Synergism of Catalysis and Reaction Center Rehybridization. An ab Initio Study of the Hydrolysis of the Parent Carbodiimide

to include compounds with important roles in a wide array of chemical applications. 3 The most important reactions of carbodiimides all involve nucleophilic attack, and the nucleophilic addition of water to dicyclohexylcarbodiimide is widely used for dehydration. 4 We are particularly interested in the hydrolysis of carbodiimides for their potential role as reactive intermediates in guanine deamination. 5 There have been a few experimental studies of the addition of carboxylic acids to dicyclohexylcarbodiimide,6 but to our knowledge, there have not been any studies of the addition of water to carbodiimide. Computational studies were performed on the parent carbodiimide, HN dCdNH, but they focused on the equilibrium structure, 7,8 the N-inversion, 9 and the torsional -rotational dynamics. 10 We report here the results of an ab initio molecular orbital study into the kinetics of the hydrolysis of the parent carbodiimide. The study shows that the catalysis by a second water molecule causes electronic relaxation that facilitates further catalysis due to H-bonding with the environment. All geometries were optimized and vibrational analyses were performed at the MP2(full)/6-31G* level. 11,13 Populations were determined using the natural bond orbital (NBO) method. 12 The relative energies include vibrational zero-point energy corrections which were scaled by the empirical value 0.9646. 14 Higher level G2 and QCISD(T)(fc)/6-311 +G(3df,2p) energies were computed for the single water hydrolysis of carbodiimide, and they gave approximately the same relative energy values for the activation barriers as the MP2(full)/6-31G* calculations. For example, the ∆E0 activation energies computed at the MP2(full)/6-31G*, G2, and QCISD(T)(fc)/6-311 +G(3df,2p) levels are 44.8, 45.4, and 46.0 kcal/mol, respectively. The hydrolysis of the parent carbodiimide, HN dCdNH, should be similar to the hydrolyses of carbon dioxide, 15 ketene, 16 and keteneimine17 since these heterocumulenes are isoelectronic. Theoretical studies into the hydration of CO 2, H2CdCdO, and H2CdCdNH showed that consideration of a second water molecule resulted in catalysis. Similar results were also obtained for the hydrolysis of SO3. Obviously, the catalysis arises in all of these cases from alleviation of steric strain in going from a four-membered to a six-membered cyclic transition-state structure. Our calculations of the van der Waals complexes and transition states for the oneand two-water hydrolyses of the parent carbodiimide (Figure 1, 1-4) resulted in activation energies of 43.7 and 32.1 kcal/mol, respectively (Figure 2). Thus, the inclusion of a second water molecule results in a catalysis of 11.6 kcal/mol, and this result can be rationalized just as in the case of the other heterocumulenes and SO 3. The consideration of the effect of a third water molecule was the next logical step. The placement of a third water molecule is not a trivial matter, and we initially considered two possibilities. The first option involved placement of the water at the site of proton transfer (Scheme 1, A). We quickly judgedA to be catalytically of little relevance because it is well-known that there is little energy gain in going from a sixto an eight-membered cyclic transition state. In fact, this was recently illustrated for the hydrolysis of carbon dioxide, 19 where the addition of a third water molecule to the site of proton transfer reduced the activation energy merely by another 2.6 kcal/mol. The second option, and the less intuitive yet the more interesting one, involved the placement of the third water molecule as shown in B20 (Scheme 1). In this scenario, the transition-state structure still involves proton transfer through a six-membered ring (thick dashed lines in B), but the C-O bond forming O-atom is H-bonded to another water molecule (boxed and with thin dashed lines in B) which is not taking part in the proton transfer. The logic behind recognizing the importance of structure B relates to hybridization effects on charge relaxation associated with the activation barriers. Comparison of 2 and4 shows that the consideration of a second water molecule results in a transition-state structure in which bond formation between the adding water (H2O) and the C-atom (C -OA) has progressed more quickly while the H-transfer (HT) has slowed; the C -OA distance decreases by 0.129 Å, and the O A-HT distance decreases by 0.068 Å. Note also that the rehybridization of the C-atom has progressed more in 4 than in2 and this is illustrated by the ∠(NC-N) angles of 147.7 ° for 2 and 139.9° for 4. Thesestructural differences between 2 and4 have important electronicconsequences during activation for the dNH group that remains an imine during the reaction (NH R) and the OA-H group where the H-atom remains bonded to O A during the reaction (OAHR). Hybridization concepts suggest that an dNH group in a diimide will be less negative than in an imine. 21a Therefore, we would predict that the change in the charge of the NH R group would be more negative for the process 3 f 4 than for1 f 2. This prediction was confirmed by natural population analysis of 1-4 which revealed∆q(NHR) values of+0.01 for 1 f 2 and -0.19 for3 f 4 (Table 1). Similarly, in the course of the addition * To whom correspondence should be addressed. Fax: (573) 882-2754. E-mail: chemrg@showme.missouri.edu. (1) Khorana, H. G.Chem. Re V. 1953, 53, 145. (2) Kurzer, F.; Douraghi-Zadeh, K. Chem. Re V. 1967, 67, 107. (3) Williams, A.; Ibrahim, I. T.Chem. Re V. 1981, 81, 589. (4) (a) Schimzu, T.; Seki, N.; Taka, H.; Kamigata, N. J. Org. Chem.1996, 61, 6013. (b) Schuster, E.; Hesse, C.; Schumann, D. Synlett1991, 12, 916. (c) Olah, G. A.; Wu, A.; Farooq, O. Synthesis1989, 7, 568. (5) Glaser, R.; Son, M.-S. J. Am. Chem. Soc. 1996, 118, 10942. (6) (a) Slebioda, M.Tetrahedron1995, 51, 7829. (b) Ibrahim, I. T.; Williams, A. J. Chem. Soc., Perkin Trans. 2 1982, 1459. (7) Nguyen, M. T.; Riggs, N. V.; Radom, L.; Winnewisser, M.; Winnewisser, B. P.; Birk, M.Chem. Phys. 1988, 122, 305. (8) Bertran, J.; Oliva, A.; Jose, J.; Duran, M.; Molina, P.; Alajarin, M.; Leonardo, C. L.; Elguero, J. Chem. Soc., Perkin Trans. 2 1992, 299. (9) (a) Nguyen, M. T.; Ha, T.-K.J. Chem. Soc., Perkin Trans. 2 1983, 1297. (b) Lehn, J. M.; Munsch, B. Theor. Chim. Acta1968, 12, 91. (10) Pracna, P.; Winnewisser, M.; Winnewisser, B. P. J. Mol. Spectrosc. 1993, 162, 127. (11) Hehre, W. J.; Radom, L.; Schleyer, P. v. R.; Pople, J. A. Ab Initio Molecular Orbital Theory; John Wiley & Sons: New York, 1986. (12) (a) Glendening, E. D.; Reed, A. E.; Carpenter, J. E.; Weinhold, F. NBO Version 3.1 . (b) Glendening, E. D.; Weinhold, F. J. Comput. Chem. 1998, 19, 628 and references therein. (13) We examined the hydrolysis of CO 2 involving two water molecules at the MP2(full)/6-31G* and MP2(full)/6-311G** levels and determined activation enthalpies a t 0 K of 31.8 and 34.3 kcal/mol, respectively. There is close agreement between these levels, and the magnitude of the effect we are discussing greatly exceeds the theoretical model dependency. (14) Pople, J. A.; Scott, A. P.; Wong, M. W.; Radom, L. Isr. J. Chem. 1993, 33, 345. (15) (a) Merz, K. M.J. Am. Chem. Soc. 1990, 112, 7973. (b) Nguyen, M. T.; Ha, T. K. J. Am. Chem. Soc. 1984, 106, 599. (16) Nguyen, M. T.; Hegarty, A. F. J. Am. Chem. Soc. 1984, 106, 1552. (17) Nguyen, M. T.; Hegarty, A. F. J. Am. Chem. Soc. 1983, 105, 3811. (18) Morokuma, K.; Muguruma, C. J. Am. Chem. Soc. 1994, 116, 10316. (19) Nguyen, N. T.; Raspoet, G.; Vanquickenborne, L. G.; Van Duijnen, P. Th.J. Phys. Chem. A1997, 101, 7379. (20) The imine isZ-configured inA, but it is E-configured inB to take advantage of the H-bonding interaction with water. The intrinisic Z-preference energy is very small. (21) (a) NBO calculations on MP2(full)/6-31G* optimized structures show that the population of thedNH group in carbodiimide is-0.40, while it is -0.52 in isourea. (b) Similar calculations show that the charge of an -OH group is-0.48 in water, while it is-0.27 in isourea. 8541 J. Am. Chem. Soc. 1998,120,8541-8542