Excited states in the adiabatic connection fluctuation-dissipation theory: Recovering missing correlation energy from the negative part of the density response spectrum

2021 ◽  
Vol 154 (16) ◽  
pp. 164102
Author(s):  
Daria Drwal ◽  
Ewa Pastorczak ◽  
Katarzyna Pernal
Keyword(s):  
Excited States ◽  
Correlation Energy ◽  
Response Spectrum ◽  
Negative Part ◽  
Fluctuation Dissipation ◽  
Density Response

Embracing local suppression and enhancement of dynamic correlation effects in a CASΠDFT method for efficient description of excited states

2020 ◽  
Vol 224 ◽  
pp. 333-347
Author(s):  
Katarzyna Pernal ◽  
Oleg V. Gritsenko
Keyword(s):  
Excited States ◽  
Correlation Energy ◽  
Correlation Effects ◽  
Dynamic Correlation

In this work we show that the presence of covalent and ionic configurations in a wavefunction gives rise to spatial regions where the effects of suppression and enhancement of correlation energy, respectively, dominate.

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 Correlation Energy Expressions from the Adiabatic-Connection Fluctuation–Dissipation Theorem Approach

2011 ◽  
Vol 7 (10) ◽  
pp. 3116-3130 ◽  
Author(s):  
János G. Ángyán ◽  
Ru-Fen Liu ◽  
Julien Toulouse ◽  
Georg Jansen
Keyword(s):  
Correlation Energy ◽  
Fluctuation Dissipation ◽  
Fluctuation Dissipation Theorem

An approximate ab initio method based on the DIM model

2000 ◽  
Vol 78 (12) ◽  
pp. 1575-1586 ◽  
Author(s):  
John M Cullen
Keyword(s):  
Ab Initio ◽  
Excited States ◽  
Electron Correlation ◽  
Correlation Energy ◽  
Basis Sets ◽  
Ab Initio Method ◽  
First Order ◽  
Hartree Fock ◽  
Modified Method ◽  
Electron Correlation Energy

Using a second quantized formulation, an approximate diatomics in molecules (DIM) theory is presented in which all three- and four-centered electronic integrals are neglected. To ameliorate the effects of this approximation, the DIM one electron operator is constructed so that the true ab initio first-order density matrix and total energy are reproduced at the Hartree–Fock level. The resulting model was extensively tested for a variety of basis sets for its capability of capturing both the dynamic and nondynamic components of the electron correlation energy as well as the energies of excited electronic states. A modified method in which the DIM one-electron operator is formed from the initial extended Hückel guess of the Hartree–Fock orbitals was also found to produce excellent results.Key words: DIM, electron correlation energy, excited states, semiempirical.

scholarly journals Correlation Energies of Many-Electron Ensembles Are More than the Sum of Their Parts

2018 ◽  
Author(s):  
Tim Gould ◽  
Stefano Pittalis
Keyword(s):  
Excited States ◽  
Variational Approach ◽  
Density Functional ◽  
Unique Feature ◽  
Correlation Energy ◽  
Energy Functional ◽  
Functional Approach ◽  
Passive State ◽  
Functional Theory ◽  
Natural Components

Density functional theory can be extended to excited states by means of a unified variational approach for passive state ensembles. This extension overcomes the restriction of the typical density functional approach to ground states, and offers useful formal and demonstrated practical benefits. The correlation energy functional in the generalized case acquires higher complexity than its ground state counterpart, however. Little is known about its internal structure nor how to effectively approximate it in general. Here we demonstrate that such a functional can be broken down into natural components, including what we call "state-" and "density-driven" correlations, with the latter being a unique feature of ensembles. Such a decomposition, summarised in eq. (10), is exact and also provides us with a pathway to general approximations.<br>

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