Main Group Thermochemistry Research Articles

A remarkably simple dispersion damping scheme and the DH24 double hybrid density functional.

In recent papers, Becke et al. [J. Chem. Phys. 158, 151103 (2023)] and then Becke [J. Chem. Phys. 159, 241101 (2023)] have developed a novel double hybrid density functional, "DH23," whose terms are based on good local physics. Its 12 coefficients are trained on the GMTKN55 (general main-group thermochemistry, kinetics, and noncovalent interactions) chemical database of Goerigk et al. [Phys. Chem. Chem. Phys. 19, 32184 (2017)]. The lowest GMTKN55 "WTMAD2" error to date for any hybrid or double hybrid density functional was obtained (1.73 kcal/mol for the revDH23 variant). Here, we simplify DH23 by introducing a dispersion damping scheme involving atomic numbers only and one global parameter. The resulting new functional, "DH24," performs as well as its predecessors.

Doubling down on density-functional theory.

In a recent paper, Becke et al. [J. Chem. Phys. 158, 151103 (2023)] presented a novel double hybrid density functional, "DH23," whose terms are based on good physics. Its 12 coefficients were trained on the GMTKN55 (general main-group thermochemistry, kinetics, and noncovalent interactions) chemical database of Goerigk et al. [Phys. Chem. Chem. Phys. 19, 32184 (2017)]. The lowest GMTKN55 "WTMAD2" error to date for any hybrid or double hybrid density functional was obtained (1.76 kcal/mol). Here, we make some revisions to DH23 and test its efficacy on reference data beyond GMTKN55, namely, organometallic reaction energies and barrier heights. The results confirm that DH23 is robust outside its training set. In the process, a slightly smaller GMTKN55 WTMAD2 of 1.73 kcal/mol is achieved.

Dispersion-corrected r2SCAN based double-hybrid functionals

The regularized and restored semi-local meta-generalized gradient approximation (meta-GGA) exchange–correlation functional r2SCAN [Furness et al., J. Phys. Chem. Lett. 11, 8208–8215 (2020)] is used to create adiabatic-connection-derived global double-hybrid functionals employing spin-opposite-scaled MP2. The 0-DH, CIDH, QIDH, and 0–2 type double-hybrid functionals are assessed as a starting point for further modification. Variants with 50% and 69% Hartree–Fock exchange (HFX) are empirically optimized (Pr2SCAN50 and Pr2SCAN69), and the effect of MP2-regularization (κPr2SCAN50) and range-separated HFX (ωPr2SCAN50) is evaluated. All optimized functionals are combined with the state-of-the-art London dispersion corrections D4 and NL. The resulting functionals are assessed comprehensively for their performance on main-group and metal-organic thermochemistry on 90 different benchmark sets containing 25 800 data points. These include the extensive GMTKN55 database, additional sets for main-group chemistry, and multiple sets for transition-metal complexes, including the ROST61, the MOR41, and the MOBH35 sets. As the main target of this study is the development of a broadly applicable, robust functional with low empiricism, special focus is put on variants with moderate amounts of HFX (50%), which are compared to the so far successful PWPB95-D4 (50% HFX, 20% MP2 correlation) functional. The overall best variant, ωPr2SCAN50-D4, performs well on main-group and metal-organic thermochemistry, followed by Pr2SCAN69-D4 that offers a slight edge for metal-organic thermochemistry and by the low HFX global double-hybrid Pr2SCAN50-D4 that performs robustly across all tested sets. All four optimized functionals, Pr2SCAN69-D4, Pr2SCAN50-D4, κPr2SCAN50-D4, and ωPr2SCAN50-D4, outperform the PWPB95-D4 functional.

Short-range screened density matrix functional for proper descriptions of thermochemistry, thermochemical kinetics, nonbonded interactions, and singlet diradicals.

Common one-electron reduced density matrix (1-RDM) functionals that depend on Coulomb and exchange-only integrals tend to underestimate dynamic correlation, preventing reduced density matrix functional theory (RDMFT) from achieving comparable accuracy to density functional theory in main-group thermochemistry and thermochemical kinetics. The recently developed ωP22 functional introduces a semi-local density functional to screen the erroneous short-range portion of 1-RDM functionals without double-counting correlation, potentially providing a better treatment of dynamic correlation around equilibrium geometries. Herein, we systematically evaluate the performance of this functional model, which consists of two parameters, on main-group thermochemistry, thermochemical kinetics, nonbonded interactions, and more. Tests on atomization energies, vibrational frequencies, and reaction barriers reveal that the ωP22 functional model can reliably predict properties at equilibrium and slightly away from equilibrium geometries. In particular, it outperforms commonly used density functionals in the prediction of reaction barriers, nonbonded interactions, and singlet diradicals, thus enhancing the predictive power of RDMFT for routine calculations of thermochemistry and thermochemical kinetics around equilibrium geometries. Further development is needed in the future to refine short- and long-range approximations in the functional model in order to achieve an excellent description of properties both near and far from equilibrium geometries.

A double-hybrid density functional based on good local physics with outstanding performance on the GMTKN55 database.

In two recent papers [A. D. Becke, J. Chem. Phys. 156, 214101 (2022) and A. D. Becke, J. Chem. Phys. 157, 234102 (2022)], we compared two Kohn-Sham density functionals based on physical modeling and theory with the best density-functional power-series fits in the literature. The best error statistics reported to date for a hybrid functional on the general main-group thermochemistry, kinetics, and noncovalent interactions (GMTKN55) chemical database of Goerigk et al. [Phys. Chem. Chem. Phys. 19, 32184 (2017)] were obtained. In the present work, additional second-order perturbation-theory terms are considered. The result is a 12-parameter double-hybrid density functional with the lowest GMTKN55 WTMAD2 "weighted total mean absolute deviation" error (1.76 kcal/mol) yet seen for any hybrid or double-hybrid density-functional approximation. We call it "DH23."

Density-functional theory vs density-functional fits: The best of both.

In a recent paper [A. D. Becke, J. Chem. Phys. 156, 214101 (2022)], we compared two Kohn-Sham density functionals based on physical modeling and theory with the best density-functional power series fits in the literature. With only a handful of physically motivated pre-factors, our functionals matched, and even slightly exceeded, the performance of the best power-series functionals on the general main group thermochemistry, kinetics, and noncovalent interactions (GMTKN55) chemical database of Goerigk et al. [Phys. Chem. Chem. Phys. 19, 32184 (2017)]. This begs the question: how much can their performance be improved by adding power-series terms of our own? We address this question in the present work. First, we describe a series expansion variable that we believe contains more local physics than any other variable considered to date. Then we undertake modest, one-dimensional fits to the GMTKN55 data with our theory-based functional corrected by power-series exchange and dynamical correlation terms. We settle on 12 power-series terms (plus six parent terms) and achieve the lowest GMTKN55 "WTMAD2" error yet reported, by a substantial margin, for a hybrid Kohn-Sham density functional. The new functional is called "B22plus."

Explicitly Correlated Double-Hybrid DFT: A Comprehensive Analysis of the Basis Set Convergence on the GMTKN55 Database.

Double-hybrid density functional theory (DHDFT) offers a pathway to accuracy approaching composite wavefunction approaches such as G4 theory. However, the Görling–Levy second-order perturbation theory (GLPT2) term causes them to partially inherit the slow ∝L–3 (with L the maximum angular momentum) basis set convergence of correlated wavefunction methods. This could potentially be remedied by introducing F12 explicit correlation: we investigate the basis set convergence of both DHDFT and DHDFT-F12 (where GLPT2 is replaced by GLPT2-F12) for the large and chemically diverse general main-group thermochemistry, kinetics, and noncovalent interactions (GMTKN55) benchmark suite. The B2GP-PLYP-D3(BJ) and revDSD-PBEP86-D4 DHDFs are investigated as test cases, together with orbital basis sets as large as aug-cc-pV5Z and F12 basis sets as large as cc-pVQZ-F12. We show that F12 greatly accelerates basis set convergence of DHDFs, to the point that even the modest cc-pVDZ-F12 basis set is closer to the basis set limit than cc-pV(Q+d)Z or def2-QZVPPD in orbital-based approaches, and in fact comparable in quality to cc-pV(5+d)Z. Somewhat surprisingly, aug-cc-pVDZ-F12 is not required even for the anionic subsets. In conclusion, DHDF-F12/VDZ-F12 eliminates concerns about basis set convergence in both the development and applications of double-hybrid functionals. Mass storage and I/O bottlenecks for larger systems can be circumvented by localized pair natural orbital approximations, which also exhibit much gentler system size scaling.

Revisiting the Orbital Energy-Dependent Regularization of Orbital-Optimized Second-Order Møller-Plesset Theory.

Optimizing orbitals in the presence of electron correlation, as in orbital-optimized second-order Møller-Plesset perturbation theory (OOMP2), can remove artifacts associated with mean-field orbitals such as spin contamination and artificial symmetry-breaking. However, OOMP2 is known to suffer from divergent correlation energies in regimes of small orbital energy gaps. To address this issue, several approaches to amplitude regularization have been explored, with those featuring energy-gap-dependent regularizers appearing to be most transferable and physically justifiable. For instance, κ-OOMP2 was shown to address the energy divergence issue in, for example, bond-breaking processes while offering a significant improvement in accuracy for the W4-11 thermochemistry data set, and a parameter of κ = 1.45 was recommended. A more recent investigation of regularized MP2 with Hartree-Fock orbitals revealed that stronger regularization (i.e., smaller values of κ) than what had previously been recommended for κ-OOMP2 may offer huge improvements in certain cases such as noncovalent interactions while retaining a high level of accuracy for main-group thermochemistry data sets. In this study, we investigate the transferability of those findings to κ-OOMP2 and assess the implications of stronger regularization on the ability of κ-OOMP2 to diagnose strong static correlation. We found similar results using κ-OOMP2 for several main-group thermochemistry, barrier height, and noncovalent interaction data sets including both closed shell and open shell species. However, stronger regularization yielded substantially higher accuracy for open-shell transition-metal (TM) thermochemistry and is necessary to provide qualitatively correct spin symmetry breaking behavior for several large and electrochemically relevant TM systems. We therefore find a single κ value insufficient to treat all systems using κ-OOMP2.

Dispersion corrected r2SCAN based global hybrid functionals: r2SCANh, r2SCAN0, and r2SCAN50.

The regularized and restored semilocal meta-generalized gradient approximation (meta-GGA) exchange-correlation functional r2SCAN [Furness et al., J. Phys. Chem. Lett. 11, 8208-8215 (2020)] is used to create three global hybrid functionals with varying admixtures of Hartree-Fock "exact" exchange (HFX). The resulting functionals r2SCANh (10% HFX), r2SCAN0 (25% HFX), and r2SCAN50 (50% HFX) are combined with the semi-classical D4 London dispersion correction. The new functionals are assessed for the calculation of molecular geometries, main-group, and metalorganic thermochemistry at 26 comprehensive benchmark sets. These include the extensive GMTKN55 database, ROST61, and IONPI19 sets. It is shown that a moderate admixture of HFX leads to relative improvements of the mean absolute deviations for thermochemistry of 11% (r2SCANh-D4), 16% (r2SCAN0-D4), and 1% (r2SCAN50-D4) compared to the parental semi-local meta-GGA. For organometallic reaction energies and barriers, r2SCAN0-D4 yields an even larger mean improvement of 35%. The computation of structural parameters (geometry optimization) does not systematically profit from the HFX admixture. Overall, the best variant r2SCAN0-D4 performs well for both main-group and organometallic thermochemistry and is better or on par with well-established global hybrid functionals, such as PW6B95-D4 or PBE0-D4. Regarding systems prone to self-interaction errors (SIE4x4), r2SCAN0-D4 shows reasonable performance, reaching the quality of the range-separated ωB97X-V functional. Accordingly, r2SCAN0-D4 in combination with a sufficiently converged basis set [def2-QZVP(P)] represents a robust and reliable choice for general use in the calculation of thermochemical properties of both main-group and organometallic chemistry.

Density functionals with full nonlocal exchange, nonlocal rung-3.5 correlation, and D3 dispersion: Combined accuracy for general main-group thermochemistry, kinetics, and noncovalent interactions.

We introduce the HF-R35-D3(BJ) functional combining full nonlocal exact (Hartree-Fock-like, HF) exchange, inexpensive rung-3.5 correlation constructed from nonlocal one-electron operators, and nonlocal D3 dispersion corrections. HF-R35-D3(BJ) is among the first full-exact-exchange functionals offering competitive accuracy for general main-group thermochemistry, kinetics, and noncovalent interactions. HF-R35-D3(BJ) gives weighted mean absolute deviation WTMAD-2 8.5kcal/mol across the entire GMTKN55 dataset, outperforming most dispersion-corrected semilocal functionals and approaching the accuracy of dispersion-corrected global hybrids. This requires six fitted parameters, three each in the nonlocal correlation and dispersion corrections. Full nonlocal exchange appears to help give accurate binding energies and reasonable energy orderings for water hexamers. These results motivate continued exploration of inexpensive nonlocal correlation corrections to nonlocal exchange.

Analysis of Recent BLYP- and PBE-Based Range-Separated Double-Hybrid Density Functional Approximations for Main-Group Thermochemistry, Kinetics, and Noncovalent Interactions.

We investigate the effects of range separation of the exchange energy on electronic ground-state properties for recently published double-hybrid density functionals (DHDFs) with the extensive GMTKN55 database for general main-group thermochemistry, kinetics, and noncovalent interactions. We include the semiempirical range-separated DHDFs ωB2PLYP and ωB2GP-PLYP developed by our group for excitation energies, together with their ground-state-parametrized variants, which we denote herein as ωB2PLYP18 and ωB2GP-PLYP18. We also include the nonempirical range-separated DHDFs RSX-0DH and RSX-QIDH. For all six DHDFs, damping parameters for the DFT-D3 dispersion correction (and for its DFT-D4 variant) are presented. We comment on when the range-separated functionals can be more beneficial than their global counterparts and conclude that range separation alone is no guarantee for overall improved results. We observe that the BLYP-based functionals generally outperform the PBE-based functionals. We finally note that the best-performing DHDFs for GMTKN55 are still the semiempirical range-separated double hybrids ωDSD3-PBEP86-D4 and ωDSD72-PBEP86-D4, the former of which includes a third-order perturbative correlation term in addition to the more conventional second-order perturbation that DHDFs are based upon.

R2SCAN-D4: Dispersion corrected meta-generalized gradient approximation for general chemical applications.

We combine a regularized variant of the strongly constrained and appropriately normed semilocal density functional [J. Sun, A. Ruzsinszky, and J. P. Perdew, Phys. Rev. Lett. 115, 036402 (2015)] with the latest generation semi-classical London dispersion correction. The resulting density functional approximation r2SCAN-D4 has the speed of generalized gradient approximations while approaching the accuracy of hybrid functionals for general chemical applications. We demonstrate its numerical robustness in real-life settings and benchmark molecular geometries, general main group and organo-metallic thermochemistry, and non-covalent interactions in supramolecular complexes and molecular crystals. Main group and transition metal bond lengths have errors of just 0.8%, which is competitive with hybrid functionals for main group molecules and outperforms them for transition metal complexes. The weighted mean absolute deviation (WTMAD2) on the large GMTKN55 database of chemical properties is exceptionally small at 7.5 kcal/mol. This also holds for metal organic reactions with an MAD of 3.3 kcal/mol. The versatile applicability to organic and metal-organic systems transfers to condensed systems, where lattice energies of molecular crystals are within the chemical accuracy (errors <1 kcal/mol).

Assessing the Applicability of the Geometric Counterpoise Correction in B2PLYP/Double-ζ Calculations for Thermochemistry, Kinetics, and Noncovalent Interactions

We present a proof-of-concept study of the suitability of Kruse and Grimme’s geometric counterpoise correction (gCP) for basis set superposition errors (BSSEs) in double-hybrid density functional calculations with a double-ζ basis set. The gCP approach only requires geometrical information as an input and no orbital/density information is needed. Therefore, this correction is practically free of any additional cost. gCP is trained against the Boys and Bernardi counterpoise correction across a set of 528 noncovalently bound dimers. We investigate the suitability of the approach for the B2PLYP/def2-SVP level of theory, and reveal error compensation effects—missing London dispersion and the BSSE—associated with B2PLYP/def2-SVP calculations, and present B2PLYP-gCP-D3(BJ)/def2-SVP with the reparametrised DFT-D3(BJ) and gCP corrections as a more balanced alternative. Benchmarking results on the S66x8 benchmark set for noncovalent interactions and the GMTKN55 database for main-group thermochemistry, kinetics, and noncovalent interactions show a statistical improvement of the B2PLYP-gCP-D3(BJ) scheme over plain B2PLYP and B2PLYP-D3(BJ). B2PLYP-D3(BJ) shows significant overestimation of interaction energies, barrier heights with larger deviations from the reference values, and wrong relative stabilities in conformers, all of which can be associated with BSSE. We find that the gCP-corrected method represents a significant improvement over B2PLYP-D3(BJ), particularly for intramolecular noncovalent interactions. These findings encourage future developments of efficient double-hybrid DFT strategies that can be applied when double-hybrid calculations with large basis sets are not feasible due to system size.

A range-separated generalized Kohn-Sham method including a long-range nonlocal random phase approximation correlation potential.

Based on our recently published range-separated random phase approximation (RPA) functional [Kreppel et al., "Range-separated density-functional theory in combination with the random phase approximation: An accuracy benchmark," J. Chem. Theory Comput. 16, 2985-2994 (2020)], we introduce self-consistent minimization with respect to the one-particle density matrix. In contrast to the range-separated RPA methods presented so far, the new method includes a long-range nonlocal RPA correlation potential in the orbital optimization process, making it a full-featured variational generalized Kohn-Sham (GKS) method. The new method not only improves upon all other tested RPA schemes including the standard post-GKS range-separated RPA for the investigated test cases covering general main group thermochemistry, kinetics, and noncovalent interactions but also significantly outperforms the popular G0W0 method in estimating the ionization potentials and fundamental gaps considered in this work using the eigenvalue spectra obtained from the GKS Hamiltonian.

Range-Separated Density-Functional Theory in Combination with the Random Phase Approximation: An Accuracy Benchmark.

A formulation of range-separated random phase approximation (RPA) based on our efficient ω-CDGD-RI-RPA [J. Chem. Theory Comput. 2018, 14, 2505] method and a large scale benchmark study are presented. By application to the GMTKN55 data set, we obtain a comprehensive picture of the performance of range-separated RPA in general main group thermochemistry, kinetics, and noncovalent interactions. The results show that range-separated RPA performs stably over the broad range of molecular chemistry included in the GMTKN55 set. It improves significantly over semilocal DFT but it is still less accurate than modern dispersion corrected double-hybrid functionals. Furthermore, range-separated RPA shows a faster basis set convergence compared to standard full-range RPA making it a promising applicable approach with only one empirical parameter.

M11plus, a Range-Separated Hybrid Meta Functional Incorporating Nonlocal Rung-3.5 Correlation, Exhibits Broad Accuracy on Diverse Databases.

We present tests of the recent M11plus Minnesota density functional for a broad range of main-group and transition-metal chemistry databases, most of which were not used in in the construction of any of the Minnesota functionals. M11plus is a range-separated hybrid meta functional combining long-range nonlocal Hartree-Fock exchange with nonlocal rung-3.5 correlation. M11plus performs well for main-group thermochemistry, kinetics, and noncovalent interactions and especially well for radical species. It is numerically well behaved, it has a computational cost that is ∼1.2 to 1.5 times that of M11 in realistic calculations, and it is particularly accurate for triplet excited states, which is a difficult challenge for density functional approximations. The results show that nonlocal rung-3.5 correlation is a broadly useful ingredient for improving the performance of density functional approximations.

Domain-based local pair natural orbital methods within the correlation consistent composite approach.

Ab initio composite approaches have been utilized to model and predict main group thermochemistry within 1 kcal mol-1 , on average, from well-established reliable experiments, primarily for molecules with less than 30 atoms. For molecules of increasing size and complexity, such as biomolecular complexes, composite methodologies have been limited in their application. Therefore, the domain-based local pair natural orbital (DLPNO) methods have been implemented within the correlation consistent composite approach (ccCA) framework, namely DLPNO-ccCA, to reduce the computational cost (disk space, CPU (central processing unit) time, memory) and predict energetic properties such as enthalpies of formation, noncovalent interactions, and conformation energies for organic biomolecular complexes including one of the largest molecules examined via composite strategies, within 1 kcal mol-1 , after calibration with 119 molecules and a set of linear alkanes. © 2019 Wiley Periodicals, Inc.

Qsar Analysis of the Estrogen Activities of Bisphenol a Analogs using Multiple Linear Regression and Artificial Neural Network

Abstract. This study gives a quantitative structure-activity relationship (QSAR) analysis of the estrogen activities of bisphenol A and analogs. The chemical structures of 23 Bisphenol A analogs have been characterized by quantum-electronic descriptors. The present study was performed using multiple regression analysis (MLR) and artificial neural network (ANN). The quantitative model was accordingly proposed and the toxicity of the compounds was interpreted based on the multivariate statistical analysis. This study shows that the results obtained by MLR were suitable and have served to predict estrogen activities, but compared to the results of the ANN model, we conclude that the prediction achieved by the latter is more effective and better than MLR model. Following to the obtained results, our proposed model may be useful to predict of Estrogen activities and risk assessment of chemicals.&#x0D; Keywords&#x0D; QSAR, Bisphenol A, multiple linear regression, artificial neural network&#x0D; References&#x0D; [1] Rezg R, El-Fazaa S, Gharbi N, Mornagui B (March 2014). "Bisphenol A and human chronic diseases: Current evidences, possible mechanisms, and future perspectives".Environment International 2014, 64, 83–90. [2] Melzer D, Rice NE, Lewis C, Henley WE, Galloway TS (2010). Zhang, Baohong, ed."Association of Urinary Bisphenol a Concentration with Heart Disease: Evidence from NHANES 2003/06". PLoS ONE 5 (1). [3] Manikkam, M.; Tracey, R.; Guerrero-Bosagna, C.; Skinner, M. K. (January 24, 2013). "Plastics derived endocrine disruptors (BPA, DEHP and DBP) induce epigenetic transgenerational inheritance of obesity, reproductive disease and sperm epimutations".PLoS ONE 8 (1). 1–16. [4] D.R. Doerge, N.C. Twaddle, M. Vanlandingham, R.P. Brown, J.W. Fisher, Toxicol. Appl. Pharmacol. 2011, 255, 261.[5] Ho SM, Tang WY, Belmonte de Frausto J, Prins GS (2006). "Developmental exposure to estradiol and bisphenol A increases susceptibility to prostate carcinogenesis and epigenetically regulates phosphodiesterase type 4 variant 4". Cancer Res. 66 (11): 5624–32. [6] Johanna R. Rochester and Ashley L. Bolden (2015 Jul) “Bisphenol S and F: A Systematic Review and Comparison of the Hormonal Activity of Bisphenol A Substitutes”. Environ Health Perspect123(7):643-50.[7] Kelly, P. C., William, A. T., Thomas, E. W., QSAR models of thein vitro estrogen activity of bisphenol A analogs, QSAR Comb.Sci., 2003, 22: 78―88.[8]. Frisch, M. J. T., G. W. et al , Gaussian 09, Revision D.01. Gaussian, Inc., Wallingford CT, 2009.[9]. Zhao, Y.; Truhlar, D., The M06 suite of density functionals for main group thermochemistry, thermochemical kinetics, noncovalent interactions, excited states, and transition elements: two new functionals and systematic testing of four M06-class functionals and 12 other functionals. Theor Chem[10] J. Devillers (1996), Strengths and Weaknesses of the Backpropagation Neural Network in QSAR and QSPR Studies, in: J. Devillers (Ed.) Neural Networks in QSAR and Drug Design, Academic Press, London, pp.1-46.[11] K. Hornik (1991), AppSroximation capabilities of multilayer feedforward networks, Neural Networks, 4 251-257.[12] A. Adad, M. Larif, R. Hmamouchi, M. Bouachrine, T. Lakhlifi, J. Comp. Meth. Mol. Des. 4(3) (2014) 72-83.[13] A. Golbraikh, A. Tropsha, Beware of q2. J. Mol. Graphics Model. 20 (2002) 269–276.&#x0D;

The Nonlocal Kernel in van der Waals Density Functionals as an Additive Correction: An Extensive Analysis with Special Emphasis on the B97M-V and ωB97M-V Approaches.

The development of van der Waals density functional approximations (vdW-DFAs) has gained considerable interest over the past decade. While in a strictest sense, energy calculations with vdW-DFAs should be carried out fully self-consistently, we demonstrate conclusively for a total of 11 methods that such a strategy only increases the computational time effort without having any significant effect on energetic properties, electron densities, or orbital-energy differences. The strategy to apply a nonlocal vdW-DFA kernel as an additive correction to a fully converged conventional DFA result is therefore justified and more efficient. As part of our study, we utilize the extensive GMTKN55 database for general main-group thermochemistry, kinetics, and noncovalent interactions [ Phys. Chem. Chem. Phys. 2017, 19, 32184], which allows us to analyze the very promising B97M-V [ J. Chem. Phys. 2015, 142, 074111] and ωB97M-V [ J. Chem. Phys. 2016, 144, 214110] DFAs. We also present new DFT-D3(BJ) based counterparts of these two methods and of ωB97X-V [ J. Chem. Theory Comput 2013, 9, 263], which are faster variants with similar accuracy. Our study concludes with updated recommendations for the general method user, based on our current overview of 325 dispersion-corrected and -uncorrected DFA variants analyzed for GMTKN55. vdW-DFAs are the best representatives of the three highest rungs of Jacob's Ladder, namely, B97M-V, ωB97M-V, and DSD-PBEP86-NL.

A Quantitative Structure – Activity Relationship Study on the Estrogen Activities of Bisphenol a Analogs using Computational Chemistry Methods and Multiple Linear Regression Technique

This article presents the results of the QSAR study of bisphenol A and its analogs. Molecular-chemical analysis of these substances is performed on base of the Density Functional Theory (DFT), using the function 6-31 + G *. The calculation of the characteristic parameters of the structure is given by optimizing molecular structures, vibrational frequencies, the molecular orbital energies with reasonable accuracy. The obtained quantum parameters and known observable activities are used as input data for constructing the QSAR model, using the classical data processing method in statistical mathematics - the multivariable linear regression.&#x0D; The constructed model QSAR has R2&gt; 0,9; and . The statistical parameters show that the model, constructing by method of multiple linear regression using the parameters of quantum chemistry can be used as a predictive model of the activity of estrogens for unexplored derivatives and BPA analogs with moderate reliability.&#x0D; Keywords&#x0D; Bisphenol A, Estrogen, Density Functional Theory, M06 hybridmeta - GGA functional, Quantitative structure – activity relationship, Multiple linear regression&#x0D; References&#x0D; Rezg R, El-Fazaa S, Gharbi N, Mornagui B (March 2014). "Bisphenol A and human chronic diseases: Current evidences, possible mechanisms, and future perspectives".Environment International 2014, 64, 83–90. [2] Melzer D, Rice NE, Lewis C, Henley WE, Galloway TS (2010). Zhang, Baohong, ed."Association of Urinary Bisphenol a Concentration with Heart Disease: Evidence from NHANES 2003/06". PLoS ONE 5 (1). [3] Manikkam, M.; Tracey, R.; Guerrero-Bosagna, C.; Skinner, M. K. (January 24, 2013). "Plastics derived endocrine disruptors (BPA, DEHP and DBP) induce epigenetic transgenerational inheritance of obesity, reproductive disease and sperm epimutations".PLoS ONE 8 (1). 1–16. [4] D.R. Doerge, N.C. Twaddle, M. Vanlandingham, R.P. Brown, J.W. Fisher, Toxicol. Appl. Pharmacol. 2011, 255, 261.[5] Ho SM, Tang WY, Belmonte de Frausto J, Prins GS (2006). "Developmental exposure to estradiol and bisphenol A increases susceptibility to prostate carcinogenesis and epigenetically regulates phosphodiesterase type 4 variant 4". Cancer Res. 66 (11): 5624–32. [6] Johanna R. Rochester and Ashley L. Bolden (2015 Jul) “Bisphenol S and F: A Systematic Review and Comparison of the Hormonal Activity of Bisphenol A Substitutes”. Environ Health Perspect123(7):643-50.[7] Kelly, P. C., William, A. T., Thomas, E. W., QSAR models of thein vitro estrogen activity of bisphenol A analogs, QSAR Comb.Sci., 2003, 22: 78―88.[8]. Frisch, M. J. T., G. W. et al , Gaussian 09, Revision D.01. Gaussian, Inc., Wallingford CT, 2009.[9]. Zhao, Y.; Truhlar, D., The M06 suite of density functionals for main group thermochemistry, thermochemical kinetics, noncovalent interactions, excited states, and transition elements: two new functionals and systematic testing of four M06-class functionals and 12 other functionals. Theor Chem Account 2008,120 (1-3), 215-241.