A universal approach for continuum solvent pK a calculations: are we there yet?

This paper reviews several pK _a calculation strategies that are commonly used in aqueous acidity predictions. Among those investigated were the direct or absolute method, the proton exchange scheme, and the hybrid cluster–continuum (Pliego and Riveros) and implicit–explicit (Kelly, Cramer and Truhlar) models. Additionally, these protocols are applied in the pK _a calculation of 55 neutral organic and inorganic acids in conjunction with various solvent models, including the CPCM-UAKS/UAHF, IPCM, SM6 and COSMO-RS, with a view to identifying a universal approach for accurate pK _a predictions. The results indicate that the direct method is unsuitable for general pK _a calculations, although moderately accurate results (MAD <3 units) are possible for certain classes of acids, depending on the choice of solvent model. The proton exchange scheme generally delivers good results (MAD <2 units), with CPCM-UAKS giving the best performance. Furthermore, the sensitivity of this approach to the choice of reference acid can be substantially lessened if the solvation energies for ionic species are calculated via the IPCM cluster–continuum approach. Reference-independent hybrid approaches that include explicit water molecules can potentially give reasonably accurate values (MAD generally ~2 units) depending on the solvent model and the number of explicit water molecules added.     

Calculations of pKa of superacids in 1,2-dichloroethane

Acidity calculations for some CH and NH superacids in 1,2-dichloroethane (DCE) were carried out using SMD and COSMO-RS continuum solvation models. After comparing the results of calculations with respective experimental pK(a) values it was found that the performance of SMD/M05-2X/6-31G* method is characterized by the mean unsigned error (MUE) of 0.5 pK(a) units and the slope of regression line of 0.915. The similar SMD/B3LYP/6-31G* approach was slightly less successful. The strong correlation over entire data set is confirmed by R(2) values of 0.990 and 0.984 for M05-2X and B3LYP functionals, respectively. The COSMO-RS method, while providing the value of the linear regression line slope similar to the corresponding values from SMD approach, characterized by rather loose correlation (R(2) = 0.823, MUE = 1.7 pK(a) units) between calculated and experimental pK(a) values in DCE solution.     

Ab Initio Quantum Mechanical Study on the Origin of the pK(a) Differences of the Proton Sponges 1,8-Bis(dimethylamino)naphthalene, 1,8-Bis(dimethylamino)-2,7-dimethoxynaphthalene, 1,6-Dimethyl-1,6-diazacyclodecane, and 1,6-Diazabicyclo[4.4.4]tetradecane

Ab initio quantum mechanical calculations were used in studying the origin of the exceptionally high basicities of four diamines (13-16) with pK(a1) values ranging from 12.1 to 25. The computational approach involved the calculation of the gas-phase proton affinities of the molecules studied at the MP2/6-31G//HF/6-31G level and the solvation energies with the polarizable continuum model at the HF/6-31G level. The calculated gas-phase and aqueous-phase proton affinities of a structurally diverse series of amines were compared with the corresponding experimental gas-phase proton affinities and pK(a1) values. The calculated values were found to be in reasonable agreement with the experimental ones. The high basicities of the studied diamines were found to originate from the nitrogen lone-pair repulsion, solvation effects, and strong intramolecular hydrogen bonds. Each of these factors were found to be able to increase the pK(a1) values of the high-basicity diamines by 2-6 pK(a) units. The relative contributions of the factors varied between the compounds. The nitrogen lone-pair repulsion was estimated to be the most important factor in increasing the pK(a1) values. In addition, barriers for proton transfers between the nitrogens of selected diamines were calculated, and comparison was made between the barrier heights and the geometries of the diamines.     

Accurate pK(a) calculations for carboxylic acids using complete basis set and Gaussian-n models combined with CPCM continuum solvation methods

Complete Basis Set and Gaussian-n methods were combined with CPCM continuum solvation methods to calculate pK(a) values for six carboxylic acids. An experimental value of -264.61 kcal/mol for the free energy of solvation of H(+), DeltaG(s)(H(+)), was combined with a value for G(gas)(H(+)) of -6.28 kcal/mol to calculate pK(a) values with Cycle 1. The Complete Basis Set gas-phase methods used to calculate gas-phase free energies are very accurate, with mean unsigned errors of 0.3 kcal/mol and standard deviations of 0.4 kcal/mol. The CPCM solvation calculations used to calculate condensed-phase free energies are slightly less accurate than the gas-phase models, and the best method has a mean unsigned error and standard deviation of 0.4 and 0.5 kcal/mol, respectively. The use of Cycle 1 and the Complete Basis Set models combined with the CPCM solvation methods yielded pK(a) values accurate to less than half a pK(a) unit.     

Probing the influence of solvent effects on the conformational behavior of 1,3-diazacyclohexane systems

The conformational behavior of a 1,3-diazacyclohexane system has been investigated using the DFT B3LYP/6-311+G** level of theory. The structural parameters and relative energies predicted that anomeric effects are operative in the conformations of 1,3-diazacyclohexane. The stability of conformers predicted in the solvent continuum model (water and acetonitrile) is similar to the gas-phase results. The explicit water molecules stabilized the least-stable conformer, and the predictive trend is opposite to that of the gas-phase results. The stability of the conformers in the gas phase is a compromise between avoiding repulsions and maximizing hyperconjugative stabilization. The NBO analysis suggests that the interactions of explicit solvent molecules with 1,3-diazacyclohexane conformers attenuate the anomeric stabilization. The hydrogen-bonding interactions of explicit solvent molecules with 1,3-diazacyclohexane swamped the anomeric effects to alter the conformational stability compared to the gas-phase and solvent continuum model studies.     

Absolute pK(a) determinations for substituted phenols

The CBS-QB3 method was used to calculate the gas-phase free energy difference between 20 phenols and their respective anions, and the CPCM continuum solvation method was applied to calculate the free energy differences of solvation for the phenols and their anions. The CPCM solvation calculations were performed on both gas-phase and solvent-phase optimized structures. Absolute pK(a) calculations with solvated phase optimized structures for the CPCM calculations yielded standard deviations and root-mean-square errors of less than 0.4 pK(a) unit. This study is the most accurate absolute determination of the pK(a) values of phenols, and is among the most accurate of any such calculations for any group of compounds. The ability to make accurate predictions of pK(a) values using a coherent, well-defined approach, without external approximations or fitting to experimental data, is of general importance to the chemical community. The solvated phase optimized structures of the anions are absolutely critical to obtain this level of accuracy, and yield a more realistic charge separation between the negatively charged oxygen and the ring system of the phenoxide anions.     

Theoretical prediction of pKa values of seleninic, selenenic, sulfinic, and carboxylic acids by quantum-chemical methods

Aqueous acid dissociation constants of substituted areneseleninic, areneselenenic, arenesulfinic, and benzoic acids are calculated by ab initio (MP2) and DFT (B3LYP) methods in combination with bulk solvation models (IEFPCM, CRSrad) from appropriate thermodynamic cycles. Mean absolute deviations (MAD) between experimental and calculated pK(a) values are quite large for basis sets without diffuse functions; however, trends are reasonably well described. Best agreement with experiment as described by MAD as well as correlation coefficient and slope of the correlation equation pK(a) = a*ΔG(calc)/RT ln(10) + b is obtained with the CPCM solvation model using the defaults optimized within COSMO-RS (CRSrad; MAD = 1.54, R(2) = 0.94, a = 0.83). Sulfenic (selenenic) acid tautomers are significantly more stable than the corresponding sulfoxide (selenoxide) forms.     

Gas-phase reactivity of 2,7-dimethyl-[1,2,4]-triazepine thio derivatives toward Cu+ cation: a DFT study

The gas-phase interactions of 2,7-dimethyl-[1,2,4]-triazepine and its thio derivatives with Cu+ were studied through the use of high-level density functional theory (DFT) calculations. The structure of all possible tautomers and their conformers was optimized at the B3LYP/6-31G(d) level of theory. Final energies were obtained at the B3LYP/6-311+G(2df,2p) level. It has been found that the direct association of Cu+ occurs at the oxygen atom attached to position 3 in the case of the dioxo derivative and at the sulfur atom in all other cases. For the dithio derivatives, the global minimum of the PES corresponds to the structure in which the metal ion bridges between the heteroatom at position 3 and the nitrogen atom at position 4 of the corresponding enolic tautomer, forming a four-membered ring structure; for the dioxo derivative, this conformer competes with the ketone tautomer. Moreover, the isomerization processes leading from the most stable adduct to the other stable conformers were investigated. Among all the considered compounds, the 3,5-dithiotriazepines-Cu+ is found to be the one that associates Cu+ more tightly in the gas phase. The calculated Cu+ binding energies show a good correlation with the experimental proton affinities.     

Ab initio procedure for aqueous-phase pKa calculation: the acidity of nitrous acid

We present an ab initio procedure for accurately calculating aqueous-phase pKa values and apply it to study the acidity of nitrous acid (HNO2, or HONO). The aqueous-phase pK(a) of nitrous acid was obtained from calculated gas-phase acidities and solvation free energies via a thermodynamic cycle and the solvation model chemistry of Barone et al. (J. Chem. Phys. 1997, 107, 3210). Solvation free energies were calculated at the HF/6-31G(d) level using the dielectric-polarizable continuum and the integral equation formalism-polarizable continuum solvent models (D-PCM and IEF-PCM, respectively), with the D-PCM model yielding the most accurate pKa values. For HF free energies of solvation, significant improvements in accuracy could be made by moving to the larger 6-311++G(3df,3pd) and aug-cc-pVQZ basis sets. Solvation free energies were also calculated using the density functional theory (DFT) methods B3LYP, TPSS, PBE0, B1B95, VSXC, B98 and O3LYP, with the most accurate methods being TPSS and VSXC, which provided average errors of less than 0.11 pKa units. Solvation free energies calculated with the different DFT methods were relatively insensitive to the basis set used. Our theoretical calculations are compared with experimental results obtained using stopped flow spectrophotometry. The pKa of nitrous acid was measured as 3.16 at 25 degrees C, and the enthalpy and entropy of nitrous acid dissociation were calculated from measurements as 6.7 kJ mol(-1) and -38.4 J mol(-1) K(-1), respectively, between 25 and 45 degrees C. The UV/visible absorption spectra of the nitrite ion and nitrous acid were also examined, and molar extinction coefficients were obtained for each.     

Gaseous arginine conformers and their unique intramolecular interactions

Extensive ab initio calculations were employed to characterize stable conformers of gaseous arginine, both the canonical and zwitterionic tautomers. Step-by-step geometry optimizations of possible single-bond rotamers at the B3LYP/6-31G(d), B3LYP/6-31++G(d,p), and MP2/6-31++G(d,p) levels yield numerous structures that are more stable than any known ones. The final electronic energies of the conformers were determined at the CCSD/6-31++G(d,p) level. The lowest energies of the canonical and zwitterionic structures are lower than the existing values by 2.0 and 2.3 kcal/mol, respectively. The relative energies, rotational constants, dipole moments, and harmonic frequencies of the stable conformers remain for future experimental verification. The conformational distributions at various temperatures, estimated according to thermodynamic principles, consist almost exclusively of the newly found structures. One striking feature is the occurrence of blue-shifting hydrogen bonds in all six of the most stable conformers. A unique feature of important conformations is the coexistence of dihydrogen and blue- and red-shifting hydrogen bonds. In addition to the hydrogen bonds, the stereoelectronic effects were also found to be important stabilization factors. The calculated and measured proton affinities agree within the theoretical and experimental uncertainties, affirming the high quality of our conformational search. The theoretical gas-phase basicity of 245.9 kcal/mol is also in good agreement with the experimental value of 240.6 kcal/mol. The extensive searches establish firmly that gaseous arginine exists primarily in the canonical and not the zwitterionic form.     

Interaction of metal ions with biomolecular ligands: how accurate are calculated free energies associated with metal ion complexation?

To address fundamental questions in bioinorganic chemistry, such as metal ion selectivity, accurate computational protocols for both the gas-phase association of metal-ligand complexes and solvation/desolvation energies of the species involved are needed. In this work, we attempt to critically evaluate the performance of the ab initio and DFT electronic structure methods available and recent solvation models in calculations of the energetics associated with metal ion complexation. On the example of five model complexes ([M(II)(CH(3)S)(H(2)O)](+), [M(II)(H(2)O)(2)(H(2)S)(NH(3))](2+), [M(II)(CH(3)S)(NH(3))(H(2)O)(CH(3)COO)], [M(II)(H(2)O)(3)(SH)(CH(3)COO)(Im)], [M(II)(H(2)S)(H(2)O)(CH(3)COO)(PhOH)(Im)](+) in typical coordination geometries) and four metal ions (Fe(2+), Cu(2+), Zn(2+), and Cd(2+); representing open- and closed-shell and the first- and second-row transition metal elements), we provide reference values for the gas-phase complexation energies, as presumably obtained using the CCSD(T)/aug-cc-pVTZ method, and compare them with cheaper methods, such as DFT and RI-MP2, that can be used for large-scale calculations. We also discuss two possible definitions of interaction energies underlying the theoretically predicted metal-ion selectivity and the effect of geometry optimization on these values. Finally, popular solvation models, such as COSMO-RS and SMD, are used to demonstrate whether quantum chemical calculations can provide the overall free enthalpy (ΔG) changes in the range of the expected experimental values for the model complexes or match the experimental stability constants in the case of three complexes for which the experimental data exist. The data presented highlight several intricacies in the theoretical predictions of the experimental stability constants: the covalent character of some metal-ligand bonds (e.g., Cu(II)-thiolate) causing larger errors in the gas-phase complexation energies, inaccuracies in the treatment of solvation of the charged species, and difficulties in the definition of the reference state for Jahn-Teller unstable systems (e.g., [Cu(H(2)O)(6)](2+)). Although the agreement between the experimental (as derived from the stability constants) and calculated values is often within 5 kcal·mol(-1), in more complicated cases, it may exceed 15 kcal·mol(-1). Therefore, extreme caution must be exercised in assessing the subtle issues of metal ion selectivity quantitatively.     

Protonation processes and electronic spectra of histidine and related ions

A full structural assignment of the neutral, protonated, and deprotonated histidine conformers in the gas phase is presented. A total of 3024 unique trial structures were generated by all combinations of internal single-bond rotamers of these species and optimized at the B3LYP/6-311G* level and further optimized at the B3LYP/6-311++G** level. A set of unique conformers is found, and their relative energies, free energies, dipole moments, rotational constants, electron affinities, ionization energies, and harmonic frequencies are determined. The population ratio of histidine and its tautomer is 1:0.16 at 298 K. Massive conformational changes are observed due to protonation and deprotonation, and the intramolecular H-bonds are characterized with the atoms in molecules theory. The calculated proton dissociation energy, gas-phase acidity, proton affinity, and gas-phase basicity are in excellent agreement with the experiments. The deprotonation and protonation of gaseous histidine both occur on the imidazole ring, explaining the versatile biofunctions of histidine in large biomolecules. The UV spectra of neutral and singly and doubly protonated histidine are investigated with the TDDFT/B3LYP/6-311+G(2df,p) calculations. The S0-S1, S0-S2, and S0-S3 excitations of histidine are mixed pipi*/npi* transitions at 5.37, 5.44, and 5.69 eV, respectively. The three excitation energies for histidine tautomer are 4.85, 5.47, and 5.52 eV, respectively. The three excitations for protonated histidine are mainly npi* transitions at 5.45, 5.67, and 5.82 eV, respectively. The S0-S1 excitation of protonated histidine produces ImH-CbetaH2-CalphaH(COOH)-NH2+, while the S0-S2 and S0-S3 transitions produce ImH-CbetaH2-CalphaH(NH2)-(COOH)+. These data may help to understand the mechanisms of the UV fragmentation of biomolecules.     

The oxidation of tyrosine and tryptophan studied by a molecular dynamics normal hydrogen electrode

The thermochemical constants for the oxidation of tyrosine and tryptophan through proton coupled electron transfer in aqueous solution have been computed applying a recently developed density functional theory (DFT) based molecular dynamics method for reversible elimination of protons and electrons. This method enables us to estimate the solvation free energy of a proton (H(+)) in a periodic model system from the free energy for the deprotonation of an aqueous hydronium ion (H(3)O(+)). Using the computed solvation free energy of H(+) as reference, the deprotonation and oxidation free energies of an aqueous species can be converted to pK(a) and normal hydrogen electrode (NHE) potentials. This conversion requires certain thermochemical corrections which were first presented in a similar study of the oxidation of hydrobenzoquinone [J. Cheng, M. Sulpizi, and M. Sprik, J. Chem. Phys. 131, 154504 (2009)]. Taking a different view of the thermodynamic status of the hydronium ion, these thermochemical corrections are revised in the present work. The key difference with the previous scheme is that the hydronium is now treated as an intermediate in the transfer of the proton from solution to the gas-phase. The accuracy of the method is assessed by a detailed comparison of the computed pK(a), NHE potentials and dehydrogenation free energies to experiment. As a further application of the technique, we have analyzed the role of the solvent in the oxidation of tyrosine by the tryptophan radical. The free energy change computed for this hydrogen atom transfer reaction is very similar to the gas-phase value, in agreement with experiment. The molecular dynamics results however, show that the minimal solvent effect on the reaction free energy is accompanied by a significant reorganization of the solvent.     

Computing Alchemical Free Energy Differences with Hamiltonian Replica Exchange Molecular Dynamics (H-REMD) Simulations

Alchemical free energy calculations play a very important role in the field of molecular modeling. Efforts have been made to improve the accuracy and precision of those calculations. One of the efforts is to employ a Hamiltonian replica exchange molecular dynamics (H-REMD) method to enhance conformational sampling. In this paper, we demonstrated that HREMD method not only improves convergence in alchemical free energy calculations but also can be used to compute free energy differences directly via the Free Energy Perturbation (FEP)algorithm. We show a direct mapping between the H-REMD and the usual FEP equations, which are then used directly to compute free energies. The H-REMD alchemical free energy calculation (Replica exchange Free Energy Perturbation, REFEP) was tested on predicting the pK(a) value of the buried Asp26 in thioredoxin. We compare the results of REFEP with TI and regular FEP simulations. REFEP calculations converged faster than those from TI and regular FEP simulations. The final predicted pK(a) value from the H-REMD simulation was also very accurate, only 0.4 pK(a) unit above the experimental value. Utilizing the REFEP algorithm significantly improves conformational sampling, and this in turn improves the convergence of alchemical free energy simulations.     

DFT study of the glutathione peroxidase-like activity of phenylselenol incorporating solvent-assisted proton exchange

Modeling of the glutathione peroxidase-like activity of phenylselenol has been accomplished using density-functional theory and solvent-assisted proton exchange (SAPE). SAPE is a modeling technique intended to mimic solvent participation in proton transfer associated with chemical reaction. Within this method, explicit water molecules incorporated into the gas-phase model allow relay of a proton through the water molecules from the site of protonation in the reactant to that in the product. The activation barriers obtained by SAPE for the three steps of the GPx-like mechanism of PhSeH fall within the limits expected for a catalytic system at physiological temperatures (DeltaG(1)++ = 19.1 kcal/mol; DeltaG(2)++= 6.6 kcal/mol; G(3)++ = 21.7 kcal/mol) and are significantly lower than studies which require direct proton transfer. The size of the SAPE network is also considered for the model of the reduction of the selenenic acid, step 2 of the GPx-like cycle. Use of a four-water network better accommodates the reaction pathway and reduces the activation barrier by 5 kcal/mol over the two-water model.     

Acidity of anilines: calculations vs experiment

The gas-phase acidities of ca. 60 monosubstituted anilines (with acidity span of almost 50 kcal mol(-1)) have been calculated using density functional theory (DFT) at the B3LYP/6-311+G** level. At this relatively simple level of theory the calculated (ΔG(calc)) and available experimental (ΔG(exp)) acidities are in reasonable quantitative correlation according to the following equation: ΔG(obs) = a + bΔG(calc), where a=20.79, b=0.942, n=27, R(2)=0.990, and s=0.78 kcal·mol(-1). The slope is not far from its ideal value. Substituent effects on the acidities were dissected separately into those operating in the neutral acid molecule and in its conjugated anion using the isodesmic homodesmotic reactions. All in all, both forms, neutral and anionic, are contributing in combination to make up the gross acidity of anilines. However, the contributions of the anions into the gross substituent effects are much larger than the substituent effects in the neutral anilines. Some of the systems were used in testing a relatively new theoretical model, COSMO-RS (conductor-like screening model for real solvents), using it for the prediction of pK(a) values in DMSO. The method proved to be rather accurate for showing pK(a) trends (R(2)=0.980 in DMSO). However, the predicted absolute pK(a) values were all somewhat lower (rmsd=2.49 kcal·mol(-1)) than the respective experimental values.     

水溶液中铵离子pKa值的理论计算

在HF/6-31+G*和B3LYP/6-31+G*水平上, 采用导体极化连续模型(CPCM)及UAKS孔穴计算了11种铵离子在水溶剂中的溶剂化自由能, 与实验值相比较, 平均误差和标准偏差分别为0.17, 12.04和0.96, 10.96 kJ/mol. 结合B3LYP/6-31+G*水平上的11种铵离子气相质子转移反应自由能, 得到了水溶剂中的绝对pKa值, 计算结果与实验数据吻合得很好, 相应的平均误差和标准偏差分别为0.05, 1.50和0.45, 1.40 pKa单位. 可见, 采用CPCM-UAKS模型能够较为精确地计算铵离子型化合物的绝对pKa值.     

Local Structures and Chemical Properties of Deprotonated Arginine

The potential energy surface of gaseous deprotonated arginine has been systematically in- vestigated by first principles calculations. At the B3LYP/6-31G(d) level, apart from the identification of several stable local structures, a new global minimum is located which is about 6.56 kJ/mol more stable than what has been reported. The deprotonated arginine molecule has two distinct forms with the deprotonation at the carboxylate group (COO^-). These two forms are bridged by a very high energy barrier and possess very different IR spectral profiles. Our calculated proton dissociation energy and gas-phase acidity of argi-nine molecule are found to be in good agreement with the corresponding experimental results. The predicted geometries, dipole moments, rotational constants, vertical ionization energies and IR spectra of low energy conformers will be useful for future experimental measurements.     

Aqueous solvation free energies of ions and ion-water clusters based on an accurate value for the absolute aqueous solvation free energy of the proton

Thermochemical cycles that involve pKa, gas-phase acidities, aqueous solvation free energies of neutral species, and gas-phase clustering free energies have been used with the cluster pair approximation to determine the absolute aqueous solvation free energy of the proton. The best value obtained in this work is in good agreement with the value reported by Tissandier et al. (Tissandier, M. D.; Cowen, K. A.; Feng, W. Y.; Gundlach, E.; Cohen, M. J.; Earhart, A. D.; Coe, J. V. J. Phys. Chem. A 1998, 102, 7787), who applied the cluster pair approximation to a less diverse and smaller data set of ions. We agree with previous workers who advocated the value of -265.9 kcal/mol for the absolute aqueous solvation free energy of the proton. Considering the uncertainties associated with the experimental gas-phase free energies of ions that are required to use the cluster pair approximation as well as analyses of various subsets of data, we estimate an uncertainty for the absolute aqueous solvation free energy of the proton of no less than 2 kcal/mol. Using a value of -265.9 kcal/mol for the absolute aqueous solvation free energy of the proton, we expand and update our previous compilation of absolute aqueous solvation free energies; this new data set contains conventional and absolute aqueous solvation free energies for 121 unclustered ions (not including the proton) and 147 conventional and absolute aqueous solvation free energies for 51 clustered ions containing from 1 to 6 water molecules. When tested against the same set of ions that was recently used to develop the SM6 continuum solvation model, SM6 retains its previously determined high accuracy; indeed, in most cases the mean unsigned error improves when it is tested against the more accurate reference data.     

On the role of the conserved aspartate in the hydrolysis of the phosphocysteine intermediate of the low molecular weight tyrosine phosphatase

The usual rate-determining step in the catalytic mechanism of the low molecular weight tyrosine phosphatases involves the hydrolysis of a phosphocysteine intermediate. To explain this hydrolysis, general base-catalyzed attack of water by the anion of a conserved aspartic acid has sometimes been invoked. However, experimental measurements of solvent deuterium kinetic isotope effects for this enzyme do not reveal a rate-limiting proton transfer accompanying dephosphorylation. Moreover, base activation of water is difficult to reconcile with the known gas-phase proton affinities and solution phase pK(a)'s of aspartic acid and water. Alternatively, hydrolysis could proceed by a direct nucleophilic attack by a water molecule. To understand the hydrolysis mechanism, we have used high-level density functional methods of quantum chemistry combined with continuum electrostatics models of the protein and the solvent. Our calculations do not support a catalytic activation of water by the aspartate. Instead, they indicate that the water oxygen directly attacks the phosphorus, with the aspartate residue acting as a H-bond acceptor. In the transition state, the water protons are still bound to the oxygen. Beyond the transition state, the barrier to proton transfer to the base is greatly diminished; the aspartate can abstract a proton only after the transition state, a result consistent with experimental solvent isotope effects for this enzyme and with established precedents for phosphomonoester hydrolysis.