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.     

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.     

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     

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     

Conformation dependence of pKa’s of the chromophores from the purple asFP595 and yellow zFP538 fluorescent proteins

Two members of the green fluorescent protein family, the purple asFP595 and yellow zFP538 proteins, are perspective fluorescent markers for use in multicolor imaging and resonance energy-transfer applications. We report the results of quantum based calculations of the solution pK_a values for selected protonation sites of the denatured asFP595 and zFP538 chromophores in the trans- and cis-conformations in order to add in the interpretation of photo-physical properties of these proteins. The pK_a values were determined from the theromodynamic cycle based on B3LYP/6-311++G(2df, 2p) calculations of the gas phase free energies of the molecules and the B3LYP/6-311++G(d, p) calculations of solvation energies. The results show that the pK_a’s of the protonation sites of the chromophore from asFP595 noticeably depend on the isomer conformation (cis- or trans-), while those of zFP538 are much less sensitive to isomerization.     

Structure and stability of gold-substituted diborane, boranes, and borohydride ions

Pseudopotential ab initio calculations were performed for species of the type BH _n (AuPH₃) _m ^k , where n+m=3 or 4, and the charge k is −2,…,+1. Some derivatives of these and diaurated diboranes were also studied. The structural data agree well with the available experimental evidence. Factors affecting the stability of these systems, including the role of aurophilic attraction, are discussed. The singly charged anions and the diaurated diboranes are predicted to be the most stable members of these series. Received: 22 January 1999 / Accepted: 2 June 1999 / Published online: 4 October 1999     

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.     

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     

A thermodynamic and kinetic study of the formation of C<Subscript>20</Subscript> compounds encapsulating H,He and Ne atoms

 Binding energies of helium, neon and atomic hydrogen encapsulated inside a C₂₀ cage were calculated using an ab initio method at the B3LYP/6-31+G⋆ level of theory. The standard equilibrium constants for the reactions of noble-gas atoms going into the C₂₀ molecular cage have also been studied. The transition states for the reactions of C₂₀ with hydrogen and helium were further obtained with an ab initio method at the B3LYP/6-31+G⋆ level and the rate constants were estimated by using conventional transition-state theory. It was found that the hydrogen and helium atoms are extremely difficult to put into the C₂₀ cage. Once inside the cage, a helium atom can hardly get out, while a hydrogen atom can easily escape from the cage. The results are expected to enrich fullerene science and be helpful for fullerene applications such as storage. Received: 2 November 2002 / Accepted: 19 December 2002 / Published online: 30 April 2003 Correspondence to: R. Q. Zhang, e-mail: aprqz@cityu.edu.hk Acknowledgements. The work described in this paper was jointly supported by a grant from the City University of Hong Kong (project no. 7001222) and a grant from the Research Grants Council of the Hong Kong Special Administrative Region, China (project no. 9040633/CityU, 1011/01P].     

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.     

Role of twisting and sliding on the solvation of a stacked cytosine dimer: an ab initio study

Ab initio calculations with inclusion of correlation effects at the MP2/6-31G* level have been used to predict the interaction energy of stacked cytosine dimer (C/C) as a function of twisting and sliding in the gas phase. Systematic calculations have also been carried out on the solvation free energies of various rotated and translated C/C dimers using a polarized continuum model approach at the HF/6-31G* level with a view to probe the role of various degrees of freedom on the free energy of solvation of the C/C dimer. The interaction energy of the C/C dimer decreases upon changing from a parallel to an antiparallel conformation in the gas phase. The 180°-rotated conformation has been found to be the most stable arrangement when compared to other rotated positions. The rotated and translated dimers exhibit lower solvation free energy than the parallel conformation. The decrease in the dipole moment upon rotation from the parallel to the antiparallel conformation indicates the cancellation of charge distribution upon rotation in the z direction of one cytosine base with respect to the other. The calculation reveals that the present approach could not yield association energy, ΔΔG _Asso, in a solvent medium. This may be due to the fact that in the case of floppy molecules the contribution from translational, rotational and vibrational free energies plays a significant role in the calculation of ΔΔG _Asso. Received: 13 December 2001 / Accepted: 25 March 2002 / Published online: 13 June 2002     

Ab initio molecular orbital study of Fe(CO) n (n = 1–3)

Geometry optimization was performed for the ground states of FeCO, Fe(CO)₂, and Fe(CO)₃ at various levels of ab initio calculations, and the bond lengths and dissociation energies obtained were in reasonable agreement with experimental results. The nature of bonding was studied for these molecules using a complete-active-space self-consistent-field method. From the Mulliken population analysis, it was found that the traditional donation and back donation mechanism is valid for these molecules, including Fe(CO)₃, which has a pyramidal structure. Received: 27 September 1999 / Accepted: 13 January 2000 / Published online: 19 April 2000     

A small-core multiconfiguration Dirac–Hartree–Fock-adjusted pseudopotential for Tl – application to TlX (X = F, Cl, Br, I)

 A relativistic pseudopotential of the energy-consistent variety simulating the Tl²¹⁺ (1s– 4f) core has been generated by adjustment to multiconfiguration Dirac–Hartree–Fock data based on the Dirac–Coulomb–Breit Hamiltonian. Valence ab initio calculations using this pseudopotential have been performed for atomic excitation energies and for spectroscopic constants of the X0⁺ and A0⁺ states of TlX (X = F, Cl, Br, I). Comparison is made to experiment and to four-component density functional results. Received: 22 June 1999 / Accepted: 5 August 1999 / Published online: 15 December 1999     

Prediction of the Raman spectrum of the aqueous formate anion by a combined density functional theory and self-consistent-reaction-field study

Formate, HCOO⁻, is a small ion that can be used as a convenient model to represent general carboxylic acids as well as the terminal side chains of glutamic and aspartic amino acids in biological systems. Several ab initio techniques (Hartree–Fock and density functional theory methods) were used to study the formate anion in aqueous solution, where the solvent was treated as an electrostatic influence by means of a self-consistent-reaction-field (SCRF) method. The comparison of calculated frequencies with Raman experimental data constitutes a good test for the solvation model employed in this work. The results showed that the application of a SCRF method not only produced smaller errors but also improved the linear correlation between predicted and experimental values. This latter characteristic enables a more efficient application of a linear scaling factor, λ, which corrects the calculated frequencies. In fact, the application of λ to the values calculated for the continuum, when compared to those obtained for a vacuum, resulted in smaller root-mean-square errors of the deviations from the experimental data. Received: 15 May 2000 / Accepted: 19 June 2000 / Published online: 11 September 2000     

Diabatic and adiabatic potential-energy surfaces for azomethane photochemistry

We propose an analytic form to represent the intersecting potential energy surfaces (PES) of the first two singlet states of azomethane. The aim is to run semiclassical simulations of photochemical events such as fragmentation and isomerization. The PES are based on ab initio calculations and corrected on the basis of available experimental data. We resort to a quasi-diabatic representation, suitable to deal with the S₀-S₁ conical intersection and to include the essential information about electronic couplings in a 2 × 2 effective hamiltonian matrix. Received: 18 February 1999 / Accepted: 12 April 1999 / Published online: 14 July 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.     

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.     

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.     

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.     

Self-consistent reaction field calculation of solvent reorganization energy in electron transfer: a dipole-reaction field interaction model

Based on the continuum dielectric model, this work has established the relationship between the solvent reorganization energy of electron transfer (ET) and the equilibrium solvation free energy. The dipole-reaction field interaction model has been proposed to describe the electrostatic solute-solvent interaction. The self-consistent reaction field (SCRF) approach has been applied to the calculation of the solvent reorganization energy in self-exchange reactions. A series of redox couples, O₂/O⁻ ₂, NO/NO⁺, O₃/O⁻ ₃, N₃/N⁻ ₃, NO₂/NO⁺ ₂, CO₂/CO⁻ ₂, SO₂/SO⁻ ₂, and ClO₂/ClO⁻ ₂, as well as (CH₂)₂C-(-CH₂-) _n -C(CH₂)₂ (n=1 ∼ 3) model systems have been investigated using ab initio calculation. For these ET systems, solvent reorganization energies have been estimated. Comparisons between our single-sphere approximation and the Marcus two-sphere model have also been made. For the inner reorganization energies of inorganic redox couples, errors are found not larger than 15% when comparing our SCRF results with those obtained from the experimental estimation. While for the (CH₂)₂C–(–CH₂–) _n –C(CH₂)₂ (n=1 ∼ 3) systems, the results reveal that the solvent reorganization energy strongly depends on the bridge length due to the variation of the dipole moment of the ionic solute, and that solvent reorganization energies for different systems lead to slightly different two-sphere radii. Received: 19 April 2000 / Accepted: 6 July 2000 / Published online: 27 September 2000