Static Response and Local Field Factor of the Electron Gas

Moroni, Saverio; Ceperley, David M.; Senatore, G.

doi:10.1103/physrevlett.75.689

Cited by 304 publications

(400 citation statements)

References 17 publications

Supporting

Mentioning

372

Contrasting

Unclassified

Order By: Relevance

“…Corradini et al (1998) gave a parametrization of the quantum Monte Carlo data of Moroni et al (1995) for the homogeneous electron gas that satisfies the theoretically known limits for small and large q. This kernel has an analytical space Fourier transform that simplifies its implementation in standard first-principles techniques.…”

Section: The Exchange-correlation Kernel F XCmentioning

confidence: 99%

“…(i) the compressibility sum rule, lim q→0 f xc (q, ϭ0) ϭd 2 ⑀ xc ( )/d 2 , where ⑀ xc ( ) denotes the exchange-correlation energy per particle; (ii) the third frequency moment sum rule: (iii) the static and frequency-dependent shortwavelength behavior: lim q→ϱ f xc (q, ϭ0)ϰc Ϫ (b/q 2 ) ͓1Ϫg(0)͔ [the correct values of the constants b and c can be found in Moroni et al (1995) instead of the values used by Gross and Kohn (1985)] and lim q→ϱ f xc (q, 0) ϭϪ (8 /3q 2 ) ͓1Ϫg(0)͔, where g(0) is the paircorrelation function evaluated at zero distance; (iv) The following relations satisfied in the highfrequency limit by the real and imaginary parts of f xc for qϽϱ: lim →ϱ Re f xc (q, )ϭf xc (0,ϱ)ϩc/ 3/2 and lim →ϱ Im f xc (q, )ϭϪc/ 3/2 , with cϭ23 /15 in the high-density limit evaluation of the irreducible polarization propagator.…”

Section: (A4)mentioning

confidence: 99%

See 1 more Smart Citation

Electronic excitations: density-functional versus many-body Green’s-function approaches

2002

View full text Add to dashboard Cite

Electronic excitations lie at the origin of most of the commonly measured spectra. However, the first-principles computation of excited states requires a larger effort than ground-state calculations, which can be very efficiently carried out within density-functional theory. On the other hand, two theoretical and computational tools have come to prominence for the description of electronic excitations. One of them, many-body perturbation theory, is based on a set of Green's-function equations, starting with a one-electron propagator and considering the electron-hole Green's function for the response. Key ingredients are the electron's self-energy ⌺ and the electron-hole interaction. A good approximation for ⌺ is obtained with Hedin's GW approach, using density-functional theory as a zero-order solution. First-principles GW calculations for real systems have been successfully carried out since the 1980s. Similarly, the electron-hole interaction is well described by the Bethe-Salpeter equation, via a functional derivative of ⌺. An alternative approach to calculating electronic excitations is the time-dependent density-functional theory (TDDFT), which offers the important practical advantage of a dependence on density rather than on multivariable Green's functions. This approach leads to a screening equation similar to the Bethe-Salpeter one, but with a two-point, rather than a four-point, interaction kernel. At present, the simple adiabatic local-density approximation has given promising results for finite systems, but has significant deficiencies in the description of absorption spectra in solids, leading to wrong excitation energies, the absence of bound excitonic states, and appreciable distortions of the spectral line shapes. The search for improved TDDFT potentials and kernels is hence a subject of increasing interest. It can be addressed within the framework of many-body perturbation theory: in fact, both the Green's functions and the TDDFT approaches profit from mutual insight. This review compares the theoretical and practical aspects of the two approaches and their specific numerical implementations, and presents an overview of accomplishments and work in progress. CONTENTS

show abstract

Section: The Exchange-correlation Kernel F XCmentioning

confidence: 99%

Section: (A4)mentioning

confidence: 99%

Electronic excitations: density-functional versus many-body Green’s-function approaches

2002

View full text Add to dashboard Cite

show abstract

“…The DMC data of Π(q, 0), together with the well-known analytical result of Π 0 (q, 0), determine G + (q, 0), which is parametrized as a function of r s and q (= |q|). 36 In particular, in the limit of q → ∞, G + (q, 0) is known as…”

Section: Sum Rulesmentioning

confidence: 99%

“…(3)- (5), for n(p). The static charge response function Q R c (q, 0) in the electron gas is calculated by Moroni, Ceperley, and Senatore (MCS) 36 in DMC for r s ≤ 10, giving the numerical data for Π(q, 0). With use of Eq.…”

Section: Sum Rulesmentioning

confidence: 99%

Emergence of an excitonic collective mode in the dilute electron gas

Takada

2016

Phys. Rev. B

View full text Add to dashboard Cite

By comparing two expressions for the polarization function Π(q, iω) given in terms of two different local-field factors, G+(q, iω) and Gs(q, iω), we have derived the kinetic-energy-fluctuation (or sixthpower) sum rule for the momentum distribution function n(p) in the three-dimensional electron gas. With use of this sum rule, together with the total-number (or second-power) and the kinetic-energy (or fourth-power) sum rules, we have obtained n(p) in the low-density electron gas at negative compressibility (namely, rs > 5.25 with rs being the conventional density parameter) up to rs ≈ 22 by improving on the interpolation scheme due to Gori-Giorge and Ziesche proposed in 2002. The obtained results for n(p) combined with the improved form for Gs(q, ω + i0 + ) are employed to calculate the dynamical structure factor S(q, ω) to reveal that a giant peak, even bigger than the plasmon peak, originating from an excitonic collective mode made of electron-hole pair excitations, emerges in the low-ω region at |q| near 2pF (pF: the Fermi wave number). Connected with this mode, we have discovered a singular point in the retarded dielectric function at ω = 0 and |q| ≈ 2pF.

show abstract

“…where κ and µ are non-empirical constants selected to recover the local-spin density linear response 69 and to satisfy the Lieb-Oxford bound 70 , and s=s(ρ,∇ρ) is a functional of the reduced density gradient.…”

Section: Theory and Approachmentioning

confidence: 99%

Ligand-Field-Dependent Behavior of Meta-GGA Exchange in Transition-Metal Complex Spin-State Ordering

2017

View full text Add to dashboard Cite

Prediction of spin-state ordering in transition metal complexes is essential for understanding catalytic activity and designing functional materials. Semi-local approximations in density functional theory, such as the generalized-gradient approximation (GGA), suffer from several errors notably including delocalization error that give rise to systematic bias for more covalently bound low-spin electronic states. Incorporation of exact exchange is known to counteract this bias, instead favoring high-spin states, in a manner that has recently been identified to be ligand-field dependent. In this work, we introduce a tuning strategy to identify the effect of incorporating the Laplacian of the density (i.e., a meta-GGA) in exchange on spinstate ordering. We employ a diverse test set of M(II) and M(III) first-row transition metal ions from Ti to Cu as well as octahedral complexes of these ions with ligands of increasing field strength (i.e., H 2 O, NH 3 , and CO). We show that the sensitivity of spin-state ordering to meta-GGA exchange is highly ligand-field dependent, stabilizing high-spin states in strong-field (i.e., CO) cases and stabilizing low-spin states in weak-field (i.e., H 2 O, NH 3 , and isolated ions) cases. This diverging behavior leads to generally improved treatment of isolated ions and strong field complexes over a standard GGA but worsened treatment for the hexa-aqua or hexa-ammine complexes. These observations highlight the sensitivity of functional performance to subtle changes in chemical bonding.2

show abstract

Static Response and Local Field Factor of the Electron Gas

Cited by 304 publications

References 17 publications

Electronic excitations: density-functional versus many-body Green’s-function approaches

Electronic excitations: density-functional versus many-body Green’s-function approaches

Emergence of an excitonic collective mode in the dilute electron gas

Ligand-Field-Dependent Behavior of Meta-GGA Exchange in Transition-Metal Complex Spin-State Ordering

Contact Info

Product

Resources

About