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Ab initio calculations on the hydration of dimethylpyrazole and indazole. Solvent effects on tautomeric energies.
Journal of Molecular Structure (Theochem), 165 (1988) 115-124 Elsevier Science Publishers B.V., Amsterdam - Printed in The Netherlands
115
AB INITIO CALCULATIONS ON THE HYDRATION OF DIMETHYLPYRAZOLE AND INDAZOLE. SOLVENT EFFECTS ON TAUTOMERIC ENERGIES.
M. HODOSCEK, D. KOCJAN and D. HAD& Boris KidriE Institute of Chemistry and Lek Works, POB. 30,61115 Ljubljana (Yugoslavia) (Received 14 September 1987)
ABSTRACT The effect of hydration upon the energies of the tautomeric pairs of indazoles and dimethylpyrazoles was investigated (i) by attaching one water molecule to each nitrogen, and (ii) by the continuum model. In the calculation (i) the STO-3G basis set was used. The geometry optimization resulted in strongly hydrogen bonded cyclic structures with notable co-operative effect. This was explored in more detail with 3,4-dimethylpyrazole hydrate using the 3-21G basis set and correction for the basis set superposition error. In the calculation (ii) on the indazole pair the 631G basis set was used together with the continuum based SCF algorithm of Tomasi and coworkers [ 11. The results of both approaches are in good agreement. The tautomeric energy of the indazole tautomers calculated by the extended basis set (10 kcal mol-‘) is 2.9 kcal smaller than that obtained from STO-3G calculations. The continuum solvent effects reduces it to 5 kcal mol-‘.
INTRODUCTION
Theoretical treatments of solvent effects on tautomeric energies of heterocyclic systems are of general interest to organic chemists and, in particular, to medicinal chemists if tautomerism is connected with pharmacological properties. However, reliable theoretical investigations of this type are demanding on computer time, especially with large molecules, and therefore comparative investigations involving economical approaches are needed. In this paper we describe the results of two computational approaches to the solvent effect on the energies of the tautomeric forms of indazole (1HIn and 2HIn) and of 3,4 (4,5) dimethylpyrazole (1HPy and 2HPy) (Fig. 1) . The first is the supramolecular approach for which one water molecule was attached to each heterocyclic nitrogen. The geometry optimization using the STO-3G basis set which included both the heterocyclic skeleton and the water molecules, yielded a cyclic structure with strong, co-operative hydrogen bonding which appeared worthy of more detailed study. In view of the well-known deficiencies of the minimal basis set in the treatment of hydrogen-bonded systems this has
0166-1280/88/$03.50
0 1988 Elsevier Science Publishers B.V.
116
Fig. 1. The tautomeric pairs of dimethylpyrazole
and indazole with numbering of atoms.
been done on the smaller system, 3,4-dimethylpyrazole (1HPy) dihydrate using the 3-21G basis set and the energy for the basis set superposition error (BSSE) corrected. Hydrogen bonding in 2HPy dihydrate was not explored in this way and only its energy was computed with both basis sets. The second approach was the one developed by Tomasi and co-workers [ 11. The SCF algorithm is based on a continuum description of the solvent. Since the coupling operator depends on the solute charges, and hence on the quality of the wave function, we recalculated the indazole pair energies and charges by the extended 6-31G basis set. Thus, a more reliable energy difference for this tautomeric pair was also obtained. This treatment was not extended to 1HPy and 2HPy because their tautomeric energy is small and no dramatic effects can be expected either from the extended basis set treatment or from the continuum solvent effect. The results of semi-empirical MNDO and “ab initio” (STO-3G basis set) calculations of tautomeric energies of free dimethylpyrazoles, indazoles and their more extended tetrahydrobenzo homologues were reported recently [ 21 and it was demonstrated that the extension of the basic heterocyclic moieties by saturated carbocyclic rings does not significantly affect the tautomeric energies. However, more influential was the effect of protonation of the amino group substituted on the saturated ring. The pharmacological importance of the tautomerism of these heterocyclic systems, explained in more detail in ref. 2, required in addition to the “in vacua” calculations the investigation of solvent effect on the tautomeric energies in order to approach more closely the conditions in the organism. The previous study [ 21 also demonstrated that the heterocyclic systems, discussed herein, are reliable models of the actual pharmacological molecules, ergolenes, azaergolenes and their partial analogues [ 31. These molecules, endowed with dopaminergic activity, are too large for “ab initio” treatment at sufficiently high level. Both approaches to solvent effects adopted in this study tend to decrease
117
the difference in energy of the tautomers without inverting their relative stability. From the methodological point of view it is interesting that both the supramolecular and the continuum models yield very similar results. METHODS
The calculations were carried out using the GAUSSIAN 80 program package [ 41. The geometry optimization of the five-membered heterocycles caused problems in convergence and in order to overcome the parameter oscillations it was necessary to prepare the initial geometry in such a way as to avoid the geometrical interdependence of certain parameters: this was achieved by fixing some selected points in the space. The best geometry of the fixed points is that given by the crystal (or microwave) structure. Next, the atoms of the molecular system were connected with free parameters to the grid of fixed points. Thus parameters which are determined without being interrelated are obtained. The bond lengths and angles of the benzenic hydrogens were kept constant during minimization. The procedure is illustrated by Fig. 2. The geometrical parameters of the dihydrates which were optimized are shown in Fig. 3. The pyrazole moiety was relaxed, according to the procedure outlined above, in optimizing the geometry of the water molecules. The BSSE was corrected by the Boys’ counterpoise method [ 51. The ener-
b
Fig. 2. Geometry optimization of indazole. Distances and angles (dashed lines) were optimized with respect to reference structure (full lines and circles - see text). Fig. 3. Illustrating the optimized geometrical parameters of the dihydrates (dashed). The OH distances represented by full lines were kept constant. The heterocyclic moiety was relaxed.
118 TABLE 1 Optimized interatomic distances (A) and angles ( ” ) of dihydrates (A, STO-3G; B, 3-21G) 3,4-Dimethylpyrazole A
CQ N,-H..*O1 N,-H. --0, Q,-H...O, O,-IJ***O, C&-H...Nz O,-IJ. . .Nz
&J1-H...O1 N,-H...O, Q1-H...02 01-IJ...02 Q,-H...N, 0,-H.. .Np
2.509 1.475 2.499 1.622 2.779 1.857
4,5-Dimethylpyrazole B
(“1 162.1 149.8 154.1
(A) 2.668 1.682 2.579 1.676 2.774 1.833
A
(“1 161.0 155.2 158.7
6) 2.532 1.506 2.517 1.637 2.794 1.872
B
(“1 161.5 150.4 154.2
6) 2.674 1.689 2.580 1.676 2.766 1.826
lH-Indazole (A)
2H-Indazole (A)
2.521 1.488 2.515 1.637 2.839 1.931
&-H...02 N&a --0, Q,-H.. ‘0, 0,-E* * -0, Q1-H...N1 0,-H.. .N,
163.0 150.0 152.0
2.473 1.421 2.469 1.591 2.755 1.839
(“1 160.6 155.4 158.5
162.3 149.9 152.7
gies modified by the continuum solvent effect were calculated with the program generously supplied by Prof. J. Tomasi (Pisa) . The solvent cavity parameter k was set to 1.5 and the dielectric constant E to 78.5. RESULTS AND DISCUSSION
Hydrogen bonding in the hydrates The energy optimization of the geometrical parameters of the cyclic hydrates (Table 1) , as well as the difference between the energy of the supermolecule (E,) and the sum of the energies of the components (E,), dE=E,-LE, (Tables 2 and 3)) indicated rather strong hydrogen bonding even considering the deficiencies of the minimal basis set. This prompted (i) the dissection of AE into pair contributions and (ii) a calculation with the 321G basis set for one example (1HPy) at least. The dimer hydrogen bond energies are defined by AEd = Ed - L’E, where Ed is the energy of the respective dimer. The geometrical parameters of the dimers and monomers were taken as they were in the optimized supermolecule. Thus the deformation energies were excluded. The results obtained with the STO-3G basis set will be discussed first. The data given in Table 1 show the NH *. -0 distances to be very short and this is
119 TABLE 2 Total (a.u.) and hydration (kcal mol-‘)
energies of 3,4-dimethylpyrazole
System
3,4-Dimethylpyrazole H,O (1) H,O(2) a : 2HzO a:O(l)Hz a:0(2)H, b:c
;: ii
H g
3-21G
STO-3G
Norm.
BSSE corr.
-299.1437 74.9621 74.9641 449.1098 374.1211 374.1146 149.9306
-301.1682 75.5852 75.5850 452.3998 376.7735 376.7693 151.1850
-301.1728 75.5926 75.5921 452.3998 376.1787 376.7770 151.1934
25.1 9.6 4.3 2.7 6.4
36.5 12.6 10.1 9.3 6.5
26.6 8.4 7.6 5.5 5.1
AE* d- (a+b+c) e- (a+b) f- (a+c) g- (b+c) AE-ZE, *For explanations see text.
TABLE 3 STO-3G energies of hydration of indazoles System
-E (a.u.)
lH-indazole H&(l)
372.77570 74.96222
lH-indazole*2H,O HzO(2) a:H,O(l) a:H,0(2) b:c
522.73984 74.96422 447.74595 447.75336
BH-indazole H@(l)
372.75418 74.96393
PH-indazole.2H,O HzO(2) a’:H,O(l) a’:H,0(2) b’:c’
522.72578 74.96137 447.73479 447.72512
*For explanations see text.
149.93122
149.92908
AE (kcal mol-‘)
d- (a+b+c) ef- (a+b) (a+c) g- (b+c) AE-ZE,
23.7 9.7 3.8 3.0 7.2
d’ - (a’ +b’ +c’) e’ f’ -- (a’ +b’) (a’ +c’) g’ - (b’ +c’) AE-CE,
29.1 12.1 4.4 2.4 10.2
*
120
also true of the water 0. - -0 distances. The hydrogen bonds are non-linear and the water dimer is obviously compressed, which explains the low A&: in the free dimer A& calculated in the same basis set is 6 kcal mol-l [ 61. The pyridinic N* * ‘Hz0 bond is also shorter than calculated by Del Bene [ 71 for various six-membered heterocycles ( N 3 A). However, d&‘s are comparable. Perhaps the most interesting result is that the sum of the components LYE, is substantially smaller than the total interaction energy AZ. This difference of 8-10 kcal mol-’ was attributed mainly to the co-operative effect in the hydrogen-bonded cyclic structure of the dihydrate. Hydrogen bonding in 2HIn.2HzO is stronger than in lHIn*2HzO using both energy and geometry criteria except for the bonding between water molecules (Table 3). N1 of 2HIn is more negatively charged (7.167 e) than the corresponding pyridinic N2 of 2HIn (7.132 e) and the pyrrolic hydrogen is more positive in the former (0.763) than in the latter (0.772). In 1HPy the charge of Nz equals that on N1 of 2HIn, but the pyrrolic hydrogen is more positive (0.772 e). LIE in 1HPy is between both indazole isomers which is in accord with the atomic charges. However, this may be fortuitous since it is known [ 71 that correlation between atomic charges and hydrogen-bond energies in mixed systems is not straightforward. The calculation on lHPy.2HzO with the 3-21G basis set yielded a higher interaction energy than with the STO-3G basis set. Most of the increase is due to water-water and N---HzO( 2) bonding. AEd of water-water bonding (9.3 kcal mol-‘) was less than in the geometry optimized water dimer (10.05 kcal mol-l). It is known from previous work on hydrogen-bonded systems that small splitvalence basis sets, including 4-31G, yield hydrogen bond energies which are too large [ 6,8] whereas the STO-3G basis set yields energies closer to experimental figures. However, the geometries are better reproduced by the splitvalence basis sets. The 0,. **0, distance is increased relative to one calculated with the STO-3G basis set whereas the N*-.H20 bond is shortened. The NIH- - *OH2 distance assumes a more realistic value of 2.67 A. The AE-C& value is 2 kcal mol-l less than in the STO-3G calculation. The geometrical parameters of both hydrated pyrazole tautomers are given in Table 4; for comparison, the parameters of the free molecules are also given. Most affected by hydration are the N - C bonds for which the differences are up to 0.027 A whereas with other bonds they are below 0.01 A. The values resulting from calculations with STO-3G and 3-21G basis sets run in parallel. The effects of hydration on the geometric parameters of the indazole skeletons are smaller than on pyrazoles and are therefore not reproduced. The principal source of the overestimation by small basis sets of the hydrogen-bond energy is the basis set superposition error (BSSE) . In order to obtain more realistic figures we have recalculated the hydration energies of 1HPy using the Boys’ counterpoise correction [ 51. The correction markedly reduces
121 TABLE 4 Bond lengths and angles of 3,4- and 4,5-dimethylpyrazole (A STO-3G, B 3-21G) 4,5_Dimethylpyrazole
3,4-Dimethylpyrazole
Bond N,-N, G-G G-C, G-G K-G N,-H
2H,O
Free
2Hz0
Free A
B
A
B
A
B
A
B
1.381 1.335 1.435 1.358 1.375 1.023
1.373 1.316 1.427 1.365 1.353 0.992
1.376 1.339 1.422 1.366 1.364 1.064
1.371 1.322 1.416 1.374 1.340 1.021
1.385 1.328 1.430 1.361 1.382 1.023
1.377 1.311 1.423 1.367 1.357 0.993
1.378 1.332 1.419 1.369 1.372 1.058
1.373 1.317 1.412 1.376 1.345 1.021
104.0 111.9 104.9 107.5 111.8 120.6
105.4 111.2 104.5 107.8 111.0 119.6
105.2 111.2 104.6 108.4 110.6 118.5
106.3 110.6 104.4 108.6 110.2 118.6
102.8 113.2 104.7 106.7 112.5 120.3
104.2 112.4 104.4 107.1 111.9 119.4
104.1 112.4 104.5 107.5 111.5 118.6
105.0 111.8 104.2 107.8 111.2 118.5
Angles N&G W& c3GGi W&J, W’Wz HN&
the hydrogen-bond energies, which appears reasonable for the 3-21G basis set. However, the cooperative effect still remains at 5.1 kcal mol-l. Obvious overcorrection occurs on the values calculated by the STO-3G basis set which are therefore not reproduced. Because the dihydrates exhibit hydrogen bonding strengthened by co-operative effects the calculations were extended to the monohydrate of 1HPy. The energy optimization of geometrical parameters places the water molecule so that both the pyrrolic N,H and the pyridinic Nz are engaged in hydrogen bonding thus forming a five-membered ring (Fig. 4). The unfavourable 0HN2 angle leads to an increase in the H-**l$ distance relative to the dihydrate. For the same reason the N,H- - - 0 distance is increased. The calculated total interaction energy of 13.8 kcal mol-l is expected to be lower by about 10% considering the BSSE computed for the dihydrate. This appears reasonable for two hydrogen bonds and confirms the cooperative effect in the dihydrate ring. It would certainly be interesting to have an experimental check on the hydration properties of pyrazoles and indazoles which may be important for the biological properties of larger molecules containing these heterocyclic moieties. Solvation effects on the tautomeric energies Of primary concern was the relative stability of the indazole tautomeric forms because of the biological properties of the parent molecule 2-azaergolene [ 31.
122
Fig. 4. Optimized geometry of the 3,4-dimethylpyrazole
monohydrate.
The indazole pair was therefore examined by recalculating the energies on the STO-3G optimized geometry using the extended 6-31G basis set and applying the method of Tomasi and co-workers [l] in order to estimate the continuum solvent effect. The energy difference between the tautomers in vacua (Table 5) is 2.9 kcal mol-’ smaller than that resulting from the STO-3G calculation: the solvent effect halves the energy difference bringing it to 5 kcal mol-’ (Table 5). This may be compared with the results of the calculation on the dihydrates although in this case the minimal basis set was used (Table 3). The energy difference between the tautomeric dihydrate pair of indazoles is 8.8 kcal mol-‘, i.e. 32% less than computed in vacua. The reduction of the tautomeric energy difference in the supermolecular approach is obviously due to the stronger hydrogen bonding by 1HIn which is the higher energy tautomer. This stronger bonding is likely to originate in the higher charge on the pyridinic nitrogen mentioned previously. This is, on the other hand, reflected in the continuum effect which takes into account the solute charges. The larger solvent effect exhibited in the latter approach was to be expected because in the supermolecular approach only the effect of the nearest solvent molecules is considered. The effect of hydration on the tautomerit energy of the dimethylpyrazoles differs between both basis sets without reversing the relative stabilities. The absolute values of the tautomeric ener-
123 TABLE 5 Total energies (a.u.) of tautomeric forms of dimethylpyrazole (A&) (kcal mol-‘)
and indazole and energy differences
Molecule
STO-3G
3-21G
3,4_Dimethylpyrazole 4,5-Dimethylpyrazole dE, (free) AE, (dihydrate)
- 299.14649 - 299.14836 1.2 0.9
lH-indazole lH-indazole solvated” BH-indazole SH-indazole solvated” AE, (free) AE, (solvated)
-372.77697
-301.16963 -301.17004 0.26 0.4 6-31G -377.28889 -377.32306 - 377.27294 - 377.31506 10.0 5.0
-372.75643 12.9 8.8
“Continuum model (ref. 1).
gies are so small that at this level of calculation it is difficult to see the reason for the discrepancy. The agreement between the supermolecular and the continuum solvent effects on the tautomeric energies of indazoles is reassuring since it shows that the relative energies of the two forms are not altered. Moreover, Tomasi’s method appears to be useful for treating the solvent effect on tautomeric systems, which is also important from the economic point of view. The relatively good agreement in the tautomeric energies computed by the minimal and split valence basis sets is probably due to the fact that in the presently examined systems there are no essential differences between the bonds involved in the tautomerism. This contrasts with the results of a comparative calculation on hydroxypyridines [ 91 in which the change between aromatic and quinonoid systems occurs along with interchange of OH and NH bonds. In this case the minimal basis set led to an erroneous result [ 91. ACKNOWLEDGEMENTS
The work was supported by Research Community of Slovenia. Thanks are due to Prof. J. Tomasi (Pisa) for the program for calculating the continuum solvent effect and to the IMP Company for free computer time on their VAX780 system.
124 REFERENCES 1 S. Miertus, E. Scrocco, and J. Tomasi, Chem. Phys., 55 (1981) 11’7. 2 D. Kocjan, M. Hodoscek, and D. Ha&i, J. Mol. Struct. (Theochem) ,152 (1987) 331. 3 N.J. Bach, E.C. Kornfeld, J.A. Clemens,E.B. SmaIstig, andR.C.A. Frederickson, J. Med. Chem., 23 (1980) 492. 4 J.S. Bingkley, R.A. Whiteside, R. Krishnan, R. Seeger, D.J. DeFrees, H.B. Schlegel, S. Topiol, L.R. Kahn, and J.A. Pople, QCPE, No. 406, Indiana University. 5 S.F. Boys and F. Bernardi, Mol. Phys., 19 (1970) 553. 6 J.D. Dill, L.C. Allen, W.C. Topp, and J.A. Pople, J. Am. Chem. Sot., 97 (1975) 1220. 7 J.E. Del Bene, Chem. Phys., 15 (1976) 463. 8 S. Ikuta, Chem. Phys. Lett., 95 (1983) 604. 9 M.J. Scanlan, I.H. Hillier, and A.A. MacDowell, J. Am. Chem. Sot., 105 (1983) 3368.
115
AB INITIO CALCULATIONS ON THE HYDRATION OF DIMETHYLPYRAZOLE AND INDAZOLE. SOLVENT EFFECTS ON TAUTOMERIC ENERGIES.
M. HODOSCEK, D. KOCJAN and D. HAD& Boris KidriE Institute of Chemistry and Lek Works, POB. 30,61115 Ljubljana (Yugoslavia) (Received 14 September 1987)
ABSTRACT The effect of hydration upon the energies of the tautomeric pairs of indazoles and dimethylpyrazoles was investigated (i) by attaching one water molecule to each nitrogen, and (ii) by the continuum model. In the calculation (i) the STO-3G basis set was used. The geometry optimization resulted in strongly hydrogen bonded cyclic structures with notable co-operative effect. This was explored in more detail with 3,4-dimethylpyrazole hydrate using the 3-21G basis set and correction for the basis set superposition error. In the calculation (ii) on the indazole pair the 631G basis set was used together with the continuum based SCF algorithm of Tomasi and coworkers [ 11. The results of both approaches are in good agreement. The tautomeric energy of the indazole tautomers calculated by the extended basis set (10 kcal mol-‘) is 2.9 kcal smaller than that obtained from STO-3G calculations. The continuum solvent effects reduces it to 5 kcal mol-‘.
INTRODUCTION
Theoretical treatments of solvent effects on tautomeric energies of heterocyclic systems are of general interest to organic chemists and, in particular, to medicinal chemists if tautomerism is connected with pharmacological properties. However, reliable theoretical investigations of this type are demanding on computer time, especially with large molecules, and therefore comparative investigations involving economical approaches are needed. In this paper we describe the results of two computational approaches to the solvent effect on the energies of the tautomeric forms of indazole (1HIn and 2HIn) and of 3,4 (4,5) dimethylpyrazole (1HPy and 2HPy) (Fig. 1) . The first is the supramolecular approach for which one water molecule was attached to each heterocyclic nitrogen. The geometry optimization using the STO-3G basis set which included both the heterocyclic skeleton and the water molecules, yielded a cyclic structure with strong, co-operative hydrogen bonding which appeared worthy of more detailed study. In view of the well-known deficiencies of the minimal basis set in the treatment of hydrogen-bonded systems this has
0166-1280/88/$03.50
0 1988 Elsevier Science Publishers B.V.
116
Fig. 1. The tautomeric pairs of dimethylpyrazole
and indazole with numbering of atoms.
been done on the smaller system, 3,4-dimethylpyrazole (1HPy) dihydrate using the 3-21G basis set and the energy for the basis set superposition error (BSSE) corrected. Hydrogen bonding in 2HPy dihydrate was not explored in this way and only its energy was computed with both basis sets. The second approach was the one developed by Tomasi and co-workers [ 11. The SCF algorithm is based on a continuum description of the solvent. Since the coupling operator depends on the solute charges, and hence on the quality of the wave function, we recalculated the indazole pair energies and charges by the extended 6-31G basis set. Thus, a more reliable energy difference for this tautomeric pair was also obtained. This treatment was not extended to 1HPy and 2HPy because their tautomeric energy is small and no dramatic effects can be expected either from the extended basis set treatment or from the continuum solvent effect. The results of semi-empirical MNDO and “ab initio” (STO-3G basis set) calculations of tautomeric energies of free dimethylpyrazoles, indazoles and their more extended tetrahydrobenzo homologues were reported recently [ 21 and it was demonstrated that the extension of the basic heterocyclic moieties by saturated carbocyclic rings does not significantly affect the tautomeric energies. However, more influential was the effect of protonation of the amino group substituted on the saturated ring. The pharmacological importance of the tautomerism of these heterocyclic systems, explained in more detail in ref. 2, required in addition to the “in vacua” calculations the investigation of solvent effect on the tautomeric energies in order to approach more closely the conditions in the organism. The previous study [ 21 also demonstrated that the heterocyclic systems, discussed herein, are reliable models of the actual pharmacological molecules, ergolenes, azaergolenes and their partial analogues [ 31. These molecules, endowed with dopaminergic activity, are too large for “ab initio” treatment at sufficiently high level. Both approaches to solvent effects adopted in this study tend to decrease
117
the difference in energy of the tautomers without inverting their relative stability. From the methodological point of view it is interesting that both the supramolecular and the continuum models yield very similar results. METHODS
The calculations were carried out using the GAUSSIAN 80 program package [ 41. The geometry optimization of the five-membered heterocycles caused problems in convergence and in order to overcome the parameter oscillations it was necessary to prepare the initial geometry in such a way as to avoid the geometrical interdependence of certain parameters: this was achieved by fixing some selected points in the space. The best geometry of the fixed points is that given by the crystal (or microwave) structure. Next, the atoms of the molecular system were connected with free parameters to the grid of fixed points. Thus parameters which are determined without being interrelated are obtained. The bond lengths and angles of the benzenic hydrogens were kept constant during minimization. The procedure is illustrated by Fig. 2. The geometrical parameters of the dihydrates which were optimized are shown in Fig. 3. The pyrazole moiety was relaxed, according to the procedure outlined above, in optimizing the geometry of the water molecules. The BSSE was corrected by the Boys’ counterpoise method [ 51. The ener-
b
Fig. 2. Geometry optimization of indazole. Distances and angles (dashed lines) were optimized with respect to reference structure (full lines and circles - see text). Fig. 3. Illustrating the optimized geometrical parameters of the dihydrates (dashed). The OH distances represented by full lines were kept constant. The heterocyclic moiety was relaxed.
118 TABLE 1 Optimized interatomic distances (A) and angles ( ” ) of dihydrates (A, STO-3G; B, 3-21G) 3,4-Dimethylpyrazole A
CQ N,-H..*O1 N,-H. --0, Q,-H...O, O,-IJ***O, C&-H...Nz O,-IJ. . .Nz
&J1-H...O1 N,-H...O, Q1-H...02 01-IJ...02 Q,-H...N, 0,-H.. .Np
2.509 1.475 2.499 1.622 2.779 1.857
4,5-Dimethylpyrazole B
(“1 162.1 149.8 154.1
(A) 2.668 1.682 2.579 1.676 2.774 1.833
A
(“1 161.0 155.2 158.7
6) 2.532 1.506 2.517 1.637 2.794 1.872
B
(“1 161.5 150.4 154.2
6) 2.674 1.689 2.580 1.676 2.766 1.826
lH-Indazole (A)
2H-Indazole (A)
2.521 1.488 2.515 1.637 2.839 1.931
&-H...02 N&a --0, Q,-H.. ‘0, 0,-E* * -0, Q1-H...N1 0,-H.. .N,
163.0 150.0 152.0
2.473 1.421 2.469 1.591 2.755 1.839
(“1 160.6 155.4 158.5
162.3 149.9 152.7
gies modified by the continuum solvent effect were calculated with the program generously supplied by Prof. J. Tomasi (Pisa) . The solvent cavity parameter k was set to 1.5 and the dielectric constant E to 78.5. RESULTS AND DISCUSSION
Hydrogen bonding in the hydrates The energy optimization of the geometrical parameters of the cyclic hydrates (Table 1) , as well as the difference between the energy of the supermolecule (E,) and the sum of the energies of the components (E,), dE=E,-LE, (Tables 2 and 3)) indicated rather strong hydrogen bonding even considering the deficiencies of the minimal basis set. This prompted (i) the dissection of AE into pair contributions and (ii) a calculation with the 321G basis set for one example (1HPy) at least. The dimer hydrogen bond energies are defined by AEd = Ed - L’E, where Ed is the energy of the respective dimer. The geometrical parameters of the dimers and monomers were taken as they were in the optimized supermolecule. Thus the deformation energies were excluded. The results obtained with the STO-3G basis set will be discussed first. The data given in Table 1 show the NH *. -0 distances to be very short and this is
119 TABLE 2 Total (a.u.) and hydration (kcal mol-‘)
energies of 3,4-dimethylpyrazole
System
3,4-Dimethylpyrazole H,O (1) H,O(2) a : 2HzO a:O(l)Hz a:0(2)H, b:c
;: ii
H g
3-21G
STO-3G
Norm.
BSSE corr.
-299.1437 74.9621 74.9641 449.1098 374.1211 374.1146 149.9306
-301.1682 75.5852 75.5850 452.3998 376.7735 376.7693 151.1850
-301.1728 75.5926 75.5921 452.3998 376.1787 376.7770 151.1934
25.1 9.6 4.3 2.7 6.4
36.5 12.6 10.1 9.3 6.5
26.6 8.4 7.6 5.5 5.1
AE* d- (a+b+c) e- (a+b) f- (a+c) g- (b+c) AE-ZE, *For explanations see text.
TABLE 3 STO-3G energies of hydration of indazoles System
-E (a.u.)
lH-indazole H&(l)
372.77570 74.96222
lH-indazole*2H,O HzO(2) a:H,O(l) a:H,0(2) b:c
522.73984 74.96422 447.74595 447.75336
BH-indazole H@(l)
372.75418 74.96393
PH-indazole.2H,O HzO(2) a’:H,O(l) a’:H,0(2) b’:c’
522.72578 74.96137 447.73479 447.72512
*For explanations see text.
149.93122
149.92908
AE (kcal mol-‘)
d- (a+b+c) ef- (a+b) (a+c) g- (b+c) AE-ZE,
23.7 9.7 3.8 3.0 7.2
d’ - (a’ +b’ +c’) e’ f’ -- (a’ +b’) (a’ +c’) g’ - (b’ +c’) AE-CE,
29.1 12.1 4.4 2.4 10.2
*
120
also true of the water 0. - -0 distances. The hydrogen bonds are non-linear and the water dimer is obviously compressed, which explains the low A&: in the free dimer A& calculated in the same basis set is 6 kcal mol-l [ 61. The pyridinic N* * ‘Hz0 bond is also shorter than calculated by Del Bene [ 71 for various six-membered heterocycles ( N 3 A). However, d&‘s are comparable. Perhaps the most interesting result is that the sum of the components LYE, is substantially smaller than the total interaction energy AZ. This difference of 8-10 kcal mol-’ was attributed mainly to the co-operative effect in the hydrogen-bonded cyclic structure of the dihydrate. Hydrogen bonding in 2HIn.2HzO is stronger than in lHIn*2HzO using both energy and geometry criteria except for the bonding between water molecules (Table 3). N1 of 2HIn is more negatively charged (7.167 e) than the corresponding pyridinic N2 of 2HIn (7.132 e) and the pyrrolic hydrogen is more positive in the former (0.763) than in the latter (0.772). In 1HPy the charge of Nz equals that on N1 of 2HIn, but the pyrrolic hydrogen is more positive (0.772 e). LIE in 1HPy is between both indazole isomers which is in accord with the atomic charges. However, this may be fortuitous since it is known [ 71 that correlation between atomic charges and hydrogen-bond energies in mixed systems is not straightforward. The calculation on lHPy.2HzO with the 3-21G basis set yielded a higher interaction energy than with the STO-3G basis set. Most of the increase is due to water-water and N---HzO( 2) bonding. AEd of water-water bonding (9.3 kcal mol-‘) was less than in the geometry optimized water dimer (10.05 kcal mol-l). It is known from previous work on hydrogen-bonded systems that small splitvalence basis sets, including 4-31G, yield hydrogen bond energies which are too large [ 6,8] whereas the STO-3G basis set yields energies closer to experimental figures. However, the geometries are better reproduced by the splitvalence basis sets. The 0,. **0, distance is increased relative to one calculated with the STO-3G basis set whereas the N*-.H20 bond is shortened. The NIH- - *OH2 distance assumes a more realistic value of 2.67 A. The AE-C& value is 2 kcal mol-l less than in the STO-3G calculation. The geometrical parameters of both hydrated pyrazole tautomers are given in Table 4; for comparison, the parameters of the free molecules are also given. Most affected by hydration are the N - C bonds for which the differences are up to 0.027 A whereas with other bonds they are below 0.01 A. The values resulting from calculations with STO-3G and 3-21G basis sets run in parallel. The effects of hydration on the geometric parameters of the indazole skeletons are smaller than on pyrazoles and are therefore not reproduced. The principal source of the overestimation by small basis sets of the hydrogen-bond energy is the basis set superposition error (BSSE) . In order to obtain more realistic figures we have recalculated the hydration energies of 1HPy using the Boys’ counterpoise correction [ 51. The correction markedly reduces
121 TABLE 4 Bond lengths and angles of 3,4- and 4,5-dimethylpyrazole (A STO-3G, B 3-21G) 4,5_Dimethylpyrazole
3,4-Dimethylpyrazole
Bond N,-N, G-G G-C, G-G K-G N,-H
2H,O
Free
2Hz0
Free A
B
A
B
A
B
A
B
1.381 1.335 1.435 1.358 1.375 1.023
1.373 1.316 1.427 1.365 1.353 0.992
1.376 1.339 1.422 1.366 1.364 1.064
1.371 1.322 1.416 1.374 1.340 1.021
1.385 1.328 1.430 1.361 1.382 1.023
1.377 1.311 1.423 1.367 1.357 0.993
1.378 1.332 1.419 1.369 1.372 1.058
1.373 1.317 1.412 1.376 1.345 1.021
104.0 111.9 104.9 107.5 111.8 120.6
105.4 111.2 104.5 107.8 111.0 119.6
105.2 111.2 104.6 108.4 110.6 118.5
106.3 110.6 104.4 108.6 110.2 118.6
102.8 113.2 104.7 106.7 112.5 120.3
104.2 112.4 104.4 107.1 111.9 119.4
104.1 112.4 104.5 107.5 111.5 118.6
105.0 111.8 104.2 107.8 111.2 118.5
Angles N&G W& c3GGi W&J, W’Wz HN&
the hydrogen-bond energies, which appears reasonable for the 3-21G basis set. However, the cooperative effect still remains at 5.1 kcal mol-l. Obvious overcorrection occurs on the values calculated by the STO-3G basis set which are therefore not reproduced. Because the dihydrates exhibit hydrogen bonding strengthened by co-operative effects the calculations were extended to the monohydrate of 1HPy. The energy optimization of geometrical parameters places the water molecule so that both the pyrrolic N,H and the pyridinic Nz are engaged in hydrogen bonding thus forming a five-membered ring (Fig. 4). The unfavourable 0HN2 angle leads to an increase in the H-**l$ distance relative to the dihydrate. For the same reason the N,H- - - 0 distance is increased. The calculated total interaction energy of 13.8 kcal mol-l is expected to be lower by about 10% considering the BSSE computed for the dihydrate. This appears reasonable for two hydrogen bonds and confirms the cooperative effect in the dihydrate ring. It would certainly be interesting to have an experimental check on the hydration properties of pyrazoles and indazoles which may be important for the biological properties of larger molecules containing these heterocyclic moieties. Solvation effects on the tautomeric energies Of primary concern was the relative stability of the indazole tautomeric forms because of the biological properties of the parent molecule 2-azaergolene [ 31.
122
Fig. 4. Optimized geometry of the 3,4-dimethylpyrazole
monohydrate.
The indazole pair was therefore examined by recalculating the energies on the STO-3G optimized geometry using the extended 6-31G basis set and applying the method of Tomasi and co-workers [l] in order to estimate the continuum solvent effect. The energy difference between the tautomers in vacua (Table 5) is 2.9 kcal mol-’ smaller than that resulting from the STO-3G calculation: the solvent effect halves the energy difference bringing it to 5 kcal mol-’ (Table 5). This may be compared with the results of the calculation on the dihydrates although in this case the minimal basis set was used (Table 3). The energy difference between the tautomeric dihydrate pair of indazoles is 8.8 kcal mol-‘, i.e. 32% less than computed in vacua. The reduction of the tautomeric energy difference in the supermolecular approach is obviously due to the stronger hydrogen bonding by 1HIn which is the higher energy tautomer. This stronger bonding is likely to originate in the higher charge on the pyridinic nitrogen mentioned previously. This is, on the other hand, reflected in the continuum effect which takes into account the solute charges. The larger solvent effect exhibited in the latter approach was to be expected because in the supermolecular approach only the effect of the nearest solvent molecules is considered. The effect of hydration on the tautomerit energy of the dimethylpyrazoles differs between both basis sets without reversing the relative stabilities. The absolute values of the tautomeric ener-
123 TABLE 5 Total energies (a.u.) of tautomeric forms of dimethylpyrazole (A&) (kcal mol-‘)
and indazole and energy differences
Molecule
STO-3G
3-21G
3,4_Dimethylpyrazole 4,5-Dimethylpyrazole dE, (free) AE, (dihydrate)
- 299.14649 - 299.14836 1.2 0.9
lH-indazole lH-indazole solvated” BH-indazole SH-indazole solvated” AE, (free) AE, (solvated)
-372.77697
-301.16963 -301.17004 0.26 0.4 6-31G -377.28889 -377.32306 - 377.27294 - 377.31506 10.0 5.0
-372.75643 12.9 8.8
“Continuum model (ref. 1).
gies are so small that at this level of calculation it is difficult to see the reason for the discrepancy. The agreement between the supermolecular and the continuum solvent effects on the tautomeric energies of indazoles is reassuring since it shows that the relative energies of the two forms are not altered. Moreover, Tomasi’s method appears to be useful for treating the solvent effect on tautomeric systems, which is also important from the economic point of view. The relatively good agreement in the tautomeric energies computed by the minimal and split valence basis sets is probably due to the fact that in the presently examined systems there are no essential differences between the bonds involved in the tautomerism. This contrasts with the results of a comparative calculation on hydroxypyridines [ 91 in which the change between aromatic and quinonoid systems occurs along with interchange of OH and NH bonds. In this case the minimal basis set led to an erroneous result [ 91. ACKNOWLEDGEMENTS
The work was supported by Research Community of Slovenia. Thanks are due to Prof. J. Tomasi (Pisa) for the program for calculating the continuum solvent effect and to the IMP Company for free computer time on their VAX780 system.
124 REFERENCES 1 S. Miertus, E. Scrocco, and J. Tomasi, Chem. Phys., 55 (1981) 11’7. 2 D. Kocjan, M. Hodoscek, and D. Ha&i, J. Mol. Struct. (Theochem) ,152 (1987) 331. 3 N.J. Bach, E.C. Kornfeld, J.A. Clemens,E.B. SmaIstig, andR.C.A. Frederickson, J. Med. Chem., 23 (1980) 492. 4 J.S. Bingkley, R.A. Whiteside, R. Krishnan, R. Seeger, D.J. DeFrees, H.B. Schlegel, S. Topiol, L.R. Kahn, and J.A. Pople, QCPE, No. 406, Indiana University. 5 S.F. Boys and F. Bernardi, Mol. Phys., 19 (1970) 553. 6 J.D. Dill, L.C. Allen, W.C. Topp, and J.A. Pople, J. Am. Chem. Sot., 97 (1975) 1220. 7 J.E. Del Bene, Chem. Phys., 15 (1976) 463. 8 S. Ikuta, Chem. Phys. Lett., 95 (1983) 604. 9 M.J. Scanlan, I.H. Hillier, and A.A. MacDowell, J. Am. Chem. Sot., 105 (1983) 3368.