Kinetic Energy Density Functionals from Models for the One-Electron Reduced Density Matrix

Chakraborty, Debajit; Cuevas-Saavedra, Rogelio; Ayers, Paul W.

doi:10.1007/978-3-319-72374-7_17

Cited by 5 publications

(8 citation statements)

References 79 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The other point is that constraints from N -representability have been developed for weighted-density approximation KEDFs based on model 1-rdms. See Chakraborty et al , and the discussion below.…”

Section: Kinetic Energy Functionalsmentioning

confidence: 99%

Section: Kinetic Energy Functionalsmentioning

confidence: 99%

“…Another interesting and potentially promising real-space route to construct KEDFs is to define a model 1-rdm that depends purely on the electron density. This was attempted by Chakraborty et al , Given a 1-rdm, γ( r , r ′), the kinetic energy associated with it is T s [ n ] = prefix− 1 2 ∫ d boldr d boldr ′ δ ( r − r ′ ) ( ∇ r 2 γ false[ n ; boldr , boldr ′ false] ) Chakraborty et al proposed model 1-rdms of the form γ [ n ; r , r ′ ] = n ( r ) n ( r ′ ) g ( k F | r − r ′ | ) This form is motivated by DFA development for the exchange energy, as well as having some resemblance to two-point functional ingredients already encountered. The effective wavevector, k F , however, is a function to be defined.…”

Section: Kinetic Energy Functionalsmentioning

confidence: 99%

“…To employ a NLPP in OFDFT, one can use a model 1-rdm. Recalling the subject of the work by Chakraborty et al, , several approaches have been proposed for formulating a model 1-rdm. Xu et al exploited a prescription in which a Gaussian decaying 1-rdm is linked to a local KEDF energy density as follows, γ [ n ] ( r , r ′ ) = ρ q ( r , r ′ ) e − s 2 ( r ) / 2 β ( r , r ′ ) [ 1 + A ( s 2 false( boldr false) 2 β false( boldr , boldr ′ false) ) 2 ] Here β ( r , r ′ ) = β ( r ) + β ( r ′ ) 2 with …”

Section: Kinetic Energy Functionalsmentioning

confidence: 99%

See 3 more Smart Citations

Orbital-Free Density Functional Theory: An Attractive Electronic Structure Method for Large-Scale First-Principles Simulations

Mi,

Luo,

Trickey

et al. 2023

Chem. Rev.

View full text Add to dashboard Cite

Kohn−Sham Density Functional Theory (KSDFT) is the most widely used electronic structure method in chemistry, physics, and materials science, with thousands of calculations cited annually. This ubiquity is rooted in the favorable accuracy vs cost balance of KSDFT. Nonetheless, the ambitions and expectations of researchers for use of KSDFT in predictive simulations of large, complicated molecular systems are confronted with an intrinsic computational cost-scaling challenge. Particularly evident in the context of firstprinciples molecular dynamics, the challenge is the high cost-scaling associated with the computation of the Kohn−Sham orbitals. Orbital-free DFT (OFDFT), as the name suggests, circumvents entirely the explicit use of those orbitals. Without them, the structural and algorithmic complexity of KSDFT simplifies dramatically and near-linear scaling with system size irrespective of system state is achievable. Thus, much larger system sizes and longer simulation time scales (compared to conventional KSDFT) become accessible; hence, new chemical phenomena and new materials can be explored. In this review, we introduce the historical contexts of OFDFT, its theoretical basis, and the challenge of realizing its promise via approximate kinetic energy density functionals (KEDFs). We review recent progress on that challenge for an array of KEDFs, such as one-point, twopoint, and machine-learnt, as well as some less explored forms. We emphasize use of exact constraints and the inevitability of design choices. Then, we survey the associated numerical techniques and implemented algorithms specific to OFDFT. We conclude with an illustrative sample of applications to showcase the power of OFDFT in materials science, chemistry, and physics.

show abstract

Section: Kinetic Energy Functionalsmentioning

confidence: 99%

Section: Kinetic Energy Functionalsmentioning

confidence: 99%

Section: Kinetic Energy Functionalsmentioning

confidence: 99%

Section: Kinetic Energy Functionalsmentioning

confidence: 99%

See 2 more Smart Citations

Orbital-Free Density Functional Theory: An Attractive Electronic Structure Method for Large-Scale First-Principles Simulations

Mi,

Luo,

Trickey

et al. 2023

Chem. Rev.

View full text Add to dashboard Cite

show abstract

“…where f i , V nl (r , r) = r | Vnl |r , and γ s (r, r ) = i f i ψ i (r)ψ * i (r ) represent the occupation number of the i-th KS orbital ψ i , the real-space representation of the nonlocal part pseudopotential, and the noninteracting density matrix, respectively. Considering that the density matrices γ s [ρ](r, r ) can be used to approximate the KEDFs [7,56,57], a nonlocal pseudopotential energy density functional (NLPPF) relying directly on the density matrices was proposed to evaluate the nonlocal electron-ion interaction energy. The nonlocal electron-ion interaction energy is then rewritten as…”

mentioning

confidence: 99%

Nonlocal Pseudopotential Energy Density Functional for Orbital-Free Density Functional Theory

Xu,

Ma,

et al. 2022

Preprint

View full text Add to dashboard Cite

Orbital-free density functional theory (OF-DFT) runs at low computational cost that scales linearly with the number of simulated atoms, making it suitable for large-scale material simulations.It is generally considered that OF-DFT strictly requires the use of local pseudopotentials, rather than orbital-dependent nonlocal pseudopotentials, for the calculation of electron-ion interaction energies, as no orbitals are available. This is unfortunate situation since the nonlocal pseudopotentials are known to give much better transferability and calculation accuracy than local ones.We report here the development of a theoretical scheme that allows the direct use of nonlocal pseudopotentials in OF-DFT. In this scheme, a nonlocal pseudopotential energy density functional is derived by the projection of nonlocal pseudopotential onto the non-interacting density matrix (instead of "orbitals") that can be approximated explicitly as a functional of electron density. Our development defies the belief that nonlocal pseudopotentials are not applicable to OF-DFT, leading to the creation of an alternate theoretical framework of OF-DFT that works superior to the traditional one.

show abstract

Recent advancements and challenges in orbital‐free density functional theory

Xu,

Ma,

et al. 2024

WIREs Comput Mol Sci

View full text Add to dashboard Cite

Orbital‐free density functional theory (OFDFT) stands out as a many‐body electronic structure approach with a low computational cost that scales linearly with system size, making it well suitable for large‐scale simulations. The past decades have witnessed impressive progress in OFDFT, which opens a new avenue to capture the complexity of realistic systems (e.g., solids, liquids, and warm dense matters) and provide a complete description of some complicated physical phenomena under realistic conditions (e.g., dislocation mobility, ductile processes, and vacancy diffusion). In this review, we first present a concise summary of the major methodological advances in OFDFT, placing particular emphasis on kinetic energy density functional and the schemes to evaluate the electron–ion interaction energy. We then give a brief overview of the current status of OFDFT developments in finite‐temperature and time‐dependent regimes, as well as our developed OFDFT‐based software package, named by ATLAS. Finally, we highlight perspectives for further development in this fascinating field, including the major outstanding issues to be solved and forthcoming opportunities to explore large‐scale materials.This article is categorized under: Electronic Structure Theory > Density Functional Theory Software > Simulation Methods Quantum Computing > Theory Development

show abstract

Kinetic Energy Density Functionals from Models for the One-Electron Reduced Density Matrix

Cited by 5 publications

References 79 publications

Orbital-Free Density Functional Theory: An Attractive Electronic Structure Method for Large-Scale First-Principles Simulations

Orbital-Free Density Functional Theory: An Attractive Electronic Structure Method for Large-Scale First-Principles Simulations

Nonlocal Pseudopotential Energy Density Functional for Orbital-Free Density Functional Theory

Recent advancements and challenges in orbital‐free density functional theory

Contact Info

Product

Resources

About