J. Phys. Chem. 1995, 99, 12525-12528
12525
Solvent Effects on the Thermodynamics and Kinetics of the Proton Transfer between Hydronium Ion and Ammonia. A Theoretical Study Using the Continuum and the Discrete Models Francisco R. Tortonda,? Juan-Luis Pascual-Ah&,* Estanislao Silla,*qs and Iiiaki Tuii6n Departamento de Quimica Fisica, Universidad de Valencia, 46100 Burjassot, Valencia, Spain Received: February 23, 1995; In Final Form: May 31, 1995@
In this work we present the results of a study of the solvent effects in the protonation of ammonia from a hydronium ion. The potential energy surface in the gas phase and the free energy surface in a continuum have been characterized at the HF/6-311G** level. Stationary points have been also relocated at the MP2/ 6-311G** level. The results obtained with the continuum model are compared with those of a discretecontinuum model in which five additional water molecules are placed around the proton acceptor and proton donor molecules. Both from the electronic and geometric points of view, solvent effects enforce the N-H bond while weakening the 0-H bond. At fixed N - 0 distances, solvent effects thermodynamically favor the proton transfer from hydronium to ammonia but make the process kinetically slower by increasing the energy barrier.
1. Introduction
Proton transfer reactions play a very important role in many chemical and biological processes.' For this reason, many theoretical works have been devoted to this subject2 However, while most of these studies have been carried out for isolated AH+-B systems, biological processes take place under the influence of complex surroundings: solvent and protein environments. Thus, it is of capital importance to include the effects of these envimoments in theoretical studies of proton transfer reactions in order to understand how these processes can take place in biological systems. Nowadays, the development of new strategies to include solvent and protein environm e n t ~on ~ ,chemical ~ processes makes it possible to achieve this goal. In a previous study, we analyzed solvent effects on the proton transfer between water and hydronium ion.9 Some interesting differences were found between the reaction path in the gas phase and in solution. In this paper we present the results of our study for the proton transfer from the hydronium ion to ammonia (H30+-NH3), which may be used as a model for the protonation of the R-NH2 group in proteins. Solvent effects on the reduced potential energy surface of the reaction are included using a continuum model. The ability of this relatively simple solvent model is discussed comparing the results with those obtained with a discrete solvation of the system. Moreover, the continuum model used here has been previously employed to calculate protonation and deprotonation free energies in aqueous solutions of methylamines and alcohols.'0," These studies, in which experimental values are quite well reproduced, seem to indicate that the continuum model can be very useful to highlight the acid-base problem in solution. 2. Methodology
Calculations in the gas phase have been carried out at the HFl6-311G**l2 level by means of the MONSTERGAUSS program.I3 Geometries were optimized with the gradient technique of Davidon,j4 up to the total gradient of less than 5 +Permanent address: I. B. Monastil, Elda, Alicante, Spain. E-mail:
[email protected]. FAX: 34-6-3864564. Abstract published in Advance ACS Absrracts, July 15, 1995. @
0022-365419512099- 12525$09.0010
Figure 1. Systems for which the proton transfers have been studied. x mdyn A-'. The reduced potential energy surface for the proton transfer in the gas phase has been constructed using the N - 0 and N-H+ distances as coordinates and optimizing the rest of the geometrical variables. Minima have been fully optimized without any restriction. The stationary points have been also optimized at the MP216-311G** level by using the Gaussian92 package. Solvent effects calculations have been carried out by means of the PCM model3-I6by using a dielectric constant of 78.4. The cavity selected for the continuum calculations was the solvent-excluding surface constructed with the GEPOL program." The radii of the initial spheres (RN = 1.86 A, Ro = 1.68 A, RH= 1.44 A) were, as in previous paper^,^.'^ 20% larger than the van der Waals radii. Further support for this selection of the radii has been recently given.I8 Calculations have also been carried out by using a modified MONSTERGAUSS program at the HF16-311G** level. The free energy surface for the proton transfer in solution has been obtained from the points calculated in the gas phase and by adding the electrostatic solvation free energy. Thus, this is a free energy surface in the sense that it incorporates electrostatic free energies of solvation, but it does not include contributions due to the intemal partition function or dispersion and cavitation terms. The MP2 calculations in solution have been carried out using the continuum model of Rivail et al.,'9.20 where the solute is placed in an ellipsoidal cavity.
0 1995 American Chemical Society
Tortonda et al.
12526 J. Phys. Chem., Vol. 99,No. 33, 1995
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Figure 2. Potential energy surface for the proton transfer in the gas phase at the HF/6-311G** level. Isoenergetic lines are in kcaVmol TABLE 1: Distances (in A), Mulliken Charges on Water Molecules Attached to Ammonia (WN)or Water (WO),and Bond Orders for the Structures Studied at the HF Level gas phase continuum discrete-continuum 2.755 (2.667)" 1.034 (1.060)
0.810 0.099 a
2.855 (2.918) 1.020 (1.042)
0.827 0.094
2.77 1 1.026 2.93 1 2.889 0.032 0.03 1 0.846 0.088
MP2 values in parentheses.
In the discrete-continuum model 2 and 3 water molecules were added, linearly hydrogen bonded, to water and ammonia molecules, respectively, as can be seen in Figure 1. The internal geometry of these five new water molecules was kept fixed to its optimized values ( I = 0.9410 A, 0 = 105.46"), and all the rest of the variables of the system were optimized to locate the minimum in the gas phase. Keeping the same gas phase geometry, the system is recalculated in a continuum using the PCM model. Calculations were also carried out at the HF/631 1G** level.
3. Results and Discussion In Figure 2 we present the reduced potential energy surface for the proton transfer in the gas phase. To obtain this surface 176 ab initio points were calculated. As previously the proton transfer from the hydronium ion to ammonia takes place in a barrierless process, and only a minimum is found on the surface. This corresponds to the ammonium ion interacting with the water molecule ( m f - H * 0 ) . As can be seen in Table 1, at the HF level, the minimum appears at a N-0 distance of 2.755 A and a N-H1 distance of 1.034 A, in good agreement with previous studies on this ~ystem.*I-*~The energy with
respect to the separate ammonium ion and water molecule is -21.43 kcal/mol. This is close to the energy obtained with more extended basis sets.23 At the MP2 level the N-0 distance at the equilibrium geometry is somewhat shorter (2.667 A), while the N-H1 distance is larger (1.060 A). The reduced free energy surface for the proton transfer in solution is presented in Figure 3. As said before, this has been obtained from the points calculated in the gas phase solvated with a continuum model. The minimum appears at a N-0 distance of 2.855 A and a N-H1 distance of 1.020 A. The relative energy of the minimum with respect to the separate molecules is now only -5.42 kcavmol. Using the ellipsoidal cavity model, the minimum in solution at the MP2 level appears at a N-0 distance of 2.918 A and at a N-H1 distance of 1.042 A. As expected, both at the HF and MP2 levels, the continuum reduces the interaction because of the trend to separate the ion and the dipole of the water molecule to solvate them better. Some interesting features can also be seen in the HF reduced free energy surface. The free energy curve for displacements in the N-0 distance around the minimum is very flat. Indeed, in the range of N-0 distances from 2.78 to 2.90 A the energy changes by less than 0.1 kcaymol. Thus, one should expect that other energetic contributions (correlation, dispersion, and cavitation) should be important to locate the minimum exactly on the reduced free energy surface. As far as the cavitation contribution's attempt to reduce the solute's surface area, a decrease of the N-0 distance could be expected by including this term. Inversely, displacements in the N-H1 coordinate, at fixed N-0 distances, require more energy than in the gas phase. The SCF force constants numerically derived from Figures 2 and 3 are 2.98 x and 1.67 x au for the N-0 bond and 3.38 x lo-' and 5.05 x lo-' au for the N-H1 bond in the gas phase and in solution, respectively. These tendencies observed in the reduced free energy surface are confirmed by the values of the force constants obtained at the MP2 level within the ellipsoidal cavity model. The MP2 force constant of the N-0 bond is reduced from 3.55 x to 0.78
Proton Transfer between Hydronium Ion and Ammonia
J.'Phys. Chem., Vol. 99, No. 33, 1995 12527
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Figure 3. Free energy surface for the proton transfer in solution ( E = 78.4) at the HF/6-311G** level. Isoenergetic lines are in kcallmol.
'+" I
x lo-* au when going from the gas phase to solution, while d(N-0)=2.85 A that of the N-H1 bond is increased from 2.91 x lo-' to 3.63 x lo-' au. It should be pointed out here that at the SCF level the ellipsoidal cavity model leads to the dissociation of the ammonium ion-water molecule complex. To evaluate the accuracy of the results obtained by means of the continuum model, it is interesting to compare with a discrete-continuum solvation model. For this purpose, we have optimized the structure of the N&+-H20 system surrounded with five discrete water molecules, as explained in the previous section. The geometry of this structure together with those obtained in the gas phase and in a continuum is given in Table 1. It can be seen that both the discrete-continuum and the continuum models reproduce the same trends in the geometrical description of the ammonium ion-water molecule minimum: 0.9 1.1 1.3 1.5 1.7 1.9 a lengthening of the N-0 distance and a shortening of the N-H W H ) (A) distance. However, while the agreement is very good for the Figure 4. Energy curves for the proton transfer in theogas phase and N-H distance, the N-0 distance in both models differs as much in solution for a nitrogen-oxygen distance of 2.85 A at the HN6as 0.09 A. This is mainly due not to deficiencies of the 311G** level. continuum model but rather to the very flat energy surface around the minimum for displacements along the N-0 coorthe proton acceptor character of the water molecule, and this dinate. As said before, in the interval of N-0 distances 2.78tries to compensate the lengthening provoked by the electrostatic 2.90 A the energies range around 0.1 kcal/mol, which is more effect. In agreement with the conclusions discussed when or less the same as the difference in the cavitation contributions comparing both energy surfaces, bond order clearly indicate that at the extreme ends of the interval. A parabolic interpolation solvent effects reinforce the N-H1 bond while decreasing the taking into account both the electrostatic and the cavitation strength of the 0-H1 bond. Conclusions with both the contributions, the last one being calculated as in ref 24, gives discrete-continuum and the continuum model are qualitatively very similar although more pronounced in the first. a distance between oxygen and nitrogen atoms for the minimum of around 2.82 A, which is in better agreement with the discrete In many biological processes the distance between the protonmodel. The remaining difference between the two models can donor and proton-acceptor atoms may be constrained by the be explained with the same argument that we used in our environments. For this reason it is interesting to analyze solvent previous works about proton transfer and proton ~ o l v a t i o n . ~ . ~ ~effects on the proton transfer for a fixed N-0 distance. In The electrostatic solvent effect tends to separate the ion and Figure 4 the energy variation, at the HF level, along the proton transfer path for a N - 0 distance of 2.85 A is shown, the the dipole to solvate them better. This effect is obviously present in the continuum model. However, when we add conclusions being very similar for other N-0 distances. Some explicit water molecules, we also have a charge transfer from interesting differences can be seen. The barrier for the proton the system to the solvation shell (see Table 1) that increases transfer from the hydronium ion to ammonia in solution (5.2
12528 J. Phys. Chem., Vol. 99, No. 33, 1995 kcaymol) is nearly twice the barrier found in the gas phase (2.5 kcallmol). However, solvent effects increase the exothermicity of the reaction with respect to the gas phase by about 1.9 kcall mol. It seems then that the electrostatic solvent effect thermodynamically favors the protonation of the ammonia from a hydronium ion but makes the process kinetically slower for systems with constraints in the donor-acceptor distance. As can be seen in the reduced energy surfaces, if the N-0 distance is not constrained, the transfer takes place without any energy barrier.
4. Conclusions Here we have presented a study of the solvent effects on the proton transfer from the hydronium ion to ammonia. Solvent effects have been simulated by means of two models: a continuum model and a discrete-continnum representation of the first solvation shell. The free energy surface for the proton transfer in solution has been obtained solvating the points of the potential energy surface in the gas phase, using the PCM model. Inclusion of electron correlation has been also considered by using the ellipsoidal cavity method at the M E level. The same trends for the solvent effect are observed with and without inclusion of electron correlation, although the geometries of the minima in the gas phase and in solution are slightly different. Some interesting differences appear between the process in the gas phase and in aqueous solution. In solution it seems that, while the force constant associated with the N-0 displacement is lowered, that corresponding to the N-H1 bond is increased, as reflected in the N-H1 and 0-H1 bond orders. These two effects should be taken into account in developing effective potentials for the protonation of R-NHz groups in solution. At fixed donor-acceptor distances, the electrostatic solvent effect, while increasing the energy barrier, thermodynamically favors the proton transfer from hydronium to ammonia. The conclusions obtained with the continuum model have been contrasted with results obtained with a discrete-continnum representation of the solvent. The two models give the same general trends, and the differences can be rationalized considering the missing terms in our continuum models (cavitation, dispersion, and charge transfer contributions). Acknowledgment. Calculations were carried out on a VAX4000 and on a RISC-6000/580 (a SEUI Project OP900042 and a grant of the Generalitat Valenciana are acknowledged). I.T. thanks a postdoctoral fellowship of the Ministerio de Educacion y Ciencia (Spain). This work was supported by
Tortonda et al. DGICYT Project PB93-0699. The authors wish to acknowledge Prof. D. Rinaldi for providing them with the last version of the Nancy continuum model and Prof. M. Ruiz-L6pez for reading the manuscript. References and Notes (1) Jeffrey, G. A.; Saenger, W. In Hydrogen Bonding in Biological Structures; Springer-Verlag: Berlin, 1991. (2) See for example: Scheiner, S.; Redfem, P.; Hillebrand, E. A. lnt. J. Quantum Chem. 1986, 29, 817. (3) Miertus, S.; Scrocco, E.; Tomasi, J. Chem. Phys. 1981, 55, 117. (4) Dillet, V.; Rinaldi, D.; Rivail, J. L. J . Phys. Chem. 1994, 98, 5034. (5) Cramer, C. J.; Truhlar, D. G. Science 1992, 256, 213. (6) Gao, J. J . Phys. Chem. 1992, 96, 537. (7) Field, M. J.; Bash, P. A.; Karplus, M. J . Comput. Chem. 1990, 11, 700. (8) Thery, V.; Rinaldi, D.; Rivail, J. L.; Maigret, B.; Ferenczy, G. G. J . Comput. Chem. 1994, 15, 269. (9) Tortonda, F. R.; Pascual-Ahuir, J. L.; Silla, E.; Tufibn, I. J . Phys. Chem. 1993, 97, 11087. (10) (a) Pascual-Ahuir, J. L.; Andres, J.; Silla, E. Chem. Phys. Lett. 1990, 169, 297. (b) TuRbn, I.; Silla, E.; Tomasi, J. J . Phys. Chem. 1992, 96, 9043. (1 1) Tufibn, I.; Silla, E.; Pascual-Ahuir, J. L. J . Am. Chem. SOC.1993, 115, 2226. (12) Krishnan, R.; Binkley, J. S.; Seeger, R.; Pople, J. A. J . Chem. Phys. 1980, 72, 650. (13) Peterson, M. R.; Poirier, R. A. University of Toronto, Canada, 1980. (14) Davidon, W. C. Math. Prog. 1975, 9, 1. (15) Frish, M. J.; Trucks, G. W.; Head-Gordon, M.; Gill, P. M. W.; Wrong, M. W.; Foresman, J. B.; Johnson, B. G.; Schlegel, H. B.; Robb, M. A.; Reprogle, E. S.; Gomperts, R.; Andres, J. L.; Raghavachari, K.; Binkley, J. S.; Gonzalez, C.; Martin, R. L.; Fox, D. J.; Defrees, D. J.; Baker, J.; Stewart, J. J. P.; Pople, J. A. Gaussian 92; Carnegie-Mellon Quantum Chemistry Publishing Unit: Pittsburgh, PA, 1992. (16) (a) Bonaccorsi, R.; Cimiraglia, R.; Tomasi, J. J . Compur. Chem. 1983, 4 , 567. (b) Pascual-Ahuir, J. L.; Silla, E.; Tomasi, J.; Bonaccorsi, R. J . Comput. Chem. 1987, 8, 778. (17) (a) Pascual-Ahuir, J. L.; Silla, E. J. Comput. Chem. 1990, 11, 1047. (b) Silla, E.; Tufibn, I.; Pascual-Ahuir, J. L. J . Comput. Chem. 1991, 12, 1077. (c) Pascual-Ahuir, J. L.; Tuiih, I.; Silla, E. J. Comput. Chem. 1994, 15, 1127. (18) Bachs, M.; Luque, F. J.; Orozco, M. J . Comput. Chem. 1994, 15, 446. (19) (a) Rivail, J. L.; Rinaldi, D.; Ruiz-Lbpez, M. F. In Theoretical Computationnl Models for Organic Chemistry; Formosinho, S. J., Amaut, L., Csizmadia, I., Eds.; Kluwer: Dordrecht, 1991; pp 79-92. (b) Rinaldi, D.; Rivail, J. L.; Rguini, N. J. Comput. Chem. 1992, 13, 675. (20) Rinaldi, D.; Pappalardo, R. R. SCRFPAC; QCPE, Indiana University: Bloomington, IN, 1992; program number 622. (21) Jaroszewski, L.; Lesyng, B.; Tanner, J. J.; McCammon, J. A. Chem. Phys. Lett. 1990, 175, 282. (22) Roszak, S.; Kaldor, U.; Chapman, D. A,; Kaufman, J. J. J . Phys. Chem. 1992, 96, 2123. (23) Del Bene, J. E. J. Phys. Chem. 1988, 92, 2874. (24) Tufibn, I.; Silla, E.; Pascual-Ahuir, J. L. Chem. Phys. Lett. 1993, 203, 289. (25) Tuiibn, I.; Silla, E.; Bertrln, J. J. Phys. Chem. 1993, 97, 5547. JP9505 19V
