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.     

Relative pKa of some anilinium derivatives in methanol,acetonitrile, and tetrahydrofurane solvents

In this study, the relative pK_a values of nine anilinium derivatives in methanol (MeOH), acetonitrile (AN), and tetrahydrofurane (THF) solutions were successfully calculated with mean absolute deviations of 0.63, 0.68, and 0.75 pK_a units, respectively. To this aim, their gas‐phase basicities were computed using the CBS‐QB3 composite method. Also, conductor‐like polarizable continuum model (CPCM) with UAHF, UAKS and UA0 cavities and SM8 solvation models at HF/6‐31+G(d) level of theory were applied for the calculation of the solvation Gibbs free energies. The obtained results indicate that there is reliable correlation between the experimental and computed pK_a values in the studied solutions. Therefore, to extend the pK_a database for anilines, correlation equations were used to predict the pK_a values in the investigated solvents.     

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.     

Thermodynamic cycle for the calculation of ab initio pKa values for hydroxamic acids

A thermodynamic cycle to calculate pK_a values (Minus log of acid dissociation constants) of hydroxamic acids is presented. Hydroxamic acids exist mainly as amide isomers in the aqueous medium. The amide form of hydroxamic acids has two deprotonation sites and may yield either an N-ion or an O-ion upon deprotonation. The thermodynamic cycle proposed includes the gas-phase N–H deprotonation of the hydroxamic acid, the solvent phase transformation of the N-ion to the O-ion and the solvation of the hydroxamic acid molecule and the O-ion in water. The CBS-QB3 method was employed to obtain gas-phase free energy differences between 12 hydroxamic acids and their respective anions. The aqueous solvation Gibbs free energy changes were calculated at the HF/6-31G(d)/CPCM and HF/6-31+G(d)/CPCM levels of theory using HF/6-31+G(d)/CPCM geometries. For the proton, literature values of the gas-phase free energy of formation and the solvation free energy change were used. The free energy change for the transformation of the N-ion to O-ion in the aqueous medium was calculated by employing CBS-QB3/CPCM in the aqueous medium. For this, the hydroxamic acids were divided in two classes according to the substituent at the carbonyl carbon. A common transformation free energy difference for aliphatic substituted hydroxamic acids and a separate common transformation free energy difference for aromatic substituted hydroxamic acids were obtained. The pK_a calculation yielded a root mean square error of 0.32 pK_a units.     

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.     

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     

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.     

Evaluation of DFT Methods and Implicit Solvation Models for Anion‐Binding Host‐Guest Systems

Although supramolecular chemistry is traditionally an experimental discipline, computations have emerged as important tools for the understanding of supramolecules. We have explored how well commonly used density functional theory quantum mechanics and polarizable continuum solvation models can calculate binding affinities of host‐guest systems. We report the calculation of binding affinities for eight host–guest complexes and compare our results to experimentally measured binding free energies that span the range from ?2.3 to ?6.1 kcal mol^?1. These systems consist of four hosts (biotin[6]uril, triphenoxymethane, cryptand, and bis‐thiourea) with different halide ions (F^?, Cl^?, Br^?) in various media including organic and aqueous. The mean average deviation (MAD) of calculated from measured ΔG_a is 2.5 kcal mol^?1 when using B3LYP‐D3 with either CPCM or PCM. This MAD value lowers even more by eliminating two outliers: 1.1 kcal mol^?1 for CPCM and 1.2 kcal mol^?1 for PCM. The best DFT and implicit solvation model combination that we have studied is B3LYP?D3 with either CPCM or PCM.     

The influence of hydrophobic amino acid side groups on the acidity of the aromatic imidazole ring of histidine: A theoretical study

In this study we have calculated the acidity constant (pKa) of imidazole ring in Histidine‐Hydrophobic amino acid dipeptides using the quantum chemistry and continuum solvation methods. Density functional theory calculations with the large basis sets are used to determine the Gibbs free energy of deprotonate in the gas and liquid phases. Based on our results ΔG_S values are located between ?69.38 and ?18.82 kcal mol^?1 which are related to His⁺–Gly and His forms, respectively. pKa of the dipeptides in the aqueous phase was obtained from the calculated gas‐phase and solvation free energies through a thermodynamic cycle and the solvation model chemistry of Martin Karplus et al. Solvation effects are treated using a self‐consistent reaction field formalism involving polarized continuum models. According to our calculations pKa values are between 5.50 and 8.19 that are belong to His⁺–ILe and His⁺–Ala forms, respectively. Natural bond orbital analysis of dipeptides reveals that the electron delocalization in imidazole ring is the most effective factor in determination of acidity order for these compounds. Structural analysis confirmed that the orientation of carbonyl group with respect to imidazole ring is an effective factor in imidazole ring stability. © 2011 Wiley Periodicals, Inc. Int J Quantum Chem, 2011     

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.     

Supramolecular Binding Thermodynamics by Dispersion‐Corrected Density Functional Theory

The equilibrium association free enthalpies ΔG_a for typical supramolecular complexes in solution are calculated by ab initio quantum chemical methods. Ten neutral and three positively charged complexes with experimental ΔG_a values in the range 0 to ?21 kcal mol^?1 (on average ?6 kcal mol^?1) are investigated. The theoretical approach employs a (nondynamic) single‐structure model, but computes the various energy terms accurately without any special empirical adjustments. Dispersion corrected density functional theory (DFT‐D3) with extended basis sets (triple‐ζ and quadruple‐ζ quality) is used to determine structures and gas‐phase interaction energies (ΔE), the COSMO‐RS continuum solvation model (based on DFT data) provides solvation free enthalpies and the remaining ro‐vibrational enthalpic/entropic contributions are obtained from harmonic frequency calculations. Low‐lying vibrational modes are treated by a free‐rotor approximation. The accurate account of London dispersion interactions is mandatory with contributions in the range ?5 to ?60 kcal mol^?1 (up to 200 % of ΔE). Inclusion of three‐body dispersion effects improves the results considerably. A semilocal (TPSS) and a hybrid density functional (PW6B95) have been tested. Although the ΔG_a values result as a sum of individually large terms with opposite sign (ΔE vs. solvation and entropy change), the approach provides unprecedented accuracy for ΔG_a values with errors of only 2 kcal mol^?1 on average. Relative affinities for different guests inside the same host are always obtained correctly. The procedure is suggested as a predictive tool in supramolecular chemistry and can be applied routinely to semirigid systems with 300–400 atoms. The various contributions to binding and enthalpy–entropy compensations are discussed.     

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     

Thermodynamic cycles and the calculation of pKa

A theoretical equation for the calculation of pK_a based on a proton transfer reaction between the acid and one water molecule is derived using the general chemical equilibrium relationship. The present result is compared with two equations recently used that were based on thermodynamic cycles, but predict different pK_a’s. It is shown that one thermodynamic cycle is wrong, and its better performance when compared with the correct cycle is due to an erroneous value used for the solvation free energy of the H₃O⁺ ion. In addition, this analysis indicates that the PCM-UAHF solvation model is inconsistently parametrized.     

SAMPL7 blind challenge: quantum–mechanical prediction of partition coefficients and acid dissociation constants for small drug-like molecules

The physicochemical properties of a drug molecule determine the therapeutic effectiveness of the drug. Thus, the development of fast and accurate theoretical approaches for the prediction of such properties is inevitable. The participation to the SAMPL7 challenge is based on the estimation of logP coefficients and pK_a values of small drug-like sulfonamide derivatives. Thereby, quantum mechanical calculations were carried out in order to calculate the free energy of solvation and the transfer energy of 22 drug-like compounds in different environments (water and n-octanol) by employing the SMD solvation model. For logP calculations, we studied eleven different methodologies to calculate the transfer free energies, the lowest RMSE value was obtained for the M06L/def2-TZVP//M06L/def2-SVP level of theory. On the other hand, we employed an isodesmic reaction scheme within the macro pK_a framework; this was based on selecting reference molecules similar to the SAMPL7 challenge molecules. Consequently, highly well correlated pK_a values were obtained with the M062X/6–311+G(2df,2p)//M052X/6–31+G(d,p) level of theory.

     

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     

Ligand‐Exchange Processes on Solvated Beryllium Cations. Part III

On the basis of DFT calculations (B3LYP/6‐311+G**), the possibility to include solvent effects is considered in the investigation of the H₂O‐exchange mechanism on [Be(H₂O)₄]²⁺ within the widely used cluster approach. The smallest system in the gas phase, [Be(H₂O)₄(H₂O)]²⁺, shows the highest activation barrier of +15.6 kcal/mol, whereas the explicit addition of five H‐bonded H₂O molecules in [{Be(H₂O)₄(H₂O)}(H₂O)₅]²⁺ reduces the barrier to +13.5 kcal/mol. Single‐point calculations applying CPCM (B3LYP(CPCM:H₂O)/6‐311+G**//B3LYP/6‐311+G**) on [Be(H₂O)₄(H₂O)]²⁺ lower the barrier to +9.6 kcal/mol. Optimization of the precursor and transition state of [Be(H₂O)₄(H₂O)]²⁺ within an implicit model (B3LYP(CPCM:H₂O)/6‐311+G** or B3LYP(PCM:H₂O)/6‐311+G**) reduces the activation energy further to +8.3 kcal/mol but does not lead to any local minimum for the precursor and is, therefore, unfavorable.     

Fluoro‐ and Perfluoralkylsulfonylpentafluoroanilides: Synthesis and Characterization of NH Acids for Weakly Coordinating Anions and Their Gas‐Phase and Solution Acidities

Fluoro‐ and perfluoralkylsulfonyl pentafluoroanilides [HN(C₆F₅)(SO₂X); X=F, CF₃, C₄F₉, C₈F₁₇] are a class of imides with two different strongly electron‐withdrawing substituents attached to a nitrogen atom. They are NH acids, the unsymmetrical hybrids of the well‐known symmetrical bissulfonylimides and bispentafluorophenylamine. The syntheses, the structures of these perfluoroanilides, their solvates, and some selected lithium salts give rise to a structural variety beyond the symmetrical parent compounds. The acidities of representative subsets of these novel NH acids have been investigated experimentally and quantum‐chemically and their gas‐phase acidities (GAs) are reported, as well as the pK_a values of these compounds in acetonitrile (MeCN) and DMSO solution. In quantum chemical investigations with the vertical and relaxed COSMO cluster‐continuum models (vCCC/rCCC), the unusual situation is encountered that the DMSO‐solvated acid Me₂SO–H‐N(SO₂CF₃)₂, optimized in the gas phase (vCCC model), dissociates to Me₂SO‐H⁺–N(SO₂CF₃)₂^? during structural relaxation and full optimization with the solvation model turned on (rCCC model). This proton transfer underlines the extremely high acidity of HN(SO₂CF₃)₂. The importance of this effect is studied computationally in DMSO and MeCN solution. Usually this effect is less pronounced in MeCN and is of higher importance in the more basic solvent DMSO. Nevertheless, the neglect of the structural relaxation upon solvation causes typical changes in the computational pK_a values of 1 to 4 orders of magnitude (4–20 kJ mol^?1). The results provide evidence that the published experimental DMSO pK_a value of HN(SO₂CF₃)₂ should rather be interpreted as the pK_a of a Me₂SO‐H⁺–N(SO₂CF₃)₂^? contact ion pair.     

Effect of Preferential Solvation on the Thermodynamic Properties of Antidepressant Drug Trazodone in Aqueous Ethanol: Linear Free‐Energy Relationships

Dissociation constants (pK_a) of trazodone hydrochloride (TZD⋅HCl) in EtOH/H₂O media containing 0, 10, 20, 30, 40, 50, 60, 70, and 80% (v/v) EtOH at 288.15, 298.15, 308.15, and 318.15 K were determined by potentiometric techniques. At any temperature, pK_a decreased as the solvent was enriched with EtOH. The dissociation and transfer thermodynamic parameters were calculated, and the results showed that a non‐spontaneous free‐energy change (Δ_dissG^o>0) and unfavorable enthalpy (Δ_dissH^o>0) and entropy (Δ_dissS^o<0) changes occurred on dissociation of trazodone hydrochloride. The free‐energy change or pK_a varied nonlinearly with the reciprocal dielectric constant, indicating the inadequacy of the electrostatic approach. The dissociation equilibria are discussed on the basis of the standard thermodynamics of transfer, solvent basicity, and solute‐solvent interactions. The values of Δ_transG^o and Δ_transH^o increased negatively with increasing EtOH content, revealing a favorable transfer of trazodone hydrochloride from H₂O to EtOH/H₂O mixtures and preferential solvation of H⁺ and trazodone (TZD). Also, Δ_transS^o values were negative and reached a minimum, in the H₂O‐rich zone that has frequently been related to the initial promotion and subsequent collapse of the lattice structure of water. The pK_a or Δ_dissG^o values correlated well with the Dimroth‐Reichardt polarity parameter E_T(30), indicating that the physicochemical properties of the solute in binary H₂O/organic solvent mixtures are better correlated with a microscopic parameter than the macroscopic one. Also, it is suggested that preferential solvation plays a significant role in influencing the solvent dependence of dissociation of trazodone hydrochloride. The solute‐solvent interactions were clarified on the basis of the linear free‐energy relationships of Kamlet and Taft. The best multiparametric fit to the Kamlet‐Taft equation was evaluated for each thermodynamic parameter. Therefore, these parameters in any EtOH/H₂O mixture up to 80% were accurately derived by means of the obtained equations.     

Proton-donating power of 100% perchloric acid: An MP2 study

The ab initio quantum chemical method MP2 with a 6-311++G(d, p) basis set is used to calculate the energy of gas-phase solvation of the H₂Cl₄⁺ cation and Cl₄⁻ anion by one perchloric acid molecule. The energy of additional solvation of the resulting complexes by liquid perchloric acid is estimated within the continuum model of solvation by the PCM method, with the acid modeled as a continuum with a large dielectric constant of ɛ = 115. The calculated data have provided an almost quantitative estimate for the energy of selfionization of 100% liquid perchloric acid. The similarly calculated energy of solvation of protons by 100% perchloric acid is 30.7 kcal/mol lower than the heat of hydration of protons in aqueous solution. This result explains the fact that anhydrous perchloric acid exhibits the properties of a superacid.     

Using polarizable POSSIM force field and fuzzy‐border continuum solvent model to calculate pKa shifts of protein residues

Our Fuzzy‐Border (FB) continuum solvent model has been extended and modified to produce hydration parameters for small molecules using POlarizable Simulations Second‐order Interaction Model (POSSIM) framework with an average error of 0.136 kcal/mol. It was then used to compute pK _a shifts for carboxylic and basic residues of the turkey ovomucoid third domain (OMTKY3) protein. The average unsigned errors in the acid and base pK _a values were 0.37 and 0.4 pH units, respectively, versus 0.58 and 0.7 pH units as calculated with a previous version of polarizable protein force field and Poisson Boltzmann continuum solvent. This POSSIM/FB result is produced with explicit refitting of the hydration parameters to the pK _a values of the carboxylic and basic residues of the OMTKY3 protein; thus, the values of the acidity constants can be viewed as additional fitting target data. In addition to calculating pK _a shifts for the OMTKY3 residues, we have studied aspartic acid residues of Rnase Sa. This was done without any further refitting of the parameters and agreement with the experimental pK _a values is within an average unsigned error of 0.65 pH units. This result included the Asp79 residue that is buried and thus has a high experimental pK _a value of 7.37 units. Thus, the presented model is capable or reproducing pK _a results for residues in an environment that is significantly different from the solvated protein surface used in the fitting. Therefore, the POSSIM force field and the FB continuum solvent parameters have been demonstrated to be sufficiently robust and transferable. © 2016 Wiley Periodicals, Inc.