Semiempirical and Ab Initio Calculations of Tautomerism in 2,3-Dihydroxypyrazine Ahmed M. El-Nahas Chemistry Department, Faculty of Science, El-Menou�¡a University, Shebin El-Kom, Egypt Semiempirical (AM1 and PM3) and ab initio (MP2/6-31 a G*//HF/6-31 a G*) calculations on the relative stabilities of different tautomers of 2,3-dihydroxypyrazine show that this species exists not only in solution but also in the gas phase predominantly as a dioxo tautomer. Owing to its signi¢çcance in many chemical and biological reactions, the tautomerism of heterocyclic compounds continues to be a matter of intense experimental and theoretical research.3 Solvent e€ects often play an important role in organic chemistry and many chemical equilibria may be substantially modi¢çed by a change of the molecular environment.23 Most theoretical and experimental studies have concentrated on the tautomerism in 2-hydroxypyridine, uracil, thymine and cytosine.8¡¾13 A theoretical study28 at the AM1 and 3-21G levels on the tautomerism of hydroxy- pyrazine and mercaptopyrazine has shown that hydroxy- pyrazine and its oxo form are present in almost equal proportions while the thiol is of greater concentration than the thione.To our knowledge there previously have been neither theoretical nor experimental investigations involving 2,3-dihydroxypyrazine. A similar compound, 2,3- dioxopiperazine, has been studied both experimentally and theoretically and it was found that the dioxo form is the most stable species in the solid state.29 In this regard, it appeared interesting to study tautomerism in 2,3-dihydroxy- pyrazine.This compound can exist in three tautomeric forms, two of which exist in more than one conformer (Fig. 1). Our aim in this study is to use semiempirical (AM11 and PM32) and ab initio calculations to predict the stabilities of the 2-hydroxy-3-oxo and 2,3-dioxo tautomers of 2,3-dihydroxypyrazine. The geometries of the investigated tautomers were optimized at the AM1 and PM3 levels in the gas phase and in aqueous solutions without any symmetry constraints.Solvent e€ects in aqueous solution are calculated using the Self-Consistent Reaction Field (SCRF) method24 available in the VAMP5.5 program.33 The optimizations of the molecular geometries were carried out within C2v (1, 3, 6) and Cs (2, 4, 5) symmetries using the Hartree¡¾Fock method37 with the 6-31 a G* basis set.38 The e€ect of electron correlation on the calculated relative energies was investigated by performing Moeller¡¾Plesset calculations40 truncated at second order (MP2) with the 6-31 a G* basis set.Relative energies for the structures displayed in Fig. 1 are listed in Table 2. A plot of relative energies at di€erent theoretical levels in the gas phase and in aqueous solution is shown in Fig. 2. Compared to HF/6-31 a G*, the average errors in calculating di€erent properties using AM1 and PM3 procedures are given in Table 4.All calculated forms of 1, 2, 4, 5, 6 (Fig. 1) are minima on the potential energy surface of 2,3-dihydroxypyrazine, while structure 3 is a saddle point of second order and is, therefore, removed from further discussion. The energy J. Chem. Research (S), 1998, 222¡¾223 J. Chem. Research (M), 1998, 1014¡¾1031 Fig. 1 Optimized conformations of 2,3-dihydroxypyrazine Table 4 Absolute errors in relative energies (kcal mol¢§1), dipole moments (Debye), and ionization potentials (eV) obtained from AM1 and PM3 methods in the gas phase (w.r.t. 6-31 a G*) RE (kcal mol¢§1) DM (Debye) IP (eV) Structure AM1 PM3 AM1 PM3 AM1 PM3 1 0.0 0.0 0.088 0.172 0.278 0.402 2 0.18 0.74 0.529 0.830 0.331 0.412 3 4.52 9.81 0.961 0.390 0.408 0.476 4 1.01 2.28 0.594 0.923 0.129 0.129 5 3.21 3.80 0.384 0.980 0.128 0.096 6 1.28 4.00 1.206 1.981 0.164 0.152 Average errors 1.77 3.44 0.627 0.879 0.240 0.278 Table 2 Relative energies (kcal mol¢§1) for the investigated molecule at semiempirical and ab initio levels Gas phase Aqueous solution Structure AM1 PM3 AM1 PM3 6-31 a G* MP2/6-31 a G*//HF/6-31 a G* 1 0.0 0.0 0.0 0.0 0.0 0.0 2 1.19 0.63 ¢§1.12 ¢§1.15 1.37 1.02 3 10.63 5.34 4.84 0.10 15.15 14.16 4 ¢§0.65 0.62 ¢§4.92 ¢§3.45 ¢§1.66 0.86 5 ¢§0.30 0.29 ¢§4.98 ¢§3.69 ¢§3.51 ¢§1.49 6 ¢§7.24 ¢§4.52 ¢§13.31 ¢§10.12 ¢§8.52 ¢§3.82 222 J.CHEM. RESEARCH (S), 1998barrier required for transformation of the dihydroxy forms 1 to 2 amounts to 3 kcal mol¢§1 while that for conversion of the dihydroxy 1 to the hydroxyoxo 4 tautomer is 143 kcal mol¢§1, at the AM1 level in the gas and liquid phases.Inspection of Fig. 2 shows that the dioxo tautomer 6 is the most stable species at all the theoretical levels while the relative stabilities of the hydroxyoxo forms 4, 5 depend on the calculational level, as these are close enough energetically. In polar solvents, the tautomeric equilibrium of 2,3- dihydroxypyrazine is shifted in favor of the more polar oxo forms.22,41 The dioxo form 6 was found to be the most stable structure, with the stability in solution increased by 16 kcal mol¢§1 compared to that found in the gas phase.In solvents of high relative permittivity, the stability of the hydroxyoxo forms 4, 5 also increases, which indicates that 2,3-dihydroxypyrazine is present in solution predomi- nantly as hydroxyoxo and dioxo tautomers. These results may explain the predominance of the similar compound, 2,3-dioxopiperazine, in the solid state.29 The a-diketone is thus stable in the gas and condensed phases and can undergo condensation and other reactions at the carbonyl groups.Fig. 2 Plot of relative energies versus theoretical levels. All energies are relative to that of 1. SCF represents HF/6-31 a G* and MP2 represents MP2/6-31 a G*//HF/6-31 a G* The author thanks Professor P. v. R. Schleyer for facili- tating ab initio calculations at Erlangen, Germany. Techniques used: Semiempirical (AM1 and PM3), ab initio and self- consistent reaction ¢çeld theory calculations.References: 43 Table 1: Heats of formation (AM1 and PM3, in kcal mol¢§1) and total energies (ab initio, in a.u.) for the investigated species Table 3: Dipole moments (Debye) and ionization potentials (eV) for the investigated species in the gas phase Table 5: Optimized geometries for di€erent structures in the gas phase Received, 18th August 1997; Accepted, 22nd December 1997 Paper E/7/06037H References cited in this synopsis 1 M.J. S. Dewar, E. G. Zoebisch, E. F. Healy and J. J. P. Stewart, J. Am. Chem. Soc., 1985, 107, 3902. 2 J. J. P. Stewart, J. Comput. Chem., 1989, 10, 209, 221. 3 J. S. Kwaitowski, T. J. Zielinski and R. Rein, Adv. Quant. Chem., 1986, 18, 85. 8 W. M. F. Fabian, J. Phys. Org. Chem., 1990, 3, 332. 9 W. M. F. Fabian, J. Mol. Struct. (Theochem), 1990, 206, 295. 10 J. Leszczynski, J. Phys. Chem., 1992, 96, 1649. 11 H. Meghezzi and A.Boucekkine, J. Mol. Struct. (Theochem), 1992, 257, 175. 12 U. Narinder, J. Mol. Struct. (Theochem), 1989, 188, 199. 13 A. R. Katritzky, M. Szafran and J. Stevens, J. Mol. Struct. (Theochem), 1989, 184, 179. 23 C. Reichardt, in Solvent and Solvent E€ects in Organic Chemistry, VCH, Weinheim, 1988. 24 G. Rauhut, T. Clark and T. Steinke, J. Am. Chem. Soc., 1993, 115, 9174. 28 J. G. Contreras and J. B. Alderete, Bol. Soc. Chil. Quim., 1992, 37, 7. 29 A. Peeters, C. V. Alesony, A. T. H. Lenstra and H. G. Geise, Int. J. Quant. Chem., 1993, 46, 73. 33 G. Rauhut, A. Alex, J. Chandrasekhar and T. Clark, in VAMP5.5, Oxford Molecular Ltd., Oxford, 1993. 37 C. C. J. Roothaan, Rev. Mod. Phys., 1951, 23, 69. 38 (a) P. C. Harriharan and J. A. Pople, Theor. Chim. Acta, 1973, 28, 213; (b) T. Clark, J. Chandrasekhar, G. W. Spitznagel and P. v. R. Schleyer, J. Comput. Chem., 1983, 4, 294. 40 (a) C. Moeller and M. S. Plesset, Phys. Rev., 1934, 46, 618; (b) J. A. Pople, J. S. Binkley and R. Seeger, Int. J. Quant. Chem., 1976, 10, 1. 41 (a) J. Frank and A. R. Katritzky, J. Chem. S., Perkin Trans. 2, 1976, 1428; (b) M. Kuzuya, A. Noguchi and T. Okuda, J. Chem. Soc., Perkin Trans. 2, 1985, 1423. J. CHEM. RESEARCH (S), 1998 223