Benchmark study of DFT functionals for late-transition-metal reactions

The performance of a wide variety of DFT exchange-correlation functionals for a number of late-transition-metal reaction profiles has been considered. Benchmark ab-initio reference data for the prototype reactions Pd + H2, Pd + CH4, Pd + C2H6 (both C-C and C-H activation), and Pd + CH3Cl are presented, while ab-initio data of lesser quality were obtained for the catalytic hydrogenation of acetone and for the low-oxidation-state and high-oxidation-state mechanisms of the Heck reaction. "Kinetics" functionals such as mPW1K, PWB6K, BB1K, and BMK clearly perform more poorly for late-transition-metal reactions than for main-group reactions, as well as compared to general-purpose functionals. There is no single "best functional" for late-transition-metal reactions, but rather a cluster of several functionals (PBE0, B1B95, PW6B95, and TPSS25B95) that perform about equally well; if main-group thermochemical performance is additionally considered, then B1B95 and PW6B95 emerge as the best performers. TPSS25B95 and TPSS33B95 offer attractive performance compromises if weak interactions and main-group barrier heights, respectively, are also important. In the ab-initio calculations, basis set superposition errors (BSSE) can be greatly reduced by ensuring that the metal spd shell has sufficient radial flexibility in the high-exponent range. Optimal HF percentages in hybrid functionals depend on the class of systems considered, increasing from anions to neutrals to cations to main-group barrier heights; transition-metal barrier heights represent an intermediate situation. The use of meta-GGA correlation functionals appears to be quite beneficial.     

Random-phase-approximation-based correlation energy functionals: benchmark results for atoms

The random phase approximation for the correlation energy functional of the density functional theory has recently attracted renewed interest. Formulated in terms of the Kohn-Sham orbitals and eigenvalues, it promises to resolve some of the fundamental limitations of the local density and generalized gradient approximations, as, for instance, their inability to account for dispersion forces. First results for atoms, however, indicate that the random phase approximation overestimates correlation effects as much as the orbital-dependent functional obtained by a second order perturbation expansion on the basis of the Kohn-Sham Hamiltonian. In this contribution, three simple extensions of the random phase approximation are examined; (a) its augmentation by a local density approximation for short-range correlation, (b) its combination with the second order exchange term, and (c) its combination with a partial resummation of the perturbation series including the second order exchange. It is found that the ground state and correlation energies as well as the ionization potentials resulting from the extensions (a) and (c) for closed subshell atoms are clearly superior to those obtained with the unmodified random phase approximation. Quite some effort is made to ensure highly converged data, so that the results may serve as benchmark data. The numerical techniques developed in this context, in particular, for the inherent frequency integration, should also be useful for applications of random phase approximation-type functionals to more complex systems.     

Hybrid exchange correlation functionals and potentials: Concept elaboration

This paper deals with hybrid functionals that contain exact exchange energy and are the most popular and effective functionals in modern density functional theory. Emphasis is laid on generalization of the notion of a “hybrid functional,” which arises from the introduction of the spatial dependence of the exact exchange admixture (local hybrid functionals). Problems inherent in hybrid functionals are considered along with problems inherent in a wider class of so-called orbital-dependent functionals. In particular, the technique for constructing the local and multiplicative potentials, including the optimized effective potential method, is considered in detail. The theoretical approaches under study are illustrated by calculations of atomization molecular energies and magnetic resonance parameters.     

Density functionals for exchange and correlation energies: Exact conditions and comparison of approximations

A set of exact conditions is compiled for the purpose of developing and testing approximations for the exchange-correlation energy as a functional of the electron density. Special emphasis is placed upon recently developed density-scaling relationships. Commonly used generalized gradient approximations are compared against several of these conditions. A direct tabular comparison of these functionals (not of calculated properties) with one another is also made. © 1994 John Wiley & Sons, Inc.     

Benchmark study of popular density functionals for calculating binding energies of three-center two-electron bonds

Density functional theory (DFT) can be used to study the three-center two-electron (3c2e) bonding mode, which is universal in catalysts containing alkaline-earth (Ae) and boron-group (Bg) elements. However, because of the delocalization pattern of the 3c2e bond, the wavefunction cannot be accurately described by DFT methods. The calculated energies of Ae and Bg catalysts therefore fluctuate greatly when different functionals are used, largely because of inconsistent DFT-calculated binding energies of 3c2e bonds. Nevertheless, with the development of supercomputers and theoretical calculation software, the DFT method is becoming increasingly popular for studying Ae and Bg catalysts. In this study, we compared the performances of 21 functionals with the high-level composite G3B3 method in calculations for the binding energies of 3c2e bonds. Several frequently used post-Hartree–Fock methods were also tested. The calculation results indicate that the M06-2X, MN12-L, and MN15 functionals give consistent and reliable binding energies for common 3c2e bonds. © 2018 Wiley Periodicals, Inc.     

The importance of middle-range Hartree-Fock-type exchange for hybrid density functionals

Hybrid functionals are responsible for much of the utility of modern Kohn-Sham density functional theory. When rigorously applied to solid-state metallic and small band gap systems, however, the slow decay of their nonlocal Hartree-Fock-type exchange makes hybrids computationally challenging and introduces unphysical effects. This can be remedied by using a range-separated hybrid which only keeps short-range nonlocal exchange, as in the functional of Heyd et al. [J. Chem. Phys. 118, 8207 (2003)]. On the other hand, many molecular properties require full long-range nonlocal exchange, which can also be included by means of a range-separated hybrid such as the recently introduced LC-omegaPBE functional [O. A. Vydrov and G. E. Scuseria, J. Chem. Phys. 125, 234109 (2006)]. In this paper, we show that a three-range hybrid which mainly includes middle-range Hartree-Fock-type exchange and neglects long- and short-range Hartree-Fock-type exchange yields excellent accuracy for thermochemistry, barrier heights, and band gaps, emphasizing that the middle-range part of the 1/r potential seems crucial to accurately model these properties.     

Short-range exchange and correlation energy density functionals: beyond the local-density approximation

We propose approximations which go beyond the local-density approximation for the short-range exchange and correlation density functionals appearing in a multideterminantal extension of the Kohn-Sham scheme. A first approximation consists of defining locally the range of the interaction in the correlation functional. Another approximation, more conventional, is based on a gradient expansion of the short-range exchange-correlation functional. Finally, we also test a short-range generalized-gradient approximation by extending the Perdew-Burke-Ernzerhof exchange-correlation functional to short-range interactions.     

Avoiding singularity problems associated with meta-GGA (generalized gradient approximation) exchange and correlation functionals containing the kinetic energy density

Convergence problems of meta-GGA (generalized gradient approximation) XC (exchange and correlation) functionals containing a self-interaction correction term are traced back to a singularity of the latter that occurs at critical points of the electron density. This is demonstrated for the bond critical point of equilibrium and stretched H2. A simple remedy is suggested that cures meta-XC functionals such as VSXC, TPSS, M05, M06, and their derivatives without extra cost.     

Nonlocal energy density functionals: Models plus some exact general results

Holas and March (Phys Rev 1995 A51, 2040) gave a formally exact expression for the force ??V_xc( r )/? r associated with the exchange‐correlation potential V_xc( r ) of density functional theory. This forged a precise link between first‐ and second‐order density matrices and V_xc( r ). Here models are presented in which these low‐order matrices can be related to the ground‐state electron density. This allows nonlocal energy density functionals to be constructed within the framework of such models. Finally, results emerging from these models have led to the derivation of some exact “nuclear cusp” relations for exchange and correlation energy densities in molecules, clusters, and condensed phases. © 2003 Wiley Periodicals, Inc. Int J Quantum Chem, 2003     

Nonlocal functionals for exchange and correlation in density functional theory: Application to atoms and to small atomic clusters

The local density approximation (LDA ) to exchange and correlation effects has well-known limitations. The nonlocal weighted density approximation (WDA ) corrects some of those defects. This is illustrated here by applications to free atoms and small atomic clusters. The WDA also induces a nonlocal kinetic energy functional that is tested for atoms. © 1995 John Wiley & Sons, Inc.     

Perfluorinated anion exchange membranes: Preparation and preliminary tests of dialysis

Using the preirradiation technique a kinetic study of the grafting of the 4-vinyl pyridine (V₄P) and an aliphatic ammonium monomer (ALAM) onto the copolymer film of ethylene–tetrafluoroethylene (ETFE) has been performed. The influence of dose, temperature, and concentration of monomer, reticular agent, and inhibitor were investigated. The results are discussed on the basis of the interactions between monomer diffusibility and viscosity of the medium. The characteristics of some membranes were determined. Their applicability to the recovery of acid by dialysis is demonstrated.     

Toward developing accelerated stress tests for proton exchange membrane electrolyzers

Proton exchange membrane water electrolysis is technically the most suitable technology for the production of green hydrogen on a large scale. Although it is still more expensive than hydrogen produced from fossil sources, it has already been commercialized. Novel components with cost-effective materials and efficient manufacturing processes are being rapidly developed. However, these components must endure durability tests that can guarantee a lifetime of at least 50,000 operation hours. Consequently, there is an urgent need to develop accelerated stress test protocols based on a deep understanding of degradation mechanisms of stack components. Recent reports show that the main degradation mechanisms are associated to anode catalyst dissolution, membrane chemical decomposition, and formation of semiconducting oxides on the metal components. These mechanisms can be accelerated by stressors such as high current density, dynamic operation, and shutdown modes. On the basis of these reports and knowledge of the operational requirements for large-scale proton exchange membrane water electrolysis, we propose an accelerated stress test protocol for the fast evaluation of newly developed cost efficient and durable components.     

Generalized gradient exchange functionals based on the gradient-regulated connection: a new member of the TCA family

A new type of generalized gradient approximation exchange functional coupled with the TCA correlation model has been proposed. Based on gradient-regulated connection, this exchange functional is able to mix performances of a modified PBE for the bulk region, to those of the PW91 for the asymptotic one, leading to a significant improvement on the modelization of weak interacting systems, while keeping a good accuracy for the atomization energies.     

About the difference between density functionals defined by energy criterion and density functionals defined by density criterion: Exchange functionals

The difference between density functionals defined by energy criterion and density functionals defined by density criterion is studied for the exchange functional. It is shown that Slater potentials are exact exchange potentials in the sense that they yield the Hartree–Fock electron density if all operators are given by local expressions. © 2016 Wiley Periodicals, Inc.     

Assessment of density functionals with long‐range and/or empirical dispersion corrections for conformational energy calculations of peptides

Density functionals with long‐range and/or empirical dispersion corrections, including LC‐ωPBE, B97‐D, ωB97X‐D, M06‐2X, B2PLYP‐D, and mPW2PLYP‐D functionals, are assessed for their ability to describe the conformational preferences of Ac‐Ala‐NHMe (the alanine dipeptide) and Ac‐Pro‐NHMe (the proline dipeptide) in the gas phase and in water, which have been used as prototypes for amino acid residues of peptides. For both dipeptides, the mean absolute deviation (MAD) is estimated to be 0.22–0.40 kcal/mol in conformational energy and 2.0–3.2° in torsion angles ? and ψ using these functionals with the 6‐311++G(d,p) basis set against the reference values calculated at the MP2/aug‐cc‐pVTZ//MP2/aug‐cc‐pVDZ level of theory in the gas phase. The overall performance is obtained in the order B2PLYP‐D ≈ mPW2PLYP‐D > ωB97X‐D ≈ M06‐2X > MP2 > LC‐ωPBE > B3LYP with the 6–311++G(d,p) basis set. The SMD model at the M06‐2X/6‐31+G(d) level of theory well reproduced experimental hydration free energies of the model compounds for backbone and side chains of peptides with MADs of 0.47 and 4.3 kcal/mol for 20 neutral and 5 charged molecules, respectively. The B2PLYP‐D/6‐311++G(d,p)//SMD M06‐2X/6‐31+G(d) level of theory provides the populations of backbone and/or prolyl peptide bond for the alanine and proline dipeptides in water that are consistent with the observed values. © 2010 Wiley Periodicals, Inc. J Comput Chem, 2010