Dispersion Corrected r2SCAN Based Global Hybrid Functionals: r2SCANh, r2SCAN0, and r2SCAN50

The re-regularized semilocal meta generalized gradient approximation (meta-GGA) exchange-correlation functional r2SCAN [J. W. Furness, A. D. Kaplan, J. Ning, J. P. Perdew, and J. Sun, J. Phys. Chem. Lett. 11, 8208–8215 (2020)] is used to create the three global hybrid functionals with varying admixtures of Hartree–Fock exact exchange (HFX). The resulting exchange-correlation functionals r2SCANh (10% HFX), r2SCAN0 (25% HFX), and r2SCAN50 (50%HFX) are combined with the recent semi-classical D4 London dispersion correction. The new functionals are assessed for molecular geometries, general main-group, and metalorganic thermochemistry at 26 comprehensive benchmark sets including such as the large GMTKN55, ROST61, and IONPI19 sets. It is shown that a moderate admixture of HFX leads to overall mean percentual improvements of −11 (r2SCANh-D4), −16 (r2SCAN0-D4), and −1% (r2SCAN50-D4) regarding thermochemistry compared to the parental meta-GGA. For organometallic reaction energies and barriers, r2SCAN0-D4 even yields a mean improvement of −35%. The computation of structural parameters does not systematically profit from HFX admixture. Overall, the most promising combination r2SCAN0-D4 performs well for both main-group and organometallic thermochemistry. It yields deviations better or on par with other very well-performing 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.

Quasi-dimensional models applied to kinetic and exchange energy density functionals

We investigate the behavior of three-dimensional 3D exchange energy functional of density-functional theory in anisotropic systems with two-dimensional 2D character and 1D character. The local density approximation (LDA), the generalized gradient approximation (GGA), and the meta-GGA behave as functions of quantum well width. We use the infinite-barrier model (IBM) for the quantum well. In the first section, we describe the problem of three-dimensional exchange functional, in the second section we introduce the quasi-2D IBM system, in the third section we introduce the quasi-1D IBM system. Using that an exact-exchange functional provides the correct approach to the true two-dimensional limit, we want to show that the 2D limit can be considered as a constraint on approximate functionals. For the 1D limit case we also propose a new functional obtained with methods completely similar to those of 2D limit.

DFT calculation of the Renner Teller Effect in NCO: Preliminary assessment of Exact Exchange Energy on the accuracy of the X2Π Renner Coefficient

Assessment of DFT methods through analysis of the Renner-Teller Effect (RTE) in the XΠ state of the NCO radical was completed. Our results suggest that the amount of exact exchange at long range is important for an accurate description of the RTE in NCO. DFT functionals from the B3LYP, PBE, TPSS, M06, and M11 families with standard Correlation Consistent, 6-311G split valence family, as well as Sadlej, and Sapporo polarized triple-ζ basis sets were assessed. Our Renner coefficients are compared with previously published theoretical and experimental results to characterize the overall accuracy of various functional/basis set combinations in determining the RTE splitting in the Π (bending) modes of NCO(XΠ). We suggest that this method of analysis can be extended to other systems, serve as an accuracy metric when selecting a functional, and provide a means to create training sets for machine learning in computational molecular physics applications.

Assessing the Accuracy of the SCAN Functional for Water Through a Many-Body Analysis of the Adiabatic Connection Formula

<div> <div> <div> <p>We present a systematic analysis of the accuracy of a series of SCANα functionals for water, with varying fractions (α) of exact exchange, which are constructed through the adiabatic connection formula. Our results indicate that that all SCANα functionals exhibit substantial errors in the representation of the water 2-body energies. Importantly, the inclusion of exact exchange is found to have opposite effects on the ability of the SCANα functionals to describe the interaction energies of water clusters with 2-dimensional and 3-dimensional hydrogen-bonding arrangements. These errors are found to directly affect the ability of the SCANα functionals to describe the structure of liquid water at ambient conditions, which is investigated using explicit many-body models (MB-SCANα) derived from the corresponding SCANα data. In particular, it is found that all MB-SCANα models predict a more compact first hydration shell, which results in a denser liquid with a more ice-like structure. These ap- parent opposite trends can be explained by the inability of all SCANα functionals to provide a balanced description of the water 2B and 3B energies at the fundamental level. The analyses presented in this study provide new insights that can guide future developments of improved exchange-correlation functionals for water.</p> </div> </div> </div>

Assessing the Accuracy of the SCAN Functional for Water Through a Many-Body Analysis of the Adiabatic Connection Formula

<div> <div> <div> <p>We present a systematic analysis of the accuracy of a series of SCANα functionals for water, with varying fractions (α) of exact exchange, which are constructed through the adiabatic connection formula. Our results indicate that that all SCANα functionals exhibit substantial errors in the representation of the water 2-body energies. Importantly, the inclusion of exact exchange is found to have opposite effects on the ability of the SCANα functionals to describe the interaction energies of water clusters with 2-dimensional and 3-dimensional hydrogen-bonding arrangements. These errors are found to directly affect the ability of the SCANα functionals to describe the structure of liquid water at ambient conditions, which is investigated using explicit many-body models (MB-SCANα) derived from the corresponding SCANα data. In particular, it is found that all MB-SCANα models predict a more compact first hydration shell, which results in a denser liquid with a more ice-like structure. These ap- parent opposite trends can be explained by the inability of all SCANα functionals to provide a balanced description of the water 2B and 3B energies at the fundamental level. The analyses presented in this study provide new insights that can guide future developments of improved exchange-correlation functionals for water.</p> </div> </div> </div>

Assessing the Accuracy of the SCAN Functional for Water Through a Many-Body Analysis of the Adiabatic Connection Formula

<div> <div> <div> <p>We present a systematic analysis of the accuracy of a series of SCANα functionals for water, with varying fractions (α) of exact exchange, which are constructed through the adiabatic connection formula. Our results indicate that that all SCANα functionals exhibit substantial errors in the representation of the water 2-body energies. Importantly, the inclusion of exact exchange is found to have opposite effects on the ability of the SCANα functionals to describe the interaction energies of water clusters with 2-dimensional and 3-dimensional hydrogen-bonding arrangements. These errors are found to directly affect the ability of the SCANα functionals to describe the structure of liquid water at ambient conditions, which is investigated using explicit many-body models (MB-SCANα) derived from the corresponding SCANα data. In particular, it is found that all MB-SCANα models predict a more compact first hydration shell, which results in a denser liquid with a more ice-like structure. These ap- parent opposite trends can be explained by the inability of all SCANα functionals to provide a balanced description of the water 2B and 3B energies at the fundamental level. The analyses presented in this study provide new insights that can guide future developments of improved exchange-correlation functionals for water.</p> </div> </div> </div>