thermodynamic stability and reactivity of the antiaromatic heterocycle 1h-azirine

13. A. J. Dobbs, "Experimental observations of chemically induced dynamic electron polarization (CIDEP)," Mol. Phys., 18, 290-294 (1973).

14. P. P. Levin and V. A. Kuz'min, "The role of spin-orbital interaction in the kinetics of geminal recombination of triplet radical pairs in micelles," Dokl. Akad. Nauk SSSR, 292, No. i, 134-137 [sic].

15. B. F. Minaev, Yu. A. Serebrennikov, and H. D. Rempel, "Non-equilibrium spin polarization on the Si-SI center in silicon induced by spin orbit coupling," Phys. Status Solidi, 148, 689-698 (1988).

THERMODYNAMIC STABILITY AND REACTIVITY OF THE

ANTIAROMATIC HETEROCYCLE IH-AZIRINE

S. M. Zavoruev and R.-I. I. Rakauskas UDC 541.13

The thermodynamic characteristics of reactions resulting in the conversion of the antiaromatic three-membered aza heterocycle iH-azirine into isomeric 2H- azirine have been calculated by the SCF-aMO-LCAO method and perturbation theory. The proton affinity has been investigated, and it has been shown that protonation occurs at a carbon atom with the subsequent transition to 2H-azirine protonated at the nitrogen atom.

Despite numerous attempts, the three-membered nitrogen-containing heterocycle iH-azirine has not yet been synthesized (see reviews [1-3]), although isomeric 2H-azirine is fairly stable. It has been postulated that iH-azirine can be an intermediate in several reactions, for example, the hydrolysis of N-phthalimido-l,2,3-triazoles or the oxidative reactions of N-aminophthalimide with alkynes [3], which probably include a common step leading to the formation of iH-azirine, which quickly isomerizes to 2H-azirine:

N N Z../\ (X = phthalimide)

If this hypothesis is correct, the existence of iH-azirine could be detected experimentally by the methods of IR spectroscopy when the appropriate conditions are selected, since its vibrational spectrum was recently calculated by theoretical methods [4, 5]. We note that such a route was previously utilized to experimentally identify a similar antiaromatic heterocycle, viz., thiirene, whose vibrational spectrum was calculated by an ab initio method in [4].

In the present work we determined the thermodynamic characteristics of reaction (i) in the case of the unsubstituted isomers, which may provide a basis for further kinetic calculations. The work also included an investigation of the reactivity of iH-azirine, particu- larly with respect to a proton, and an examination of the structural consequences of protonation. Other isomerization channels, which may be both thermodynamically and kinetically preferable, are possible [6-8], but we confined ourselves to reaction (I) in the present investigation.

Calculation Method. The calculation was carried out by the SCF-MO-LCAO method with the 6-31G(d, p) basis set [9], which includes d-type polarization functions on the nitrogen and carbon atoms and p-type polarization functions on the hydrogen atoms. Partial consideration of electron correlation was carried out according to second-order Moller-Plesset perturbation theory in accordance with the algorithm in [i0] with the use of the 6-31G basis set [Ii]. The correlation corrections obtained were used together with the relative energies of the

! Vil'nyus University. Translated from Teoreticheskaya i ~ksperimental naya Khimiya, Vol. 25, No. 4, pp. 481-486, Jnly-August, 1989. Original article submitted July 13, 1987.

0040-5760/89/2504-0445512.50 �9 1990 Plenum Publishing Corporation 445

0 a 5

7 6

�84

ZgJ f001

/ 6 80

4 60

5

2O

~Y

// 8 lO~T,, deg I

Fig. 1 Fig. 2

Fig. i. Structural formulas and numbering of atoms: a) IH- azirine; b) 2H-azirine; c) 1H-azirine protonated at the nitrogen atom; d) iH-azirine protonated at a carbon atom; Q is the projection of the H atom onto the plane of the ring.

Fig. 2. Dependence of the values of the logarithms of the equilibrium constant of the isomerization reaction iH-azirine ~ 2H-azirine on the temperature: i) 6-31G(d, p); 2) (MP2/6-31G)/6-31G(d, p).

TABLE i. Equilibrium Geometric Parameters of the Neutral iH-Azirine Molecule and the Analog Protonated at the Nitrogen Atom*

l P -arameter I IH-azirine iH-azirine protonated at the N

I atom .

Bond length, pm C2--C3 126,8 (126,5) 126,5 (125,5) NI--C2 152,8 (149,0) 152,1 (148,5) C2--H5 105,8 (106,4) 106,2 (106,8) NI--H4 101,0 (100,9) 100,! (I00,5)

Angle, deg H4--N l - -Q ** 67,4 (69,2) 57,3 (65,6) C3--C2--Q 155,8 160,6 (161,0) H5--C2--Q 11,2 0 (0)

*The values calculated with the use of the 6-31G(d, p) basis set [16] are given in parentheses. **Here Q is the projection of the H atom onto the plane of the ring.

isomers calculated in the 6-31G(d, p) basis, since their additivity had been demonstrated for reactions not accompanied by changes in the total number of electron pairs [12, 13]. The geometric parameters of 2H- and iH-azirine, as well as the protonated forms (Fig. i) were completely optimized with the use of the 6-31G basis set and were presented in [5, 14]. Previously calculated (with the 6-31G basis) values of the harmonic vibrational frequencies [5] were used to calculate the vibrational statistical sums and the energies of the zero vibrational levels. The geometric parameters selected in the present work (Tables 1 and 2) differ somewhat from those given in [5] for the following reasons. I. They were reoptimized with the use of the GAUSSIAN 80 program [15] by a gradient method, since systematic optimization in the internal coordinates with approximation of the cross sections of the potential- energy surface by parabolas in the case of gently sloping surfaces can lead to greater in- definiteness in the position of the minimum than calculations employing a gradient method. The difference between the geometric parameters optimized by the two methods does not exceed i run for the bond lengths and 0.i-0.2 ~ for the angles. 2. The optimization of the geometric parameters of the molecule of iH-azirine was carried out under the assumption that the methylene hydrogen atoms are found in the plane of the ring. The removal of this restriction (with maintenance of the symmetry plane perpendicular to the plane of the ring) resulted in the departure of the methylene bonds from the plane just indicated by 11.2 ~ in the direction opposite to the N-H bond.

446

TABLE 2. Its Protonated Form

2H-azirine ~rotonated Parameter i 2H-azirine

Equilibrium Geometric Parameters of 2H-Azirine and

Bond l eng th , pm

N l--C2 124,5 124,2 N t--C3 155,6 152,2 C2--C3 146,1 148,1 C2--H4 106,4 I (}6,8 C3--H5 107,1 107,1

2H-azirine Protonated Parameter 2H-azirine

Angle, deg

C2--C3--Q * 164,2 162,4 H5--C3--H6 116,1 118,5 N1--C2--H4 150,3 147,8 H7--NI--C3 - - 99,8 H7--N 1--C2 - - 145,5

*Here Q is the projection of the H atom onto the plane of the ring.

TABLE 3. Calculated Rotational Constants and Energies of the Zero Vibrational Levels in the Case of the Usual Iso- topes (12C, 14N, and IH)

Rotational constants, GHz

Mo I ecu i e A l c

Ezv , kJ'mole -I

2H-Azirine 36,314 22,158 15,133 114,5 (35,616) * (22,224) * (15,065) *

I H - A z i r i n e ' 32,399 23,655 14,275 111,8

*Experimental values [17].

We note that the use of split-valence basis sets of the 3-21G and 4-31G types leads to similar results for iH-azirine (see [4]) and that the inclusion of polarization functions in the basis results in some shortening of the skeletal bond~; therefore, Table 1 presents only the results of a recently published investigation [16], in which the 6-31G(d, p) basis set was used, for comparison. The equilibrium geometric parameters obtained were used in calculations on the 6-31G(d, p) and MP2/6-31G levels.

RESULTS AND DISCUSSION

Equilibrium Gas-Phase Isomerization Reaction. The logarithm of the equilibrium constant for the gas-phase isomerization reaction is defined by the expressions

In Ka, r =--AG~/RT = A~r/R--AHo/RT Here

AO ~ = A (G~---Ho~

(2)

(3) is the reduced Gibbs energy, and

AHg = AEo = A E ~ + A E z v , ( 4 )

where AE~ is the change in the energy for the particular electronic state, and AEzv is the difference between the energies of the zero vibrational levels of the isomers. The reduced Gibbs energy was calculated with the use of the "rigid-rotor-harmonic-oscillator" approximation. The matrices of the tensor of the moment of inertia were calculated from the values of the equilibrium geometric parameters in the Cartesian coordinate system, and their subsequent diagonalization gave the moments of inertia and the rotational constants (Table 3). Since the experimental rotational constants for 2H-azirine coincide with the theoretically predicted values with an accuracy of 2%, similar accuracy may be postulated for the calculated rotational constants of iH-azirine. Table 3 also presents the values of the energies of the zero vibrational levels, which were calculated from the harmonic vibrational frequencies and scaled by a factor of 0.899. The scaling factor compensates the deficiencies of the use of the harmonic approximation and the incompleteness of the basis sets, as well as the fact that electron correlation was not taken into account, to a considerable extent. It was found by the least-squares method for the isoelectronic molecules of cyclopropene and 3H-diazirine [5] with known experimental values of the vibrational frequencies, and, as was shown in [5], the error in the determination of Ezv does not exceed 4 kJ.mole -I in this case.

Table 4 presents the total and relative energies of the original and protonated mole-

447

TABLE 4. Total (au)* and Relative (kJ'mole -I) Energies of the Neutral and Protonated Molecules Investigated**

I (MP2 / 6- 3 IG)*"~"~/ I (MP216"3 IG) =wwr Molecule 6-31S(d,p) 6-31G (d, p) 6-31G (d, p) 6-310 (d, p)

2H-hzirine --131,844040 --132,145462 0 0 1H-Azirine --131,781319 --132,077313 164,7 178,9 IH-Azlrin~(C) --132,177369 --132,462305 0 0 1H-Azirine(N) --132,167316 --132,454921 26,4 19,4

*i au = 2625.5 kJ'mole -I **The stability of iH-azirine relative to 2H-azirine in the calculation employing the 6-31G basis set equals 140.0 kJ.mole -I, and the stability of iH-azirine protonated at the N atom relative to the analog protonated at the C atom equals 12.1 kJ'mole -I ***The MP2/6-31G correlation correction.

TABLE 5.

T,K

Calculated Values of the Reduced Gibbs Energy

2H-azirine I iH-azirine 2H-azirine I iH-azirine-

Ar J-mole-l.deg -I

100 172,57 173,01 200 195.72 196,30 298,15 209.66 210,65 400 220,91 222,49

T.K Ar J'mole-l.deg -I

500 230,46 232,63 600 239,13 241,83 700 247,16 250,34 800 254,69 258,28

cules along with the relative energies calculated with the use of the 6-31G basis set. As follows from the data presented for the neutral molecules, both expansion of the basis and consideration of electron correlation lower the stability of iH-azirine relative to 2H-azirine. The values of the reduced Gibbs energy (Table 5) were calculated from the corresponding vibrational and rotational statistic sums for different temperatures. Assessing the accuracy of the values of CT, we note that it is a sum of two components: the error in the "rigid-rotor-harmonic-oscillator" model itself, which is usually assumed to be equal to 5%, and the error associated with the inaccuracy of the determination of the molecular constants, which may be assumed to be equal to several percent in ~he present calculation (when the calculation is carried out according to the formula presented in [18], this results in an abso- lute error not exceeding i-3 J'mole-1"deg -I in the temperature range considered).

Figure 2 presents plots of the dependence of the logarithms of the equilibrium constant of isomerization reaction (i) on the temperature. As follows from the data presented, the equilibrium constant decreases significantly as the temperature is increased, and this should result in an increase in the concentration of less stable iH-azirine. However, it should not be forgotten that the populations of the excited vibrational levels and, consequently, the rate of the corresponding monomolecular isomerization reaction undergo increases as the temperature is increased, which have the opposite effect when the barrier to the reaction is low. We note that the reaction resulting in the formation of iH-azirine from singlet ni- trene (14) and acetylene is exothermic to a considerable extent (~H~ = -241.6 kJ/mole) and should occur without passage over a barrier [19]. The iH-azirine formed would then be sta- bilized by collisions or isomerize, and an increase in the temperature should consequently result in its additional kinetic destabilization. Despite numerous attempts, we have been unable in localizing the transition state of isomerization (i); therefore, the question of the rate of this reaction and, accordingly, the lifetime of iH-azirine remains open.

Reactivity. iH-Azirine may be regarded as a member of the series of the cyclic ena- mines R2C = CR'NR~, in which two centers, viz., the amino nitrogen atom and the carbon atom can undergo electrophilic attack [20, 21]. A calculation of the relative energies of the two protonated forms, the enammonium and iminium ions, showed that the former is less stable (Table 4). Although the effects of expansion of the basis set and consideration of electron correlation have qualitatively different influences on the relative stability of the isomers, the difference is sufficiently large to prevent the occurrence of a change in the order of the stability in calculations employing either basis sets near the Hartree-Fock limit or methods for more complete consideration of the energy of electron correlation. The struc-

448

tural consequences of the protonation of iH-azirine at the carbon atom include geometric and electronic relaxation with a transition to N-protonated 2H-azirine (Fig. id). The possible subsequent deprotonation results, of course, in the formation of 2H-azirine, rather than its antiaromatic isomer as a consequence of the greater difference in stability. Therefore, the failure to detect iH-azirine may be attributed both to its small concentration and to its very rapid conversion into isomeric 2H-azirine:

H H H

V V / r n N ~ ' - /~k -~§ ~/~c (5)

}/~--c\H H~ \H H~ ~ '~i H~ \~ H h H

We note that the electrostatic model of a base-proton interaction based on a calculation of the molecular electrostatic potential [22] is not adequate in the case of IH-azirine, since the deepest potential minimum corresponds to the lone pair of the nitrogen atom, and there are no potential minima near the carbon atoms. This is attributed to the profound geometric reorganization of the molecular skeleton, which is accompanied by the loss of antiaromaticity and the corresponding release of considerable amounts of energy.

LITERATURE CITED

i. F. W. Fowler, "Synthesis and reactions of l-azirines," Adv. Heterocycl. Chem., 13, 45- 76 (1971).

2. M. Tores, E. M. Lown, H. E. Gunning, and O. P. Strausz, "4n-~ electron antiaromatic Heterocycles," Pure Appl. Chem., 52, No. 6, 1623-1643 (1980).

3. R. K. Smalley, "3-, 4-, and 7-Membered aza-heterocycles," in: D. Barton and W. D. Ollis (editors), Comprehensive Organic Chemistry, Vol. 4: Heterocyclic Compounds, Pergamon Press, Oxford (1979), pp. 565-604 [Russian translation: Vol. 8, Khimiya, Moscow (1985)].

4. Carsky, B. A. Hess, and L. J. Schaad, "Ab initio study of the structures and vibrational spectra of the Huckel 4n heterocycles azirene, oxirene, thiirene," J. Am. Chem. Soc., 105, No. 3, 396-402 (1983).

5. S. M. Zavoruev and R.-I. I. Rakauskas, "Ab initio investigation of three-membered nitrogen-containing heterocycles, i. Structure and vibrational analysis of unsaturated cy- cles," Lit. Fiz. Sb., 27, No. i, 115-117 (1987).

6. A. C. Hopkinson, M. H. Lien, K. Yates, and I. G. Csizmadia, "A nonempirical molecular orbital study of valence tautomers of C2H3N," Int. J. Quant. Chem., 12, No. 2, 355-368 (1977).

7. E.-U. Wurthwein, "Structures and stabilities of C2H4N + isomers: an ab initio molecular orbital study," J. Org. Chem., 49, No. 16, 2971-2978 (1984).

8. M. T. Nguyen and T.-K. Ha, "Ab initio SCF study of the molecular structure and relative stabilities of the C2H~N + cation isomers," J. Chem. Soc. Perkin Trans. II, No. 8, 1401- 1405 (1984).

9. P. C. Hariharan and J. A. Pople, "The influence of polarization functions on molecular orbital hydrogenation energies," Theor. Chim. Acta, 28, No. 2, 213-222 (1973).

i0. P. Carsky, B. A. Hess, and L. J. Schaad, "Use of molecular symmetry in two-electron integral transformation: an MP2 program compatible with HONDO5," J. Comput. Chem., ~, No. 3, 280-287 (1984).

Ii. W. J. Hehre, R. Ditchfield, and J. A. Pople, "Self-consistent molecular orbital methods. 12. Further extensions of Gaussian-type basis sets for use in molecular orbital studies of organic molecules," J. Chem. Phys., 56, No. 5, 2257-2261 (1972).

12. R. H. Nobes, W. J. Bouma, and L. Radom, "The additivity of polarization function and electron correlation effects in ab initio molecular orbital calculations," Chem. Phys. Lett., 89, No. 6, 497-500 (1982).

13. M. L. McKee and N. Lipscomb, "Study of additivity of correlation and polarization effects in relative energies," J. Am. Chem. Soc., 103, No. 16, 4673-4676 (1981).

14. S. M. Zavoruev and R.-I. I. Rakauskas, "Ab initio investigation of three-membered nitrogen-containing heterocycles. 5. Proton affinity," Lit. Fiz. Sb., 27, No. 2, 245-247 (1987).

15. J. S. Binkley, R. Whiteside, R. Krishnan, et al., GAUSSIAN 80. QCPE 406, Indiana Univ., Bloomington (1981).

16. O. Mo, J. L. G. de Paz, and M. Yanez, "Protonation of three-membered ring heterocycles. An ab initio molecular orbital study," J. Phys. Chem., 91, No. 26, 6484-6490 (1987).

449

17. M. Bogey, J.-L. Destombes, J. M. Denis, and J.-C. Guillemin, "The millimeter wave rota-

tional spectrum of 2H-azirine, NCH2CH/M," 115, No. i, 1-14 (1986). 18. L. V. Gurvich, I. V. Veitts, V. A. Medvedev, et al., Thermodynamic Properties of Indi-

vidual Substances [in Russian], Vol. i, Part i, Nauka, Moscow (1978). 19. S. M. Zavoruev, "Calculation of the potential surfaces, vibrational spectra, and thermo-

dynamics of gas-phase reactions of three-membered aza heterocyles," Author's abstract of dissertation for the degree of Candidate of Chemical Sciences, Moscow (1988).

20. R. A. Eades, D. A. Weil, M. R. Ellenberger, et al., "Electronic structure of vinylamine. Proton affinity and conformational analysis," J. Am. Chem. Soc., i03, No. 18, 5372-5377 (1981).

21. M. R. E11enberger, D. A. Dixon, and W. J. Farneth, "Proton affinity and the protonation of enamine in the gas phase," ibid., 103, No. 18, 5377-5382 (1981).

22. S. M. Zavoruev, R.-I. I. Rakauskas, and Yu. K. Shulskus, "Ab initio investigation of three-membered nitrogen-containing heterocycles. 4. Molecular electrostatic potential," Lit. Fiz. Sb., 27, No. 2, 243-245 (1987).

QUANTUM-CHEMICAL INVESTIGATION OF TAUTOMERISM OF

HYDROPHOSPHORYL COMPOUNDS

Yu. V. Babin, V. M. Mamaev, Yu. A. Ustynyuk, and V. V. Gorchakov

UDC 539.19:547.241:541.623

The tautomerization energies for the reaction R2P(O)H Z R2P--OH, where R= OH, OCH 3, OC2Hs, CH3, and CF s, have been calculated by the CNDO/2 method with optimization of the exponents of the Slater 3d AO's according to the criterion of a minimum total energy for the molecule. The results are in qualitative agreement with the experimental data. The MNDO and CNDO/2 calculations with the use of a standard sp basispredict greater stability for the structures with a three-coordinate phosphorus atom, in contradiction to experiment.

A large portion of the acids of trivalent phosphorus are stable in the form of the hydrophosphoryl compound (I) [i]:

H I

. a\OH R R

d) (#) Tautomer II is detected when R = R' = Alk, AlkO, as well as in the case of bis(pentafluoro- phenyl)phosphinous acid and some cyclic esters of phosphorous acid [i, 2]. In the case of strong acceptor substituents, such as when R = R' = CF3, only form II exists [i]. Therefore, the position of the prototropic equilibrium in the P-O diad system depends on the substituents at the phosphorus atom. Reliable theoretical evaluations of the relative thermodynamic stability of tautomers I and II as a function of R and R' would undoubtedly be a stimulus for the development of synthetic investigations in the area of the chemistry of hydrophosphoryl compounds.

The nonempirical Hartree-Fock-Eoothaan method was employed in the STO-2G* and 3-21G*, and 6-31G* basis sets in calculations of the tautomerization energies (~E ~ of the model molecule H3PO [3]. According to [3], this molecule is stable in form II, and the value of &E ~ is equal to 21 kJ/mole. The replacement of one of the hydrogen atoms at the phosphorus by another substituent renders the structure with a phosphoryl bond (P=O) more stable. The tautomerization energy for the case of the equilibrium (MeO)2P(O)H ~ (MeO)2P-OH was measured

Moscow University. Translated from Teoreticheskayai ~ksperimental'naya Khimiya, Volo 25, No. 4, pp. 486-490, July-August, 1989. Original article submitted June 8, 1987.

450 0040-5760/89/2504-0450512.50 �9 1990 Plenum Publishing Corporation

thermodynamic stability and reactivity of the antiaromatic heterocycle 1h-azirine

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