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.     

Estimation of uncertainty in p<Emphasis Type="Italic">K</Emphasis><Subscript>a</Subscript> values determined by potentiometric titration

A procedure is presented for estimation of uncertainty in measurement of the pK(a) of a weak acid by potentiometric titration. The procedure is based on the ISO GUM. The core of the procedure is a mathematical model that involves 40 input parameters. A novel approach is used for taking into account the purity of the acid, the impurities are not treated as inert compounds only, their possible acidic dissociation is also taken into account. Application to an example of practical pK(a) determination is presented. Altogether 67 different sources of uncertainty are identified and quantified within the example. The relative importance of different uncertainty sources is discussed. The most important source of uncertainty (with the experimental set-up of the example) is the uncertainty of pH measurement followed by the accuracy of the burette and the uncertainty of weighing. The procedure gives uncertainty separately for each point of the titration curve. The uncertainty depends on the amount of titrant added, being lowest in the central part of the titration curve. The possibilities of reducing the uncertainty and interpreting the drift of the pK(a) values obtained from the same curve are discussed.     

The SAMPL6 challenge on predicting aqueous p<Emphasis Type="Italic">K</Emphasis><Subscript>a</Subscript> values from EC-RISM theory

The “embedded cluster reference interaction site model” (EC-RISM) integral equation theory is applied to the problem of predicting aqueous pK_a values for drug-like molecules based on an ensemble of tautomers. EC-RISM is based on self-consistent calculations of a solute’s electronic structure and the distribution function of surrounding water. Following-up on the workflow developed after the SAMPL5 challenge on cyclohexane-water distribution coefficients we extended and improved the methodology by taking into account exact electrostatic solute–solvent interactions taken from the wave function in solution. As before, the model is calibrated against Gibbs energies of hydration from the “Minnesota Solvation Database” and a public dataset of acidity constants of organic acids and bases by adjusting in total 4 parameters, among which only 3 are relevant for predicting pK_a values. While the best-performing training model yields a root-mean-square error (RMSE) of 1 pK unit, the corresponding test set prediction on the full SAMPL6 dataset of macroscopic pK_a values using the same level of theory exhibits slightly larger error (1.7 pK units) than the best test set model submitted (1.7 pK units for corresponding training set vs. test set performance of 1.6). Post-submission analysis revealed a number of physical optimization options regarding the numerical treatment of electrostatic interactions and conformational sampling. While the experimental test set data revealed after submission was not used for reparametrizing the methodology, the best physically optimized models consequentially result in RMSEs of 1.5 if only improved electrostatic interactions are considered and of 1.1 if, in addition, conformational sampling accounts for quantum-chemically derived rankings. We conclude that these numbers are probably near the ultimate accuracy achievable with the simple 3-parameter model using a single or the two best-ranking conformations per tautomer or microstate. Finally, relations of the present macrostate approach to microstate pK_a results are discussed and some illustrative results for microstate populations are presented.     

Infrared spectra of Hoffmann-<Emphasis Type=Italic>T</Emphasis><Subscript><Emphasis Type=Italic>d</Emphasis></Subscript>-type benzene clathrates

Six new title compounds in the form of Cd(cyclobutylamine)₂M′(CN)₄ · 2G (M′ = Cd or Hg; G = benzene, 1,2-dichlorobenzene, or 1,3-dichlorobenzene) have been prepared in powder form. Their spectral data were found to be consistent with the structure of the Hofmann-T _d -type clathrates.     

Interactions of Puerarin with Micelles: p<Emphasis Type="Italic">K</Emphasis><Subscript>a</Subscript> Shifts and Thermodynamics

In this paper, the effect of varying hydrophobic chain lengths on the acid-base equilibrium of an isoflavone, puerarin, in cationic micelles has been studied. The interaction of puerarin with three types of micelles of identical positively charged head groups and varying tail lengths, viz., DTAB, TTAB and CTAB, shows that there is a shift in the apparent pK _a in the direction that favors the displacement of the acid-base equilibrium of puerarin towards the base form. The relative location depth of puerarin in micelles is determined according to their dielectric values (D) taking into account that lower D values correspond to deeper location. It is evident that the reduction of polarity favors the deprotonation of puerarin. The isothermal titration calorimetry measurements show that the effect of puerarin on the thermodynamic properties of micellization is enhanced in the order CTAB>TTAB>DTAB and the results illustrate that puerarin has more affinity for micelles with greater chain length.     

Catalytic hydrogenation of persubstituted <Emphasis Type=Italic>p</Emphasis>-nitrosophenols

Catalytic hydrogenation of dialkyl 2-hydroxy-4,6-dimethyl-5-nitrosobenzene-1,3-dicarboxylates over Pd/C gave the corresponding previously unknown dialkyl 5-amino-2-hydroxy-4,6-dimethylbenzene-1,3-dicarboxylates. The first-order rate constants for the hydrogenation process were found to be linearly related to steric constants of the alkyl groups.     

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.     

Benchmarking and validating algorithms that estimate p<Emphasis Type="Italic">K</Emphasis><Subscript>a</Subscript> values of drugs based on their molecular structures

The REGDIA regression diagnostics algorithm in S-Plus is introduced in order to examine the accuracy of pK _a predictions made with four updated programs: PALLAS, MARVIN, ACD/pKa and SPARC. This report reviews the current status of computational tools for predicting the pK _a values of organic drug-like compounds. Outlier predicted pK _a values correspond to molecules that are poorly characterized by the pK _a prediction program concerned. The statistical detection of outliers can fail because of masking and swamping effects. The Williams graph was selected to give the most reliable detection of outliers. Six statistical characteristics (F _exp, R ², , MEP, AIC, and s(e) in pK _a units) of the results obtained when four selected pK _a prediction algorithms were applied to three datasets were examined. The highest values of F _exp, R ², , the lowest values of MEP and s(e), and the most negative AIC were found using the ACD/pK _a algorithm for pK _a prediction, so this algorithm achieves the best predictive power and the most accurate results. The proposed accuracy test performed by the REGDIA program can also be applied to test the accuracy of other predicted values, such as log P, log D, aqueous solubility or certain physicochemical properties of drug molecules.     

Outliers detection in the statistical accuracy test of a p<Emphasis Type="Italic">K</Emphasis><Subscript>a</Subscript> prediction

The regression diagnostics algorithm REGDIA in S-Plus is introduced to examine the accuracy of pK _a predicted with four programs: PALLAS, MARVIN, PERRIN and SYBYL. On basis of a statistical analysis of residuals, outlier diagnostics are proposed. Residual analysis of the ADSTAT program is based on examining goodness-of-fit via graphical diagnostics of 15 exploratory data analysis plots, such as bar plots, box-and-whisker plots, dot plots, midsum plots, symmetry plots, kurtosis plots, differential quantile plots, quantile-box plots, frequency polygons, histograms, quantile plots, quantile-quantile plots, rankit plots, scatter plots, and autocorrelation plots. Outliers in pK _a relate to molecules which are poorly characterized by the considered pK _a program. Of the seven most efficient diagnostic plots (the Williams graph, Graph of predicted residuals, Pregibon graph, Gray L–R graph, Index graph of Atkinson measure, Index graph of diagonal elements of the hat matrix and Rankit Q–Q graph of jackknife residuals) the Williams graph was selected to give the most reliable detection of outliers. The six statistical characteristics, F_exp,R²,R_P²,MEP,AIC{F_{\rm exp},R^{2},R_{\rm P}^{2},{\it MEP},{\it AIC}}, and s in pK _a units, successfully examine the specimen of 25 acids and bases of a Perrin’s data set classifying four pK _a prediction algorithms. The highest values F_exp,R²,R_P²{F_{\rm exp},R^{2},R_{\rm P}^{2}} and the lowest value of MEP and s and the most negative AIC have been found for PERRIN algorithm of pK _a prediction so this algorithm achieves the best predictive power and the most accurate results. The proposed accuracy test of the REGDIA program can also be extended to test other predicted values, as log P, log D, aqueous solubility or some physicochemical properties.     

Bleaching of solutions of chlorophylls <Emphasis Type=Italic>a</Emphasis> and <Emphasis Type=Italic>b</Emphasis> with blue and red light

The dependences of the reaction rate constant for bleaching of solutions of chlorophyll under the action of light with a wavelength of 434 and 670 on the type of solvent and additives (O₂, H₂O, HCl, and anthocyanins) have been studied.     

X-ray crystal structures of <Emphasis Type=Italic>p</Emphasis>-halogenated 6,6-diphenylfulvenes

Crystal structures of a series of p-halogenated 6,6-diphenylfulvenes 2–5 are reported and comparatively discussed including the known structure of the non-halogenate parent compound 1. The molecular structures show twisted conformations of the plane aryl and fulvene subunits against each other, rather unaffected by the different halogen substituents. The packing structures exclusively involve C–H···X (X = F, Cl, π) contacts while Hal···Hal and π-stacking interactions do not occur.