Theoretical calculation of the pKa values of some drugs in aqueous solution

In this work, calculations of pK_a values have been performed on benzoic acid and its para‐substituted derivatives and some drugs by using Gaussian 98 software package. Gas‐phase energies were calculated with HF/6‐31 G** and B3LYP/6‐31 G** levels of theory. Free energies of solvation have been computed using the polarizable continuum model (PCM), conductor‐like PCM (CPCM), and the integral equation formalism‐PCM at the same levels which have been used for geometry determination in the gas‐phase. The results that show the calculated pK_a values using the B3LYP are better than those using the corresponding HF. In comparison to the other models, the results obtained indicate that the PCM model is a suitable solvation model for calculating pK_a values. For the investigated compounds, a good agreement between the experimental and the calculated pK_a values was also observed. © 2011 Wiley Periodicals, Inc. Int J Quantum Chem, 2011     

Accurate pKa Calculation of the Conjugate Acids of Alkanolamines,Alkaloids and Nucleotide Bases by Quantum Chemical Methods

The pK_a of the conjugate acids of alkanolamines, neurotransmitters, alkaloid drugs and nucleotide bases are calculated with density functional methods (B3LYP, M08‐HX and M11‐L) and ab initio methods (SCS‐MP2, G3). Implicit solvent effects are included with a conductor‐like polarizable continuum model (CPCM) and universal solvation models (SMD, SM8). G3, SCS‐MP2 and M11‐L methods coupled with SMD and SM8 solvation models perform well for alkanolamines with mean unsigned errors below 0.20 pK_a units, in all cases. Extending this method to the pK_a calculation of 35 nitrogen‐containing compounds spanning 12 pK_a units showed an excellent correlation between experimental and computational pK_a values of these 35 amines with the computationally low‐cost SM8/M11‐L density functional approach.     

A reliable and efficient first principles‐based method for predicting pKa values. 4. organic bases

The ionization (dissociation) constant (pK_a) is one of the most important properties of a drug molecule. It is reported that almost 68% of ionized drugs are weak bases. To be able to predict accurately the pK_a value(s) for a drug candidate is very important, especially in the early stages of drug discovery, as calculations are much cheaper than determining pK_a values experimentally. In this study, we derive two linear fitting equations (pK_a = a × ΔE + b; where a and b are constants and ΔE is the energy difference between the cationic and neutral forms, i.e., ΔE = E_neutral?E_cationic) for predicting pK_as for organic bases in aqueous solution based on a training/test set of almost 500 compounds using our previously developed protocol (OLYP/6‐311+G**//3‐21G(d) with the the conductor‐like screening model solvation model, water as solvent; see Zhang, Baker, Pulay, J. Phys. Chem. A 2010 , 114, 432). One equation is for saturated bases such as aliphatic and cyclic amines, anilines, guanidines, imines, and amidines; the other is for unsaturated bases such as heterocyclic aromatic bases and their derivatives. The mean absolute deviations for saturated and unsaturated bases were 0.45 and 0.52 pK_a units, respectively. Over 60% and 86% of the computed pK_a values lie within ±0.5 and ±1.0 pK_a units, respectively, of the corresponding experimental values. The results further demonstrate that our protocol is reliable and can accurately predict pK_a values for organic bases. © 2012 Wiley Periodicals, Inc.     

Experimentation with different thermodynamic cycles used for pKa calculations on 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 Barone and Cossi's implementation of the polarizable conductor model (CPCM) continuum solvation methods to calculate pK_a values for six carboxylic acids. Four different thermodynamic cycles were considered in this work. An experimental value of ?264.61 kcal/mol for the free energy of solvation of H⁺, ΔG_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. Thermodynamic cycles that include an explicit water in the cycle are not accurate when the free energy of solvation of a water molecule is used, but appear to become accurate when the experimental free energy of vaporization of water is used. This apparent improvement is an artifact of the standard state used in the calculation. Geometry relaxation in solution does not improve the results when using these later cycles. 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. © 2001 John Wiley & Sons, Inc. Int J Quantum Chem, 2001     

Calculating pKa values for substituted phenols and hydration energies for other compounds with the first‐order fuzzy‐border continuum solvation model

We have computed pK_a values for 11 substituted phenol compounds using the continuum Fuzzy‐Border (FB) solvation model. Hydration energies for 40 other compounds, including alkanes, alkenes, alkynes, ketones, amines, alcohols, ethers, aromatics, amides, heterocycles, thiols, sulfides, and acids have been calculated. The overall average unsigned error in the calculated acidity constant values was equal to 0.41 pH units and the average error in the solvation energies was 0.076 kcal/mol. We have also reproduced pK_a values of propanoic and butanoic acids within about 0.1 pH units from the experimental values by fitting the solvation parameters for carboxylate ion carbon and oxygen atoms. The FB model combines two distinguishing features. First, it limits the amount of noise which is common in numerical treatment of continuum solvation models by using fixed‐position grid points. Second, it uses either second‐ or first‐order approximation for the solvent polarization, depending on a particular implementation. These approximations are similar to those used for solute and explicit solvent fast polarization treatment which we developed previously. This article describes results of using the first‐order technique. This approximation places the presented methodology between the Generalized Born and Poisson‐Boltzmann continuum solvation models with respect to their accuracy of reproducing the many‐body effects in modeling a continuum solvent. © 2012 Wiley Periodicals, Inc.     

Determination of aqueous acid‐dissociation constants of aspartic acid using PCM/DFT method

Determination of acid‐dissociation constants, pK_a, of aspartic acid in aqueous solution, using density functional theory calculations combined with the conductor‐like polarizable continuum model (CPCM) and with integral‐equation‐formalism polarizable continuum model (IEFPCM) based on the UAKS and UAHF radii, was carried out. The computed pK_a values derived from the CPCM and IEFPCM with UAKS cavity model of bare structures of the B3LYP/6‐31+G(d,p)‐optimized tetrahydrated structures of aspartic acid species are mostly close to the experimental pK_a values. © 2007 Wiley Periodicals, Inc. Int J Quantum Chem, 2008     

Calculation of dissociation constants and chemical hardness of some biologically important molecules: A theoretical study

The gas‐phase geometries of neutral, protonated, and deprotonated forms of some biologically important molecules, alanine (Ala), glycine (Gly), phenylalanine (Phe), and tyrosine (Tyr), were optimized using density functional theory at B3LYP/6‐311++G(d) and the ab initio HF/6‐311++G(d) level of theories. The neutral and different stable ionic states of Ala, Gly, Phe, and Tyr have also been solvated in aqueous medium using polarizable continuum model for the determination of solvation free energies in the aqueous solution. The gas‐phase acidity constants of above four molecules have been also calculated at both levels of theories and found that the values calculated at HF/6‐311++G(d) method are in good agreement with experimental results. A thermodynamic cycle was used to determine the solvation free energies for the proton dissociation process in aqueous solution and the corresponding pK_a values of these molecules. The pK_a values calculated at B3LYP/6‐311++G(d) method are well supported by the experimental data with a mean absolute deviation 0.12 pK_a units. Additionally, the chemical hardness and the ionization potential (IP) for these molecules have been also explored at both the level of theories. The Tyr has less value of chemical hardness and IP at both levels of theories compared with other three molecules, Ala, Gly, and Phe. The calculated values of chemical hardness and IP are decreasing gradually with the substitution of the various functional groups in the side chain of the amino acids. © 2010 Wiley Periodicals, Inc. Int J Quantum Chem, 2011     

Experimental and computational study of the pKa of coumaric acid derivatives

The dissociation constant (pK_a) of a drug is a key parameter in drug discovery and pharmaceutical formulation. The hydroxy substituent has a significant effect on the acidity of hydroxycinnamic acid. In this work, the acidic constants of coumaric acids are obtained experimentally by spectrophotometry using the chemometric method and calculated theoretically using ab initio quantum mechanical method at the HF/6‐31G* level of theory in combination with the SMD continuum solvation method. Rank annihilation factor analysis (RAFA) is an efficient chemometric technique based on the elimination of the contribution of one of the chemical components from the data matrix. RAFA cannot be performed because the pure spectrum of HA^? is not available. So, two‐rank annihilation factor analysis (TRAFA) is proposed for the determination of the pK_a OF H₂A. A comparison between the pK_a values obtained previously by TRAFA for the molecules o‐coumaric acid (4.13, 9.58), m‐coumaric acid (4.48, 10.35), and p‐coumaric acid (4.65, 9.92) makes it clear that there is good agreement between the results obtained by TRAFA and ab initio quantum mechanical method.     

Incorporating solvation effects into density functional theory: Calculation of absolute acidities

An approach to the calculation of molecular electronic structures, solvation energies, and pK_a values in condensed phases is described. The electronic structure of the solute is described by density functional quantum mechanics, and electrostatic features of environmental effects are modeled through external charge distributions and continuum dielectrics. The reaction potential produced by a mode of the molecular charge distribution is computed via finite-difference solutions to the Poisson-Boltzmann equation and incorporated into the self-consistent field procedure. Here we report results on three sets of organic acids, whose pK_a values range over 16 pH units. The first set provides models for ionizable side chains in proteins; the second set considers the effects of substituting one to three chlorine atoms for hydrogens in acetic acid; and the final set consists of 4-substituted-bicyclo-[2.2.2]-octanecarboxylic acids. Successful prediction of “absolute” pK_a values places stringent requirements on the computation of gas-phase proton affinities and on the response to solvation. In some cases the current model shows substantial errors, but overall the results and trends are in good agreement with experiment. Prospects for extending this approach to more complex systems such as proteins are briefly discussed. © 1997 John Wiley & Sons, Inc.     

Computation of the influence of chemical substitution on the pK a of pyridine using semiempirical and ab initio methods

The physical properties of chemicals are strongly influenced by their protonation state, affecting, for example, solubility or hydrogen-bonding characteristics. The ability to accurately calculate protonation states in the form of pK _as is, therefore, desirable. Calculations of pK _a changes in a series of substituted pyridines are presented. Computations were performed using both ab initio and semiempirical approaches, including free energies of solvation via reaction-field models. The selected methods are readily accessible with respect to both software and computational feasibility. Comparison of calculated and experimental pK _as shows the experimental trends to be reasonably reproduced by the computations with root-mean-square differences ranging from 1.22 to 4.14 pK _a units. Of the theoretical methods applied the best agreement occurred using the second-order M?ller–Plesset/6-31G(d)/isodensity surface polarized continuum solvation model, while the more computationally accessible Austin model 1/Solvent model 2 (SM2) approach yielded results similar to the ab initio methods. Analysis of component contributions to the calculated pK _as indicates the largest source of error to be associated with the free energies of solvation of the protonated species followed by the gas-phase protonation energies; while the latter may be improved via the use of higher levels of theory, enhancements in the former require improvements in the solvation models. The inclusion of alternate minimum in the computation of pK _as is also indicated to contribute to differences between experimental and calculated pK _a values. Received: 27 April 1999 / Accepted: 27 July 1999 / Published online: 2 November 1999     

Linear Free‐Energy Relationships between a Single Gas‐Phase Ab Initio Equilibrium Bond Length and Experimental pKa Values in Aqueous Solution

Remarkably simple yet effective linear free energy relationships were discovered between a single ab initio computed bond length in the gas phase and experimental pK_a values in aqueous solution. The formation of these relationships is driven by chemical features such as functional groups, meta/para substitution and tautomerism. The high structural content of the ab initio bond length makes a given data set essentially divide itself into high correlation subsets (HCSs). Surprisingly, all molecules in a given high correlation subset share the same conformation in the gas phase. Here we show that accurate pK_a values can be predicted from such HCSs. This is achieved within an accuracy of 0.2 pK_a units for 5 drug molecules.     

Diethyl Fluoronitromethylphosphonate: Synthesis and Application in Nucleophilic Fluoroalkyl Additions

Diethyl fluoronitromethylphosphonate ( 3 ), a previously unknown compound, was synthesized by electrophilic fluorination of diethyl nitromethylphosphonate with Selectfluor. Base‐induced decomposition of 3 was studied by NMR spectroscopy, which identified diethyl fluorophosphate and fluoronitromethane as the main decomposition products. C?H acidities [pK_a values in dimethyl sulfoxide (DMSO)] of 3 , 1‐fluoro‐1‐phenylsulfonylmethanephosphonate ( 1 ; McCarthy’s reagent), tetraethyl fluoromethylenebisphosphonate ( 2 ), and some nonfluorinated phosphonates were computed, and a good correlation between calculated and experimental pK_a values was found. The calculated C?H acidities increased in the sequence 2 < 1 < 3 . Diethyl fluoronitromethylphosphonate ( 3 ) was applied in the Horner–Wadsworth–Emmons reaction with aldehydes and trifluoromethyl ketones to provide new 1‐fluoro‐1‐nitroalkenes with good to high stereoselectivities. Alkylation of 3 was successful only with iodomethane, however, conjugate additions of 3 to Michael acceptors such as α,β‐unsaturated carbonyl compounds, sulfones, and nitro compounds allowed access to variously modified diethyl 1‐fluoro‐1‐nitrophosphonates.     

Thermodynamic Estimate of pKa Values of the Carboxylic Acids in Aqueous Solution with the Density Functional Theory

The 96 pK_a values of 85 carboxylic acids in aqueous solution were calculated with the density functional theory method at the level of B3LYP/6‐31+G(d,p) and the polarizable continuum model (PCM) was used to describe the solvent. In the calculations of pK_a values, the dissociation Gibbs free energies were directly calculated using carboxylic acid dissociation reactions in aqueous solution, i. e., no thermodynamic cycle was employed, which is different from the previous literatures. A highly significant correlation of R²=0.95 with a standard deviation (SD) of 0.36 between the experimental pK_a values and the calculated dissociation Gibbs free energies [ΔG(calc.)] was found. The slope of pK_a vs. (G(calc.)/(20303RT) is only 47.6% of the theoretically expected value, which implies that the ΔG(calc.) value from the theoretical calculation is larger than the actual one for all 85 carboxylic acids studied. Thus, by adding the 0.476 scaling‐factor into the slope, we can derive a reliably procedure that can reproduce the experimental pK_a values of carboxylic acids. The pK_a values furnished by this procedure are in good agreement with the experimental results for carboxylic acids in aqueous solution.     

Potentiometric and Voltammetric Study of 6‐Benzylaminopurine and Its Derivatives

The protonation‐deprotonation equilibrium of 6‐benzylaminopurine (6‐BAP) and its derivatives was studied by potentiometry and voltammetry. The effect of Cl‐ or OCH₃‐group in position 2′, 3′ and 4′ of the benzene ring of 6‐BAP on both pK_a values was investigated. To determine the enthalpy and entropy, the temperature dependence of pK_a was employed. It was found that with increasing temperature the pK_a decreased. In comparison with 6‐BAP the chloro‐ or methoxy‐ group resulted in pK_a increase. The first pK_a values were also determined by linear sweep (LSV) and elimination voltammetry with linear scan (EVLS). New approaches were shown not only for the determination of pK_a from voltammetric titration curves but also for the evaluation of the reduction processes of benzylaminopurines.     

Theoretical Study of Firefly Luciferin pKa Values—Relative Absorption Intensity in Aqueous Solutions

Ground‐state vibrational analyses of firefly luciferin and its conjugate acids and bases are performed. The Gibbs free energies obtained from these analyses are used to estimate pK_a values for phenolic hydroxy and carboxy groups and the N–H⁺ bond in the N‐protonated thiazoline or benzothiazole ring of firefly luciferin. The theoretical pK_a values are corrected using the experimental values. The concentrations of these chemical species in solutions with different pH values are estimated from their corrected pK_a values, and the pH dependence of their relative absorption intensities is elucidated. With the results obtained we assign the experimental spectra unequivocally. Especially, the small peak near 400 nm at pH 1–2 in experimental absorption spectra is clarified to be due to the excitation of carboxylate anion with N‐protonated thiazoline ring of firefly luciferin. Our results show that the pK_a values of chemical species, which are contained in the aqueous solutions, are effective to assign experimental absorption spectra.     

Avoiding gas-phase calculations in theoretical p<Emphasis Type="Italic">K</Emphasis><Subscript>a</Subscript> predictions

CBS-QB3, two simplified and less computationally demanding versions of CBS-QB3, DFT-B3LYP, and HF quantum chemistry methods have been used in conjunction with the CPCM continuum solvent model to calculate the free energies of proton exchange reactions in water solution following an isodesmic reaction approach. According to our results, the precision of the predicted pK _a values when compared to experiment is equivalent to that of the thermodynamic cycles that combine gas-phase and solution-phase calculations. However, in the aqueous isodesmic reaction schema, the accuracy of the results is less sensitive to the presence of explicit water molecules and to the global charges of the involved species since the free energies of solvation are not required. In addition, this procedure makes easier the prediction of pK _a values for molecules that undergo large conformational changes in solvation process and makes possible the pK _a prediction of unstable species in gas-phase such as some zwitterionic tautomers. The successive pK _a values of few amino acids corresponding to the ionization of the α-carboxylic acid and α-amine groups, which is one of the problematic cases for thermodynamic cycles, were successfully calculated by employing the aqueous isodesmic reaction yielding mean absolute deviations of 0.22 and 0.19 pK _a units for the first and second ionization processes, respectively.     

Improving the study of proton transfers between amino acid side chains in solution: choosing appropriate DFT functionals and avoiding hidden pitfalls

We have studied the influence of implicit solvent models, inclusion of explicit water molecules, inclusion of vibrational effects, and density functionals on the quality of the predicted pK _a of small amino acid side chain models. We found that the inclusion of vibrational effects and explicit water molecules is crucial to improve the correlation between the computed and the experimental values. In these micro-solvated systems, the best agreement between DFT-computed electronic energies and benchmark values is afforded by BHHLYP and B97-2. However, approaching experimental results requires the addition of more than three explicit water molecules, which generates new problems related to the presence of multiple minima in the potential energy surface. It thus appears that a satisfactory ab initio prediction of amino acid side chain pK _a will require methods that sample the configurational space in the presence of large solvation shells, while at the same time computing vibrational contributions to the enthalpy and entropy of the system under study in all points of that surface. Pending development of efficient algorithms for those computations, we strongly suggest that whenever counterintuitive protonation states are found in a computational study (e.g., the presence of a neutral aspartate/neutral histidine dyad instead of a deprotonated aspartate/protonated histidine pair), the reaction profile should be computed under each of the different protonation micro-states by constraining the relevant N–H or O–H bonds, in order to avoid artifacts inherent to the complex nature of the factors contributing to the pK _a.     

Intrinsic Acid–Base Properties of a Hexa‐2′‐deoxynucleoside Pentaphosphate,d(ApGpGpCpCpT): Neighboring Effects and Isomeric Equilibria

The intrinsic acid‐base properties of the hexa‐2′‐deoxynucleoside pentaphosphate, d(ApGpGpCpCpT) [=(A1?G2?G3?C4?C5?T6)=(HNPP)^5?] have been determined by ¹H NMR shift experiments. The pK_a values of the individual sites of the adenosine (A), guanosine (G), cytidine (C), and thymidine (T) residues were measured in water under single‐strand conditions (i.e., 10 % D₂O, 47 °C, I=0.1 M , NaClO₄). These results quantify the release of H⁺ from the two (N7)H⁺ (G?G), the two (N3)H⁺ (C?C), and the (N1)H⁺ (A) units, as well as from the two (N1)H (G?G) and the (N3)H (T) sites. Based on measurements with 2′‐deoxynucleosides at 25 °C and 47 °C, they were transferred to pK_a values valid in water at 25 °C and I=0.1 M . Intramolecular stacks between the nucleobases A1 and G2 as well as most likely also between G2 and G3 are formed. For HNPP three pK_a clusters occur, that is those encompassing the pK_a values of 2.44, 2.97, and 3.71 of G2(N7)H⁺, G3(N7)H⁺, and A1(N1)H⁺, respectively, with overlapping buffer regions. The tautomer populations were estimated, giving for the release of a single proton from five‐fold protonated H₅(HNPP)^±, the tautomers (G2)N7, (G3)N7, and (A1)N1 with formation degrees of about 74, 22, and 4 %, respectively. Tautomer distributions reveal pathways for proton‐donating as well as for proton‐accepting reactions both being expected to be fast and to occur practically at no “cost”. The eight pK_a values for H₅(HNPP)^± are compared with data for nucleosides and nucleotides, revealing that the nucleoside residues are in part affected very differently by their neighbors. In addition, the intrinsic acidity constants for the RNA derivative r(A1?G2?G3? C4?C5?U6), where U=uridine, were calculated. Finally, the effect of metal ions on the pK_a values of nucleobase sites is briefly discussed because in this way deprotonation reactions can easily be shifted to the physiological pH range.     

SAMPL6: calculation of macroscopic p<Emphasis Type="Italic">K</Emphasis><Subscript>a</Subscript> values from ab initio quantum mechanical free energies

Macroscopic pK_a values were calculated for all compounds in the SAMPL6 blind prediction challenge, based on quantum chemical calculations with a continuum solvation model and a linear correction derived from a small training set. Microscopic pK_a values were derived from the gas-phase free energy difference between protonated and deprotonated forms together with the Conductor-like Polarizable Continuum Solvation Model and the experimental solvation free energy of the proton. pH-dependent microstate free energies were obtained from the microscopic pK_as with a maximum likelihood estimator and appropriately summed to yield macroscopic pK_a values or microstate populations as function of pH. We assessed the accuracy of three approaches to calculate the microscopic pK_as: direct use of the quantum mechanical free energy differences and correction of the direct values for short-comings in the QM solvation model with two different linear models that we independently derived from a small training set of 38 compounds with known pK_a. The predictions that were corrected with the linear models had much better accuracy [root-mean-square error (RMSE) 2.04 and 1.95 pK_a units] than the direct calculation (RMSE 3.74). Statistical measures indicate that some systematic errors remain, likely due to differences in the SAMPL6 data set and the small training set with respect to their interactions with water. Overall, the current approach provides a viable physics-based route to estimate macroscopic pK_a values for novel compounds with reasonable accuracy.     

Improving the Capture of CO2 by Substituted Monoethanolamines: Electronic Effects of Fluorine and Methyl Substituents

The influence of electronic and steric effects on the reaction between CO₂ and monoethanolamine (MEA) absorbents is investigated using computational methods. The pK_a of the alkanolamine, the reaction enthalpy for carbamate formation, and the hydrolytic carbamate stability are important factors for the efficiency of CO₂ capture. The steric and electronic effects of CH₃, CH₂F, CHF₂, CF₃, F, dimethyl, difluoro, and bis(2‐trifluoromethyl) substituents at the α carbon of MEA on this reaction are investigated. Density functional theory (DFT) (B3LYP, M06‐2X, M08‐HX and M11‐L) and ab initio methods [spin component‐scaled second‐order Møller‐Plesset theory (SCS‐MP2), G3], each coupled with solvent models [conductor‐like polarizable continuum model (CPCM) and universal solvation models (SM8 and SMD)], are shown to yield accurately calculated pK_a values of the substituted MEAs. Specifically, G3, SCS‐MP2, and M11‐L methods coupled with the SMD and SM8 solvation models perform well with a mean unsigned error (MUE) of only 0.15, 0.24 and 0.25 pK_a units, respectively. SCS‐MP2 is used to calculate the reaction enthalpy for carbamate formation and the carbamate stability towards hydrolysis. With the introduction of β‐fluoro substituents (especially the CH₂F moiety) the reaction enthalpy for the formation of carbamates can be fine‐tuned to be less exothermic than that using the unsubstituted MEA. This implies a reduced energy requirement for the solvent‐regeneration step in the post‐combustion carbon‐capture method, which is currently the energy‐limiting step in efficient CO₂ capture. β‐Fluoro‐substituted MEAs are also shown to form less stable carbamates than MEA. Thus, β‐fluoro‐substituted MEAs display a great potential for the use in the post‐combustion carbon‐capture process. Finally, a clear correlation is observed between the gas‐phase basicity and the tendency to form carbamates. This allows for the rapid prediction of which species will be formed experimentally, and thus the CO₂‐absorbing capacities of alkanolamines can be estimated.