scholarly journals Multi-State Density Functional Theory for Ground and Excited States

2021 ◽  
Author(s):  
Yangyi Lu ◽  
Jiali Gao
Keyword(s):  
Density Functional Theory ◽  
Excited States ◽  
Ground State ◽  
Density Functional ◽  
Energy Functional ◽  
State Density ◽  
Hamiltonian Matrix ◽  
Functional Theory ◽  
Practical Applications ◽  
Exact Density

We report a rigorous formulation of multi-state density functional theory (MSDFT) that extends the Kohn-Sham (KS) energy functional for the ground state to a Hamiltonian matrix functional H[D] of the density matrix D in the space spanned by the lowest N adiabatic states. We establish a variational principle of MSDFT, which guarantees that the variational optimization results in a Hamiltonian matrix, whose eigenvalues are the lowest N eigen-energies of the system. We present an explicit expression of H[D] and introduce the correlation matrix functional. Akin to KS-DFT for the ground state, a universal multi-state correlation potential is derived for a two-state system as an illustrative example. This work shows that MSDFT is an exact density functional theory that treats the ground and excited states on an equal footing and provides a framework for practical applications and future developments of approximate functionals for excited states.

Some Fundamental Issues in Ground-State Density Functional Theory: A Guide for the Perplexed

2009 ◽  
Vol 5 (4) ◽  
pp. 902-908 ◽  
Author(s):  
John P. Perdew ◽  
Adrienn Ruzsinszky ◽  
Lucian A. Constantin ◽  
Jianwei Sun ◽  
Gábor I. Csonka
Keyword(s):  
Density Functional Theory ◽  
Ground State ◽  
Density Functional ◽  
State Density ◽  
Functional Theory ◽  
Ground State Density

Density functional theory is straying from the path toward the exact functional

Science ◽  
2017 ◽  
Vol 355 (6320) ◽  
pp. 49-52 ◽  
Author(s):  
Michael G. Medvedev ◽  
Ivan S. Bushmarinov ◽  
Jianwei Sun ◽  
John P. Perdew ◽  
Konstantin A. Lyssenko
Keyword(s):  
Density Functional Theory ◽  
Density Distribution ◽  
Ground State ◽  
Electron Density Distribution ◽  
Density Functional ◽  
Electron System ◽  
The Other ◽  
Functional Theory ◽  
The Core ◽  
Exact Density

The theorems at the core of density functional theory (DFT) state that the energy of a many-electron system in its ground state is fully defined by its electron density distribution. This connection is made via the exact functional for the energy, which minimizes at the exact density. For years, DFT development focused on energies, implicitly assuming that functionals producing better energies become better approximations of the exact functional. We examined the other side of the coin: the energy-minimizing electron densities for atomic species, as produced by 128 historical and modern DFT functionals. We found that these densities became closer to the exact ones, reflecting theoretical advances, until the early 2000s, when this trend was reversed by unconstrained functionals sacrificing physical rigor for the flexibility of empirical fitting.

scholarly journals Ensemble Density Functional Theory Reloaded

2020 ◽  
Author(s):  
Tim Gould ◽  
Gianluca Stefanucci ◽  
Stefano Pittalis
Keyword(s):  
Density Functional Theory ◽  
Excited States ◽  
Ground State ◽  
Density Functional ◽  
Low Cost ◽  
Ground States ◽  
Exchange Energy ◽  
Functional Theory ◽  
Fluctuation Dissipation ◽  
Fluctuation Dissipation Theorem

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.<br><br>

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

2020 ◽  
Author(s):  
Tim Gould ◽  
Gianluca Stefanucci ◽  
Stefano Pittalis
Keyword(s):  
Density Functional Theory ◽  
Excited States ◽  
Ground State ◽  
Density Functional ◽  
Low Cost ◽  
Ground States ◽  
Exchange Energy ◽  
Functional Theory ◽  
Fluctuation Dissipation ◽  
Fluctuation Dissipation Theorem

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.

scholarly journals Coordinate Scaling in Time-Independent Excited-State Density Functional Theory for Coulomb Systems

Computation ◽  
2019 ◽  
Vol 7 (4) ◽  
pp. 59
Author(s):  
Ágnes Nagy
Keyword(s):  
Density Functional Theory ◽  
Excited State ◽  
Excited States ◽  
Density Functional ◽  
Coulomb Systems ◽  
State Theory ◽  
State Density ◽  
Functional Theory ◽  
Exchange Correlation ◽  
Coordinate Scaling

A time-independent density functional theory for excited states of Coulomb systems has recently been proposed in a series of papers. It has been revealed that the Coulomb density determines not only its Hamiltonian, but the degree of excitation as well. A universal functional valid for any excited state has been constructed. The excited-state Kohn–Sham equations bear resemblance to those of the ground-state theory. In this paper, it is studied how the excited-state functionals behave under coordinate scaling. A few relations for the scaled exchange, correlation, exchange-correlation, and kinetic functionals are presented. These relations are expected to be advantageous for designing approximate functionals.

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