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.     

On the conjoint gradient correction to the Hartree—Fock kinetic and exchange energy density functionals

The kinetic and the exchange energy functionals are expressed in the form T[ρ] = C_TF∫ drρ^5/3(r)f_t(s) and K[ρ] = C_D∫ drρ^4/3(r)f_K(s), where C_TF = (3/10)(3π²)^2/3 and C_D = −(3/4)(3/π)^4/3 are the Thomas-Fermi and the Dirac coefficients, respectively, and s = |∇ρ(r)|/C_sρ^4/3(r), with C_s = 2(3π²)^1/3. These expressions are used to perform a comparison of f_T(s) and f_K(s) in terms of their generalized gradient expansion approximations. It is shown that f_κ(s) and is congruent to f_T(s) in the range characteristic of the interior regions of atoms and many solids and that the second-order gradient expansion of the kinetic energy provides a rather reasonable approximation to the generalized gradient expansion approximation of both the kinetic and the exchange energy functionals. © 1996 John Wiley & Sons, Inc.     

Influence of the exchange screening parameter on the performance of screened hybrid functionals

This work reexamines the effect of the exchange screening parameter omega on the performance of the Heyd-Scuseria-Ernzerhof (HSE) screened hybrid functional. We show that variation of the screening parameter influences solid band gaps the most. Other properties such as molecular thermochemistry or lattice constants of solids change little with omega. We recommend a new version of HSE with the screening parameter omega=0.11 bohr(-1) for further use. Compared to the original implementation, the new parametrization yields better thermochemical results and preserves the good accuracy for band gaps and lattice constants in solids.     

Magnetic exchange couplings evaluated with Rung 3.5 density functionals

Rung 3.5 exchange-correlation functionals are assessed for the calculation of magnetic exchange coupling parameters and atomic spin populations for a variety of inorganic and organic magnetic systems. Density functional theory calculations of exchange couplings sensitively depend on nonlocal contributions to the exchange-correlation functional. Semilocal functionals, Rungs 1-3 on "Jacob's Ladder" of density functional approximations, yield excessively delocalized electrons and overestimated absolute exchange couplings. Fourth-rung hybrid functionals admixing nonlocal exchange improve the results. We show that new "Rung 3.5" functionals give magnetic properties intermediate between semilocal and hybrid functionals, providing additional evidence that these functionals incorporate some desirable aspects of nonlocal exchange. Results for ferromagnetic complexes indicate areas for future improvement.     

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.     

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.     

On the exchange of cyanide with acetonitrile. A test of theoretical calculations

- The theoretically predicted formation of an adduct between cyanide and anhydrous acetonitrile was tested experimentally; no evidence for such a complex was found. The previously reported radioactivity loss in the reactions of cyanide - ¹⁴C in acetonitrile solutions was possibly due to protonation and loss of hydrogen cyanide, since no exchange between cyanide and acetonitrile was evidenced within the sensitivity limits of ¹³C labelling. Potassium cyanide and carbonate in the presence of 18-crown-6 ether catalyze the H/D exchange between acetonitrile and trideuteroacetonitrile.     

Spin-depolarisation in energetic atomic collisions by the exchange of electrons

The use of spin-polarized particles in atomic collision experiments may allow to study specific details of the reaction. In case of (at least) two active electrons, a spin-depolarisation may result from the exchange of electrons. The effect depends on the electron-electron interaction during the collision. Electron exchange is discussed and a model calculation is performed.     

Hartree-Fock exchange computed using the atomic resolution of the identity approximation

In this work, we apply the atomic resolution of the identity (ARI) fitting approximation to the computation of Hartree-Fock exchange. The ARI approximation is a local modification of the RI approximation that produces an energy which is differentiable with respect to nuclear motion, unlike other local applications of RI. We justify empirically the use of locality and present timing comparisons of ARI, RI, and exact computation for one-, two-, and three-dimensional carbon systems. ARI is found to reduce significantly the cost of RI for large systems, while retaining accuracy.     

Is combining meta‐GGA correlation functionals with the OPTX exchange functional useful?

The recent generalized gradient approximation (GGA) density functional OCS1 of Handy and Cohen is implemented in the deMon code and tested on a carefully selected set of problems. OCS1 is found to be accurate for molecular atomization energies, transition metal–ligand bonds, and systems with intramolecular hydrogen bonds. However, OCS1 encounters problems for systems with intermolecular hydrogen bonds. It also tends to elongate bond lengths systematically, and sometimes significantly. The OPTX exchange is combined with three meta‐GGA correlation functionals, Lap3, τ1, and τ2, the latter reported for the first time. The new meta‐GGA scheme OPTX exchange plus τ2 correlation called Oτ2 yields improved molecular geometries, NMR shielding constants, and an improved barrier height for the H+H₂ reaction. © 2005 Wiley Periodicals, Inc. Int J Quantum Chem, 2006     

On the atomic weight of potassium

A brief survey of data is made, which indicates the possibility that the present internationally accepted value for the atomic weight of potassium (39.102) is too high. Additional experimental evidence is brought to light, which also supports this conclusion.     

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.     

Benchmark results for empirical post-GGA functionals: difficult exchange problems and independent tests

Many of the most promising new density functionals have improved the treatment of non-local exchange effects with the help of semi-empirical information and more sophisticated recipes for combining Hartree-Fock and local exchange approximations. In order to quantify recent advancements and identify directions for improvement, we have examined a broad spectrum of test problems. We evaluate the performance of several new hybrid density functionals (ωB97, ωB97X, ωB97X-D, LRC-ωPBEh, M06, M06-2X, and M06-HF) on a variety of chemical problems, some sensitive to the treatment of exact exchange (which we have hoped to systematically improve) and some which require a balanced treatment of correlation. Since all of the functionals under consideration are parameterized with ground-state thermochemical data, the benchmark aims to determine the applicability of the new density functionals to cases that have not been considered in the optimization of the semi-empirical parameters. The first class of benchmarks includes the excitation energies of 21 molecules (83 states) primarily from a recent benchmark conducted by Tozer and co-workers, with some additional references from data made available from the groups of Thiel and Truhlar. We briefly examine the conformational preferences of a small peptide and complete our study with two recently published sets of data that have shown large, systematic errors in simple alkane thermochemistry. While our results indicate that the more general hybrids currently under development perform well for problems outside of their parameterization and improve over the standard hybrid density functionals in an essentially systematic way, there is still a significant self-interaction error in the more difficult cases. Functionals based on a range-separation of exchange and functionals depending on the kinetic-energy density both perform comparably, and there is evidence for complementary strengths.     

Comparative performance of exchange and correlation density functionals in determining intermolecular interaction potentials of the methane dimer

We have calculated the interaction potentials of the methane dimer for the minimum-energy D(3d) conformation using the density functional theory (DFT) with 90 density functionals chosen from the combinations of nine exchange and 10 correlation functionals. Several hybrid functionals are also considered. While the performance of an exchange functional is related to the large reduced density gradient of the exchange enhancement factor, the correlation energy is determined by the low-density behavior of a correlation enhancement factor. Our calculations demonstrate that the correlation counterpart plays an equally important role as the exchange functional in determining the van der Waals interactions of the methane dimer. These observations can be utilized to better understand the seemingly unsystematic DFT interaction potentials for weakly bound systems.     

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.     

On the reliability of atomic transition integrals

A simple procedure due to Layzer and Garstang for estimating the reliability of calculated dipole-length transition integrals is re-examined. Some recent Hartree—Fock f-values of Ghoshal, Dutta and Sengupta for helium-sequence transitions are analyzed and corrected, and are shown to be of generally high accuracy.