The Hydrolysis of Amides and the Proficiency of Amidohydrolases. The Burden Borne by k w

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1 See discussions, stts, nd uthor profiles for this publiction t: The Hydrolysis of Amides nd the Proficiency of Amidohydrolses. The Burden Borne by k w Article in The Journl of Physicl Chemistry B July 2007 DOI: /jp Source: PubMed CITATIONS 17 READS 72 2 uthors, including: Kenneth M Merz Michign Stte University 280 PUBLICATIONS 26,918 CITATIONS SEE PROFILE Avilble from: Kenneth M Merz Retrieved on: 20 September 2016

2 J. Phys. Chem. B 2007, 111, The Hydrolysis of Amides nd the Proficiency of Amidohydrolses. The Burden Borne by k w Guillermin Estiu nd Kenneth M. Merz, Jr.* Deprtment of Chemistry nd the Quntum Theory Project, 2328 New Physics Building, P.O. Box , UniVersity of Florid, GinesVille, Florid ReceiVed: NoVember 20, 2006; In Finl Form: Mrch 2, 2007 The hydrolysis of smll mides hs grnered mjor ttention due to its relevnce to peptide hydrolysis, one of the most fundmentl rections of biology. Both experimentl nd theoreticl reserch efforts hve studied the rection in different medi, nd consensus hs been reched regrding the specific cid- nd bsectlyzed rection pthwys. Nevertheless, for the wter rection, lrge discrepncies between theoreticl nd experimentl results re found in the literture. Herein, we report the results of theoreticl clcultions of formmide nd ure hydrolysis t different ph vlues. Model systems hve been built clustering one nd two wter molecules with the rective mide. A creful nlysis of the rection pthwys t different tempertures hs llowed us to ccurtely reproduce vilble experimentl dt nd to seprte the wter rections from their cid nd bse counterprts. The relevnce of the results in providing n ccurte definition of the proficiency of midohydrolses is discussed. Introduction The rection mechnisms for cid- nd bse-ctlyzed hydrolysis of simple mides hve received much ttention due to their relevnce to vrious biologicl processes After intensive experimentl nd theoreticl reserch, these rections re mong the best understood of ny chemicl process. At high ph, the system follows the bse-ctlyzed route, in which hydroxide ion performs nucleophilic ttck on the crbonyl crbon tom next to n mide bond, forming tetrhedrl intermedite. 4,5,10,15-23 At low ph, protontion of the crbonyl oxygen tom followed by nucleophilic ttck crried out by wtermoleculeisknownsthe cid-ctlyzed pthwy. 5,10,16,18-20,24-29 However, the nonctlyzed wter rection, which is more relevnt for physiologicl ph, remins somewht controversil. 1,3-5,7,8,10-12,17-20,30-32 The rection is known to be very slow process t room temperture, nd in spite of limited experimentl evidence of its occurrence, 10,18 bse-ctlyzed mechnism seems to be fvored, even in neutrl queous solution. The bse-ctlyzed hydrolysis of formmide is by fr the most extensively studied rection of this type. 4,5,9,10,17-20,22,26,33,34 The ctivtion energy hs been ccurtely determined, nd theoreticl clcultions hve reproduced the experimentl vlues within cceptble errors. 4,10,17,18,22,26,33,34 From these studies, the need to properly model the queous environment hs become evident, becuse the formtion of the tetrhedrl intermedite, tht follows hydroxide ttck t the crbonyl crbon, proceeds with no pprent brrier in the gs phse. 4,12 Moreover, in spite of its ssocited exothermicity, this gs-phse rection is unlikely to occur due to the preference for hydrogen bstrction from n mine group by the rectnt hydroxide. Monte Crlo simultions tht ccount for the influence of solvent correct this trend nd led to clculted free energy brrier of 27 kcl/ mol. 4 This number is in close greement with the one derived by Wrshel et l. 33 A better greement with experiment hs been ttined by Klein nd co-workers 35,36 (devition of only 1 kcl/ mol from the experimentl free energies) from the computtion of 100 ps bised Cr-Prrinello MD trjectories. The sme uthors evluted the role of wter prticipting ctively in the rection mechnism, which cn ct s the nucleophile fter trnsferring proton to the recting OH. These two theoreticl models ttin the best greement with the vilble experimentl observtions. 5,10,18 The very recent work of Xiong nd Zhn 34 lso ttined ner quntittive greement with experiment. The mechnism of the cid hydrolysis of mides hs been extensively studied s well, 5,10,12,18-20,24,25 but theoreticl pproches including the influence of the queous environment re recent, nd most of them use N-methylcetmide (NMA) s the model system. 24,25 For this substrte, Cr-Prrinello moleculr dynmics (CPMD) simultions support mechnism in which proton is detched from the incoming nucleophile (wter) while it pproches the protonted crbonyl group. The relesed proton is solvted by n dditionl wter molecule nd protontes the mine group of NMA. 24,25 This mechnism hs been previously proposed for formmide on the bsis of experimentl studies, 5 nd the CPMD clculted ctivtion free energy for NMA is in good greement with these experiments. 24 A similr mechnism hs been nlyzed s possible rection pthwy for the unctlyzed hydrolysis of NMA but ws found to be unlikely using CPMD. 30 Insted, concerted mechnism ws proposed, in which hydroxide of two-wter ensemble ttcks the crbonyl crbon while proton of the second wter is donted to the mine end (free energy 35), yielding wter ssisted ddition cross the C-N bond. 30 The sme intermedite hs been previously proposed by Antonczk et l. fter quntum mechnicl (QM) clcultions tht only incorported two wter molecules 3 (compred with the CPMD pproch, which included 56 wter molecules). The nlysis of these results demonstrtes tht the inclusion of more thn two wter molecules in the theoreticl model does not open new mechnistic routes. Severl wter molecules hve lso been considered in recent QM clcultions of the unctlyzed hydrolysis of formmide. 8 The QM-bsed mechnism relies on the ssumption tht formmide is stbilized in wter s solvted structure built from the /jp CCC: $ Americn Chemicl Society Published on Web 05/18/2007

3 6508 J. Phys. Chem. B, Vol. 111, No. 23, 2007 Estiu nd Merz simultneous hydrogen bond coordintion of five wter molecules. The hydrogen bond interctions re rerrnged long the rection pthwy, but the number of molecules in the first coordintion sphere is retined throughout. Nonetheless, only two wter molecules re mechnisticlly relevnt, leding to CO ddition. 8 The concerted mechnism is t odds with the results of steered CPMD simultions, which concluded tht there is no need to disrupt the wter coordintion sphere of formmide, nor tht of the incoming wter molecule during rection. 17 From the comprison of the different theoreticl pproches employed to dte, it becomes evident tht modeling solvent is crucil. Through the yers, the ppliction of different levels of theory nd different solvent pproches to the study of the unctlyzed hydrolysis of mides hs resulted in reported free energy vlues rnging from 57 to 35 kcl/mol. 3,4,7-9,11,12,15,17,30 Nevertheless, even the smller clculted vlue does not led to the experimentl rte constnt reported for the wter rection, which ws estimted to be s -1 from two-point Arrhenius plot tht uses dt determined t high temperture (329 nd 393 K). 18 A vlue closer to the experimentl vlue hs been derived through the ppliction of QM methodologies in recently published rticle, but the clculted results were, we believe (Vide infr), obtined using n inpproprite kinetic nlysis. 8 A rte constnt of the sme order of mgnitude hs been estimted for the unctlyzed hydrolysis of ure, by nlogy to the experimentlly determined vlue for tetrmethylure (10-11 s -1 ). The ltter hs been extrpolted from mesurements t tempertures higher thn 400 K, in solutions buffered t ph Theoreticl clcultions hve not yet ddressed this system to our knowledge. In spite of the overll lck of success with quntum mechnicl methods to dte in explining the unctlyzed hydrolysis rection, there is still significnt experimentl nd theoreticl interest in explining the mechnism of mide wter hydrolysis, becuse the unctlyzed rection defines the reference stte used to quntify the proficiency of hydrolytic enzymes Moreover, the neutrl hydrolysis of mide bonds is complicted by the potentil vilbility of the cid nd/or bse rection chnnels. This dded mechnistic compliction mkes theoreticl study even more difficult s the observed rte constnt cn be superposition of severl rection chnnels. A rigorous experimentl study of formmide hydrolysis hs still left this issue s n open question. 18 After thorough nlysis of the rection t different phs nd tempertures (56 C (329 K) nd 120 C (393 K)), Slebock-Tilk et l. concluded tht the wter rection cn never contribute more thn 40% to the observed rte t the respective ph minim. 18 In principle, theoreticl clcultions, t n pproprite level of theory, should be cpble of reproducing the experimentl dt nd from there predict the kinetic dt tht cnnot be determined experimentlly. This kind of nlysis would be certinly helpful for full understnding of this deceptively simple rection. This rticle describes detiled nlysis of the cid-ctlyzed, bse-ctlyzed, nd unctlyzed hydrolysis of formmide nd ure using theoreticl tools. Our im is to compre our results with the vilble experimentl kinetic dt. To this end, we hve nlyzed the energy ssocited with the first stge of nucleophilic ttck, which defines the rte-determining step. Clcultions hve been done s function of the temperture, in order to llow rigorous comprison with the vilble experimentl dt. The hydrolysis of tetrmethylure is lso nlyzed, using kinetic descriptors derived using the inverse of the nlogy pplied by Cllhn, Yun, nd Wolfenden. 31 Methodology All of the clcultions hve been performed t the MP2/ G** level of theory, using the Gussin 03 suite of progrms. 47 Structurl prmeters nd energies for rectnts, products, stble intermedites, nd trnsition sttes were obtined using full geometry optimiztions, with no imposed constrints. The serch for sttionry points on the potentil energy surfce followed grdient-bsed lgorithms nd qudrtic synchronous trnsit (QST2) pproches. Criticl points were further chrcterized by determintion of the vibrtionl frequencies t the sme level of theory. Bulk solvent effects (queous solution) were modeled vi polrizble continuum model. 48,49 This pproch does not llow us to explicitly model the desolvtion or shedding of explicit wter molecules s the rection proceeds (s hs been noted by other uthors), 17 but through the explicit incorportion of solvent molecules, we hve cptured some of these effects. For exmple, the influence of second wter molecule ws nlyzed by modeling it in discrete mnner nd then compring the results with those previously reported. 3,11 Moreover, we find tht the rte-determining step in ll cses is the formtion of the tetrhedrl intermedite, so t lest in our hnds, desolvtion effects pper to be less importnt tht bond formtion. The thermodynmic functions (free energy (G), entropy (S), nd enthlpy (H)) were obtined from the pproprite prtition functions, clculted t the temperture of interest using MP2/ G** frequencies. The vibrtionl frequencies were obtined using the hrmonic pproximtion, nd t some of the higher tempertures exmined herein, this pproximtion is less stisfctory. However, no indictions tht this pproximtion suffered ctstrophic filures were observed in the results reported herein. Results nd Discussion The Hydrolysis of Formmide. The Bse-Ctlyzed Rection. The mechnism of the bse-ctlyzed rection hs been extensively studied both experimentlly nd theoreticlly. 4,5,10,17-20,22,26,33,34 The rection is first order in hydroxide concentrtion, with free energy of ctivtion of 21.5 kcl/ mol. 18 Recent experimentl studies hve nlyzed the rection t different tempertures using kinetic isotope effects nd supported mechnism involving the direct nucleophilic ttck of hydroxide on the crbonyl crbon tom to form tetrhedrl intermedite. 18 As previously discussed, inclusion of the queous environment in the clcultions prevents proton bstrction from formmide by the hydroxide ion. 4 The ltter is fvored by 26 kcl/mol in the gs phse reltive to nucleophilic ttck t the crbonyl crbon. In order to ccount for this, different solvent pproches hve been used to model the queous environment, leding to clculted ctivtion free energies tht brcket those derived from experiment. 4,17 For exmple, steered CPMD simultions gve vlue of 15 kcl/mol, 17 while Monte Crlo simultions predicted vlue of 27 kcl/mol. 4 We hve chosen to use continuum pproch, nd to nlyze in detil the different steps of the experimentl study of the bse-ctlyzed hydrolysis. 18 A similr study nd pproch hs been reported recently by Xiong nd Zhn, nd they were ble to obtin excellent greement with experiment. 34 With this gol in mind, we hve evluted the thermodynmic quntities ssocited with this rection t 25, 56, nd 120 C. The solvent corrected optimized geometry of the trnsition stte hs C-O hyd distnce of 2.04 Å. At this internucler distnce, the C-O hyd -H hyd ngle is 112 (see TSFORN; see Figure 1). These structurl chrcteristics closely resemble those obtined using steered CPMD simultions, which gve reported

4 Hydrolysis of Amides J. Phys. Chem. B, Vol. 111, No. 23, Figure 1. Computed geometry for the formmide nion/wter hydrogenbonded complex (FORNWAT) nd the TS for the ddition of hydroxide to formmide (TSFORN). Color code: red, oxygen; blue, nitrogen; cyn, crbon; white, hydrogen. TABLE 1: Free Energies for the Stble Species Associted with Bse-Ctlyzed Formmide Hydrolysis FOR + OH FORN + WAT FORNWAT TSFORN 298 K K K Energies (kcl/mol) re reltive to FORNWAT (see more detils in the text). Positive vlues indicte less stble species. Formmide (FOR), formmide nion (FORN), hydroxide ion (OH), nd wter (WAT). For FORNWAT nd TSFORN, see Figure 1. vlues of 2.2 Å nd 110, respectively. 17 In order to properly determine the energy of the rection, we hve nlyzed in detil the reltive stbility of the different species tht define the initil stte. Formmide nd hydroxide re known to coexist in equilibrium with the formmide nion nd wter. We hve found third minimum on the potentil energy surfce, which cn be described s wter molecule hydrogen bonded to the formmide nion (wter/formmide nion dduct, FORNWAT, see Figure 1). Both the formmide nion nd the FORNWAT complex re more stble thn formmide nd hydroxide (see Tble 1). Nevertheless, complex formtion fter the pproch of the nucleophile positions the rective species in n optimum configurtion to proceed to the next stge of the rection, with no need to seprte wter from the formmide nion. In other words, becuse the equilibrium for proton trnsfer is fst nd reversible, the most fvored rection chnnel follows FORN- WAT formtion, nd the rection brrier will be determined by the difference between its energy nd the trnsition stte (TS) energy (TSFORN). For this rection pthwy, the clculted ctivtion free energy (21.4 kcl/mol (clcd), see Tble 1) is in excellent greement with experiment (21.5 kcl/ mol (expt) t 298 K). 18 To better highlight the greement between our dt nd those reported in ref 18, we used the Eyring eqution to clculte the rte constnts t the sme tempertures used in the experiments. We obtin rte constnts of 4 s -1 (398 K), s -1 (329 K), nd s -1 (298 K), versus the experimentlly derived vlues of 3.2 s -1 (398 K) nd s -1 (329 K). 18 The comprison considers pseudo-first-order kinetics, nd therefore, the free energies re computed under stndrd conditions ([OH - ] ) 1). The Acid-Ctlyzed Rection. The experimentl study of the cid-ctlyzed hydrolysis of formmide hs led to mechnism tht is initited by protontion of the crbonyl oxygen of the mide, which ctivtes it towrd nucleophilic ttck by wter. 5 Nucleophilic ttck is ssisted by second wter molecule, tht cptures proton which yields the neutrl tetrhedrl intermedite nd H 3 O +, thereby voiding formtion of the unstble O-protonted tetrhedrl intermedite. H 3 O + lso plys role in the second step of the rection, ssisting in the relese of Figure 2. Computed geometry for protonted formmide hydrogen bonded with one nd two wter molecules (FORPW, FORPW2). Color code s in Figure 1. TABLE 2: Free Energies for the Species Associted with Acid-Ctlyzed Formmide Hydrolysis FOR + H 3O FORP + WAT FORPW TSFP3 TSFP4 298 K K K Energies (kcl/mol) re reltive to FORPW (see more detils in the text). Positive vlues indicte less stble species. Formmide (FOR), protonted formmide (FORP), hydronium ion (H 3O), nd wter (WAT). For FORPW, see Figure 2, nd for TSFP, see Figure 3. NH 3 through protontion of the nitrogen tom. The rection hs been studied by solvent kinetic isotope effects, which show tht the oxygen toms in the tetrhedrl intermedite re in equilibrium between the protonted nd deprotonted sttes. 5 The nlysis of the kinetics s function of temperture resulted in n ctivtion free energy of 22.8 kcl/mol. 18 The proposed mechnism hs been studied theoreticlly for NMA using CPMD. 25 The simultions used the pth smpling lgorithm of Chndler nd co-workers, 50 for the rectnts defined s the O-protonted mide nd wter, nd supported the trnsfer of proton of the rective wter to n djcent one. No rection brriers were computed due to the computtionl expense of the clcultions, but previous constrined CPMD simultions gve free energy of ctivtion of 19 kcl/mol, 24 in close greement with the experimentl vlue 22.8 kcl/mol. 13,14 We hve nlyzed different possible rection pthwys, serching for trnsition sttes nd compring the stbility of the species tht define the initil stte of the rection. Proton trnsfer from H 3 O + to formmide is computed to be fvored by 16 kcl/mol t room temperture. Anlogous to the previous study in bsic medi, n dditionl minimum ws found in which wter molecule is hydrogen bonded to protonted formmide through both the oxygen nd the nitrogen toms of the molecule (FORPW, see Figure 2). This dduct is nerly isoenergetic with the system consisting of formmide nd H 3 O + t room temperture (FOR + H 3 O, see Tble 2) but is stbilized s the temperture increses, becoming 8 kcl/mol more stble t 398 K (see Tble 2). However, it remins, t this temperture, 9 kcl/mol less stble thn protonted formmide plus wter molecule (FORP + WAT, see Tble 2). Moreover, in order to ccount for the experimentlly proposed mechnism, second wter molecule hs to be modeled in the rection pthwy, which will ssist the nucleophilic ttck through the relese of H 3 O +. This model uses H 2 O/H 3 O + cluster s the rective species, responsible for protonting the crbonyl oxygen nd forming the gem-diol intermedite fter H 3 O + relese. The optimized structure of the two-wter dduct is lso shown in Figure 2 (FORPW2). The reltive energies re listed in Tble 3. Following the sme resoning s tht for the bsectlyzed rection, we hve chosen the dducts s the sttes tht define the rectnts, since once they re formed s prt

5 6510 J. Phys. Chem. B, Vol. 111, No. 23, 2007 Estiu nd Merz TABLE 3: Energies for the Species Associted with Acid-Ctlyzed Formmide Hydrolysis, Following the Two-Wter Mechnism FOR + H 3O + WAT FORPW + WAT FORPW2 TSFP2 298 K K K Energies (kcl/mol) re reltive to FORPW2 (see more detils in the text). Positive vlues indicte less stble species. Figure 3. Computed geometries for severl trnsition sttes identified in this work. Color code s in Figure 1. of the proton trnsfer rection, the rection chnnels of lowest energy re directly vilble. In the serch for the TS, we first modeled the experimentlly proposed mechnism: concerted ddition of two wter molecules to protonted formmide with the second wter molecule cpturing proton to stbilize the gem-diol intermedite. We identified two lmost isoenergetic TS structures (TSFP1 nd TSFP2, see Figure 3) in which the proton of the rective wter hs been trnsferred to the second one, nd cn be formlly described s H 3 O + species hydrogen bonded to n incoming OH -. The ltter is forming n elongted bond with the crbonyl crbon. TSFP2 is 2 kcl/mol lower in energy thn TSFP1 nd 24 kcl/mol higher in free energy thn the rectnts, defined s FORPW2. TSFP2 llows the relesing H 3 O + to ssist the second step of the rection, trnsferring proton to the mide end. From the nlysis of the structure of TSFP2, it cn be determined tht the sme H 3 O + relesed fter proton subtrction cn be involved in the second step of the rection. The clculted free energy brrier (23.8 kcl/mol) is in excellent greement with the experimentl vlue (22.8 kcl), 18 nd, hence, supports the previously proposed mechnism. The previous mechnism hs been suggested s wy to overcome the fct tht H 3 O + is not strong nucleophile per se. As consequence, the initil protontion of formmide becomes necessry to ssist the rection to proceed through nucleophilic pthwy. Nevertheless, wter is still poor nucleophile, nd even in the cse of protonted formmide, where the electrophilicity of the crbonyl crbon tom hs been enhnced by protontion, wter ddition to either the CN (TSF3, see Figure 3) or the CO bond (TSF4, see Figure 3) leds to ctivtion free energies of 45 nd 51 kcl/mol, respectively. As for the bse-ctlyzed rection, we clculted the kinetic rte constnts using the Eyring eqution nd the free energy vlues for the most fvored pthwy t different tempertures. The clculted rte constnts cn gin be compred with the experimentlly reported vlues. The clculted vlues of 0.77 s -1 (398 K), s -1 (329 K), nd s -1 (298 K) re in good ccord with the experimentl vlues of 0.15 s -1 (398 K) nd s -1 (329 K). 18 The Wter Rection. The interest in the unctlyzed hydrolysis of mides lies in the quntittive determintion of the proficiency of hydrolytic enzymes. 7,18,44,51 Most of the work in this re hs been crried out by Wolfenden nd co-workers, who studied the hydrolysis of smll dipeptides, reporting rte constnts close to s The simplest mide, formmide, hs been frequently used s the de fcto model of the peptide bond. However, its neutrl hydrolysis hd not been considered in detil until 1981, when Hine estimted the rte constnt for this rection from kinetic mesurements t high temperture (80 C). 10 Hine s reserch hs been followed by Slebock-Tilk et l., who mesured the kinetics of the hydrolysis of formmide s function of ph t tempertures of 56 nd 120 C. 18 In both cses, the observed kinetics hs been fitted to generl expression, k obsd ) k H + [H3 O + ] + k OH - [OH - ] + k w, from which k w ws derived. In this wy, rte constnts for k w vlues of s -1 (56 C) nd s -1 (120 C) hve been estimted. In ddition, vlue of k w ) s -1 hs been estimted t 25 C from two-point fitting to n Arrhenius plot. These studies tken together hve led to the conclusion tht it is unlikely tht conditions will be found tht llow for the isoltion of the wter term from the corresponding cid nd bse rections. 18 In spite of the dvnces on the experimentl front, the mechnism of the wter rection hs not been uniquely determined. Theoreticl studies hve been numerous, nd hve certinly contributed since 1990, following the development of improved solvent tretments. Nevertheless, neither the modeling of the solvent using continuum pproch 11 nor the definition of discrete wter molecules tht prticipte in the rection, 3,11 or even the tretment of 27 solvent molecules t the QM level using Cr-Prinello MD simultions, 17 hs succeeded in reproducing the experimentlly determined rte constnt but resulted in clculted free energies close to 50 kcl/mol. The results of quntum chemicl clcultions hve been recently thoroughly reviewed nd compiled by Gorb et l., 8 nd will not be re-exmined in detil here. An inspection of the dt published to dte shows tht the primry origin of the difference between the vlues reported by different groups relies on the definition of the initil stte. 8,11,17 This choice is complicted by the fct tht the formmide molecule in solution is solvted, nd the rective wter cn either belong to the solvtion shell or to bulk solvent. In the cse of the bse- nd cid-ctlyzed rections, wter molecule properly positioned for nucleophilic ttck cn be viewed s helping the hydrolytic pthwy. However, the soclled dducts re lower in energy thn the seprted species in the ctlyzed rections (mking it cler tht they need to be included in the nlysis) but higher in energy in the unctlyzed one. 11 At the present level of theory, when polrizble continuum model (PCM) pproch is used to model the solvent, wter nd formmide re stbilized s seprted species by solvtion, minly due to the contribution of the entropic term to the free energy. In the bse- nd cid-ctlyzed rections, the interctions between the nucleophile nd electrophile overcome this effect. In this wy, in neutrl queous environment

6 Hydrolysis of Amides J. Phys. Chem. B, Vol. 111, No. 23, TABLE 4: Free Energies for the Stble Species Associted with Unctlyzed Formmide Hydrolysis FOR + H 2O FORWAT TSFOR 298 K K K Formmide (FOR), formmide/wter complex (FORWAT), nd wter (WAT). For TSFOR, see Figure 5. Energies given in kcl/mol, reltive to the seprted species. See more detils in the text. TABLE 5: Free Energies for the Species Associted with Unctlyzed Formmide Hydrolysis FOR + 2H 2O FORWAT2N FORWAT2O TSFOR2CN TSFOR2CO 298 K K K Formmide (FOR), formmide/wter complex (FORWAT), nd wter (WAT). For FORWAT2N nd FORWAT2O, see Figure 4. For TSFOR2CN nd TSFOR2CO, see Figure 5. Energies in kcl/mol re reltive to the seprted species. nd t the present level of theory, seprted formmide nd wter re 9.7 kcl/mol lower in energy thn formmide/wter dduct, nd 20 kcl/mol lower thn formmide/two-wter complex (Tbles 4 nd 5). Nevertheless, it hs been recently proposed, on the bsis of the results of MD simultions with QM/moleculr mechnicl (MM) methods, tht formmide is stbilized in wter through hydrogen bond interctions with five wter molecules, 6 nd the entire system yields TS 35 kcl/ mol higher in energy thn the originl cluster. In this mechnism, only two wter molecules out of the five chnge their coordintion on the wy to the TS, defining rection pthwy tht cn be described s two-wter CO ddition. 8 This description is somewht rbitrry, becuse it does not consider how the hydrogen bonds of the nonrecting wter molecules chnge long the scent to the trnsition stte. The TS ssocited with two-wter CO ddition, s well s similr one involving two-wter ssisted CN ddition, hve been previously described by Antonczek et l. 3 nd by Kllies nd Mitzer. 11 A free energy of 38 kcl/mol ws clculted in the first cse, with no model for the solvent, which led to the overstbiliztion of the formmide/two-wter dduct. 3 Solvent corrections included in the work of Kllies et l. incresed this vlue to 48 kcl/mol. 11 A different description of the neutrl hydrolysis hs been derived from steered Cr-Prrinello MD simultions, which fvored rection pthwy in which the recting wter does not belong to the formmide solvtion shell but to the bulk wter. 17 Within this frmework, the wter/formmide pproch does not induce relevnt chnges in either of the rectnt s solvtion shells. These results gve free energy of 40 kcl/mol, nd hve been criticized for being bsed on the definition of constrined rection coordinte tht does not llow one to cpture concerted rections. 30 A similr mechnism ws supported by Monte Crlo simultions, leding to clculted free energy of 27.3 kcl/ mol. 4 In spite of the proximity of this vlue to the experimentl one, it hs to be noted tht the ssocited TS ws obtined using CNO ngle constrined to the vlue optimized for the tetrhedrl intermedite, nd my correspond to lte TS. 4 Our results re summrized in Tbles 4 nd 5 nd the structures shown in Figures 4 nd 5 (dducts nd TS s, respectively). The results in Tble 4 show tht one-wter CO ddition leds to clculted free energy of 50.7 kcl/mol reltive to FORWAT nd 60.4 kcl/mol reltive to the seprted species. Figure 4. Computed geometries for severl hydrogen-bonded complexes identified in this work. Color code s in Figure 1. When second wter is considered to ssist the rection, inspection of the dt in Tble 5 shows preference for CN ddition over CO ddition. The free energies re 36.5 nd 43.8 kcl/mol reltive to the two-wter/formmide dducts but 60 nd 64 kcl/mol reltive to the seprted species. When mesured reltive to the seprted species, the ctivtion free energy decreses t 398 K to 54 nd 57 kcl/mol, respectively. Our results cn be compred with those of Gorb et l., 8 who obtined similr ctivtion free energy for the CO ddition (35 kcl/mol) t the B3LYP/6-31(G) level of theory, for the energies corrected for solvent effects (PCM) fter gs-phse optimiztion. This level of theory ws unble to identify TS for CN ddition. Moreover, in the TS for CO ddition reported in ref 8, proton trnsfer from wter molecule to the crbonyl oxygen is more dvnced thn in ours, fct tht we ssocite with the lck of solvent modeling during the optimiztion. The kinetic rte constnts derived from ll of the clculted free energies re slower thn the experimentl vlues regrdless of the definition of the rectnts. 18 Nevertheless, t this point, the comprison between experimentl nd theoreticlly derived kinetic prmeters deserves further discussion. In ny comprison between experimentl nd clculted rte constnts, one should note tht the experimentl vlues correspond to pseudo-first-order constnts (k ); tht is, they include the concentrtion of wter, ccording to Hence, if we compre the rte constnt derived from the free energy difference between the seprted species nd the TS, we hve to multiply the resulting k vlue by 55 M. However, if we consider the rection strting from the dduct (FORWAT or FORWAT2), the concentrtion of wter term no longer hs to be included in the eqution. For the rection involving two wter molecules, the kinetic expression to be used is 52,53 where K eq1 is the equilibrium constnt for the rection nd K eq2 corresponds to rte ) k[form][wt] ) k [form] (1) rte ) k [FORWAT2] ) k K eq1 [FORWAT][wt] ) k K eq1 K eq2 [form][wt] 2 (2) FORMWAT + WAT w FORWAT2 (3) FORM + WAT w FORWAT (4) The rte constnt clculted for the rection strting from the dduct (k ) hs to be corrected by the equilibrium constnt if the wter concentrtion is included in the kinetic expression.

7 6512 J. Phys. Chem. B, Vol. 111, No. 23, 2007 Estiu nd Merz Figure 5. Computed geometries for severl trnsition sttes identified in this work. TSFOR represents one-wter trnsition stte, while TSFOR2CN nd TSFOR2CO represent two-wter trnsition sttes where wter is dded cross the CN nd CO bonds, respectively. Color code s in Figure 1. These constnts re ssocited with free energy vlues ccording to k ) A exp(- G /RT) (5) K eq ) exp(- G eq )/RT (6) The combintion of eqs 5 nd 6 leds to ln k + ln K ) ln A - ( G + G eq )/RT ) ln k (7) where, ccording to eq 2, k is the rte constnt ssocited with the rection strting from the seprted species. Using n pproprite tretment of the kinetic equtions implies the use of k rther thn k when the concentrtion of wter is included in the eqution. This procedure ws not followed by Gorb et l., who multiplied their clculted k vlue by the concentrtion of wter to the second power. 8 Even fter correction by the wter concentrtion, we obtin rte constnts of the order of or s -1 for the rections involving one or two wter molecules, respectively, reltive to the seprted species. A vlue closer to experiment ( Versus s -1 ) is obtined when the rection is considered to strt from the two-wter/formmide dduct, ssuming tht the species hve reched equilibrium when the kinetic experiment strts. However, our bility to mtch experiment quite closely for the cid- nd bse-ctlyzed rections strongly suggests tht we still do not hve the correct model for this rection mechnism. In the cse of the cid- nd bse-ctlyzed rections, we worked from the dducts (or the initilly formed complexes fter protontion or deprotontion) rther thn the seprted species. This ws becuse the dducts were more stble. Moreover, it ws essentil to work from these dducts rther thn the seprted species in order to obtin ner quntittive greement with experiment. In the cse of the unctlyzed rection, the complexes re significntly less stble thn the first formed dducts, suggesting tht these rections should hve their thermodynmic quntities evluted from the seprted species. When this is done, very lrge free energies of ctivtions for the unctlyzed rection re obtined, nd even if one strts the thermodynmic nlysis from the two-wter/ formmide complexes, only qulittively correct greement with experiment is obtined. As physicl chemist, one is trined to strt from the lowest energy rectnts, which in this cse re the seprted species; however, the model we re working from involves continuum solvtion shell tht hs one or two dditionl explicit wter molecules brought into the proximity of formmide. Potentilly the pproprite strting stte is relly the one- or two-wter dduct, since upon the dissolution of formmide into wter n entropic penlty is pid to bring wter molecules into the solvtion shell of formmide. Hence, by including the lrgely entropic penlty in our clcultions, we my be double-counting this when we compre our results to experiment. Furthermore, if we ssume tht the wter molecules re in equilibrium with the dducts, it cn be shown using stndrd kinetics nlysis tht the brrier is defined from the dduct to the trnsition stte nd not from the seprted species (see the Supporting informtion). Regrdless, further nlysis of this rection is necessry to reconcile the differences between theory nd experiment. We now hve ll of the necessry informtion to ddress this in detil below. The ObserVed Wter Rte Constnt. In order to compre our results with those determined experimentlly, 18 we need to relize tht the experimentlly observed vlue is built from three contributions: k w is determined s the observed rte constnt for the ph t which the other contributions re minim. 18 It cn be esily demonstrted (zeroing the derivtive of k obsd s function of ph) tht this minimum will occur when For this ph, k obsd ) k H +[H 3 O + ] + k OH -[OH - ] + k w (8) [H + ] ) (k OH -K w /k H +) 1/2 (9) k obsd ) 2(k H +k OH -K w ) 1/2 + k w (10) where K w is the wter utoprotolysis constnt. If we insert our clculted vlues into eqs 9 nd 10 [K w ) t 393 K, K w ) t 293 K; see Slebock-Tilk et l. (2002)], we obtin minimum ph of 5.64 nd n observed rte constnt of s -1 for the rection t 393 K, in excellent greement with experiment (ph 5.4 nd k ) s -1, respectively). 18 The resulting vlue is not dependent on whether we use the k w vlue clculted from the seprted species ( s -1, one-wter rection; s -1, two-wter rection) or from the dduct ( s -1, one wter molecule; s -1, two wter molecules), becuse the first term in eq 10 is t lest 1 order of mgnitude lrger. For the rection t 329 K, the clculted vlues (ph 6.04, pk obsd ) 8.16) re lso in excellent greement with experiment (ph 6.1, pk obsd ) 8.1). 18 Nor in this cse does k w ffect the vlue of k obsd, s the clculted vlues ( s -1, onewter rection; s -1, two-wter rection; s -1, one-wter dduct; s -1, two-wter dduct) re lmost 3 orders of mgnitude smller thn the first term of eq 10 ( s -1 ). This comprison indictes tht the vlue of k obsd tht mtches the experimentl dt is determined by the rte constnts for the cid- nd bse-ctlyzed hydrolysis, nd does not depend on the vlue of k w. Moreover, the greement between theory nd experiment is excellent. For the rection t room temperture, the minimum ph would be 6.13, nd the observed rte constnt, k obsd ) s -1. The vlue of k w gin does not ffect k obsd either, becuse it is computed to

8 Hydrolysis of Amides J. Phys. Chem. B, Vol. 111, No. 23, Figure 6. Red line: NLLSQ fit of the dt reported in ref 18 for 120 C (blck dots), using the eqution k obsd ) k H + [H3O + ] + k OH - KW/[H 3O + ] + k w(chi 2 ) , R 2 ) ). be s -1 (two-wter dduct), s -1 (onewter dduct), s -1 (one-wter rection), nd s -1 (two-wter rection). Going one step further, we hve nlyzed the fitting procedure used by Slebock-Tilk et l. to derive the rte constnt for the wter rection. The uthors derived k w by fitting of the experimentl vlues to eq 8, with nd without the k w term. We hve reproduced their nlysis for the dt reported t 120 C, obtining the results shown in Figure 6. From this fitting (red line, Figure 6, ll rte constnts re s -1 ), the vlues k H + ) ( , k OH - ) ( , nd kw ) ( ( ) 10-6 hve to be compred with k H + ) ( , koh - ) ( , k w ) ( ( ) 10-6, reported in ref 18. The green lines represent the vlues corresponding to the fitting without the lst term of the eqution. The difference between the two lines t minimum ph hs been ssocited with the contribution of the wter rection. However, if the errors ssocited with the fit re exmined in more detil, the blue lines in Figure 6 re obtined fter ddition nd subtrction of the ssocited errors. It is esily seen tht the green curve lies within the estimted error. Becuse of this, we do not consider tht this mthemticl tretment of the experimentl dt llows for the direct determintion of k w. The error ssocited with the numericl fitting of the experimentl dt ws lso noted by Slebock-Tilk et l., where they noted tht it is unfortunte tht our best-fit wter constnts must hve 10-30% error which limits our bility to mke conclusions nd predictions. However, our fitting of the sme dt suggests tht the errors re lrge enough to obscure the true vlue for k w. In light of this, we cn mke computtionl predictions regrding the vlue of k w, nd these re, t 298 K, s -1 (two-wter dduct), s -1 (one-wter dduct), s -1 (one-wter rection), nd s -1 (two-wter rection). These previous nlyses lend further support to the ccurcy of the computtionl results presented in this rticle. From this nlysis, we believe tht the experimentl vlue for k w hs not been relized for formmide. Indeed, in order to reconcile theory nd experiment, the unmbiguous determintion of k w is criticl nd this is the chllenge fced by experiment. The Hydrolysis of Ure. Ure is unusully stble due to its resonnce stbiliztion (estimted to be kcl/mol), 54 mking the hydrolytic decomposition very slow rection. Its experimentl determintion is further complicted by the existence of competitive rection, in which ure decomposes unimoleculrly, to give isocynic cid nd the mmonium ion. 1,2,16,55-63 Becuse the ltter is fvored t ny ph, the hydrolytic decomposition of ure hs never been observed. In spite of this, reserch hs been crried out, 7,11,31,55-57,64,65 in prt to determine the proficiency of urese nd relted midohydrolses. As prt of this effort, the kinetic prmeters of the wter rection hve been recently extrpolted for ure from the vlues determined for tetrmethylure, using the methyltion of the mino groups to block the elimintion pthwy. 31 The experimentl results were not in good greement with those obtined theoreticlly for the unctlyzed hydrolysis of ure. 7,64 Recently, Alexndrov nd Jorgensen 66 hve reported combined QM/MM simultion of the elimintion rection nd neutrl hydrolysis of ure in wter using the PM3/PDDG Hmiltonin. While their computed ctivtion energy for elimintion ( 37 kcl/mol) ws higher thn experiment (4.5-9 kcl/mol depending on the experimentl vlue used), neutrl hydrolysis ws only 3 kcl/mol higher ( 40 kcl/mol), giving rte rtio of the hydrolysis Versus elimintion pthwy tht is in good greement with experiment on TMU. 31 In the following sections, we discuss the kinetics of the bse-, cid-, nd wter-ctlyzed hydrolysis of ure, following the sme pproch s tht used for formmide, whose ccurcy reltive to experiment hs been demonstrted lredy. We show the results of clcultions for tempertures between 298 nd 498 K, imed t compring the kinetics with the experimentl vlues reported for tetrmethylure. In doing so, we re wre of the fct tht N-substitution not only prevents the elimintion mechnism but lso chnges the electrophilicity of the crbonyl crbon tom. However, s noted by Wolfenden nd co-workers,

9 6514 J. Phys. Chem. B, Vol. 111, No. 23, 2007 Estiu nd Merz Figure 7. Computed geometry for the ure/hydroxide hydrogen-bonded complex (URNWAT) nd the trnsition stte for the ddition of hydroxide to ure (TSURN). TABLE 6: Free Energies for the Stble Species Associted with Bse-Ctlyzed Ure Hydrolysis UR + OH URN + WAT URNWAT TSURN 298 K K K Energies (kcl/mol) re reltive to URNWAT (see more detils in the text). Positive vlues indicte less stble species. Ure (UR), ure/ hydroxide complex (URNWAT), hydroxide + ure ddition TS (TSURN), nd hydroxide ion (HO). See Figure 7 for URNWAT nd TSURN. tetrmethylure should be good model for ure hydrolysis nd Vice Vers. In our efforts, we tke dvntge of the sme principle espoused by Wolfenden nd co-workers, but in our cse, it reduces the computtionl cost of doing detiled clcultions on tetrmethylure. Bse-Ctlyzed Hydrolysis. The experimentl studies of the decomposition of ure in bsic medi indicted tht the rection follows n elimintion mechnism. 58,62,63 This rection is first order in ure, with no nucleophilic ttck involved. The hydrolytic decomposition hs never been cptured, nor hs it been theoreticlly studied to our knowledge. We found the rection to follow similr pthwy s the one described for formmide. In this cse, the trnsition stte shows C-O hyd distnce of 2.05 Å nd C-O hyd -H hyd ngle of 98 (see TSURN, Figure 7). The bending of the OH llows wek hydrogen bond between the hydroxyl hydrogen tom nd the crbonyl oxygen tom. As in the cse of formmide, we found tht proton bstrction by hydroxide is fvored t tempertures between 298 nd 498 K (see Tble 5). A third stble species ws lso identified on the potentil surfce, in which hydroxide is stbilized by hydrogen bond coordintion with both mino ends of ure (see Figure 7). Proton trnsfer to the hydroxide ion is not completed in this dduct (URNWAT, see Figure 7), s ws found in the cse of formmide (see FORNWAT, Figure 1), in greement with the lower cidity of ure. 67 This OH/UREA dduct is 9.6 kcl/mol higher in energy thn the nion of ure plus wter t 298 K but nerly isoenergetic with the sme species t 498 K. In this wy, t high temperture, it offers more fvorble rection pthwy for the rection to proceed to the TS (see Tble 6). The experimentl study of the hydrolysis of tetrmethylure, from which the kinetic prmeters for neutrl hydrolysis of ure hve been estimted, ws performed between 400 nd 525 K. 31 At these tempertures, the kinetic prmeters re determined by the free energy difference between the TS nd the dduct (URNWAT). For these conditions, we clculte free energy of ctivtion of 26 kcl/mol (498 K), which leds to kinetic rte constnts of s -1 (298 K), s -1 (398K), nd 48 s -1 (498 K). At room temperture, the seprted species re more stble thn the dduct. However, s previously Figure 8. Computed geometries for severl hydrogen-bonded complexes of ure identified in this work. TABLE 7: Free Energies for the Species Associted with Acid-Ctlyzed Ure Hydrolysis UR + H 3O + WAT URPWN URPWO TSURPWN TSURPWO 298 K K K Energies (kcl/mol) re reltive to URPWN (see more detils in the text). Positive vlues indicte less stble species. Ure (UR), protonted ure (URP), wter hydrogen-bonded complex to mino hydrogens (URPWN), wter hydrogen-bonded complex to the protonted ure crbonyl (URPWO), hydronium ion (H 3O + ), nd wter (WAT). For URPWN nd URPWO, see Figure 8. discussed for the cse of formmide, we pointed out tht the dduct cn be formed during the (fst) proton trnsfer step, nd the mechnism cn then proceed from this dduct before wter relese. Under this ssumption, the rectnt is defined by the dduct (URNWAT), even t lower tempertures. Regrdless of the temperture, the rte constnts re smller thn the corresponding ones for formmide. This observtion is in greement with the lower resonnce stbiliztion of the ltter, which results in smller energy penlty for pyrmidliztion of the crbonyl crbon. Acid-Ctlyzed Hydrolysis. Similr to the bse-ctlyzed rection, the cid-ctlyzed hydrolysis of ure follows n elimintion rection to give isocynic cid nd NH ,59,61-63,68 No experimentl or theoreticl studies hve been reported for the hydrolytic decomposition pthwy to our knowledge. In our theoreticl nlysis, we found tht protontion of the crbonyl forming URP + WAT stbilizes the system by 23 kcl/mol reltive to ure nd H 3 O + t ny of the tempertures considered. Nevertheless, the wter molecule cn be stbilized by hydrogen bond coordintion to protonted ure (see URPWN nd URPWO, Figure 8). Bifurcted coordintion with both mino ends gve structure tht is only 5 kcl/mol less stble thn protonted ure nd wter t 298 K nd is more stble by 1 kcl/mol t 498 K (see Tble 7). Another coordintion mode is possible, which includes the protonted crbonyl oxygen nd one of the mino ends (URPWO). The dt in Tble 7 show tht the resulting dduct is 12.2 kcl/mol higher in energy thn the first one t room temperture nd 11.4 kcl/mol higher t 498 K. We hve considered the possibility of second wter ssisting the ttck on protonted ure by cpturing proton of the rective wter in mnner similr to wht ws described for formmide. For consistent model, the dduct involved in proton trnsfer, from which the rection proceeds, hs to include two wter molecules coordinted to protonted ure. Two possible coordintion modes were considered, which re shown in Figure 9. Their reltive energies re reported in Tble 8. In spite of the lck of experimentl informtion on the possible mechnism of the cid-ctlyzed hydrolysis of ure,

10 Hydrolysis of Amides J. Phys. Chem. B, Vol. 111, No. 23, Figure 9. Computed geometries for hydrogen-bonded complexes of protonted ure nd two wter molecules identified in this work. TABLE 8: Free Energies for the Stble Species Associted with Acid-Ctlyzed Ure Hydrolysis UR + H 3O + WAT URPWN + WAT URPW2N URPW2O TSURP1 298 K K K Ure (UR), two-wter hydrogen-bonded complex to the mino hydrogens (URPW2N), two-wter hydrogen-bonded complex to the protonted ure crbonyl (URPW2O), hydronium ion (H 3O + ), nd wter (WAT). For URPW2N nd URPW2O, see Figure 9. For TSURP1, see Figure 10. Energies (kcl/mol) re reltive to URPWN (see more detils in the text). Positive vlues indicte less stble species. we hve serched for trnsition stte structures similr to those found for formmide. However, we cnnot support unmbiguously one mechnism over nother. For the cse of formmide, there were experimentl dt to which our theoreticl model could be compred, while in the cse of ure (or tetrmethylure) this is lcking. 5,10,18,26 For the cse of ure, one cn ssume tht similr mechnism would be followed, but there is no experimentl evidence tht my help to further discern the most fvored rection pthwy. Moreover, even ssuming similr rection pthwy, there is n dditionl uncertinty for the cse of ure, which is ssocited to whether URPW2N or URPW2O would define the first step of the rection. Nevertheless, unlike the one-wter dducts, the two-wter dducts re nerly isoenergetic. On the bsis of our experience with formmide, we were ble to identify trnsition stte similr to TSFORP1 (see TSURP1, Figure 10). However, in the cse of ure, the H-bond interctions do not clerly describe proton bstrction from the rective wter. The H-O distnce is only elongted to 1.07 Å when the O(wter)-C distnce is 1.54 Å (see Figure 10). This TS is 36.6 kcl/mol higher in energy thn the most stble two-wter dduct (URPW2O) t 298 K. The different chrcteristics of the TS structures for ure nd formmide hydrolysis cn be understood on the bsis of the higher chrge (or enhnced electrophilic chrcter) on the crbonyl crbon in the former reltive to the ltter (clculted Mulliken popultions on the crbon tom: 0.46 for ure, 0.24 for formmide). This higher chrge ppers to llow wter ttck without further ssistnce of second wter molecule. Thus, we hve lso nlyzed the rection pthwys for one-wter ddition in detil for ure. Two TS s were identified, ssocited with wter ddition cross the C-N bond of ure protonted on the crbonyl oxygen tom, nd with wter ddition cross the CO bond of ure protonted on n mino nitrogen tom. The TS structures re shown in Figure 10, nd the clculted free energies re reported in Tble 8. The ctivtion free energy is gin dependent on the stte tht we ssocite with rectnts. Figure 10. Computed TS geometries for the cid-ctlyzed hydrolysis of ure. Color code s in Figure 1. From our computed results, the comprison of the totl energies of TSURP1 ( hrtrees) nd TSURPWO + WAT ( hrtrees) shows tht the former is more stble by 13 kcl/mol. This chrcteristic is independent of the rectnt reference stte. The lower energy of the two-wter TS reltive to the one-wter TS is certinly indictive of preference for two-wter rection pthwy in the cid ctlysis of ure. The present clcultions demonstrte tht, in the cse of cid ctlysis, two wter molecules prticipte ctively s rectnts, nd hve to be included explicitly in the model (regrdless of the electrophilic nture of the crbonyl crbon). In this wy, ssuming tht the free ctivtion energy is determined by the two-wter ssisted rection strting with URPW2N (Tble 8, 36.6 kcl/mol), we cn clculte the rte constnts for cid ctlysis s function of the temperture. We obtin vlues of s -1 t 298 K, s -1 t 398 K, nd s -1 t 498 K. We predict tht the cid-ctlyzed hydrolysis of ure is much slower thn the corresponding one for formmide. We ssocite the different rectivity with the lrger resonnce stbiliztion of ure reltive to formmide. Wter Rection. The decomposition of ure hs been extensively studied since the erly 1950s, 1,2,59,62,68,69 nd the kinetic prmeters for the elimintion rection hve been determined. 1,2,68 For this decomposition mechnism, experimentl nd theoreticl dt gree on rte constnt of 10-7 s -1. 1,2,7,68 The low brrier for the elimintion rection hs prevented the experimentl detection of the hydrolytic pthwy. However, the rte constnt for the wter rection hs been estimted from the one determined for tetrmethylure (Me 4 Ur) t neutrl ph. 31 For Me 4 Ur, the rte constnt t room temperture hs been extrpolted from experimentl determintions between 400 nd 520 K. As further pproximtion, correction fctor of 2.8 hs been pplied ssuming tht N-dimethyltion will hve the sme effect for ure s for cetmide. 70 On this bsis, rte constnt of s -1 t 298 K hs been estimted. 31 This rection hs lso been studied in gret detil using modern theoreticl tools, resulting in slower predicted kinetics nd ctivtion free energies close to 50 kcl/mol (rte constnts on the order of ). 7,11 The wter environment ws simulted using continuum models, nd one 7 to three 11 wter molecules