First principles pKa calculations on carboxylic acids using the SMD solvation model: effect of thermodynamic cycle, model chemistry, and explicit solvent molecules

Mechanisms of hydrogen evolution by six-coordinate cobalt complexes: a density functional study on the role of a redox-active pyridinyl-substituted diaminotriazine benzamidine ligand as a proton relay

The hydrogen evolution reaction is an important process for energy storage. The six-coordinate cobalt complex [CoIII(L1-)(LH)]2+ (LH = N-(4-amino-6-(pyridin-2-yl)-1,3,5-triazin-2-yl)benzamidine) was found to catalyze photocatalytic hydrogen evolution. In this work, we performed density functional calculations to obtain the reduction potentials and the proton-transfer free energy of possible intermediates to determine the preferred pathways for proton reduction. The mechanism involves the metal-based reduction of Co(III) to Co(II) before the protonation at the amidinate N on the pyridinyl-substituted diaminotriazine benzamidinate ligand L1- to form [CoII(LH)(LH)]2+. Essentially, the subsequent electron transfer is not metal-based reduction, but rather ligand-based reduction to form [CoII(LH)(LH˙1-)]1+. Through a proton-coupled electron transfer process, the cobalt hydride [CoIIH(LH)(LH2˙)]1+ is formed as the key intermediate for hydrogen evolution. As the cobalt hydride complex is coordinatively saturated, a structural change is required when the hydride on Co is coupled with the proton on pyridine. Notably, the redox-active nature of the ligand results in the low acidity of the protonated pyridine moiety of LH2˙, which impedes its function as a proton relay. Our findings suggest that separating the proton relay fragment from the electron reservoir fragment of the redox-active ligand is preferred for fully utilizing both features in catalytic H2 evolution.

Advantages of Multidimensional Biasing in Accelerated Dynamics: Application to the Calculation of the Acid pKa for Acetic Acid

The use of accelerated sampling methods such as metadynamics has shown a significant advantage in calculations that involve infrequent events, which would otherwise require sampling a prohibitive number of configurations to determine the difference in free energies between two or more chemically distinct states such as in the calculation of acid dissociation constants Ka. In this case, the most common method is to bias the system via a single collective variable (CV) representing the coordination number of the proton donor group, which yields results in reasonable agreement with experiments. Here we study the deprotonation of acetic acid using the reactive force field ReaxFF and observe a significant dependence of Ka on the simulation box size when biasing only the coordination number CV, which is due to incomplete sampling of the deprotonated state for small simulation systems and inefficient sampling for larger ones. Incorporating a second CV representing the distance between the H3O+ cation and the acetate anion results in substantially more efficient sampling, both accelerating the dynamics and virtually eliminating the computational box size dependence.

Investigation of substituent effect on O–C bond dissociation enthalpy of methoxy group in meta- and para-substituted anisoles

This paper is focused on the theoretical investigation of O-C Bond Dissociation Enthalpy (BDE) of methoxy OCH₃ group in 15 meta- and 15 para-substituted anisoles in gas phase, non-polar environment, and water. Density Functional Theory (DFT) calculations were carried out using M06-2X functional and 6-311++G(d,p) basis set. Obtained BDEs were correlated with Brown and Okamoto σ_p⁺ and Hammett σ_m constants representing commonly used descriptors of electron-donating or electron-withdrawing substituent effect. Obtained linear dependences allow the prediction of substituent effect on BDE using σ_p⁺ and σ_m constants. Calculated reaction enthalpies were also compared with available experimental and theoretical ab initio G4 values. Found results suggest that employed method may provide reliable thermochemistry data for demethylation of naturally occurring (poly)phenolic compounds, as well. In all studied environments, substituent induced changes in O-C BDE can be considered equal to those observed for the dissociation of phenolic O-H bond of substituted phenols.

Inverse Electron-Demanding Diels-Alder Reactions in the Chemical Synthesis of Prenylated Indole Alkaloids Containing a Bicycle[2.2.2]diazaoctane Moiety: A Theoretical Study

The Diels-Alder reaction is believed to be a key step in the biosynthesis of prenylated indole alkaloids containing a bicycle[2.2.2]diazaoctane moiety. Many chemical syntheses of bicyclic structures by Diels-Alder reactions have been reported, but the reaction mechanism remains underexplored. We have carried out DFT calculations on both acid- and base-promoted Diels-Alder reactions in these syntheses and reveal that the reactions occur through an inverse-electron demand mechanism. We hope that the new mechanism is helpful for the mechanistic understanding of the biosynthesis of this class of important natural products.

Molecular design of redox carriers for electrochemical CO2 capture and concentration

Developing improved methods for CO₂ capture and concentration (CCC) is essential to mitigating the impact of our current emissions and can lead to carbon net negative technologies. Electrochemical approaches for CCC can achieve much higher theoretical efficiencies compared to the thermal methods that have been more commonly pursued. The use of redox carriers, or molecular species that can bind and release CO₂ depending on their oxidation state, is an increasingly popular approach as carrier properties can be tailored for different applications. The key requirements for stable and efficient redox carriers are discussed in the context of chemical scaling relationships and operational conditions. Computational and experimental approaches towards developing redox carriers with optimal properties are also described.

Mechanism of iron complexes catalyzed in the N-formylation of amines with CO2 and H2: the superior performance of N-H ligand methylated complexes

CO2 hydrogenation into value-added chemicals not only offer an economically beneficial outlet but also help reduce the emission of greenhouse gases. Herein, the density functional theory (DFT) studies have been carried out on CO2 hydrogenation reaction for formamide production catalyzed by two different N-H ligand types of PNP iron catalysts. The results suggest that the whole mechanistic pathway has three parts: (i) precatalyst activation, (ii) hydrogenation of CO2 to generate formic acid (HCOOH), and (iii) amine thermal condensation to formamide with HCOOH. The lower turnover number (TON) of a bifunctional catalyst system in hydrogenating CO2 may attribute to the facile side-reaction between CO2 and bifunctional catalyst, which inhibits the generation of active species. Regarding the bifunctional catalyst system addressed in this work, we proposed a ligand participated mechanism due to the low pKa of the ligand N-H functional in the associated stage in the catalytic cycle. Remarkably, catalysts without the N-H ligand exhibit the significant transfer hydrogenation through the metal centered mechanism. Due to the excellent catalytic nature of the N-H ligand methylated catalyst, the N-H bond was not necessary for stabilizing the intermediate. Therefore, we confirmed that N-H ligand methylated catalysts allow for an efficient CO2 hydrogenation reaction compared to the bifunctional catalysts. Furthermore, the influence of Lewis acid and strong base on catalytic N-formylation were considered. Both significantly impact the catalytic performance. Moreover, the catalytic activity of PNMeP-based Mn, Fe and Ru complexes for CO2 hydrogenation to formamides was explored as well. The energetic span of Fe and Mn catalysts are much closer to the precious metal Ru, which indicates that such non-precious metal catalysts have potentially valuable applications.

Nuclear quantum effects on autoionization of water isotopologs studied by ab initio path integral molecular dynamics

In this study, we investigate the nuclear quantum effects (NQEs) on the acidity constant (pK_A) of liquid water isotopologs under the ambient condition by path integral molecular dynamics (PIMD) simulations. We compared simulations using a fully explicit solvent model with a classical polarizable force field, density functional tight binding, and ab initio density functional theory, which correspond to empirical, semiempirical, and ab initio PIMD simulations, respectively. The centroid variable with respect to the proton coordination number of a water molecule was restrained to compute the gradient of the free energy, which measures the reversible work of the proton abstraction for the quantum mechanical system. The free energy curve obtained by thermodynamic integration was used to compute the pK_A value based on probabilistic determination. This technique not only reproduces the pK_A value of liquid D₂O experimentally measured (14.86) but also allows for a theoretical prediction of the pK_A values of liquid T₂O and aqueous HDO and HTO, which are unknown due to their scarcity. It is also shown that the NQEs on the free energy curve can result in a downshift of 4.5 ± 0.9 pK_A units in the case of liquid water, which indicates that the NQEs plays an indispensable role in the absolute determination of pK_A. The results of this study can help inform further extensions into the calculation of the acidity constants of isotope substituted species with high accuracy.

On the Accuracy of the Direct Method to Calculate pKa from Electronic Structure Calculations

The direct method (HA_(soln) ⇌ A_(soln)^– + H_(soln)⁺) for calculating pK_a of monoprotic acids is as efficient as thermodynamic cycles. A selective adjustment of proton free energy in solution was used with experimental pK_a data. The procedure was analyzed at different levels of theory. The solvent was described by the solvation model density (SMD) model, including or not explicit water molecules, and three training sets were tested. The best performance under any condition was obtained by the G4CEP method with a mean absolute error close to 0.5 units of pK_a and an uncertainty around ±1 unit of pK_a for any training set including or excluding explicit solvent molecules. PM6 and AM1 performed very well with average absolute errors below 0.75 units of pK_a but with uncertainties up to ±2 units of pK_a, using only the SMD solvent model. Density functional theory (DFT) results were highly dependent on the basis functions and explicit water molecules. The best performance was observed for the local spin density approximation (LSDA) functional in almost all calculations and under certain conditions, as high as those obtained by G4CEP. Basis set complexity and explicit solvent molecules were important factors to control DFT calculations. The training set molecules should consider the diversity of compounds.

Development of a New Borax-Based Formulation for the Removal of Pyrite Scales

In the oil and gas industry, pyrite forms one of the most hardened scales in reservoirs, which hinders the flow of fluids. Consequently, this leads to blockage of the downhole tubular, formation damage, and complete shutdown of production and operational processes. Herein, a new green formulation based on borax (K2B4O7) is proposed for pyrite scale removal. The temperature effect, disk rotational speed, and borax concentration have been investigated using a rotating disk apparatus. Also, XPS and SEM-EDX analyses were conducted on the pyrite disk surface before and after the treatment with the green formulation. The new formulation showed the potential ability to dissolve pyrite without generating the toxic hydrogen sulfide (H2S). The dissolution rate of the scale in the new formulation is increased by 16% compared to that in a previous green formulation composed of 20 wt %DTPA+9 wt % K2CO3. Molecular modeling technique using DFT was used to study the solvation energies of Fe2+ and Fe3+. The latter had a higher solvation energy than the former, which confirmed that upon using the borax-based formulation to oxidize Fe2+ to Fe3+. It will aid the dissolution of pyrite scales. The new formulation achieved a corrosion rate that is 25 times lower than that of 15 wt % HCl, which is commercially used in treating scales. Finally, the proposed new formulation does not require the use of corrosion inhibitors; hence, it is expected to result in a more economical scale treatment method.

Chemical Equilibrium of Zinc Acetate Complexes in Ethanol Solution. A Theoretical Description through Thermodynamic Cycles

The Gibbs free energy of complexation between the Zn(II) species and acetate ligands, forming the [Zn(OAc)_n]^2-n complexes with n = 1, 2 in an ethanol solution, was assessed by two different theoretical protocols based on thermodynamic cycles. In both approaches, the solution phase Gibbs free energy of each reaction is computed by summing up contributions from gas phase thermochemistry calculations to solvation Gibbs free energies obtained in a hybrid fashion, i.e., each (neutral or electrically charged) solute was first solvated by explicit solvent molecules in order to capture relevant (micro) solute-solvent and/or solvent-solvent interactions and then, a continuum model calculation is performed in order to get the corresponding bulky solute-solvent contributions. For our first thermodynamic protocol, here denominated as variant 1, a set of x independent solvent molecules are used to screen each of the involved solutes, while the variant 2 strategy uses the fact that a set of solvent molecules may exist as aggregates (or molecular clusters) in the solvent macroscopic media, before the solvation process of solutes. Our selected quantum theoretical protocol was the M05-2X/6-31+G(d)/SMD level. We made a systematic exploration about the influence of several sources of errors, such as the solvent conformation, the number of solvent molecules used to screen each of the involved solutes, the coordination geometry of the metallic center before and after the complexation process, and the pertinence of using molecular geometries optimized in gas phase and in ethanol solution, for the computation of the Gibbs free energy variation regarding the two chemical reactions under study. We set an accuracy threshold equal or less than 4.0 kcal·mol^-1, with respect to the corresponding experimental records. The robustness of our thermodynamic strategies was then tested by computing the gas phase free energy contributions to the (solution phase) reaction free energies here assessed, using different density functional approximations, namely the M05-2X, BH&HLYP, PBE0, ωb97X-D and M06-2X functionals in conjunction with the larger 6-311+G(d,p) basis set.

Hydrogen-Deuterium Exchange in Basic Near-Critical and Supercritical Media: An Experimental and Theoretical Study

Treatment of homo- and heterocyclic aromatic substrates with basic deuterium oxide under near- or supercritical conditions results in rapid base-catalyzed hydrogen-deuterium exchange (HDE) in aromatic and benzylic positions. It has been postulated that HDE follows a simple deprotonation-reprotonation mechanism, but little evidence has been provided to date. This study correlates experimentally observed proton exchanges in n-butylbenzene with ab initio calculations of the acidities and potential energy (PE) profiles. In addition to providing further support for carbanion intermediacy in HDE, these results offer new insights into substrate acidities in near- and supercritical aqueous media and the optimal conditions required for their isotope exchange.

Density Functional Calculations for Aqueous Silver Clusters Containing Water and Nitrate Ligands

The incorporation of a nitrate ion into silver-water aqueous clusters has been examined using PBE0 density functional theory with the solvent model density (SMD) solvation model. The Gibbs free energy of solvation and other thermodynamic variables are calculated using the harmonic/rigid rotor/ideal gas model at 298.15 K for aqueous solutes including the effects of solute relaxation in water and with London dispersive forces at the D3 level. Free energies of solvation for Ag⁺ and NO₃^- were found to agree well with experimental values of -118.2 and -60.1 kcal/mol, respectively, calculated using cluster-continuum models with six to eight water molecules and including solute relaxation and London D3 dispersive interactions. An analysis of data of varying cluster size upon calculated free energy is presented. A direct procedure is applied to aqueous clusters such as Ag_n^z(NO₃^-)(H₂O)₅, Ag_n^z(H₂O)₅, and (NO₃^-)(H₂O)₆ n = 1-4; z = 0, +1 in the SMD solvent representation to calculate equilibrium constants for nitrate association with silver clusters in solution that includes fully relaxed solutes. The equilibrium structures of the nitrate-containing clusters involve one or more bonds from nitrate oxygen to positive silver clusters. Water molecules interact with nitrate through H atoms, and overall, the structure represents a silver nitrate cluster with water ligands having similarity to a close ion pair in many aspects. The neutral silver atom is attached to nitrate through H-bonded water molecules. The ratio of nitrate-containing silver clusters to nitrate-free clusters using a calculated equilibrium constant of 0.51 L/mol for Ag⁺ is small in the range of many experiments. Similar values are found for positive silver clusters up to four atoms in size. The resulting procedures were applied to aqueous clusters of Ag_n(NO₃)_m^+(n-m) that have been previously experimentally studied for silver reduction in aqueous solution. A chain-like structure with collinear and bidentate oxygen bonds to silver was found, and the equilibrium constants for clustering were determined. A simplified model calculation for the reduction of Ag(H₂O)₆⁺ clusters in the presence of silver clusters in aqueous media was studied to understand catalytic effects observed in these systems. The reduction potentials vary with silver cluster size indicating a more favorable reduction caused by the presence of larger silver clusters.

Prediction of Aqueous pK a Values for Guanidine-Containing Compounds Using Ab Initio Gas-Phase Equilibrium Bond Lengths

In this work, we demonstrate the existence of linear relationships between gas-phase equilibrium bond lengths of the guanidine skeleton of 2-(arylamino)imidazolines and their aqueous pK _a value. For a training set of 22 compounds, in the most stable conformation of their lowest energy tautomeric form, three bonds were found to exhibit r ² and q ² values >0.95 and root-mean-squared-error of estimation values ≤0.25 when regressed individually against pK _a. The equations describing these one-bond-length linear relationships, in addition to a multiple linear regression model using all three bond lengths, were then used to predict the experimental pK _a values of an external test set of further 27 derivatives. The optimal protocol we derive here shows an overall mean absolute error (MAE) of 0.20 and standard deviation of errors of 0.18 for the test set. Predictions for a second test set of diphenyl-based bis(2-iminoimidazolidines) yielded an MAE of 0.27 and a standard deviation of 0.10. The predictive power of the optimal model is further demonstrated by its ability to correct erroneously reported experimental values. Finally, a previously established guanidine model is recalibrated at a new level of theory, and predictions are made for novel phenylguanidine derivatives, showing an MAE of just 0.29. The protocols established and tested here pass both of Roy's modern and stringent MAE-based criteria for a "good" quantitative structure-activity relationship/quantitative structure-property relationship model predictivity. Notably, the ab initio bond length high correlation subset protocol developed in this work demonstrates lower MAE values than the Marvin program by ChemAxon for all test sets.

Concerning the mechanism of iodine(iii)-mediated oxidative dearomatization of phenols

The iodine(iii)-mediated oxidative dearomatization of phenols has proven to be a general method for the preparation of cyclohexadienones. While this is a widely used reaction, there is still a great deal of uncertainty regarding the mechanistic pathway followed by these reactions. In part, this is due to the highly unstable nature of many of the key intermediates, which makes their direct detection extremely difficult. In order to gain some insight into these mechanistic questions, DFT calculations [M06-2X/6-31+G(d) for C, H, and O and LANL2DZdp for iodine] were used to evaluate the two most commonly proposed reaction mechanisms. These results show that unimolecular fragmentation of an oxygen-bound intermediate to give a phenoxenium ion (TS1) is preferred over direct addition of the nucleophile to the aromatic ring of the activated phenol (TS3). In addition, results are presented that suggest protonation and/or hydrogen bonding may play a key role in lowering the energy of the unimolecular fragmentation pathway.

An efficient protocol for computing the pKa of Zn-bound water

We present an efficient and accurate method for computing absolute pK_w values in Zn²⁺ complexes.

Acidity Constant (pKa ) Calculation of Large Solvated Dye Molecules: Evaluation of Two Advanced Molecular Dynamics Methods

pH‐Sensitive dyes are increasingly applied on polymer substrates for the creation of novel sensor materials. Recently, these dye molecules were modified to form a covalent bond with the polymer host. This had a large influence on the pH‐sensitive properties, in particular on the acidity constant (pK_a). Obtaining molecular control over the factors that influence the pK_a value is mandatory for the future intelligent design of sensor materials. Herein, we show that advanced molecular dynamics (MD) methods have reached the level at which the pK_a values of large solvated dye molecules can be predicted with high accuracy. Two MD methods were used in this work: steered or restrained MD and the insertion/deletion scheme. Both were first calibrated on a set of phenol derivatives and afterwards applied to the dye molecule bromothymol blue. Excellent agreement with experimental values was obtained, which opens perspectives for using these methods for designing dye molecules.

Calculations of the Energetics of Oxidation of Aqueous Nucleosides and the Effects of Prototropic Equilibria

Recently the calculated standard reduction potentials of the radical-cations of N-methyl substituted DNA bases have been reported that agree fairly well with the experimental results. However, there are issues reflecting the fact that the experimental results usually relate to the couple E(o)(Nuc(•),H(+)/NucH(+)), whereas the calculated results are for the E(o)(Nuc(•+)/Nuc) couple. To calculate the midpoint reduction potential at pH 7 (Em7), it is important to have accurate acid dissociation constants (pKs) for both ground-state bases and their radicals, and the effects of uncertainty in some of these values (e.g., that of the adenosine radical) must be considered. Calculations of the pKs of the radicals of the nucleic acid bases (as nucleosides) have been performed to explore the effects the various pKs have on calculating the values of Em7 and to see what improvements can be made with the accuracy of the calculations.

Density functional theory investigations on the binding modes of amidoximes with uranyl ions

η¹-O of tautomerized amidoximes and η¹-O/η²-N–O of anionic amidoximes are all plausible coordination modes for amidoximes in ligating uranyl ions.

Modeling the antisymmetric and symmetric stretching vibrational modes of aqueous carboxylate anions

The infrared spectra of six aqueous carboxylate anions have been calculated at the M05-2X/cc-pVTZ level of theory with the SMD solvent model, and validated against experimental data from the literature over the region of 1700 cm(-1) to 1250 cm(-1); this region corresponds to the stretching modes of the carboxylate group, and is often interrogated when probing bonding of carboxylates to other species and surfaces. The anions studied here were formate, acetate, oxalate, succinate, glutarate and citrate. For the lowest energy conformer of each anion, the carboxylate moiety antisymmetric stretching peak was predicted with a mean signed error of only 4 cm(-1) using the SMD solvent model, while the symmetric peak was slightly overestimated. Performing calculations in vacuum and scaling was found to generally over-predict the antisymmetric vibrational frequencies and under predict the symmetric peak. Different conformers of the same anion were found to have only slightly different spectra in the studied region and the inclusion of explicit water molecules was not found to significantly change the calculated spectra when the implicit solvent model is used. Overall, the use of density functional theory in conjunction with an implicit solvent model was found to result in infra-red spectra that are the best reproduction of the features found experimentally for the aqueous carboxylate ions in the important 1700 cm(-1) to 1250 cm(-1) region. The development of validated model chemistries for simulating the stretching modes of aqueous carboxylate ions will be valuable for future studies that investigate how carboxylate anions complex with multivalent metal cations and related species in solution.

Synthesis of endoperoxides by domino reactions of ketones and molecular oxygen

Domino reactions of ketones with molecular oxygen in the presence of potassium hydroxide and potassiumt-butoxide afford cyclic hydroperoxy acetals (3,5-dihydroxy-1,2-dioxanes).

Solvation and protonation of coumarin 102 in aqueous media: a fluorescence spectroscopic and theoretical study

The ground- and excited-state protonation of Coumarin 102 (C102), a fluorescent probe applied frequently in heterogeneous systems with an aqueous phase, has been studied in aqueous solutions by spectroscopic experiments and theoretical calculations. For the dissociation constant of the protonated form in the ground state, pKa = 1.61 was obtained from the absorption spectra; for the excited-state dissociation constant, pKa* = 2.19 was obtained from the fluorescence spectra. These values were closely reproduced by theoretical calculations via a thermodynamic cycle (the value of pKa* also by calculations via the Förster cycle) using an implicit–explicit solvation model (polarized continuum model + addition of a solvent molecule). The theoretical calculations indicated that (i) in the ground state, C102 occurs primarily as a hydrogen-bonded water complex, with the oxo group as the binding site, (ii) this hydrogen bond becomes stronger upon excitation, and (iii) in the ground state, the amino nitrogen atom is the protonation site, and in the excited state, the carboxy oxygen atom is the protonation site. A comprehensive analysis of fluorescence decay data yielded the values kpr = 3.27 × 10(10) M(–1) s(–1) for the rate constant of the excited-state protonation and kdpr = 2.78 × 10(8) s(–1) for the rate constant of the reverse process (kpr and kdpr were treated as independent parameters). This, considering the relatively long fluorescence lifetimes of neutral C102 (6.02 ns) and its protonated form (3.06 ns) in aqueous media, means that a quasi-equilibrium state of excited-state proton transfer is reached in strongly acidic solutions.

Solv-ccCA: Implicit Solvation and the Correlation Consistent Composite Approach for the Determination of pKa

Direct theoretical methods are advantageous for the prediction of pKa, as relative methods rely upon the experimental values of reference acid molecules that can limit application of the method to well-characterized systems. Here, a direct route is introduced, which incorporates the SMD universal solvation model1 within the correlation consistent Composite Approach (ccCA). This Solv-ccCA methodology has been used for the prediction of theoretical pKa values for nitrogen-containing species to within a mean absolute deviation (MAD) of 1.0 pKa unit from experimental values by utilizing a thermodynamic cycle that combines gas-phase and solution-phase calculations. Several density functionals, including B3LYP, B97-1, B97-2, B98, BMK, M06, and M06-2X, were also evaluated for use with SMD and for comparison to Solv-ccCA.

Lipophilicity assessment of ruthenium(II)-arene complexes by the means of reversed-phase thin-layer chromatography and DFT calculations

The lipophilicity of ten ruthenium(II)-arene complexes was assessed by reversed-phase thin-layer chromatography (RP-TLC) on octadecyl silica stationary phase. The binary solvent systems composed of water and acetonitrile were used as mobile phase in order to determine chromatographic descriptors for lipophilicity estimation. Octanol-water partition coefficient, logK_OW, of tested complexes was experimentally determined using twenty-eight standard solutes which were analyzed under the same chromatographic conditions as target substances. In addition, ab initio density functional theory (DFT) computational approach was employed to calculate logK_OW values from the differences in Gibbs' free solvation energies of the solute transfer from n-octanol to water. A good overall agreement between DFT calculated and experimentally determined logK_OW values was established (R² = 0.8024–0.9658).

Predicting pKa in Implicit Solvents: Current Status and Future Directions

Computational prediction of condensed phase acidity is a topic of much interest in the field today. We introduce the methods available for predicting gas phase acidity and pKas in aqueous and non-aqueous solvents including high-level electronic structure methods, empirical linear free energy relationships (LFERs), implicit solvent methods, explicit solvent statistical free energy methods, and hybrid implicit–explicit approaches. The focus of this paper is on implicit solvent methods, and we review recent developments including new electronic structure methods, cluster-continuum schemes for calculating ionic solvation free energies, as well as address issues relating to the choice of proton solvation free energy to use with implicit solvation models, and whether thermodynamic cycles are necessary for the computation of pKas. A comparison of the scope and accuracy of implicit solvent methods with ab initio molecular dynamics free energy methods is also presented. The present status of the theory and future directions are outlined.