The protonation of azanaphthalenes and azabenzenes has been studied theoretically using CNDO/2 wavefunctions and perturbation theory in order to examine the correlation between pKa values and quantum-mechanical quantities

Meer, Douwe van der

Weijer, Peter van de

English

van de Weijer, Peter

van der Meer, Douwe

NARCIS 

Theoretical study on the protonation of AZA-aromatics

University of Twente Research Information

Theoret. Chim. Acta (Berl.) 38, 223--229 (1975) © by Springer-Verlag 1975 Theoretical Study on the Protonation of AZA-Aromatics Peter van de Weijer and Douwe van der Meer Chemical Physics Laboratory, Twente University of Technology, Enschede, The Netherlands Johan L. Koster Theoretical Chemistry Group, Rijksuniversiteit, Utrecht, The Netherlands Received September 2, 1974/March 10, 1975 The protonation of azanaphthalenes and azabenzenes has been studied theoretically using CNDO/2 wavefunctions and perturbation theory in order to examine the correlation between pK a values and quantum-mechanical quantities. Key words: Aza-aromatics, protonation of 1. Introduction Much attention has been given in the past to the theoretical study of proto- nation reactions [-1-3]. These early works were rather limited, because of the use of very simplified methods, mainly ~-electron theories. In the last ten years, however, more advanced methods have become available, semi-empirical as well as ab initio, which have been used for a study on this subject [4-9]. In this paper we present the results of a theoretical study on the protonation of aza- aromatics. This study, which is based on the CNDO/2 method and perturbation theory, is concerned with the correlation between the experimentally deter- mined pK a values of the azanaphthalenes [-10] and the theoretical calcu- lations. 2. Theory The energy change in solution (AEz) accompanying the proton transfer reaction R H + ~ R + H  + (1) can be calculated from the gas phase protonation energy A E  o and the solvation energy terms E s as follows: AE~ = - AEg + E~(R) - Es(RH +) + E~(H +) (2) where A E o is defined by: A E  o = Eo(RH +) - Eo(R ) . (3) In our study A E  o has been calculated quantum-mechanically (see below). The solvation energies of R and RH + are obtained using the classical model of Hylton et al. [11] and Es(H +) is a constant known from experiment. 224 P. van de Weijer et al, In view of the large size of the molecules to be studied, AEo has been determined using the CNDO/2 method [12-14J and perturbation theory. This calculation has been carried out in three steps. First we have performed a CNDO/2 calculation on the neutral molecule R in order to obtain E0(R ) and the corresponding wave-function. In the second step the position of the proton has been determined by calculating the mole- cular electrostatic potential [15] of the molecule R, following a procedure similar to that of Petrongolo and Tomasi [16]. The electrostatic potential gives a first order approximation of AEo, commonly called the Coulomb energy (Ec). By evaluating E c at several points in space one or more minima may be found which correspond - to first order - to the sites of protonation in the molecule. This type of calculation is much less time consuming than minimization of Eg(RH +) by a full CNDO/2 calculation. In the final step - with the proton placed at one of the E c minima - we have first carried the perturbation approach - of which E c is the first order term - to higher order. In this way we obtain the induction energy E~, resulting from polarization of the molecular charge distribution in the field of the proton [17, 18]. It has been shown that reliable values for E~ can be obtained, employing a slightly modified second order energy expression based on Brillouin-Wigner perturbation energy [19] (see Refo [18] for further details). Secondly, polar- ization as well as charge transfer is taken into account by performing a CNDO/2 calculation on the protonated species, giving E0(RH+). Subtracting E0(R ) from Eo(RH +) we obtain the gas phase protonation energy AEg. However, it is well known that these protonation energies are overestimated by the CNDO/2 method [4, 16]. Since they appear to be about 4/3 times as large as the corresponding energies obtained from minimal basis set ab initio calculations, we have scaled down our AE o values by a factor 3/4. Having determined the various terms which contribute to AE~, the energy change in solution, it is necessary to make some assumptions before we can correlate AE~ with experimental pK a values. At 298 °K the latter are related to the free energy difference in solution (A Gz) as follows: AG l = - R T  lnK a = 1.36 pKa (4) where A Gl is in kcal/mole. If we assume that, apart from a symmetry factor, the entropy difference of the reaction is constant and that changes in volume can be neglected, Eq. (4) reduces to: AE l = 1.36 pK' a + constant (5) where pK' a incorporates the symmetry factor mentioned above (pK', = pK,  - 0.30 for the symmetrical diazanaphthalenes and pK' a = p K ,  otherwise). Since the solvation energy of the proton (Es(H+)) is also constant, it is convenient to re- write Eq. (5) as: - AE = 1.36 pK'~ - Es(H +) + constant (6) where AE is defined by [cf. Eq. (2)]: AE = A E  o - Es(R) + Es(RH +) (7) The Protonation of AZA-Aromatics 225 3. Results and Discussion A difficulty in our calculations for the 12 azanaphthalenes is that the mole- cular structure is not known for all of them. We therefore assumed the "benzene" geometry for all molecules: Rcc = RcN = R•N = 1.397 ~,  RcH = 1.084 and all angles 120 ° . The results of the calculations are shown in Table 1 (for a tom numbering see Fig. 1). Using these results we have examined how the pK '  a values correlate with E o E c + E~, A E  o, and A E  in order to establish the relative importance of these terms. Table 1. Protonation energyterms ~razanaphthalenes.  Allenergiesin kcal/mole b Compound No. -E C -E I -AEg a -AE pK~ Cinnoline (l,2-diazanaphthalene Quinazoline (l,3-diazanaphthalene Quinoxaline (l,4-diazanaphthalene 1,5-naphthyridine (l,5-diazanaphthalene 1,6-naphthyridine (l,6-diazanaphthalene 1,7-naphthyridine (l,7-diazanaphthalene 1 , 8 - n a p h t h y r i d i n e  (l,8-diazanaphthalene Phthalazine (2,3-diazanaphthalene 2,6-naphthyridine (2,6-diazanaphthalene 2,7-naphthyridene (2,7-diazanaphthalene Quinoline (l-azanaphthalene) Isoquinoline (2-azanaphthalene) 1 ~ 88.35 75.00 256.41 290.85 87.66 70.43 253.50 288.76 2.27 2 e 91.30 73.09 261.72 296.46 3.43 B 85.84 72.17 256.96 292.34 3 77.44 74.20 258.17 293.12 0.26 4 88.23 75.16 259.88 295.27 2.61 5 ~ 81.19 74.32 261.41 297.02 3.78 8 83.32 70.87 258.44 294.00 6 ~ 78.75 73.79 260.06 295.57 8 82.33 70.53 257.39 292.99 3.63 7 103.10 74.37 262.67 297.42 3.09 8 81.08 70.41 257.44 292.19 3.17 9 88.23 71.41 256.68 293.21 3.18 10 90.11 71.56 257.69 294.04 3.43 Ii 82.96 72.18 263.78 298.60 4.94 12 96.26 72.99 258.93 294.10 5.40 these values have been scaled down by a factor 3/4 (see text) for pK a values see Ref. [i0] 8 i 6 3 5 4 Fig. 1. Numbering of the positions in a naphthalene molecule 226 P. van de Weijer et al. 300- o 29o- <3 f oll o7 02 e5 ~ 0 1 0  012 e 9  el  pK~ Fig. 2. Correlation between AE and pK', for azanaphthalenes. The numbers in the figure cor- respond to the numbers in Table 1 If we consider the Coulomb energy E c we find hardly any correlation with pK'a, the correlation coefficient c being 0.35. Especially the large Coulomb energy of 1,8-naphthyridine is striking. The correlation becomes even worse if we include the induction energy E~: c = 0.23. The protonation energy in the gas phase A E o gives a correlation with the pK' a values slightly better than that of the Coulomb energy (c = 0.41). Inclusion of the solvation energy terms gives a further improvement (c = 0.46). The correlation line corresponding to A E  is shown in Fig. 2. The slope of this line is 0.82 which is somewhat less than the expected value of 1.36 [cf. Eq. (6)]. The intercept is 292.1 kcal/mole. This should be approximately equal to the solva- tion energy of the proton, as we expect the constant in Eq. (6) not to be larger than 10 kcal/mole [20]. Since the solvation energy of the proton is 261kcal/mole [-21], one may infer that the adjustment of A E  o (based on minimal basis set ab init io calculations) still leads to slightly overestimated protonation energies (cf. Ref. [9]). Although A E  gives a better correlation than E o E c + E  ~ or A E  o, the final correlation (c--0.46) is not satisfactory. We will now consider some possible sources of error which may be responsible for this poor correlation. a) We have placed the proton at the minimum of the Coulomb energy. In further calculations this position is not changed, though we might expect the optimized geometry of the protonated molecule to be different, not only with regard to the proton position, but also as a consequence of some deformation of the reacting molecule. However, it would cost a tremendous amount  of com- putation time to find this geometry. b) Another, perhaps a more serious, error is that for all molecules we have used the "benzene" structure, which may differ considerably from the ex- perimental structure. We have investigated this error by performing similar calculations on four azabenzenes for which the experimental structure is known [-22-25]. The various contributions to A E  for both the "benzene" structure and the experimental structure have been determined in the same way as before. The results are given in Table 2 and Fig. 3. From the correlation lines given in Fig. 3, which refer to A E  versus pK'a, it is seen that the influence of the structure is surprisingly small as far as the slope is concerned, both slopes being 0.89. However, the correlation coefficients differ considerably - c=0 .70  and The Protonation of AZA-Aromatics  Table 2. Protonation energy terms for azabenzenes. All energies in kcal/mole 227 Compound No. -E c -E I -dEg c -dE P aK" d Pyridine 139 83.77 67.83 252.36 297.49 (l-azabenzene) 13 D 83.59 67.33 245.78 290.94 Pyridazine 14~ 84.65 68.96 246.31 291.02 (l,2-diazabenzene) 14 D 81.08 66.33 241.98 287.18 Pyrimidine 159 83.71 68.96 249.08 294.68 (l,3-diazabenzene) 15 D 77.50 67.96 242.50 288.08 Pyrazine 169 78.56 68.78 247.17 292.75 (l,4-diazabenzene) 16 D 70.91 66.58 240.26 286.10 5.23 2.03 1.00 0.35 a "benzene" structure b experimental structure c these values have been scaled down by a factor 3/4 (see text) d for pK a values see [28] T 295- o E 285. J • 14 pK~ Fig. 3. Correlation between AE and pK'  a for azabenzenes. The upper line corresponds to the aza- benzenes with "benzene" geometry, the lower line to the azabenzenes with experimental geometry. For numbering see Table 2 c = 0.93 - thus underlining the importance of the use of experimental geo- metries. This difference in correlation coefficients is mainly due to the large deviation found for pyridazine ("benzene" structure). This is not surprising, since the departure from the "benzene" structure will be most pronounced when two nitrogen atoms are attached to each other. In the case of diazanaphthalenes the same phenomenon may be noticed for cinnoline and phthalazine (see Fig. 2). Reasonable correlations for azabenzenes (experimental structure) are also obtained between pK'  a and E o E c + E  I and AEo: c=0.84,  c=0 .84  and c=0.95 respectively. These results indicate that for correlation with pK', values within a given series the induction and solvation energy terms are relatively unimportant. It is seen from Fig. 2 and Fig. 3 that the correlation line of the azanaphthalenes and that of the azabenzenes ("benzene" structure) nearly coincide (as they should): both lines have the same intercept (292.1 kcal/mole) and about the same slope (0.82 and 0.89 respectively). This would not be the case if the solvation energy - which is largely dependent on the size of the molecules - had been omitted, a fact which has been noted before [26]. 228 P. van de Weijer et al. c) In the case of the asymmetrical diazanaphthalenes an additional diffi- culty is the fact that two different protonation sites are possible (we have always used the lowest energy value for our correlations). For cinnoline and quinazoline our results clearly indicate position 1 (the e-position) as the most favourable site of protonation. However, for 1,6- and 1,7-naphthyridine the Coulomb energy favours position 6 and 7 respectively (the fl-position), whereas according to AE o and AE, protonation will take place at the a-position. A similar discrepancy between E c and AE o is sometimes encountered in ab initio calculations (see e.g. the results for cyclopropene in Ref. [27]). Experimental work to determine the actual site of protonation is in pro- gress. 4. Conclusions Our calculations on azanaphthalenes have resulted in a rather poor correla- tion between AE and pK' a. However, similar calculations on azabenzenes have shown that to a large extent this may be due to the lack of experimental geo- metries in the former case. For  correlation with pK'a values within a series of structurally similar mole- cules one should use either the Coulomb energy or - preferably - the gas phase protonation energy. The induction and solvation energy terms have been shown to be relatively unimportant. With regard to the site of protonation in the asymmetrical diazanaphthalenes our results indicate that for cinnoline and quinazoline the a-position is the most favourable site of attack. However, for 1,6- and 1,7-naphthyridine the present results are not conclusive. Acknowledgement. We wish to thank Prof. Dr. D. Feil and Dr. F. B. van Duijneveldt for criti- cally reading the manuscript. The investigations were supported in part by the Netherlands Foundation for Chemical Research (SON) with financial aid from the Netherlands Organization for the Advancement of Pure Research (zwo). References 1. Longuet-Higgins, H.C.: J. Chem. Phys. 18, 275 (1950) 2. Chalvet, O., Pages, M., Roux, M., Buu-Hoi, N.P., Royer, R.: J. Chim. Phys. 51, 548 (1954) 3. Pullman, A, Nakajima, T.: J. Chim. Phys. 55, 793 (1958) 4. Schuster, P.: Theoret. Chim. Acta (Berl.) 19, 212 (1970) 5. Kollmar, H., Smith, H. O.: Chem. Phys. Letters 5, 7 (1970) 6. Leibovici, C.: Intern. J. Quantum Chem. 8, 193 (1974) 7. Hopkinson, A.C., Holbrook, N.K., Yates, K., Csizmadia, I.G.: J. Chem. Phys. 49, 3596 (1968) 8. Lathan, W.A., Hehre, W.J., Curtiss, L.A., Pople, J.A.: J. Am. Chem. Soc. 93, 6377 (1971) 9. Hopkinson, A. C., Csizmadia, L. G.: Can. J. Chem. 52, 546 (1974) 10. van den Ham, D. M. W.: private communication 11. Hylton, J., Christoffersen, R.E., Hatl, G.G.: Chem. Phys. Letters 24, 501 (1974) 12. Pople, J.A., Santry, D. P., Segal, G.A.: J. Chem. Phys. 43, S 129 (1965) 13. Pople, J.A., Segal, G.A.: J. Chem. Phys. 43, S 136 (1965) 14. Pople, J.A., Segal, G.A.: J. Chem. Phys. 44, 3289 (1966) 15. Bonaccorsi, R., Scrocco, E., Tomasi, J.: J. Chem. Phys. 52, 5270 (1970) The Protonation of AZA-Aromatics 229 16. Petrongolo, C., Tomasi, J.: Chem. Phys. Letters 20, 201 (1973) 17. van Duijneveldt, F.B.: Thesis, University of Utrecht 1969 18. Koster, J.L.: Thesis, University of Utrecht 1975; copies are available on request 19. Hameka, H.F.: Introduction to quantum theory. New York: Harper & Row 1967 20. Arnett, E. M., Jones III, F. M., Taagepera, M., Henderson, W.G., Beauchamp, J. L., Holtz, D., Taft, R.W.: J. Am. Chem. Soc. 94, 4724 (1972) 21. Kebarle, P., Searles, S. K., Zolla, A., Scarborough, J., Arshadi, M.: J. Am. Chem. Soc. 89, 6393 (1967) 22. Bak, B., Hansen-Nygaard, L., Rastrup-Andersen, J.: J. Mol. Spectry. 2, 361 (1958) (pyridine) 23. Innes, K. K., Lukas, R. M.,Jr.: J. Mol. Spectry. 24, 247 (1963) (pyridazine) 24. Wheatley, P.J.: Acta Cryst. 13, 80 (1960) (pyrimidine) 25. Merrit, J.A., Innes, K. K.: Spectrochim. Acta 16, 945 (1960) (pyrazine) 26. Daudel, R.: Quantum theory of chemical reactivity. Boston: D. Reidel Publishing Company 1967 27. Ghio, C., Tomasi, J.: Theoret. Chim. Acta (Berl.) 30, 151 (1973) 28. Albert, A.: Physical methods in heterocyclic chemistry, Vol. I. New York: Academic Press 1963 Dr. D. van der Meer Chemical Physics Laboratory Twente University of Technology Postbus 217 Enschede, The Netherlands 

Theoretical study on the protonation of AZA-aromatics

Abstract

Similar works

Full text

Available Versions

NARCIS

University of Twente Research Information