as 6 = 1 - X1/X2), and hence is a measure of the charge delocalization on a given plane. Furthermore, it is also possible to define the gradient paths determining the lines of maximum electron density between two nuclei (usually called bond paths) which in turn allows us to define the bond lengths, which in strained rings are not identical to the interatomic dis- tances. Then, for a given compound, the set of bond critical points and the network of the max- imum electron density paths define the correspond- ing molecular graph, which has been shown to be very useful in the description of strained systems [30-321.

In the present study these topological calcu- lations were carried out using the MP2 electronic charge densities in order to take into account explicitly the electron correlation effects. For this purpose, the AIMPAC series of programs [33] was employed.

3. Results

3.1. Geometries

The geometrical data referred to the formula

711

H 112-Cl

\ H

/

/

N+-C 3

‘H H22.7C2

I HP1

4

shown above are reported in Table 1. It can be seen that, in this case, electron corre-

lation effects are not very important. In general, the bond angles obtained at the MP2 level differ from

Table 1 Characteristics of the optimized geometries of compound 4

Method HF/6-3lG* MP2/6-3 lG*

Bond length (A)

N+-Cl

Cl-C2

Cl-HI I”

1.454 1.462

1.481 1.497

1.074 1.085

Bond angle (deg)

Cl-N+-C2

N+-Cl-C2

Cl-N+-C3

61.2 61.6

59.4 59.2

137.8 137.6

N+-Cl-HI1 114.8 114.7

C2-Cl-HI2 119.2 118.9

Hll-Cl-HI2 116.5 116.9

a Identical to Cl-Hl2, C2-H21, C2-H22, etc.

the HF ones by less than 0.5” while, as expected, the bond lengths increase by 0.08 A or more.

3.2. Ring strain

To analyse the ring strain in compound 4 we

c /H C

+/ H

N N\H

10 11

thought it useful to compare its bonding character- istics with those of the neutral monocyclic com- pound, aziridine (10) and its protonated form (11).

In this comparison we are assuming that some similarities might exist between protonated aziridine (11) and the azoniaspiro cation (4), since both systems are positively charged and have a tetracoordinated nitrogen atom. The MP2 optimized structures of aziridine and protonated aziridine were taken from Ref. 34. In Fig. 1 we present the molecular graphs of these three species. Firstly, it should be noted that the values reported in this figure for the bond path lengths, bond path angles, bond critical point charge densities and ring critical point charge densities of 10 and 11 are not very different from the SCF values published by Cremer and Kraha [30]. In general, the charge densities at the bond critical

48 A. Martinez et al./J. Mol. Struct. (Theochem) 309 (1994) 45-52

(‘A’7 (60.3) \ ~

A 75.6 \ I

0.250 ‘*lt“ /

p.35 83 (1*47g1

a

(1.4

C

Fig. 1. Molecular graphs of (a) aziridine (lo), (b) protonated aziridine (ll), and (c) aziridineaziridinium ion (4), obtained using the MP2 electronic density. Bond path lengths are in r%ngstrijms and bond path angles are in degrees. The geometrical bond lengths and bond angles are given within parentheses. The densities (e a.u.-3) at the bond critical points (0) and at the ring critical points (+). The ellipticities of the bonds are given in square brackets.

points and at the ring critical points are slightly smaller, which is in-keeping with the fact that the bonds are slightly longer at the MP2 level. This is a direct consequence of the influence of excited anti- bonding configurations at the MP2 level. However, the most significant differences correspond to the total atomic charges, obtained by means of a Mulliken population analysis.

It can be seen from Table 2 that SCF theory tends to exaggerate the electronegativity of the

nitrogen atom, while it slightly underestimates that of carbon; these observations are also reflected in the values of the corresponding dipole moments. As we shall illustrate later, these electron correlation effects play a non-negligible role in the description of these three strained systems.

The corresponding Laplacians of the electronic charge densities are presented in Fig. 2. It can be seen that protonation of aziridine implies a signifi- cant activation of the C-N bonds, while the C-C

A. Martinez et al/J. Mol. Struct. (Theochem) 309 (1994) 45-52

Table 2 TotaI Mulliken charges of species 4, 10 and 11, obtained using a 6-31G* basis set

Species N c H(C)

49

H(N)

HF MP2 HF MP2 HF MP2 HF MP2

4 -0.485 -0.323 -0.184 -0.216 +0.271 +0.273 _ _ 10 -0.625 -0.548 -0.220 -0.240 +0.1!38 CO.183 +0.346 +0.327 11 -0.728 -0.632 -0.209 -0.233 +0.297 +0.291 +0.477 +0.466

linkage becomes slightly reinforced. These acti- vation phenomena upon gas-phase protonation have been discussed fully elsewhere 1231. Here we discuss again only the most si~ifi~nt features. Upon nitrogen protonation, the nitrogen lone- pair becomes a c-bonding orbital. To do so, it gains p character, and by orthogonality the hybrids involved in the C-N bonds should increase their s character. These hybridization changes must involve an increase in the angle between these two hybrids, as found when com- paring the corresponding bond path angles of neutral (75.1”) and protonated (76.1”) aziridine. This increase in s character also implies an increase in the electronegativity of the nitrogen atom, which depopulates the C-N bond. The charge depletion in the C-N bonding region causes a polarization of the charge density around both carbon atoms, which results in a reinforce- ment of the C-C linkage. The most significant consequence of the depopulation of the C-N bonds is that the corresponding paths become inwardly curved, while their ellipticities become almost twice those in the neutral form. The first feature implies that the N-C-C bond path angles are much smaller in the protonated species than in the neutral one, which should be reflected (as we show later) in a greater ring strain. It should also be noted that these charge redistributions are not reflected in the geometrical bond angles, which always undergo changes opposite to those described above for the corresponding bond path angles. This apparent contradiction can be easily understood if one takes into account the fact that the C-N bond lengths increase while the C-C bond length decreases upon proton- ation. Consequently, the C-N-C bond angle should be slightly smaller in the protonated

form and the N-C-C ones slightly larger. Hence hybridization changes in strained rings cannot be discussed in terms of geometrical angles, but must be discussed by considering changes in bond path angles.

The increase in the ellipticity of the C-N bonds is a consequence of the decrease in the magnitude of Xz, which is an indication of the weakness of the cyclic structure with regard to a ring-opening process. As shown by Bader 1281, the opening of a ring structure results from the coalescence of the ring critical point and a bond critical point, which takes place when Xz vanishes. This is far from true for protonated aziridine, but both the molecular graphs and the Laplacian of p clearly show (see Figs. 1 and 2) a weakening of the cychc structure. It must be stated that the SCF calculations clearly overestimate these effects, because at the SCF level the ellipticities of the C-N bonds increase by a factor of 3, as a consequence of the overestimation of the el~tronegativity of nitrogen, as mentioned above.

The situation for the Spiro cation (4) is not very different from that described above for the proton- ated form of aziridine, but the effects are quantita- tively smaller. The charge densities at the C-N bonds are also smaller than in neutral aziridine (lo), but are greater than those in protonated azir- idine (11). As a consequence, the corresponding bond paths are also inwardly curved, but to a smaller extent than in protonated aziridine. There are, however, some significant differences between the bonding of these two molecular ions, in parti- cular with regard to the C-N-C bond path angle. As illustrated in Fig. 1, this angle is considerably greater in 4 than in 10 or 11. This is a consequence of the geometrical restrictions imposed by the existence of the two cyclic structures in the former.

50 A. Martinez et ai./J. Mol. Struct. (Theochem) 309 (1994) 45-52

t

: a

Fig. 2. Contour maps of the Laplacian of the MP2 charge densities of (a) aziridine (lo), (b) protonated aziridine (ll), and (c) aziridineaziridinium ion (4). Positive values of V’p are denoted by solid lines and negative values by dashed lines. The values of the contour lines are f0.05, ~tO.25, 3~0.50, f0.75 and f0.95 a.u.

Let us consider one of the two identical subunits of orbitals involved in the C-N bonds can be of the 4. Similarly to what has been found for 11, in order of 76” because the other two hybrids (those molecule 4 the existence of a positive charge also involved in the N-H bonds) have no restrictions results in an increase in the electronegativity of with respect to their spatial orientation (the angle the nitrogen atom, which should be reflected in between them opens up to 1139, this possibility is an increase in the angle between its hybrid orbitals. hindered in compound 4 where these two hybrids However, while in 11 the angle between the hybrid are also forced to subtend an angle smaller than

A. Martinez et al./J. Mol. Struct. (Theochem) 309 (1994) 45-52 51

90”, because they are involved in the C-N bonds of the second cyclic subunit.

A second difference is related to the charge delo- calization that occurs in three-membered rings. Obviously, in species 4 this delocalization is con- siderably greater than in the monocyclic counter- parts, as it takes place in both aziridinium subunits. The most striking consequence of this is the rather small net charge at the nitrogen atom (half of the protonated aziridine and almost half of the neutral aziridine). This may be the reason why, in spite of the depopulation of the C-N bonds of 4 with respect to 10, the corresponding bond lengths are slightly shorter in the former than in the latter.

Table 3 Total energies (E) and zero-point energies (ZPE) of the com- pounds involved in reactions (l)-(3) evaluated at the 6-31G* level

Compound ;.u.,

ZPE (kcal mol-‘)

Ethane Propane Aziridine Protonated aziridine Dimethylamine Protonated dimethylamine Aziridineaziridinium ion

-79.22875 50.0 - 118.26365 69.4 -133.03856 47.6 -133.40795 57.2 -134.23885 62.4 -134.61353 72.7 -210.27334 79.6 -210.96301a

The main conclusion of this topological analysis is that 4, similarly to 11, should be more strained than aziridine itself.

Tetramethylammonium ion -212.68514 110.4

a Total energy obtained at the MP2/6-3 lG* level.

To check this from a more quantitative point of view we considered the three isodesmic reactions shown below, where the three systems under consideration are compared with the appropriate strain-free aliphatic compounds. The structures of these reference systems were also optimized at the 6-31G* level. As far as we know, the structure of tetramethylammonium ion has never been reported at this level; it is available from the authors upon request. The enthalpies of reactions (l)-(3) were obtained using the HF/6-31G* total energies, after including the corresponding zero-point- energy corrections (Table 3).

predicted by using reaction (3). Consistent with our previous discussion, protonated aziridine is predicted to be more strained than the correspond- ing neutral molecule. Similarly, if one considers the strain in 4 for each cyclic subunit to be half the enthalpy of reaction (3), one finds that on going from aziridine (10) to the aziridineaziridinium ion (4) there is an increase in the ring strain of the same order as that found for protonation of the former.

4. Conclusion

It can be seen that the three reactions are Contrary to expectations, we have shown by exothermic, showing that the cyclic species present means of a topological analysis of the electronic a considerable strain. Quite significantly, the charge densities and their Laplacians and by the exothermicity of the first two processes is in fairly energetics of appropriate isodesmic reactions that good agreement with the estimations (about 24.3 the azoniaspiro[2.2]pentane cation has a ring strain and -28.9 kcalmol-‘) obtained using the corre- similar to that of protonated aziridine, although sponding experimental heats of formation at there are some differences in the details of the 298 K [35]. Hence we may have some confidence bonding of the two species. Both protonated in our estimation for the ring strain of 4 as aziridine (11) and the aziridineaziridinium ion (4)

EN--H+ 3 CHa-C&*C&-NH-CH3 + 2 CH,-CY-CH,, AH =-22.8 kcal mot’ (1)

I> +,H N,

H + 3 CH&HpC&-NH*-Ct-$ + 2 CH,-CH2-CH,, AH =-25.5 kcal mot’ (2)

c3 N* + 6 CH3-C&e (CH&N++ 4 CH3-CH,-CH3, AH =-51.7 kcal mot’ (3)

52 A. Martinez et al.lJ. Mol. Struct. (Theochem) 309 (1994) 45-52

are more labile with regard to a ring-opening pro- cess than is aziridine. However, taking into account that protonated aziridine is a stable cyclic structure and that the aziridineaziridinium cation has a similar ring strain, one might conclude that the latter should also be stable, in spite of the fact that it has never been isolated.

5. Acknowledgement

Financial support from CICYT (Project Nos. FAR90-746 and PB90-0228X02-01) is gratefully acknowledged.

6. References

[l] L. Audier, M. Azzaro, A. Cambon and R. Guedj, Bull. Sot. Chim. Fr., (1968) 1013.

[2] L. Audier, M. Azzaro, A. Cambon and R. Guedj, Bull.

[31

[41

[51

bl 171

PI

[91

[lOI

[ill

WI

v31 v41

Sot. Chim. Fr., (1968) 1021. L.I. Petlichnaya, E. Besyadetskaya, MS. Oleiovskaya and O.G. Demchuk, Farm. Zh., (1976) 34. (Chem. Abs., 86, 171687). M. Teulade and P. Savignac, Phosphorus Sulfur, 21 (1984) 23. M.G. Avetyan, A.V. Kazaryan and S.G. Matsoyan, Arm. Khim. Zh., 38 (1985) 658. (Chem. Abs., 104, 167682). J. Potel and N. Brock, Azneim. Forsch., 21 (1971) 1250. C. Ho and S. Ludeman, J. Labelled Comput. Radio- pharm., 28 (1990) 587. G.R. Pettit, J.A. Settepani and R.A. Hill, Can. J. Chem., 43 (1965) 1792. S.V. Yakovlev, V.B. Ukraintsev, O.M. Nozdrina and Yu.N. Kukushkin, Zh. Obshch. Khim., 60 (1990) 1321. (Chem. Abs., 114, 34768). M.G. Avetyan, M.G. Sarkisyan and S.G. Matsoyan, Arm. Khim. Zh., 27 (1974) 225. (Chem. Abs., 81, 91266). D. Maysinger, P.C. Tagari and C. Cuello, Biochem. Pharmacol., 35 (1986) 3583. P. Vieles and J. Galsomias, Bull. Sot. Chim. Fr., (1967) 1598. G.W. Fischer and K. Lohs, Z. Chem., 8 (1968) 416. J.G. Demirchoghyan, S.A. Papoyan, O.V. Babasyan,

D.A. Galstyan and MS. Oganesyan, Zh. Eksp. Klin. Med., 16 (1976) 33. (Chem. Abs., 87,95833).

[15] J. Hine, Physical Organic Chemistry, McGraw-Hill, New York, 1962, p. 146.

[ 161 J.R. Sowa and CC. Price, J. Org. Chem., 34 (1969) 474. [17] O.Mo, J.L.G.dePazandM.Yaiiez, J.Phys.Chem.,91

(1987) 6484. [18] 0. M6, M. Yaiiez and J. Elguero, J. Mol. Struct.

(Theochem), 201 (1989) 17. [19] M.J. Frisch, M. Head-Gordon. G.W. Trucks.

Lw

1211

J.B. Foresman, H.B. Schlegel, K. Raghavachari; J.S. Binkley, C. Gonzalez, D.J. DeFrees, D.J. Fox, R.A. Whiteside, R. Seeger, C.F. Melius, J. Baker, R.L. Martin, L.R. Kahn, J.J.P. Stewart, S. Topiol and J.A. Pople, GAUSSIAN 90, Revision I, Gaussian, Inc., Pittsburgh PA, 1992. P.C. Hariharan and J.A. Pople, Theor. Chim. Acta, 28 (1973) 213. J.A. Pople, K. Ragavachari, H.B. Schlegel and J.S. Binkley, Int. J. Quantum Chem. Symp., 13 (1979) 225.

PI

~231

1241

v51

P61

1271

1281

[x91 1301

[311

[321

1331

[341

[351

P.v.R. Schleyer, Watoc’93, Toyohashi, Japan, 1993, p. 40. M. Alcami, 0. M6, M. Yaiiez, J.L.-M. Abboud and J. Elguero, Chem. Phys. Lett., 172 (1990) 471. M. Essefar, M. El Mouhtadi, V. Lopez and M. Yafiez, J. Mol. Struct. (Theochem), 255 (1992) 393. J. Tortajada, A. Total, J.P. Morizur, M. Alcami, 0. M6 and M. Yafiez, J. Phys. Chem., 96 (1992) 8309. R.F.W. Bader, P.J. MacDougall and C.D.H. Lau, Am. Chem. Sot., 106 (1984) 1594. K.W. Wiberg, R.F.W. Bader and C.D.H. Lau, J. Am. Chem. Sot., 109 (1987) 985. R.F.W. Bader, Atoms in Molecules. A Quantum Theory, Oxford University Press, New York, 1990. R.F.W. Bader, Chem. Rev., 91 (1991) 893. D. Cremer and E. Kraha, J. Am. Chem. Sot., 107 (1985) 3800. D. Cremer and J. Gauss, J. Am. Chem. Sot., 108 (1986) 7467. K.B. Wiberg, R.F. Bader and C.D.H. Lau, J. Am. Chem. Sot., 109 (1987) 1001. The AIMPAC programs package was provided by J. Cheeseman and R.F.W. Bader, McMaster Univer- sity, Hamilton, Ont. M. Alcami, 0. M6 and M. Yafiez, J. Am. Chem. Sot., 115 (1993) 11074. S.G. Lias, J.E. Bartness, J.B. Liebman, J.L. Holmes, R.D. Levin and W.G. Mallard, J. Phys. Chem. Ref. Data, 17 (Suppl. 1) (1988).