For more than three decades, nearly freeelectron elemental metals have been a topic of debate because the computed bandwidths are significantly wider in the local density approximation to densityfunctional theory (DFT) than indicated by angleresolved photoemission (ARPES) experiments. Here, we systematically investigate this using first principles calculations for alkali and alkalineearth metals using DFT and various beyondDFT methods such as metaGGA, G_{0}W_{0}, hybrid functionals (YSPBE0, B3LYP), and LDA + eDMFT. We find that the static nonlocal exchange, as partly included in the hybrid functionals, significantly increase the bandwidths even compared to LDA, while the G_{0}W_{0}bands are only slightly narrower than in LDA. The agreement with the ARPES is best when the local approximation to the selfenergy is used in the LDA + eDMFT method. We infer that even moderately correlated systems with partially occupied
 Award ID(s):
 1939528
 NSFPAR ID:
 10326297
 Editor(s):
 M. Lewin, Rupert L.
 Date Published:
 Journal Name:
 The Elliott Lieb Anniversary Volume
 Format(s):
 Medium: X
 Sponsoring Org:
 National Science Foundation
More Like this

Abstract s orbitals, which were assumed to approximate the uniform electron gas, are very well described in terms of shortrange dynamical correlations that are only local to an atom. 
Approaching periodic systems in ensemble density functional theory via finite onedimensional models
Abstract Ensemble density functional theory (EDFT) is a generalization of groundstate DFT, which is based on an exact formal theory of finite collections of a system’s ground and excited states. EDFT in various forms has been shown to improve the accuracy of calculated energy level differences in isolated model systems, atoms, and molecules, but it is not yet clear how EDFT could be used to calculate band gaps for periodic systems. We extend the application of EDFT toward periodic systems by estimating the thermodynamic limit with increasingly large finite onedimensional ‘particle in a box’ systems, which approach the uniform electron gas (UEG). Using ensemblegeneralized Hartree and local spin density approximation exchangecorrelation functionals, we find that corrections go to zero in the infinite limit, as expected for a metallic system. However, there is a correction to the effective mass, with results comparable to other calculations on 1D, 2D, and 3D UEGs, which indicates promise for nontrivial results from EDFT on periodic systems.

We argue that the success of DFT can be understood in terms of a semiclassical expansion around a very specific limit. This limit was identified long ago by Lieb and Simon for the total electronic energy of a system. This is a universal limit of all electronic structure: atoms, molecules, and solids. For the total energy, ThomasFermi theory becomes relatively exact in the limit. The limit can also be studied for much simpler model systems, including noninteracting fermions in a onedimensional well, where the WKB approximation applies for individual eigenvalues and eigenfunctions. Summation techniques lead to energies and densities that are functionals of the potential. We consider several examples in one dimension (fermions in a box, in a harmonic well, in a linear halfwell, and in the PöschlTeller well. The effects of higher dimension are also illustrated with the threedimensional harmonic well and the Bohr atom, noninteracting fermions in a Coulomb well. Modern density functional calculations use the KohnSham scheme almost exclusively. The same semiclassical limit can be studied for the KohnSham kinetic energy, for the exchange energy, and for the correlation energy. For all three, the local density approximation appears to become relatively exact in this limit. Recent work, both analytic and numerical, explores how this limit is approached, in an effort to deduce the leading corrections to the local approximation. A simple scheme, using the EulerMaclaurin summation formula, is the result of many different attempts at this problem. In very simple cases, the correction formulas are much more accurate than standard density functionals. Several functionals are already in widespread use in both chemistry and materials that incorporate these limits, and prospects for the future are discussed.more » « less

The natural determinant reference (NDR) or principal natural determinant is the Slater determinant comprised of the N most strongly occupied natural orbitals of an Nelectron state of interest. Unlike the Kohn–Sham (KS) determinant, which yields the exact groundstate density, the NDR only yields the best idempotent approximation to the interacting oneparticle reduced density matrix, but it is welldefined in common atomcentered basis sets and is representationinvariant. We show that the underdetermination problem of prior attempts to define a groundstate energy functional of the NDR is overcome in a grandcanonical ensemble framework at the zerotemperature limit. The resulting grand potential functional of the NDR ensemble affords the variational determination of the ground state energy, its NDR (ensemble), and select ionization potentials and electron affinities. The NDR functional theory can be viewed as an “exactification” of orbital optimization and empirical generalized KS methods. NDR functionals depending on the noninteracting Hamiltonian do not require troublesome KSinversion or optimized effective potentials.

Our ability to understand and simulate the reactions catalyzed by iron depends strongly on our ability to predict the relative energetics of spin states. In this work, we studied the electronic structures of Fe 2+ ion, gaseous FeO and 14 iron complexes using Kohn–Sham density functional theory with particular focus on determining the ground spin state of these species as well as the magnitudes of relevant spinstate energy splittings. The 14 iron complexes investigated in this work have hexacoordinate geometries of which seven are Fe( ii ), five are Fe( iii ) and two are Fe( iv ) complexes. These are calculated using 20 exchange–correlation functionals. In particular, we use a local spin density approximation (LSDA) – GVWN5, four generalized gradient approximations (GGAs) – BLYP, PBE, OPBE and OLYP, two nonseparable gradient approximations (NGAs) – GAM and N12, two metaGGAs – M06L and M11L, a metaNGA – MN15L, five hybrid GGAs – B3LYP, B3LYP*, PBE0, B973 and SOGGA11X, four hybrid metaGGAs – M06, PW6B95, MPW1B95 and M08SO and a hybrid metaNGA – MN15. The density functional results are compared to reference data, which include experimental results as well as the results of diffusion Monte Carlo (DMC) calculations and ligand field theory estimates from the literature. For the Fe 2+ ion, all functionals except M11L correctly predict the ground spin state to be quintet. However, quantitatively, most of the functionals are not close to the experimentally determined spinstate splitting energies. For FeO all functionals predict quintet to be the ground spin state. For the 14 iron complexes, the hybrid functionals B3LYP, MPW1B95 and MN15 correctly predict the ground spin state of 13 out of 14 complexes and PW6B95 gets all the 14 complexes right. The local functionals, OPBE, OLYP and M06L, predict the correct ground spin state for 12 out of 14 complexes. Two of the tested functionals are not recommended to be used for this type of study, in particular M08SO and M11L, because M08SO systematically overstabilizes the high spin state, and M11L systematically overstabilizes the low spin state.more » « less