G4CEP: A G4 theory modification by including pseudopotential for molecules containing first-, second- and third-row representative elements

New Insights in the Computational pKb Determination of Primary Amines and Anilines

Extensive research has already provided reliable methods for the in silico prediction of pKa, while a trustworthy strategy for pKb determination is still being sought. Indeed, the approaches previously exploited for computing pKa have shown their weakness in predicting pKb. In the light of the exceptional reliability demonstrated in the pKa calculation of a wide panel of organic acids, in this work, we exploited our "easy to use methodology", based on the direct approach, to predict the pKb of primary amines. Herein, CAM-B3LYP was compared to WB97XD and B3PW91, exploring the solvation model based on density (SMD) and the polarizable continuum model (PCM), in the presence of two explicit water molecules. Noteworthy, CAM-B3LYP and WB97XD returned completely different solvent accessible surfaces (SAS) and electron potential maps (EPM) for the bases and the conjugated acids, independently from the nature of the substituents. Once again, CAM-B3LYP/SMD/2H2O method confirmed its remarkable reliability, leading to a minimum average error (MAE) lower than 0.3. This outstanding result strengthens the trustworthiness of our method, already successfully applied to predict the pKa of different substituted phenols and carboxylic acids. Thus, our "easy-to-use" process can predict also the pKb of primary ammines and anilines, always ensuring consistent outputs.

Easy to Use DFT Approach for Computational pKa Determination of Carboxylic Acids

In pKa computational determination, the challenge in exploring and fostering new methodologies and approaches goes in parallel with the amelioration of computational performances. In this paper a "ready to use methodology" has been compared to other strategies, such as the re-shaping in solvation cavity (Bondi radius re-shaping), wanting to assess its reliability in predicting the pKa of a broad list of carboxylic acids. Thus, the functionals B3LYP and CAM-B3LYP have been selected, using SMD as continuum solvation model. Exploiting our previous results, two water molecules were made explicit on the reaction centre. Data show that our model (CAM-B3LYP/2H2 O) is capable to accurately predict pKa, leading to mean absolute error (MAE) values lower than 0.5. Noteworthy, good results were achieved in computing the pKa of substituents bearing nitro and cyano groups. Focusing on B3LYP, eventually remarkable outputs were obtained only when Bondi correction was applied to the complex with two water molecules. Hence, massive outcomes were obtained in foreseeing the trichloro and trifluoro acetic acid pKa. These findings demonstrated that no complex level of theory nor external factor is required to accurately predict carboxylic acids pKa, with MAE well below 0.5 units.

Brueckner Doubles variation of W1 theory (W1BD) adapted to pseudopotential: W1BDCEP theory

Composite methods are the combination of ab initio calculations used to achieve high precision in the face of a computational reduction. Weizmann-n theories (n = 1, 2, 3, and 4) stand out for presenting a high precision, and a version of the W1 theory is the W1BD theory that uses ab initio Brueckner Doubles (BD) methods. One way to reduce the computational cost of composite methods and maintain accuracy is to use pseudopotentials in the calculation steps; in this context, W1BDCEP composite method was developed from the respective W1BD all-electron version by considering the implementation of compact effective pseudopotential (CEP). The test set used to evaluate the theory were 8 proton affinities (PA₀), 46 electron affinities (EA₀), 54 ionization energies (IE₀), 80 enthalpies of formation (Δ_fH⁰), and 10 bond dissociation energies (BDE). The mean absolute deviation values (MADs) for W1BD and for the version adapted to the pseudopotential, W1BDCEP, were similar, with values of 0.97 kcal mol^-1 and 1.03 kcal mol^-1, respectively, when the properties PA₀, EA₀, IE₀, and Δ_fH⁰ were evaluated together. Comparing the versions of the theories that employ ab initio Brueckner Doubles calculations with the W1 and W1CEP theories, it is possible to observe that the W1BD and W1BDCEP theories are more accurate than the W1 theory (MAD_W1 = 1.25 kcal mol^-1) and W1CEP (MAD_W1CEP = 1.44 kcal mol^-1), proving the accuracy of using the BD method. Pseudopotential reduces computational time by up to 30% and thus enables more accurate calculations with less computational time.

Determination of the standard enthalpy of formation of iodine compounds through the G2 and G3(MP2)//B3-SBK theories

The domain of application of the G3(MP2)//B3-SBK theory was expanded, and its efficiency was evaluated to determinate enthalpies of formation of forty-one iodine compounds. The results were compared to those obtained with the G2 theory for the same set of molecules. The G3(MP2)//B3-SBK theory showed a mean deviation and deviation standard equal to 3.7 kcal mol^-1 and 6.0 kcal mol^-1, respectively. The G2 theory (mean deviation = 3.1 kcal mol^-1 and standard deviation = 4.9 kcal mol^-1) presented a lower error and standard deviation, but at a significantly higher computational cost. For a more complete evaluation, as a secondary part of the work, it also used different functionals B3LYP, M06-2X, WB97XD, and MP2 method with four different basis sets 6-311G(d,p), LANL2DZ, jorge-ADZP, and CEP-31G(d). The best density functional/basis set combination was obtained with M06-2X/CEP-31G(d) among the three mentioned functionals. However, the produced mean deviation is significant and equal to 17.3 kcal mol^-1, with a standard deviation equal to 23.0 kcal mol^-1. The 6-311G(d,p) basis achieved the best performance with the MP2 method, generating an equally significant mean deviation of 12.8 kcal mol^-1 with a standard deviation equal to 18.7 kcal mol^-1.

Systematic Convergence of the Numerical Taylor Series to the Best Standard and Its Potential Implication for the Development of Composite Methods

The numerical Taylor series is used as an alternative to systematically converge to a high-level calculation showing that it has the potential to be used in the development of composite methods. Five methods are tested, with two of them differing in the truncation of the series expansion and basis sets, namely, Taylor-Dunning and Taylor-Pople, and three of the interpretations of the G4, ccCA-TZ, and CBS-QB3, which are referred to as G4-Taylor, ccCA-TZ-Taylor, and CBS-QB3-Taylor, respectively. The Taylor-Dunning and Taylor-Pople methods restricted to second-order expansion show mean absolute errors of 1.16 and 1.11 kcal mol^-1, respectively, for a training set involving enthalpies of formation, ionization energies, and electronic affinities. The G4-Taylor, ccCA-TZ-Taylor, and CBS-QB3-Taylor methods achieve the lowest mean absolute errors of 0.96, 1.54, and 0.58 kcal mol^-1, respectively. The CBS-QB3-Taylor method is submitted to a validation step. The method using either forward or backward derivatives achieves a mean absolute error of 0.82 kcal mol^-1. These results show that the numerical Taylor series and possibly other series expansions can be applied systematically for the development of accurate alternatives for composite methods.

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.

Assessment of pKa Determination for Monocarboxylic Acids with an Accurate Theoretical Composite Method: G4CEP

For 22 monoprotic acids, pK_a values were calculated using the G4CEP composite theory. The solvation effect was included considering the continuous SMD solvation model; SMD and one explicit water molecule; and SMD, one water molecule, and linear correction with respect to the experimental pK_a values. The three tests provided mean absolute errors equal to 0.83, 0.51, and 0.30 pK_a units, respectively, indicating excellent performance of the G4CEP method. Comparison with density functional theory at the B3LYP and BMK levels showed that these results are quickly obtained but with a significant error. The best performance of the functionals was obtained from the combination of SMD, one explicit water molecule, linear regression correction, and basis set including diffuse functions. However, the dispersion of the results with DFT can lead to deviations of up to two pK_a units, whereas for G4CEP the largest deviations seldom exceed one pK_a unit.

Partial combination of composite strategy and the B3LYP functional for the calculation of enthalpies of formation

The B3LYP functional was re-optimized using partially composite methods for the calculation of standard enthalpies of formation. Two initial methods (B3LYP-MCM1 and B3LYP-MCM2) differing in the type and number of optimized parameters were analyzed using B3LYP/6-31 + G(2df,p) as the reference energy. For the first method (B3LYP-MCM1), the exchange-correlation and higher-level correction parameters (HLC) were optimized and for the second method (B3LYP-MCM2), in addition to the previous parameters, scaling of the basis functions responsible for large errors in the enthalpy of formation were also optimized. The best parameters were also used as adapted functionals generating two other methods referred to as: B3LYP-MF1 and B3LYP-MF2. The best-performing results (B3LYP-MCM2 and B3LYP-MF2) presented mean absolute errors near 2.3 kcal mol^-1 for the G3/05 test set. This is a significant improvement when compared with the respective results from B3LYP/6-31 + G(2df,p), which yielded a mean absolute error of 5.3 kcal mol^-1. The errors were larger for B3LYP-MCM1 (4.17 kcal mol^-1) and B3LYP-MF1 (3.98 kcal mol^-1). The scaling of the experimental atomization energies used for the calculation of enthalpy of formation was also tested for all four methods. This empirical adjustment reduced the errors to 2 kcal mol^-1. The uncertainty of the best results with 95% confidence tended to be ± 5.5 kcal mol^-1. Substantial improvements were associated with the basis set adjustments.