Ensemble Density Functional Theory Reloaded

Excited States ◽

Ground State ◽

Density Functional ◽

Low Cost ◽

Ground States ◽

Exchange Energy ◽

Functional Theory ◽

Fluctuation Dissipation ◽

Density functional theory can be generalized to mixtures of ground and excited states, for the purpose of determining energies of excitations using low-cost density functional approximations. Adapting approximations originally developed for ground states to work in the new setting would fast-forward progress enormously. But, previous attempts have stumbled on daunting fundamental issues. Here we show that these issues can be prevented from the outset, by working from a fluctuation dissipation theorem (FDT). We thereby show that existing exchange energy approximations are readily adapted to excited states, when combined with a rigorous exact Hartree term that is different in form from its ground state counterpart, and counterparts based on ensemble ansatze. Applying the FDT to correlation energies also provides insights into ground state-like and ensemble-only correlations. We thus provide a comprehensive and versatile framework for ensemble density functional approximations.

Ensemble Density Functional Theory Reloaded

10.26434/chemrxiv.12456146.v2 ◽

2020 ◽

Author(s):

Tim Gould ◽

Gianluca Stefanucci ◽

Stefano Pittalis

Keyword(s):

Excited States ◽

Ground State ◽

Density Functional ◽

Low Cost ◽

Ground States ◽

Exchange Energy ◽

Functional Theory ◽

Fluctuation Dissipation ◽

Density functional theory can be generalized to mixtures of ground and excited states, for the purpose of determining energies of excitations using low-cost density functional approximations. Adapting approximations originally developed for ground states to work in the new setting would fast-forward progress enormously. But, previous attempts have stumbled on daunting fundamental issues. Here we show that these issues can be prevented from the outset, by using a fluctuation dissipation theorem (FDT) to dictate key functionals. We thereby show that existing exchange energy approximations are readily adapted to excited states, when combined with a rigorous exact Hartree term that is different in form from its ground state counterpart, and counterparts based on ensemble ansatze. Applying the FDT to correlation energies also provides insights into ground state-like and ensemble-only correlations. We thus provide a comprehensive and versatile framework for ensemble density functional approximations.

Ensemblization of density-functional theory: Insight from the fluctuation-dissipation theorem

10.26434/chemrxiv.12456146.v3 ◽

2020 ◽

Cited By ~ 1

Author(s):

Tim Gould ◽

Gianluca Stefanucci ◽

Stefano Pittalis

Keyword(s):

Excited States ◽

Ground State ◽

Density Functional ◽

Low Cost ◽

Ground States ◽

Exchange Energy ◽

Functional Theory ◽

Fluctuation Dissipation ◽

Density functional theory can be generalized to mixtures of ground and excited states, for the purpose of determining energies of excitations using low-cost density functional approximations. Adapting approximations originally developed for ground states to work in the new setting would fast-forward progress enormously. But, previous attempts have stumbled on daunting fundamental issues. Here we show that these issues can be prevented from the outset, by using a fluctuation dissipation theorem (FDT) to dictate key functionals. We thereby show that existing exchange energy approximations are readily adapted to excited states, when combined with a rigorous exact Hartree term that is different in form from its ground state counterpart, and counterparts based on ensemble ansatze. Applying the FDT to correlation energies also provides insights into ground state-like and ensemble-only correlations. We thus provide a comprehensive and versatile framework for ensemble density functional approximations.

Ensemblization of density-functional theory: Insight from the fluctuation-dissipation theorem

10.26434/chemrxiv.12456146 ◽

2020 ◽

Author(s):

Tim Gould ◽

Gianluca Stefanucci ◽

Stefano Pittalis

Keyword(s):

Excited States ◽

Ground State ◽

Density Functional ◽

Low Cost ◽

Ground States ◽

Exchange Energy ◽

Functional Theory ◽

Fluctuation Dissipation ◽

Density functional theory can be generalized to mixtures of ground and excited states, for the purpose of determining energies of excitations using low-cost density functional approximations. Adapting approximations originally developed for ground states to work in the new setting would fast-forward progress enormously. But, previous attempts have stumbled on daunting fundamental issues. Here we show that these issues can be prevented from the outset, by using a fluctuation dissipation theorem (FDT) to dictate key functionals. We thereby show that existing exchange energy approximations are readily adapted to excited states, when combined with a rigorous exact Hartree term that is different in form from its ground state counterpart, and counterparts based on ensemble ansatze. Applying the FDT to correlation energies also provides insights into ground state-like and ensemble-only correlations. We thus provide a comprehensive and versatile framework for ensemble density functional approximations.

Ensemble Density Functional Theory: Insight from the Fluctuation-Dissipation Theorem

Physical Review Letters ◽

10.1103/physrevlett.125.233001 ◽

2020 ◽

Vol 125 (23) ◽

Author(s):

Tim Gould ◽

Gianluca Stefanucci ◽

Stefano Pittalis

Keyword(s):

Density Functional ◽

Functional Theory ◽

Fluctuation Dissipation ◽

Approximately self-consistent ensemble density functional theory: toward inclusion of all correlations

10.26434/chemrxiv.12382595 ◽

2020 ◽

Author(s):

Tim Gould

Keyword(s):

Excited States ◽

Density Functional ◽

Low Cost ◽

Recent Theory ◽

Functional Theory ◽

Effective Potentials ◽

Simple Theories ◽

Promising Tool ◽

Cost Studies

Recent theory developments in ensemble density functional theory (EDFT) promise to bring decades of work for ground-states to the practical resolution of excited-states - provided newly-discovered "density-driven correlations" can be dealt with and adequate effective potentials can be found. This Letter introduces simple theories for both; and shows that EDFT using these theories outperforms ΔSCF DFT and time-dependent DFT for low-lying gaps in most of the small atoms and molecules tested, even when all use the same density functional approximations. It thus establishes EDFT as a promising tool for low-cost studies of excited states; and provides a clear route to practical EDFT implementation of arbitrary functional approximations.

Thermal Density Functional Theory: Time-Dependent Linear Response and Approximate Functionals from the Fluctuation-Dissipation Theorem

Physical Review Letters ◽

10.1103/physrevlett.116.233001 ◽

2016 ◽

Vol 116 (23) ◽

Cited By ~ 35

Author(s):

Aurora Pribram-Jones ◽

Paul E. Grabowski ◽

Kieron Burke

Keyword(s):

Linear Response ◽

Density Functional ◽

Time Dependent ◽

Functional Theory ◽

Fluctuation Dissipation ◽

Fluctuation-dissipation theorem density-functional theory

The Journal of Chemical Physics ◽

10.1063/1.1884112 ◽

2005 ◽

Vol 122 (16) ◽

pp. 164106 ◽

Cited By ~ 166

Author(s):

Filipp Furche ◽

Troy Van Voorhis

Keyword(s):

Density Functional ◽

Functional Theory ◽

Fluctuation Dissipation ◽

TREATMENTS OF THE EXCHANGE ENERGY IN DENSITY-FUNCTIONAL THEORY

International Journal of Modern Physics B ◽

10.1142/s0217979208039344 ◽

2008 ◽

Vol 22 (14) ◽

pp. 2225-2239

Author(s):

TAMÁS GÁL

Keyword(s):

Ground State ◽

Density Functional ◽

Common Ground ◽

Particle Density ◽

Exchange Energy ◽

Density Functionals ◽

Simple Derivation ◽

Functional Theory ◽

Hartree Fock

Following a recent work [Gál, Phys. Rev. A64, 062503 (2001)], a simple derivation of the density-functional correction of the Hartree–Fock equations, the Hartree–Fock–Kohn–Sham equations, is presented, completing an integrated view of quantum mechanical theories, in which the Kohn–Sham equations, the Hartree–Fock–Kohn–Sham equations and the ground-state Schrödinger equation formally stem from a common ground: density-functional theory, through its Euler equation for the ground-state density. Along similar lines, the Kohn–Sham formulation of the Hartree–Fock approach is also considered. Further, it is pointed out that the exchange energy of density-functional theory built from the Kohn–Sham orbitals can be given by degree-two homogeneous N-particle density functionals (N = 1, 2, …), forming a sequence of degree-two homogeneous exchange-energy density functionals, the first element of which is minus the classical Coulomb-repulsion energy functional.