J . Phys. Chem. 1990, 94, 5499-5501
5499
Tautomerism of 1,2,3- and 1,2,4-Triazoie h the Gas Phase and in Aqueous Solution: A Combined ab Initio Quantum Mechanics and Free Energy Perturbation Study James R. COX; Stephen Woodcock, Ian H. Hillier,* and Mark A. Vincent Chemistry Department, University of Manchester, Manchester M13 9PL. U.K. (Received: November 1. 1989; In Final Form: February 5, 1990)
The energy differences between the tautomers of 1,2,3- and 1,2,4-triazolehave been estimated at the 6-31G**(MP2)//3-21G level including zero-point effects. The results confirm that only a single tautomer of each isomer is expected to be observed in the gas phase. In aqueous solution the free energy separation of each pair of tautomers is considerably reduced and has been estimated by use of the free energy perturbation method. These calculations agree with the experimental findings that for 1,2,3-triazole both tautomers are observed in a polar solvent, whereas for 1,2,4-triazole the concentration of the rare tautomer is still extremely low.
Introduction Due largely to the pioneering work of Pople and collaborators, it is now possible to carry out accurate a b initio calculations to predict the electronic structure of quite large molecular systems, including electron correlation effects. There is now considerable interest in building into such studies the effect of the environment, where, of necessity, potentially less rigorous methods may be involved. As examples, the environment may be a part of the molecule that takes no direct part in the chemistry being studied, such as parts of an enzyme distant from the active site, or it may be the solvent. In this paper we describe a theoretical study of the latter situation, involving tautomerism in the gas phase and in aqueous solution utilizing “state-of-the-art” a b initio quantum mechanical and free energy perturbation methods. Accurate a b initio calculations of molecular structure and energetics continue to be of value in many studies of tautomeric phenomena as shown by recent studies.’ Such studies often have biological implications as in the Occurrence of the rare tautomers of the pyrimidine bases and their role in mutagenesk2 Of particular interest is the effect of environment, particularly solvent, on the tautomeric equilibria. Thus, in the case of the well-studied 2-pyridone/2-hydroxypyridineequilibrium, the energy difference between the two tautomers is very small in the gas phase, while in the solid state and in polar solvents the 2-pyridone tautomer is d ~ m i n a n t . ~ The accurate prediction of tautomeric equilibria in solution requires high-accuracy quantum mechanical calculations of the structure and energetics of the isolated molecules, where frequently the structures of only the dominant tautomers are known experimentally, together with estimates of the solvent-solute interactions. The review by Elguero et ala4describes many situations where tautomeric equilibria are poorly understood. For example, they describe the tautomerism of 1,2,3-triazole as ”... still the most confused of all the cases of annular tautomerism”. In this paper we describe theoretical studies of the equilibria involving the 2 H tautomer (I) and the 1 H tautomer (11) of 1,2,3-triazole and also that involving the 1 H tautomer (111) and 4 H tautomer (IV) of 1,2,4-triazole. In the case of 1,2,3-triazole, microwaves and photoelectron’ spectroscopy studies conclude that in the gas phase the 2 H tautomer (I) is the only species observed. However, in solution, both the 2 H and the 1H tautomer (11) are often observed. Thus, ‘H NMR studies in CD2C12indicate that both tautomers are present in solution, their relative proportion depending upon temperature and concentration.* Two circumstantial but independent arguments have recently been presented that both give the result that the 2 H tautomer is favored in aqueous solution over the 1 H tautomer by a factor of about 2.9 For 1,2,4-triazole, microwave ‘Present address: Shell Research Center, Sittingbourne, Kent ME9 8AG,
U.K.
N=C
N=C
I
\
H/N\CIN
I
\
N\,/N-H
I
H
IH
UUl
IN1
studies have concluded that the 1H tautomer predominates overwhelmingly in the gas phase.I0 A photoelectron spectroscopic study has also concluded that the 4 H tautomer is not present at detectable levels’ in the vapor phase. As far as solution studies are concerned, a proton NMR study of 1,2,4-triazole indicates that the relative concentration of the 4H tautomer in tetrahydrofuran (THF) is less than 1% at -70 OC.* In this paper we shall describe calculations of the relative energetics of the tautomers of both isomers of triazole in the gas phase and in aqueous solution. First, calculations of the molecular geometries of the four species will be described followed by calculations of their energies including both correlation and zero-point effects. To quantitatively estimate the changes in the (1) L a , A.; Adamowicz, L.; Bartlett, R. J. J . Phys. Chem. 1989,93,4001. Kwiatkowski, J. S.; Bartlett, R. J.; Person, W. B. J. Am. Chem. SOC.1988, 110, 2353. (2) Topal, M. D.; Fresco, J. R. Nature (London) 1976, 263,285; 1976, 263, 289. (3) Beak, P.; Fry, S.; Lee, J.; Steele, F. J . Am. Chem. Soc. 1976, 98, 171. Beak, P. Ace. Chem. Res. 1977, IO, 186. (4) Elguero, J.; Marzin, C.; Katritzky, A. R.; Linda, P. The Tautomerism of Heterocycles; Academic Press: New York. 1976; p 283. ( 5 ) Nygaard, L. Reported in ref 6. (6) Palmer, M. H.; Simpson, I.; Findlay, R. H. 2.Naturforsch. 1981,36a, 34. (7) Palmer, M. H.; Simpson, I.; Wheller, J. R. 2.Naturforsch. 1981,360, 1246. (8) Lunazzi, L.; Parisi, F.;Macciantclli, D. J . Chem. Soc., Perkin Trans. 2 1984, 1025. (9) Albert, A.; Taylor, P. J. J . Chem. Soc., Perkin Trans. 2 1989, 1903. (IO) Bolton, K.; Brown, R. D.; Burden, F. R.; Mishra, A. J . Mol. Srrucr. 1975,27, 261. Bolton, K.; Brown, R. D.; Burden, F. R.; Mishra, A. J . Chem. Soc., Chem. Commun. 1970, 873.
0022-3654/90/2094-5499%02.50/00 1990 American Chemical Society
5500 The Journal of Physical Chemistry, Vol. 94, No. 14, 1990
Cox et al.
free energy of solvation between different species, the free energy perturbation method has been shown to be successful. In this work, we use this method in molecular dynamics simulations to estimate the changes in the free energy of solvation between the different tautomers of each isomer of triazole.
TABLE I: c h & k t h s to tbe Tocrl EM.rw (in au) of 1H-l,2,3-Triazde (1H-123) 28-1,2,3-Triuole , (28-123), 1H-1,2,4-Triazole (lH-l24),a d 4H-l,2,4-Triazok (48-124)
Computational Details
IH-123 2H-123 4H-124 1H-124
The geometric structuresof the four triazole species (I-IV) were obtained at the 3-21G basis set level" by using the program G A M E S S . ~ ~ At these optimized geometries large basis set (631G**)l3calculationswere carried out and correlation effects were estimated using second-order Maller-Plesset (MP2) perturbation theory.I4 Zero-point energies were estimated by calculating the harmonic frequencies at the 3-21G level. These calculations were carried out by use of the program CADPAC." Subsequent to the quantum mechanical calculations, one tautomer was transformed into another in solution by using the free energy perturbation methodt6 in molecular dynamics simulations to obtain the solvation free energy differences (AAG) between the two tautomers, as implemented in the program AMBER." The atomic partial charges for the four species studied were obtained by using the following strategy proposed by Singh and Kollman.'* Following geometry optimization at the 3-21G level, single-point calculations were carried out using a 6-31G* basis." The 6-31G* wave functions were then used to calculate the electrostatic potential around the molecules which lead to the determination of the partial atomic charges. The charges used in the molecular dynamics simulation were rescaled by a factor of 0.95 to take account of the overestimation of the molecular dipole moments given by the SCF wave functions. The molecular dynamics simulations were carried out at T = 300 K and 1-atm pressure in a water bath that contained 547 or 552 TIP3P water molecules. The initial configurations of water molecules were taken from a Monte Carlo simulation of TIP3P water. The walls of the simulated box were chosen to be at least 12 A from the most peripheral solute atoms. In the free energy perturbation method, the transformation between the two species involved in the equilibrium is carried out in a number of small steps involving the coupling parameter A. The molecular mechanics energy of the system is expressed in terms of the parameter X as in ref 19. For the tautomeric equilibria studied herein the transformation involves the simultaneous loss and growth of a proton at different nitrogen atoms of the heterocycle. As far as the molecular mechanics parameters are concerned, the van der Waals parameters were taken from ref 20, and the intramolecular parameters for the tautomers were chosen to obtain a good fit to the derived 3-21G geometries. The perturbation calculationsz1 were carried out in a series of 21 "windows" where the values of A differed by 0.05. For each value of A, 500 steps of equilibration followed by 500 steps of data collection with a time step of 0.002 ps at constant pressure and temperature (300 K)were performed using periodic boundary conditions. We have also investigated the usefulness of the reaction field continuum model (RFCM)22to estimate the solvation effects in (1 I ) Binkley, J. S.;Pople, J. A.; Hehre, W. J. J . Am. Chem. Soc. 1980, 102, 939. (12) Guest, M. F.; Kendrick, J. GAMESS User Manual, CCP1/86/1; Daresbury Laboratory, 1986. (13) Hariharan, P. C.; Pople, J. A. Theor. Chim. Acro 1973, 28, 213. (14) Mailer, C.; Plessct, M. S. Phys. Reu. 1934, 46, 618. ( I 5 ) Amos, R. D.; Rice, J. E. CADPAC, The Cambridge Analytic Derivatives Package, Issue 4.0; Cambridge, 1987. (16) Jorgensen, W. L.; Ravimohan, C. J . Chem. Phys. 1985, 83, 3050. (17) Singh, U. C.; Weiner, P. K.; Caldwell, J. W.; Kollman, P. A. AMBER (UCSF), Version 3.0; Department of Pharmaceutical Chemistry, University of California, San Francisco, 1986. (18) Singh, U. C.; Kollman, P. A. J . Compur. Chem. 1984, 5 , 129. (19) S i h , U. C.; Brown, F. K.; Bash, P. A.; Kollman, P. A. J . Am. Chem. Soc. 1987, 109, 1607. (20) Weiner, S.J.; Kollman, P. A.; Nguyen, D. T.; Case, D. A. J. Compur. Chem. 1986, 7, 230. (21) Cieplak, P.; Bash, P.; Singh, C.; Kollman, P. A. J . Am. Chem. Soc. 1987, 109,6283. (22) Rein, R.; Renugopalakrishnan, V.; Nir, S.;Swissler, T. J. In!. J . Quantum Chem. 1975, S2, 99.
ESCF 3-21G//3-21G -239.3927 -239.3990 -239.4220 -239.4280
EM" 6-31G1*//3-2IG -0.7896 -0.7881 -0.7786 -0.7780
6-3IG8*//3-21G' -240.7719 (4.6) -240.7793 (0.5) -240.7965 (6.0) -240.8076 (2.9)
'The values in parentheses are the calculated dipole moments (debyes). TABLE II: Relative Stabilities of Triazdes (kJ md-') (2H-123)(1H-124)(IH-I23) ( ~ 1 2 4 ) SCF 3-21G//3-21G -16.5 -1 5.7 SCF 6-31Gi*//3-21G -19.5 -29.2 SCF DZ//(7s3p/3s)' -15.9 -21.4 ZPE 3-2 1GJl3-21G 0.8 1.3 MP2 6-31G**//3-21G 3.9 1.6 total relative stability, -14.8 -26.3 SCF(6-3 1G**//3-2 1G) + ZPE + MP2 Reference 7.
.H
0 9 d H
.H /H
122
b @ 1 2 3 1 JYP-6 1141\ \
11063
H H
ID)
H
I
11 062
\ IN1
I
H/C-N
Figure 1. Structuresoptimized at 3-21G level: (I) 2H-I,2,3-triade; (11) 1H-l,2,3-triazole; (111) IH-1,2,4-triazole; (IV) 4H-1,2,4-triazole.
the systems studied herein. In this model the solute molecule is assumed to be a point dipole located at the center of a cavity within the solvent which is represented as a dielectric continuum. The interaction of the dipole with the reaction field induced in the solvent by the dipole itself gives rise to the stabilization. For a spherical cavity of radius a, and a solute molecule with dipole p and polarizability a,the energy is -fP2 -fa)
G=where
2(E - 1 )
= (26
+ 1)a:
Here E is the dielectric constant of the solvent. For the triazole systems studied here, the calculated dipole moments are scaled
The Journal of Physical Chemistry, Vol. 94, No. 14, 1990 5501
Tautomerism of 1,2,3- and 1,2,4-Triazole TABLE III: Cdculrted Free Jhergy Differences (W mot') and Equilibrium Colet~ntsfor Tautomerimtion for I,%> and 1,2&Trirzoks in H20 at 300 K N H20 in MD tautomer pair AAG& simuln AAG, LId I 11 I I1 I1 I 1/11 547
-
111
-
-8.9
I
I1
+9.6
IV
552
111
-
IV
-16.5
IV
-
-5.6
IV
0.5
111
-9.5 & 0.4
IO III/IV 46
I11
+17.1
by the factor 0.95, as previously discussed, the polarizabilities are estimated by the method of Miller and Sa~chik:~and a cavity radius of 3.2 A was assumed for each species.
Computational Results Gas-Phase Results. Tables I and I1 summarize the results of the calculations on the isolated triazole molecules as far as energetics are concerned. The structures optimized at the 3-21G level are shown in Figure 1. Comparison with the experimental geometry*' of lH-1,2,4-triazole yields agreement to better than 0.03 A and 2O for bond lengths and angles, respectively. The 2H tautomer of 1,2,3-triazole and the 1H tautomer of 1,2,4-triazole are found to be the most stable tautomers, the energy separation from the less stable tautomer being considerable in both cases. The use of the larger basis (6-31G**) increases the energy separation between the tautomers, this effect being particularly pronounced in the case of 1 ,2,4-triazole0 The energy separations we obtain at the 3-21G level are similar to the values obtained from a DZ//(7s3p/3s) cal~ulation.~ The relative stabilities of the tautomers may be readily understood in terms of the unfavorable lone pair-lone pair repulsion in the less stable tautomers. Correlation effects estimated at the MP2 level reduce the energy differences between the tautomers, although this reduction is quite modest. Such an effect of correlation is not unexpected in view of the unfavorable electron repulsion effects previously discussed. Zero-point-energy contributions to the relative stabilities of the tautomers are smaller than the effects of electron correlation,being close to 1 kJ mol-' in both systems studied. Our final estimates of the relative energies of the tautomers in the gas phase (Table 11) allow the equilibrium constants (I 11; 111 IV) involving the tautomer pairs to be estimated. The values are 2 X for for 1,2,4-triazole,values in line with 1,2,3-triazole and 2 X the observation that no rare tautomers are detected in the gas phase. Solution Studies. In Table I11 we summarize the free energies and equilibrium constants obtained from the calculationsdescribed herein. The free energy differences between the tautomers in solution (AAGtot) were estimated by using the equation
TABLE I V Energy Differems (W mor1)for Tautomers of 1,2,3and 1.2.4-Triazoles in H,O Calculated Usinn RFCM ~
~~~
--
tautomer pair
I1 IV
I 111
AAG&
AAGtc4
+21.3 +28.2
+6.5 +1.9
is preferentially stabilized in aqueous solution on account of its greater dipole moment compared to that of the dominant tautomer (Table I). Thus for the pair of 1,2,3-triazole tautomers, the energy separation is reduced from 14.8 kJ mol-' in the gas phase to 5.6 kJ mol-' in aqueous solution. For 1,2,4-triazole the reduction is from 26.3 kJ mol-' to 9.5 kJ mol-'. These free energy estimates lead to equilibrium constants of 10 for 1,2,3-triazole and 46 for 1,2,4-triazole in aqueous solution. The arguments of Albert and Taylor? with an equilibrium constant of -2 for 1,2,3-triazole would imply a value of AAGtot near 2 kJ mol-'. However, we would expect uncertainties of -4 kJ mol-' in the solvation contribution to the free energy differences, so that our calculations agree extremely well with the conclusions of Albert and Taylor. As far as comparison with NMR data in the solvents CD2C12and THF is concerned? our calculationswhich model aqueous solution should be of relevance in view of the similar dipole moments of all three solvents. Thus the experimental occurrence of both tautomers of 1,2,3-triazole in CD2C12and less than 1% of 4H 1,2,4-triazole in THF at -70 "C are in line with our calculated equilibrium constants (Table 111). The considerably simpler reaction field continuum model (Table IV) predicts the same trends as the simulation studies although the calculated solvation energies are considerably larger in magnitude. This results in an inversion of the populations of the tautomers on going from the gas phase to aqueous solution, a result in disagreement with the conclusions of Albert and Taylor for 1,2,3-triazole and unlikely in view of the NMR data for 1,2,4-triazole.
Here AAG& is the solvation free energy difference between the tautomers obtained from the molecular dynamics calculations, A&,, is the difference in the energy of the isolated tautomers, including zero-point effects, obtained from ab initio calculations (Table II), and ASq,,,is the difference in the entropies which could be calculated by quantum mechanical methods, but which are generally assumed to be negligible.21We first note that the most stable tautomer for each system is the same in solution as in the gas phase. However, the less stable tautomer in the gas phase
Discussion The results of our quantum mechanical calculations confirm conclusions of previous studies of tautomeric equilibria that use of a large basis (6-31G**) is needed to obtain accurate energy differences and that calculations at a lower level (3-21G) are probably adequate as far as geometry optimization is concerned.' Indeed, we find that for both isomers the calculated energy separation between the tautomer pairs at the 6-31G**//3-21G level (Table 11) is essentially unaltered at the 6-31G**//6-31G level,25 in agreement with a recent report by Catalan et al.26on 1,2,3triazole. We find that correlation effects reduce the energy separation between the tautomers to a small extent and that zero-point contributions can be essentially neglected. Similar conclusions were drawn from our previous calculations of the tautomers of uraciL2' The molecular dynamics simulations predict a reduced free energy separation for both tautomeric pairs upon solvation in water, in line with experiment. Comparison of our calculated equilibrium constants with the limited amount of experimental data available confirms the predictive value of these calculations, shown by previous studies.21 In contrast, the reaction field continuum model is found to seriously overestimate solvation energy differences for at least one of the isomers studied. Acknowledgment. We thank P. J. Taylor and Dr.C. Reynolds for helpful discussions and the SERC for support of this research. These calculations were carried out on the CRAY-XMP/48 of the Rutherford Appleton Laboratory and on the AMDAHL VPl 100 of the Manchester Computing Center. R@hy NO. I, 288-35-7; 11,288-36-8,111,288-88-0; IV, 63598-71-0.
(23) Miller, K. J.; Savchik, J. A. J . Am. Chem. Soc. 1979, 101, 7206. (24) Jeffrey, G. A.: Ruble, J. R.; Yates, J. H. Acta C r p r a h r . 1983,839, 388.
(25) Cox, J. R. Ph.D. Thesis, University of Manchester, 1987. (26) Catalan, J.; Sanchez-Cabezudo, M.; de Paz, J. L. G.; Elguero, J.; Taft, R. W.; Anvia, F. J . Compur. Chem. 1989, 10, 426. (27) Gould, I. R.; Hillier, I. H. J. Chem. Soc., Perkin Trans. 2 1990,329.
- -
AAGtot = PAC,,,
+ AEqm+ ASq,,,
