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Meta-Local Density Functionals: A New Rung on Jacob's Ladder.

ABSTRACT: The homogeneous electron gas (HEG) is a key ingredient in the construction of most exchange-correlation functionals of density-functional theory. Often, the energy of the HEG is parameterized as a function of its spin density n_σ, leading to the local density approximation (LDA) for inhomogeneous systems. However, the connection between the electron density and kinetic energy density of the HEG can be used to generalize the LDA by evaluating it on a geometric average n_σ^avg(r) = n_σ^1-x(r)ñ_σ^x(r) of the local spin density n_σ(r) and the spin density ñ_σ(r) of a HEG that has the local kinetic energy density τ_σ(r) of the inhomogeneous system. This leads to a new family of functionals that we term meta-local density approximations (meta-LDAs), which are still exact for the HEG, which are derived only from properties of the HEG and which form a new rung of Jacob's ladder of density functionals [ AIP Conf. Proc. 2001, 577, 1]. The first functional of this ladder, the local τ approximation (LTA) of Ernzerhof and Scuseria [ J. Chem. Phys. 1999, 111, 911] that corresponds to x = 1 is unfortunately not stable enough to be used in self-consistent field calculations because it leads to divergent potentials, as we show in this work. However, a geometric averaging of the LDA and LTA densities with smaller values of x not only leads to numerical stability of the resulting functional but also yields more accurate exchange energies in atomic calculations than the LDA, the LTA, or the tLDA functional (x = 1/4) of Eich and Hellgren [ J. Chem. Phys. 2014, 141, 224107]. We choose x = 0.50, as it gives the best total energy in self-consistent exchange-only calculations for the argon atom. Atomization energy benchmarks confirm that the choice x = 0.50 also yields improved energetics in combination with correlation functionals in molecules, almost eliminating the well-known overbinding of the LDA and reducing its error by two thirds.

SUBMITTER: Lehtola S

PROVIDER: S-EPMC8023657 | biostudies-literature |

REPOSITORIES: biostudies-literature

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Project description:BackgroundChinese topography appears a three-rung ladder-like distribution of decreasing elevation from northwest to southeast, which is divided by two sloping edges. Previous studies have reported that prevalence of thyroid diseases differed by altitude, and geographical factors were associated with thyroid disorders. To explore the association between three-rung ladder-like regions and thyroid disorders according to unique Chinese topographic features, we conducted an epidemiological cross-sectional study from 2015-2017 that covered all 31 mainland Chinese provinces.MethodsA total of 78,470 participants aged ≥ 18 years from a nationally representative cross-sectional study were included. Serum thyroid peroxidase antibody, thyroglobulin antibody, and thyroid-stimulating hormone levels; urine iodine concentration; and thyroid volume were measured. The three-rung ladder-like distribution of decreasing elevation from northwest to southeast in China was categorized into three topographic groups according to elevation: first ladder, > 3000 m above sea level; second ladder, descending from 3000-500 m; and third ladder, descending from 500 m to sea level. The third ladder was further divided into groups A (500-100 m) and B (< 100 m). Associations between geographic factors and thyroid disorders were assessed using linear and binary logistic regression analyses.ResultsParticipants in the first ladder group were associated with lower thyroid peroxidase (β = -4.69; P = 0.00), thyroglobulin antibody levels (β = -11.08; P = 0.01), and the largest thyroid volume (β = 1.74; P = 0.00), compared with the other groups. The second ladder group was associated with autoimmune thyroiditis (odds ratio = 1.30, 95% confidence interval [1.18-1.43]) and subclinical hypothyroidism (odds ratio = 0.61, 95%confidence interval [0.57-0.66]) (P < 0.05) compared with the first ladder group. Group A (third ladder) (500-100 m) was associated with thyroid nodules and subclinical hypothyroidism (P < 0.05). Furthermore, group B (< 100 m) was positively associated with autoimmune thyroiditis, thyroid peroxidase and thyroglobulin antibody positivity, and negatively associated with overt hypothyroidism, subclinical hypothyroidism, and goiter compared with the first ladder group(P < 0.05).ConclusionWe are the first to investigate the association between different ladder regions and thyroid disorders according to unique Chinese topographic features. The prevalence of thyroid disorders varied among the three-rung ladder-like topography groups in China, with the exception of overt hyperthyroidism.

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Meta-Local Density Functionals: A New Rung on Jacob's Ladder.

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