scholarly journals Density Functional Theory for Strongly-Interacting Electrons

2014 ◽  
pp. 153-168
Author(s):  
Francesc Malet ◽  
André Mirtschink ◽  
Klaas J. H. Giesbertz ◽  
Paola Gori-Giorgi
Keyword(s):  
Density Functional Theory ◽  
Density Functional ◽  
Functional Theory ◽  
Strongly Interacting ◽  
Interacting Electrons ◽  
Strongly Interacting Electrons

Fully Nonlocal Functionals Along the Adiabatic Connection of Density Functional Theory

2019 ◽  
Author(s):  
Stefan Vuckovic
Keyword(s):  
Density Functional Theory ◽  
Strong Correlation ◽  
Density Functional ◽  
Correlation Energy ◽  
Electronic Effects ◽  
Functional Theory ◽  
Strongly Interacting ◽  
Kinetic Component ◽  
Exact Exchange ◽  
New Framework

Inspired by the exact form of the strongly interacting limit of density functional theory, Vuckovic and Gori Giorgi have recently proposed [J. Phys. Chem. Lett. 2017, 8, 2799] the multiple radii functional (MRF), a new framework for the construction of exchange-correlation (xc) energy approximations able to describe strong correlation electronic effects. To facilitate the construction of improved approximations based on the MRF functional, in the present work we use reverse engineering strategies to reveal the forms of the MRF functional which reproduce the exact xc functional for small atoms. We also develop a procedure that allows the MRF functional to be built on the top of exact exchange. Using the adiabatic connection representation of the xc functional, we also investigate routes for the construction of the correlation functional by combining information from the physical, weakly and strongly interacting regimes. We highlight the advantages of this approach over previous adiabatic connection-based approaches for the treatment of strong correlation and discuss how it can be used for recovering the presently missing kinetic component of the correlation energy in the MRF framework.<br> <pre><br></pre>

scholarly journals Range-Separation and the Multiple Radii Functional Approximation Inspired by the Strongly Interacting Limit of Density Functional Theory

2019 ◽  
Author(s):  
Stefan Vuckovic ◽  
Tim Gould
Keyword(s):  
Density Functional Theory ◽  
Density Functional ◽  
Approximate Theory ◽  
Exact Results ◽  
Strong Correlations ◽  
Functional Theory ◽  
One Dimensional ◽  
Strongly Interacting ◽  
Correlation Problem ◽  
Exactly Solvable

The strongly-interacting limit of density functional theory has attracted considerable attention recently due to its ability to deal with the difficult strong correlation problem. Recent work [JPCL 8, 2799-2805 (2017)] introduced the "multiple radii functional" (MRF) approximation, inspired by this limit, which is designed to work well for strong correlations between dissociated fragments. Here, we analyse the MRF in exactly solvable one-dimensional molecules, to uncover how it matches, and deviates from, exact results; and use range-separation of the Coulomb potential in both exact and approximate theory to explore how this varies in space. Our work opens a path to new approximations incorporating the MRF, amongst other ingredients.<br><br>

scholarly journals Fully Nonlocal Functionals Along the Adiabatic Connection of Density Functional Theory

2019 ◽  
Author(s):  
Stefan Vuckovic
Keyword(s):  
Density Functional Theory ◽  
Strong Correlation ◽  
Density Functional ◽  
Correlation Energy ◽  
Electronic Effects ◽  
Functional Theory ◽  
Strongly Interacting ◽  
Kinetic Component ◽  
Exact Exchange ◽  
New Framework

Inspired by the exact form of the strongly interacting limit of density functional theory, Vuckovic and Gori Giorgi have recently proposed [J. Phys. Chem. Lett. 2017, 8, 2799] the multiple radii functional (MRF), a new framework for the construction of exchange-correlation (xc) energy approximations able to describe strong correlation electronic effects. To facilitate the construction of improved approximations based on the MRF functional, in the present work we use reverse engineering strategies to reveal the forms of the MRF functional which reproduce the exact xc functional for small atoms. We also develop a procedure that allows the MRF functional to be built on the top of exact exchange. Using the adiabatic connection representation of the xc functional, we also investigate routes for the construction of the correlation functional by combining information from the physical, weakly and strongly interacting regimes. We highlight the advantages of this approach over previous adiabatic connection-based approaches for the treatment of strong correlation and discuss how it can be used for recovering the presently missing kinetic component of the correlation energy in the MRF framework.<br> <pre><br></pre>

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