Basic time-independent density-functional theorems for ground states and excited states

2001 ◽  
Author(s):  
Mel Levy
Keyword(s):  
Excited States ◽  
Density Functional ◽  
Ground States

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.

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 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.<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 Exploitation of Baird Aromaticity and Clar’s Rule for Tuning the Triplet Energies of Polycyclic Aromatic Hydrocarbons

Chemistry ◽  
2021 ◽  
Vol 3 (2) ◽  
pp. 532-549
Author(s):  
Felix Plasser
Keyword(s):  
Polycyclic Aromatic Hydrocarbons ◽  
Excited States ◽  
Aromatic Hydrocarbons ◽  
Density Functional ◽  
Materials Science ◽  
Chemical Shifts ◽  
Qualitative Description ◽  
Triplet States ◽  
Excitation Energies ◽  
Polycyclic Aromatic

Polycyclic aromatic hydrocarbons (PAH) are a prominent substance class with a variety of applications in molecular materials science. Their electronic properties crucially depend on the bond topology in ways that are often highly non-intuitive. Here, we study, using density functional theory, the triplet states of four biphenylene-derived PAHs finding dramatically different triplet excitation energies for closely related isomeric structures. These differences are rationalised using a qualitative description of Clar sextets and Baird quartets, quantified in terms of nucleus independent chemical shifts, and represented graphically through a recently developed method for visualising chemical shielding tensors (VIST). The results are further interpreted in terms of a 2D rigid rotor model of aromaticity and through an analysis of the natural transition orbitals involved in the triplet excited states showing good consistency between the different viewpoints. We believe that this work constitutes an important step in consolidating these varying viewpoints of electronically excited states.

scholarly journals Study of Anharmonicity in Zirconium Hydrides Using Inelastic Neutron Scattering and Ab-Initio Computer Modeling

Inorganics ◽  
2021 ◽  
Vol 9 (5) ◽  
pp. 29
Author(s):  
Jiayong Zhang ◽  
Yongqiang Cheng ◽  
Alexander I. Kolesnikov ◽  
Jerry Bernholc ◽  
Wenchang Lu ◽  
...  
Keyword(s):  
Neutron Scattering ◽  
Excited States ◽  
Lattice Dynamics ◽  
Density Functional ◽  
Inelastic Neutron Scattering ◽  
Inelastic Neutron ◽  
Vibrational States ◽  
Functional Theory ◽  
Hydrogen Deuterium ◽  
Zirconium Hydrides

The anharmonic phonon behavior in zirconium hydrides and deuterides, including ϵ-ZrH2, γ-ZrH, and γ-ZrD, has been investigated from aspects of inelastic neutron scattering (INS) and lattice dynamics calculations within the framework of density functional theory (DFT). The harmonic model failed to reproduce the spectral features observed in the experimental data, indicating the existence of anharmonicity in those materials and the necessity of further explanations. Here, we present a detailed study on the anharmonicity in zirconium hydrides/deuterides by exploring the 2D potential energy surface of hydrogen/deuterium atoms and solving the corresponding 2D single-particle Schrödinger equation to obtain the eigenfrequencies, which are then convoluted with the instrument resolution. The convoluted INS spectra qualitatively describe the anharmonic peaks in the experimental INS spectra and demonstrate that the anharmonicity originates from the deviations of hydrogen potentials from quadratic behavior in certain directions; the effects are apparent for the higher-order excited vibrational states, but small for the ground and first excited states.

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