Theoretical Studies on the Tautomerism of 1,5,6,7-Tetrahydro-4H-indazol-4-ones

Abstract

Computational studies on three tautomeric forms of four 1,5,6,7-tetrahydro-4H-indazol-4-one derivatives: 1,5,6,7-tetrahydro-4H-indazol-4-one (1), 6,6-dimethyl-1,5,6,7-tetrahydro-4H-indazol-4-one (2), 3-methyl-1,5,6,7-tetrahydro-4H-indazol-4-one (3) and 3,6,6-trimethyl-1,5,6,7-tetrahydro-4H-indazol-4-one (4), have been performed at different levels, ranging from semiempirical AM1, ab initio Hartree-Fock HF/6-31G* and HF/6-31G** to B3LYP/6-31G** density functional calculations. These calculations have been used to establish the most stable tautomer, which in all cases was in agreement with the experimental data.

Introduction

Annular tautomerism of pyrazole and indazole derivatives has been investigated in depth both theoretically and experimentally [1,2]. A theoretical estimation of the annular tautomerism of 52 NH-indazoles concluded that although in most cases the 1H-tautomer is the most stable, in some indazoles, the 2H-tautomer was more stable than the 1H one [3]. Recently we approached the study of the tautomerism of tetrahydroindazoles (also known as tetramethylenepyrazoles) bearing a trifluoromethyl group at the 3-position and we found that in all cases they exist as 1H-3-CF₃ tautomers [4]. We present here our studies on the tautomerism of a more complex case, that of the 1,5,6,7-tetrahydro-4H-indazol-4-ones 1-4, in which three tautomeric forms have been considered (Scheme 1).

Scheme 1.

Scheme 1.

Results and Discussion

The results of the calculations at the semiempirical AM1 level are gathered in Table 1, showing that the OH form in which the heterocyclic ring loses its aromaticity is clearly unfavorable.

Table 1. AM1 Differences in energy (kJ mol^–1), energies in brackets (kJ mol^–1) and dipole moments (Debye).

	E			μ
Comp.	1H	2H	OH	1H	2H	OH
1	3.01	0.0 [74.42625]	60.78	5.08	2.05	5.64
2	2.43	0.0 [46.31270]	60.15	5.11	2.03	5.67
3	8.63	0.0 [36.13512]	63.18	4.67	1.85	5.54
4	8.02	0.0 [8.03202]	75.67	4.70	1.82	7.52

Table 1. AM1 Differences in energy (kJ mol^–1), energies in brackets (kJ mol^–1) and dipole moments (Debye).

	E			μ
Comp.	1H	2H	OH	1H	2H	OH
1	3.01	0.0 [74.42625]	60.78	5.08	2.05	5.64
2	2.43	0.0 [46.31270]	60.15	5.11	2.03	5.67
3	8.63	0.0 [36.13512]	63.18	4.67	1.85	5.54
4	8.02	0.0 [8.03202]	75.67	4.70	1.82	7.52

The corresponding ab initio energies based on geometries optimized at the HF/6-31G* and HF/6-31G** levels are shown in Table 2 and Table 3. They are consistent and show the expected decrease in energy with the increasing level of the basis set used [5].

Table 2. HF/6-31G* Differences in energy (kJ mol^–1), energies in brackets (hartree) and dipole moments (Debye).

	E			μ
Comp.	1H	2H	OH	1H	2H	OH
1	0.0 [-453.48686]	0.59	135.24	5.64	2.14	8.61
2	0.0 [-531.55518]	0.81	134.34	5.63	2.14	8.56
3	1.86	0.0 [-492.53055]	134.65	5.25	1.96	8.40
4	1.73	0.0 [-570.59882]	125.38	5.23	1.97	5.80

Table 2. HF/6-31G* Differences in energy (kJ mol^–1), energies in brackets (hartree) and dipole moments (Debye).

	E			μ
Comp.	1H	2H	OH	1H	2H	OH
1	0.0 [-453.48686]	0.59	135.24	5.64	2.14	8.61
2	0.0 [-531.55518]	0.81	134.34	5.63	2.14	8.56
3	1.86	0.0 [-492.53055]	134.65	5.25	1.96	8.40
4	1.73	0.0 [-570.59882]	125.38	5.23	1.97	5.80

Table 3. HF/ 6-31G** Differences in energy (kJ mol^–1), energies in brackets (hartree) and dipole moments (Debye).

	E			μ
Comp.	1H	2H	OH	1H	2H	OH
1	0.0 [-453.50210]	0.45	127.80	5.66	2.12	8.63
2	0.0 [-531.57666]	0.68	128.14	5.65	2.12	8.58
3	2.03	0.0 [-492.54888]	129.67	5.25	1.94	8.42
4	1.89	0.0 [-570.62340]	120.56	5.24	1.94	5.84

Table 3. HF/ 6-31G** Differences in energy (kJ mol^–1), energies in brackets (hartree) and dipole moments (Debye).

	E			μ
Comp.	1H	2H	OH	1H	2H	OH
1	0.0 [-453.50210]	0.45	127.80	5.66	2.12	8.63
2	0.0 [-531.57666]	0.68	128.14	5.65	2.12	8.58
3	2.03	0.0 [-492.54888]	129.67	5.25	1.94	8.42
4	1.89	0.0 [-570.62340]	120.56	5.24	1.94	5.84

Finally, the values obtained at the density functional B3LYP/6-31G** level are reported in Table 4.

Table 4. B3LYP/ 6-31G** Differences in energy (kJ mol^–1), energies in brackets (hartree) and dipole moments (Debye).

		E			μ
Comp.		1H	2H	OH	1H	2H	OH
1		0.93	0.0 [-456.29158]	121.97	5.27	2.18	8.32
	+ZPE	1.18	0.0 [-456.14543]	118.91
2		0.65	0.0 [-534.92481]	121.22	5.26	2.17	8.28
	+ZPE	0.91	0.0 [-534.72310]	118.07
3		3.81	0.0 [-495.61836]	125.25	4.80	2.00	8.11
	+ZPE	3.64	0.0 [-495.44438]	121.39
4		3.30	0.0 [-574.25151]	115.92	4.79	2.00	5.67
	+ZPE	3.14	0.0 [-574.02222]	113.22

Table 4. B3LYP/ 6-31G** Differences in energy (kJ mol^–1), energies in brackets (hartree) and dipole moments (Debye).

		E			μ
Comp.		1H	2H	OH	1H	2H	OH
1		0.93	0.0 [-456.29158]	121.97	5.27	2.18	8.32
	+ZPE	1.18	0.0 [-456.14543]	118.91
2		0.65	0.0 [-534.92481]	121.22	5.26	2.17	8.28
	+ZPE	0.91	0.0 [-534.72310]	118.07
3		3.81	0.0 [-495.61836]	125.25	4.80	2.00	8.11
	+ZPE	3.64	0.0 [-495.44438]	121.39
4		3.30	0.0 [-574.25151]	115.92	4.79	2.00	5.67
	+ZPE	3.14	0.0 [-574.02222]	113.22

An analysis of the data in Table 1, Table 2, Table 3 and Table 4 shows that, for the gas phase, according to the semiempirical AM1 and DFT B3LYP/6-31G** methods, the 2H tautomer is the most stable one in all cases, followed by the 1H one and distantly by the OH forms.

The linear regression between the AM1 and B3LYP/6-31G** calculated energy values afforded r² coefficients of 0.997 and 0.995 (+ZPE), showing that in the present tautomerism study, similarly to what has been reported in reference [3], the inexpensive AM1 method can be used as exploratory tool with good results.

Ab initio Hartree-Fock calculations with the 6-31G* and 6-31G** basis sets, give rise to a different stability order: i) 1H > 2H > OH in 1,5,6,7-tetrahydro-4H-indazol-4-one (1) and 6,6-dimethyl-1,5,6,7-tetrahydro-4H-indazol-4-one (2) and ii) 2H > 1H > OH in 3-methyl-1,5,6,7-tetrahydro-4H-indazol-4-one (3) and 3,6,6-trimethyl-1,5,6,7-tetrahydro-4H-indazol-4-one (4). However, the energy differences between the 1H and 2H tautomers are very small in all cases, with an average value of 1 kJ mol^–1.

All the theoretical methods predict the 4-hydroxy tautomer as the most unfavorable one, the explanation being the loss of the aromaticity of the pyrazole ring [6]. Finally, an analysis of the calculated dipole moments show that the 1H-tautomers have higher dipole moments than the 2H-tautomers (Table 1, Table 2, Table 3 and Table 4). As the influence of the solvent on the tautomeric equilibrium is related to the dipole moment, the higher the dipole moment the more stable the corresponding tautomer in polar solvents. Therefore the conclusions reached for the gas phase can be modified in solution or in solid phases. We can advance that the foregoing theoretical results are in agreement with the experimental data obtained by multinuclear NMR in solution and in solid state for all compounds [7]. As an example, we reproduce here the ¹³C-NMR spectra of compound 4, proving that in solid state it exists only as the tautomer, while in DMSO-d₆ solution both the and forms are observed in a ratio of ca. .

Figure 1. ¹³C CPMAS NMR spectrum (aromatic region) of compound 4 at 298 K.

Figure 1. ¹³C CPMAS NMR spectrum (aromatic region) of compound 4 at 298 K.

Figure 2. ¹³C-NMR spectrum (aromatic region) of compound 4 in DMSO-d₆ at 298 K.

Figure 2. ¹³C-NMR spectrum (aromatic region) of compound 4 in DMSO-d₆ at 298 K.

Conclusions

AM1 and B3LYP/6-31G** calculations on 1,5,6,7-tetrahydro-4H-indazol-4-ones 1-4 provide similar results concerning the stability of the tautomeric forms and reproduce the experimental results. In the case of compound 4, the 2H-tautomer is experimentally more stable than the 1H-one by 0.5 kJ mol^–1 at 298 K (in DMSO-d₆). The closest calculated values are found in Table 2 (1.7 kJ mol^–1) and Table 3 (1.9 kJ mol^–1). Besides, the dipole moment favours the 1H-tautomer in DMSO solution explaining why the difference is so small.

Experimental

The SPARTAN program [8] working on a Silicon Graphics Octane Workstation has been used to build and optimize the structures of the 1H, 2H and OH tautomers of the 1,5,6,7-tetrahydro-4H-indazol-4-ones 1-4 at the different computational levels (AM1, HF/6-31G*, HF/6-31G** and B3LYP/6-31G**). No symmetry restriction has been imposed in the optimization process.