Alternative Representations of the Correlation Energy in Density‐Functional Theory: A Kinetic‐Energy Based Adiabatic Connection

Teale, Andrew M.; Helgaker, Trygve; Savin, Andreas

doi:10.1002/jccs.201500132

Cited by 11 publications

(11 citation statements)

References 44 publications

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“…Eq. ( 15) generalizes results for the ground state-only case [39][40][41] to the ensembles considered in this work.…”

supporting

confidence: 81%

Electronic excited states in extreme limits via ensemble density functionals

Gould¹,

Kooi²,

Gori‐Giorgi³

et al. 2022

Preprint

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Ensemble density functional theory (EDFT) is a promising cost effective approach to address low-lying excitations in many-electron systems. Yet the corresponding functionals depend on the structure of the excitation in a challenging fashion; a fact which hinders a general and agile exploitation of the methodology. Here, we demonstrate that such a dependence become trivial as electrons become strictly correlated, because EDFT functionals become equivalent to pure ground state DFT functionals. This finding forms a most remarkable exact condition to deal with excitations in the low-density limit of all systems. An immediate consequence of which, excitations in Wigner systems can be dealt with non-empirically and universally.

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“…Eq. ( 15) generalizes results for the ground state-only case [39][40][41] to the ensembles considered in this work.…”

supporting

confidence: 81%

Electronic excited states in extreme limits via ensemble density functionals

Gould¹,

Kooi²,

Gori‐Giorgi³

et al. 2022

Preprint

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“…Models based on DFT are continuously improved, Fig. 4 (h), 98,99 e.g., to incorporate new concepts for excited state simulations. [100][101][102] Many people are working on improving the functional via alternative formulations [103][104][105] for better predictions of transition metals, stretched bonds, and Mott insulators.…”

Section: Reliable and Predictivementioning

confidence: 99%

From Prescriptive to Predictive: an Interdisciplinary Perspective on the Future of Computational Chemistry

Rommel

2021

Preprint

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Reliable predictions of the behaviour of chemical systems are essential across many industries, from nanoscale engineering over validation of advanced materials to nanotoxicity assessment in health and medicine. For the future we therefore envision a paradigm shift for the design of chemical simulations across all length scales from a prescriptive to a predictive and quantitative science. This paper presents an integrative perspective about the state-of-the-art of modelling in computational and theoretical chemistry with examples from data-and equation-based models. Extension to include reliable risk assessments and quality control are discussed. To specify and broaden the concept of chemical accuracy in the design cycle of reliable and robust molecular simulations the fields of computational chemistry, physics, mathematics, visualisation science, and engineering are bridged. Methods from electronic structure calculations serve as examples to explain how uncertainties arise: through assumed mechanisms in form of equations, model parameters, algorithms, and numerical implementations. We

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“…This requires the integration of an appropriate kernel along a path where the potential for the electronic system is interpolated between the potential of a non-interacting system to the one of the fully interacting system. This approach can feature kernels of various kinds, such as derived from the electron-electron interaction or from the electronic kinetic energy 38 . Following Refs.…”

Section: B the Adiabatic Connectionmentioning

confidence: 99%

“…One involves formulating the smearing distribution function (here below we will choose Fermi-Dirac), and the other involves choosing a path connecting the Aufbau solution to the statically correlated one. In regards to the latter, because the occupations are monotonic functions of the coupling strength 38 , λ, the integral Eq. ( 12) can be expressed in terms of an integration over the value of the occupations, from P 0 i to P s,1 i .…”

Section: Change Of Variable λ → P For the Adiabatic Connection Integralmentioning

confidence: 99%

Static Correlation Density Functional Theory

Martín-Ramos¹,

Pavanello²

2019

Preprint

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Over the years, several schemes have been proposed to describe multireference systems with Kohn-Sham Density Functional Theory. Problematic is the combination of two aspects: the Kohn-Sham reference wavefunction is usually taken to be a single Slater determinant, and approximate exchange-correlation functionals are typically derived form the local density approximation. In this work, we develop a theoretical framework that foregoes the single Slater determinant and instead employs thermal states as reference states for zero-temperature interacting systems. We provide convenient definitions of static and dynamic correlation functionals via an adiabatic connection approach. The formalism and computational results indicate that the entropic term of the thermal reference state is a good approximation to the static correlation functional. Hence, this work validates several reported results in the literature and motivates additional developments of static correlation density functionals.

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Alternative Representations of the Correlation Energy in Density‐Functional Theory: A Kinetic‐Energy Based Adiabatic Connection

Cited by 11 publications

References 44 publications

Electronic excited states in extreme limits via ensemble density functionals

Electronic excited states in extreme limits via ensemble density functionals

From Prescriptive to Predictive: an Interdisciplinary Perspective on the Future of Computational Chemistry

Static Correlation Density Functional Theory

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