Exchange and correlation in atoms, molecules, and solids by the spin-density-functional formalism

In non-self-consistent calculations of the total energy within the random-phase approximation (RPA) for electronic correlation, it is necessary to choose a single-particle Hamiltonian whose solutions are used to construct the electronic density and noninteracting response function. Here we investigate the effect of including a Hubbard-U term in this single-particle Hamiltonian, to better describe the on-site correlation of 3d electrons in the transition metal compounds ZnS, TiO 2 , and NiO. We find that the RPA lattice constants are essentially independent of U , despite large changes in the underlying electronic structure. We further demonstrate that the non-selfconsistent RPA total energies of these materials have minima at nonzero U . Our RPA calculations find the rutile phase of TiO 2 to be more stable than anatase independent of U , a result which is consistent with experiments and qualitatively different from that found from calculations employing U -corrected (semi)local functionals. However we also find that the +U term cannot be used to correct the RPA's poor description of the heat of formation of NiO.

show abstract

“…Within the adiabatic-connection fluctuation-dissipation formulation of DFT [12,13,43,44], E Tot is decomposed as…”

Section: A Non-self-consistent Rpa Total Energymentioning

confidence: 99%

Hubbard-Ucorrected Hamiltonians for non-self-consistent random-phase approximation total-energy calculations: A study of ZnS,TiO2, and NiO

Patrick

Thygesen

2016

Phys. Rev. B

View full text Add to dashboard Cite

show abstract

“…From the limit N ~ ~, we obtain excellent agreement with surface tensions and work functions evaluated for an infinite plane metal surface. [3]. The ground-state density of the system is determined by minimizing the energy E [p].…”

mentioning

confidence: 99%

Semiclassical variational calculation of liquid-drop model coefficients for metal clusters

Seidl¹,

Spina²,

Brack³

1991

Small Particles and Inorganic Clusters

View full text Add to dashboard Cite

Abstract.We report on semiclassical density variational calculations for spherical alkali metal clusters in the jellium model. We derive liquid-drop model expansions for total energy, ionisation potential and electron affinity and test the coefficients numerically for clusters with up to N = 10 5 atoms. From the limit N ~ ~, we obtain excellent agreement with surface tensions and work functions evaluated for an infinite plane metal surface. ;(r) = r-/r -R 5 7"* Work partially supported by Deutsche Forschungsgemeinschaft and minimizing the energy with respect to the three parameters Po, a and ?,. R is used for normalization to the number z of excess electrons in a cluster with N atoms. Due to the semiclassical nature of the ETF kinetic energy functional and the form (1) of our variational densities, we cannot account for shell effects which are due to the quantal nature of the electronic single-particle states (see, e.g., [4]). We can, however, obtain a selfconsistent description of average static properties of alkali clusters. Indeed, our results reproduce very well on the average the microscopic Kohn-Sham results for spherical clusters [4, 1], as well as for metal surfaces [5, 6] (using the limit N---, ~).Our approach is particularly well suited for studying the asymptotic behaviour of cluster properties in the limit N ~ ~. Our present aim is to investigate this limit, both analytically and numerically, for the total ground-state energy E(N, z) and two quantities derived from it: the ionisation potential I and the electron affinity AIn order to study the asymptotic behaviour of these quantities, we start from a leptodermous expansion of the energy E(N, z) in powers of the small quantity a/R, which leads to a liquid-drop model type expansion in powers of N-1/3. (See, e.g., [7] for a similar expansion of the total binding energy of atomic nuclei). This is very difficult to perform analytically with the density profile (1). However, for simple analytic profiles (e.g., a symmetric doubleexponential or trapezoidal form) we arrive at the following result for the leading terms: E(N, z) = E~(N, z) -zAq~ °~ + eb(N + z)

show abstract

“…Due to the spherical symmetry of the system and because the spin-orbit interaction is not considered, the eigenstates of H must also be eigenstates of the angular momentum operators L 2 and M L , spin operators S 2 and M S . The advantage of the spherical symmetry is that rigorous upper-bound theorems apply for QMC and ground state DFT can be generalized 31 for the lowest energy state states of each value of L and S. Therefore, meaningful phase diagrams can be constructed with each method.…”

Section: Methodsmentioning

confidence: 99%

Simple impurity embedded in a spherical jellium: Approximations of density functional theory compared to quantum Monte Carlo benchmarks

et al. 2011

View full text Add to dashboard Cite

We study the electronic structure of a spherical jellium in the presence of a central Gaussian impurity. We test how well the resulting inhomogeneity effects beyond spherical jellium are reproduced by several approximations of density functional theory (DFT). Four rungs of Perdew's ladder of DFT functionals, namely local density approximation (LDA), generalized gradient approximation (GGA), meta-GGA and orbital-dependent hybrid functionals are compared against our quantum Monte Carlo (QMC) benchmarks. We identify several distinct transitions in the ground state of the system as the electronic occupation changes between delocalized and localized states. We examine the parameter space of realistic densities (1 ≤ rs ≤ 5) and moderate depths of the Gaussian impurity (Z < 7). The selected 18 electron system (with closed-shell ground state) presents 1d → 2s transitions while the 30 electron system (with open-shell ground state) exhibits 1f → 2p transitions. For the former system, the accuracy for the transitions is clearly improving with increasing sophistication of functionals with meta-GGA and hybrid functionals having only small deviations from QMC. However, for the latter system, we find much larger differences for the underlying transitions between our pool of DFT functionals and QMC. We attribute these failures to an insufficiently accurate treatment of exchange by these functionals. Additionally, we amplify the inhomogeneity effects by creating the system with spherical shell which leads to even larger errors in DFT approximations.

show abstract

Exchange and correlation in atoms, molecules, and solids by the spin-density-functional formalism

Cited by 3,578 publications

References 105 publications

Hubbard-Ucorrected Hamiltonians for non-self-consistent random-phase approximation total-energy calculations: A study of ZnS,TiO2, and NiO

Hubbard-Ucorrected Hamiltonians for non-self-consistent random-phase approximation total-energy calculations: A study of ZnS,TiO2, and NiO

Semiclassical variational calculation of liquid-drop model coefficients for metal clusters

Simple impurity embedded in a spherical jellium: Approximations of density functional theory compared to quantum Monte Carlo benchmarks

Contact Info

Product

Resources

About