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

scholarly journals Exact Generalized Kohn-Sham Theory for Hybrid Functionals

2019 ◽  
Author(s):  
Rachel Garrick ◽  
Amir Natan ◽  
Tim Gould ◽  
Leeor Kronik
Keyword(s):  
Density Functional Theory ◽  
Density Functional ◽  
Density Functional Theory Calculations ◽  
State Density ◽  
Hybrid Functional ◽  
Functional Theory ◽  
Hybrid Functionals ◽  
The Many ◽  
Ground State Density ◽  
Equivalent Description

p.p1 {margin: 0.0px 0.0px 0.0px 0.0px; line-height: 18.0px; font: 15.8px Helvetica; color: #000000; -webkit-text-stroke: #000000; background-color: #ffffff} span.s1 {font-kerning: none} span.s2 {font-kerning: none; color: #000000} <p>Hybrid functionals have proven to be of immense practical value in density functional theory calculations. While they are often thought to be a heuristic construct, it has been established that this is in fact not the case. Here, we present a rigorous and formally exact generalized Kohn-Sham (GKS) density functional theory of hybrid functionals, in which exact remainder exchange-correlation potentials combine with a fraction of Fock exchange to produce the correct ground state density. Specifically, we generalize the well-known adiabatic con- nection theorem to the case of exact hybrid functional theory and use it to provide a rigorous distinction between multiplicative exchange and correlation components. We examine the exact theory by inverting reference electron densities to obtain exact GKS potentials for hybrid functionals, showing that an equivalent description of the many-electron problem is obtained with any arbitrary global fraction of Fock exchange. We establish the dependence of these exact components on the fraction of Fock exchange and use the observed trends to shed new light on the results of approximate hybrid functional calculations.</p>

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.

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