Applying density functional theory on tautomerism in 3,4-dihydropyrimidin-2(1H)-ones

Abstract

In the present study, the density functional theory (DFT) and Gibbs free energy calculations were performed to investigate the stability and tautomerism of C4-substituted-3,4-dihydropyrimidin-2(1H)-ones. Three different forms are possible for the ethyl 3,4-dihydropyrimidinones (ethyl 4-aryl-6-methyl-3,4-dihydropyrimidin-2(1H)-one-5-carboxylates, ethyl 4-aryl-2-hydroxy-6-methyl-1,4-dihydropyrimidine-5-carboxylates and ethyl 4-aryl-2-hydroxy-6-methyl-3,4-dihydropyrimidine-5-carboxylates) forms that the most stable form is ethyl 4-aryl-6-methyl-3,4-dihydropyrimidin-2(1H)-one-5-carboxylates (keto-form). The obtained data showed that the substitution on the C4-substitut position can be effective on the equilibrium constant (K_eq).

Keywords

Gibbs free energy / density functional theory (DFT) / tautomerism / dihydropyrimidin-2(1H)-ones / Keto-Form

Introduction

In 1893, the Italian chemist Pietero Bigginelli reported a condensation reaction between ethyl acetoacetate, benzaldehyde and urea to obtain a heterocyclic system of 3, 4-dihydropyrimidinone (DHPM), which is known as Biginelli reaction [1].

The 3,4-dihydropyrimidinones (DHPMs) compounds have aroused much interest in recent years due to their wide spectra of biologic activities and medicinal application as calcium channel blockers, antihypertensive, antibacterial, antitumor and anti-inflammatory agents [2-6].

Recently, computational methods have begun to be employed in studying the geometry of the 3,4-dihydropyrimidinones [7-9]. Furthermore, they used the details obtained from the optimization of the DHPMs as very useful substrate in the mechanistic studies of the oxidation reactions [7-9]. However a vast amount of information on these DHPMs is available including determination of the crystal structures of these compounds [10-13].

Heterocycles often display tautomerism as a result of the transfer of a proton, such as keto-enol, amine-enol and imine-amine equilibrium. However, several theoretical and experimental papers were published about the tautomerism of these compounds [14-16]. In all these experimental studies, the keto form of DHPMs are confirmed [11,17-19], but the aim of this study is to carry out systematic theoretical investigation of the keto-iminol form of these compounds.

Calculation methods

The quantum chemical calculations were performed with GAUSSIAN 98 suite of programs [20]. Full geometry optimizations were carried out using the density functional theory (DFT) calculations with the B3LYP/6-31+ + G** and B3LYP/6-31G** levels.

Results and discussion

Considering the importance of the configuration of the aryl group at the C4-position of heterocyclic ring on the biologic and pharmacological activities of DHPMs, in the present study, we used B3LYP/6-31+ + G** computations to study the structure of the keto-iminol form of these compounds. To obtain enthalpies, free energies and calculation of the gas phase equilibrium constant reactions of DHPMs, a vibrational analysis seemed necessary.

We studied the general structures of the DHPMs with aryl-up (antagonist) conformation in previous paper [9]. The data obtained from optimization of ethyl 4-aryl-2-hydroxy-6-methyl-1,4-dihydropyrimidine-5-carboxylates show that the structures of these compounds are similar to ethyl 4-aryl-6-methyl-3,4-dihydropyrimidin-2(1H)-one-5-carboxylates. The general structure of these compounds is shown in Fig. 1.

The geometries of 1,4-dihydropyrimidines were optimized using DFT B3LYP method with 6-31+ + G** basis set. The analysis of the optimized structures of dihydropyrimidines shows that the six-member ring adopt a boat conformation, flatted at N₁ toward an envelope conformation, with a pseudo-axial orientation of the C4-substituent, i.e., in all derivatives, the C4-substitution adopts the up orientation with respect to the heterocyclic ring boat plane. Furthermore, the conformation of the carboethoxy group (C₇ = O₈) can be considered approximately as s-trans with respect to their adjacent C₅ = C₆ bonds of the 1,4-dihydropyrimidines ring.

Thermochemical analysis

The enthalpies \left(\mathrm{\Delta }{H}_{\mathrm{f}}^{\circ }\right) and Gibbs free energies \left(\mathrm{\Delta }{G}^{\circ }\right) of the tautomerism reaction of 1,4-dihydropyrimidines are calculated based on the equilibrium reaction given in Fig. 2 using the B3LYP hybrid functional with geometry optimization and frequencies at the B3LYP/6-31G** level. These parameters are calculated for the three forms of ethyl 4-aryl-6-methyl-3,4-dihydropyrimidin-2(1H)-one-5-carboxylate (I), ethyl 4-aryl-2-hydroxy-6-methyl-1,4-dihydropyrimidinone-5-carboxylate (II)and ethyl 4-aryl-2-hydroxy-6-methyl-3,4-dihydropyrimidinone-5-carboxylate (II).

The results of these calculations of the enthalpies (formation and the equilibrium reaction, \mathrm{\Delta }{H}_{\mathrm{f}}^{\circ },\mathrm{\Delta }{H}_{\mathrm{e}\mathrm{q}}^{\circ }) and Gibbs free energies (formation and the equilibrium reaction, \left(\mathrm{\Delta }{G}_{\mathrm{f}}^{\circ },\mathrm{\Delta }{G}_{\mathrm{e}\mathrm{q}}^{\circ }\right)) of these compounds are reported in the Tables 1 and 2.

The analysis of the data reported in Table 1 shows that the formation enthalpies \left(\mathrm{\Delta }{H}_{\mathrm{f}}^{\circ }\right) (of 3,4-dihyropyrimidi-2(1H)-ones are larger than the 1,4-dihydropyrimidines because the energy of C₂ = O₇ bond is more than that of the C₂ = N₃ bond and the bond length of carbonyl group is smaller than that of the imine group. (The bond lengths for a′ and a compounds are 1.22670 Å, 1.26695 Å respectively).

According to the equilibrium reaction enthalpies data reported in the Table 1 for 3,4-dihyropyrimidin-2(1H)-ones and 1,4-dihydropyrimidines, we confirm the dynamic nature of 3,4-dihyropyrimidin-2(1H)-ones.

The calculations of the formation Gibbs free energies of 3,4-dihyropyrimidin-2(1H)-ones and 1,4-dihydropyrimidines compounds show that the keto forms of dihydropyrimidinones are more stable than iminol forms of these compounds. For example, the formation Gibbs free energies \left(\mathrm{\Delta }{G}_{\mathrm{f}}^{\circ }\right) of b′ and b compounds are -2407778 and -2407704 KJ/mol respectively. It appears that ethyl 4-(4-methylphenyl)-6-methyl-3,4-dihydropyrimidin-2(1H)-one-5-carboxylate is more stable than the ethyl 4-(4-methylphenyl)-2-hydroxy-6-methyl-1,4-dihydropyrimidin-5-carboxylate. Furthermore, the analysis of the equilibrium constant (K_eq) data reported in Table 2 shows that the value of 1,4-dihydropyrimidine compounds is less than that of the 3,4-dihydropyrimidin-2(1H)-one compounds. For example, the K_eq for f′ and f is 3.49 × 10^-13. However, the analysis of the data in Table 2 shows that K_eq also depends on the type and position of the substituent on the aryl ring. For example, K_eq for 4-methyl aryl (b) is larger than K_eq for 4-methoxy aryl (c) ring. (K_eq for these compounds are 1.45 × 10^-13, 7.90 × 10^-14 respectively).

According to the K_eq data shown in Table 2, the compounds with donating electron substituent on the aryl ring have the least K_eq compared with the compounds with acceptor electron substituent on aryl ring. For example, K_eq for 4-methoxy (c) and 4-nitro (l) substituent on the aryl ring are 7.90 × 10^-14 and 9.35 × 10^-13 respectively. This can be attributed to the charge density on the N3-H atom. For example, the charge density on the N3-H atom in the c and l compounds are+ 0.247 and+ 0.280 respectively. It seems that increasing the acidity of N3-H atom cases makes the iminol form increase as well.

Furthermore, in this paper we investigate the tautomerism between I and III compounds. Figure 3 shows that the formation enthalpy \left(\mathrm{\Delta }{H}_{\mathrm{f}}^{\circ }\right) of ethyl 2-hydroxy-6-methyl-4-phenyl-3, 4-dihydropyrimidine-5-carboxylate (III) is -570.9 kJ/mol. However, the formation enthalpy of tautomerism reaction is 59.0 KJ/mol. The data obtained from the formation and the equilibrium reaction Gibbs free energies \left(\mathrm{\Delta }{G}_{\mathrm{f}}^{\circ },\mathrm{\Delta }{G}_{\mathrm{e}\mathrm{q}}^{\circ }\right) are -2304587 and 58.5 kJ/mol respectively. Based on these data, the equilibrium constant for this reaction is 5.52 × 10^-11.

The obtained data suggest that the keto form (I) is more stable than the iminol form (III). The comparison of the thermodaynatic data of ethyl 2-hydroxy-6-methyl-4-phenyl-3,4-dihydropyrimidine-5-carboxylate (III) and ethyl 2-hydroxy-6-methyl-4-phenyl-1,4-dihydropyrimidine-5-carboxylate (II) shows that the tautomeric form III is more stable than form II. In the previous paper [9], we reported the charge density of the N₁ and N₃ atoms for some 3,4-dihydropyrimidinones. The data showed that the charge density on the N₃ atom is slightly higher than that on the N₁ atom. However, generation of the tautomeric form II is more likely than the tautomeric form II.

Conclusion

The B3LYP/6-31+ + G(d,p) optimized structures show that in all 1,4-dihydropyrimidines, the heterocyclic ring has a flat boat conformation, and the aryl ring prefers a pseudo-axial position on C₄. Furthermore, in the B3LYP optimized structures, the carbonyl group at C5-position is oriented s-trans with respect to the C₅ = C₆ bond of the 1,4-dihydropyrimidine ring. On the other hand, the structures of these compounds are quite similar to 3,4-dihydropyrimidinones. The present calculations show that the 3,4-dihydropyrimidin-2(1H)-one form (I) (keto form) is more stable than the 1,4-dihydropyrimidine (II) and 3,4-dihydropyrimidine (III) forms (iminol form). Based on the results of the present work, we have confirmed that the generation of the 1,4-dihydropyrimidine (I) form is more likely than 3,4-dihydropyrimidine (II) form because the charge density on the N₃ atom is slightly higher than that on the N₁ atom.

References

[1] Biginelli,P., Gazz. Chim. Ital.1898, 23, 360–413

[2] Cho,H.; Ueda,M.; Shima,K.; Mizuno,A.; Hayashimatsu,M.; Ohnaka,Y.; Takeuchi,Y.; Hamaguchi,M.; Aisaka,K.; Hidaka,T.; Noguchi,T., J. Med. Chem.1989, 32, 2399–2406

[3] Atwal,K. S.; Rovnyak,G. C.; Kimball,S. D.; Floyd,D. M.; Moreland,S.; Swanson,B. N.; Gougoutas,J. Z.; Schwartz,J.; Smillie,K. M.; Malley,M. F., J. Med. Chem.1990, 33, 2629–2635

[4] Rovnyak,G. C.; Kimball,S. D.; Beyer,B.; Cucinotta,G.; DiMarco,J. D.; Gougoutas,J.; Hedberg,A. O.; Malley,M.; McCarthy,J. P.; Zhang,R.; Moreland,S., J. Med. Chem.1995, 38, 119–129

[5] Atwal,K. S.; Swanson,B. N.; Unger,S. E.; Floyd,D. M.; Moreland,S.; Hedberg,A. O.; O’Reilly,B. C., J. Med. Chem.1991, 34, 806–811

[6] Grover,G. J.; Dzwonczyk,S.; McMullen,D. M.; Normandin,D. E.; Parham,C. S.; Sleph,P. G.; Moreland,S., J. Cardiovasc. Pharmacol.1995, 26, 289–294

[7] Memarian,H. R.Farhadi,A.; Sabzyan,H.; Soleymani,M., J. Photochem. Photobiol. Chem.2010, 209, 95–103

[8] Memarian,H. R.; Sabzyan,H.; Farhadi,A., Z. Naturforsch.2009, 64b, 532–540

[9] Memarian,H. R.; Sabzyan,H.; Farhadi,A., Monatsh. Chem.2010, 141, 1203–1212

[10] Kappe,C. O.; Fabian,M. F., Tetrahedron1997, 53, 2803–2816

[11] Kappe,C. O.; Peters,K.; Peters,E. M., J. Org. Chem.1997, 62, 3109–3118

[12] Dondoni,A.; Massi,A.; Minghini,E.; Sabbatini,S.; Bertolasi,V., J. Org. Chem.2003, 68, 6172–6183

[13] Marubayashi,N.; Ogawa,T.; Hamasaki,T.; Hirayama,N., J. Chem. Soc., Perkin Trans. 21997, 1309–1314

[14] Ozimiński,W. P.; Dobrowolski,J. C.; Mazurek,A. P., J. Mol. Struct. THEOCHEM2004, 680, 107–115

[15] Trofimenko,S.; Yap,G. P. A.; Jove,F. A.; Claramunt,R. M.; García,M. Á.; Santa Maria,M. D.; Alkorta,I.; Elguero,J., Tetrahedron2007, 63, 8104–8111

[16] Alkorta,I.; Blanco,F.; Elguero,J., Tetrahedron2010, 66, 5071–5081

[17] Kappe,C. O., Tetrahedron1993, 49, 6937–6963

[18] Dondoni,A.; Massi,A., Tetrahedron Lett.2001, 42, 7975–7978

[19] Mandhane,P. G.; Joshi,R. S.; Nagargoje,D. R.; Gill,C. H., Tetrahedron Lett.2010, 51, 3138-3140

[20] Frisch,M. J.; Trucks,G. W.; Schlegel,H. B.; Scuseria,G. E.; Robb,M. A.; Cheeseman,J. R.; Zakrzewski,V. G.; Montgomery,J. A. Jr; Stratmann,R. E.; Burant,J. C.; Dapprich,S.; Millam,J. M.; Daniels,A. D.; Kudin,K. N.; Strain,M. C.; Farkas,O.; Tomasi,J.; Barone,V.; Cossi,M.; Cammi,R.; Mennucci,B.; Pomelli,C.; Adamo,C.; Clifford,S.; Ochterski,J.; Petersson,G. A.; Ayala,P. Y.; Cui,Q.; Morokuma,K.; Malick,D. K.; Rabuck,A. D.; Raghavachari,K.; Foresman,J. B.; Ciolowski,J.; Ortiz,J. V.; Stefanov,B. B.; Liu,G.; Liashenko,A.; Piskorz,P.; Komaromi,I.; Gomperts,R.; Martin,R. L.; Fox,D. J.; Keith,T.; Al-Laham,M. A.; Peng,C. Y.; Nanayakkara,A.; Gonzalez,C.; Challacombe,M.; Gill,P. M. W.; Johnson,B.; Chen,W.; Wong,M. W.; Andres,J. L.; Head-Gordon,M.; Replogle,E. S.; Pople,J. A., Gaussian 98, Gaussian Inc., Pittsburg PA, 1998

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