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 Exact Generalized Kohn-Sham Theory for Hybrid Functionals

2020 ◽  
Author(s):  
Rachel Garrick ◽  
Amir Natan ◽  
Tim Gould ◽  
Leeor Kronik
Keyword(s):  
Density Functional Theory ◽  
Density Functional ◽  
Formal Theory ◽  
Density Functional Theory Calculations ◽  
State Density ◽  
Hybrid Functional ◽  
Functional Theory ◽  
Exchange Correlation ◽  
Hybrid Functionals ◽  
The Many

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 analysis of 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. First, we extend formal GKS theory by proving a generalized adiabatic connection theorem. We then use this extension to derive two different definitions for a rigorous distinction between multiplicative exchange and correlation components - one new and one previously postulated. We examine their density-scaling behavior and discuss their similarities and differences. We then present a new algorithm for obtaining exact GKS potentials by inversion of accurate reference electron densities and employ this algorithm to obtain exact potentials for simple atoms and ions. We establish that an equivalent description of the many-electron problem is indeed obtained with any arbitrary global fraction of Fock exchange and we rationalize the Fock-fraction dependence of the computed remainder exchange-correlation potentials in terms of the new formal theory. Finally, we use the exact theoretical framework and numerical results to shed light on the exchange-correlation potential used in approximate hybrid functional calculations and to assess the consequences of different choices of fractional exchange.<br><br>

scholarly journals Exact Generalized Kohn-Sham Theory for Hybrid Functionals

2020 ◽  
Author(s):  
Rachel Garrick ◽  
Amir Natan ◽  
Tim Gould ◽  
Leeor Kronik
Keyword(s):  
Density Functional Theory ◽  
Density Functional ◽  
Formal Theory ◽  
Density Functional Theory Calculations ◽  
State Density ◽  
Hybrid Functional ◽  
Functional Theory ◽  
Exchange Correlation ◽  
Hybrid Functionals ◽  
The Many

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 analysis of 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. First, we extend formal GKS theory by proving a generalized adiabatic connection theorem. We then use this extension to derive two different definitions for a rigorous distinction between multiplicative exchange and correlation components - one new and one previously postulated. We examine their density-scaling behavior and discuss their similarities and differences. We then present a new algorithm for obtaining exact GKS potentials by inversion of accurate reference electron densities and employ this algorithm to obtain exact potentials for simple atoms and ions. We establish that an equivalent description of the many-electron problem is indeed obtained with any arbitrary global fraction of Fock exchange and we rationalize the Fock-fraction dependence of the computed remainder exchange-correlation potentials in terms of the new formal theory. Finally, we use the exact theoretical framework and numerical results to shed light on the exchange-correlation potential used in approximate hybrid functional calculations and to assess the consequences of different choices of fractional exchange.<br><br>

scholarly journals Exact Generalized Kohn-Sham Theory for Hybrid Functionals

2020 ◽  
Author(s):  
Rachel Garrick ◽  
Amir Natan ◽  
Tim Gould ◽  
Leeor Kronik
Keyword(s):  
Density Functional Theory ◽  
Density Functional ◽  
Formal Theory ◽  
Density Functional Theory Calculations ◽  
State Density ◽  
Hybrid Functional ◽  
Functional Theory ◽  
Exchange Correlation ◽  
Hybrid Functionals ◽  
The Many

<div>Hybrid functionals have proven to be of immense practical value in density functional theory calculations.</div><div>While they are often thought to be a heuristic construct, it has been established that this is in fact not the</div><div>case. Here, we present a rigorous and formally exact generalized Kohn-Sham (GKS) density functional theory</div><div>of hybrid functionals, in which exact remainder exchange-correlation potentials combine with a fraction of</div><div>Fock exchange to produce the correct ground state density. First, we extend formal GKS theory by proving a</div><div>generalized adiabatic connection theorem. We then use this extension to derive two different definitions for a</div><div>rigorous distinction between multiplicative exchange and correlation components - one new and one previously</div><div>postulated. We examine their density-scaling behavior and discuss their similarities and differences. We then</div><div>present a new algorithm for obtaining exact GKS potentials by inversion of accurate reference electron densities</div><div>and employ this algorithm to obtain exact potentials for simple atoms and ions. We establish that an equivalent</div><div>description of the many-electron problem is indeed obtained with any arbitrary global fraction of Fock exchange</div><div>and we rationalize the Fock-fraction dependence of the computed remainder exchange-correlation potentials in</div><div>terms of the new formal theory. Finally, we use the exact theoretical framework and numerical results to shed</div><div>light on the exchange-correlation potential used in approximate hybrid functional calculations and to assess the</div><div>consequences of different choices of fractional exchange.</div>

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 Investigation of the cis–trans structures and isomerization of oligoprolines by using Raman spectroscopy and density functional theory calculations: solute–solvent interactions and effects of terminal positively charged amino acid residues

RSC Advances ◽  
2020 ◽  
Vol 10 (57) ◽  
pp. 34493-34500
Author(s):  
Mei-Chun Huang ◽  
Wei-Hao Chen ◽  
Chen-Wei Huang ◽  
Kuei-Yen Huang ◽  
Jia-Cherng Horng ◽  
...  
Keyword(s):  
Density Functional Theory ◽  
Raman Spectroscopy ◽  
Density Functional ◽  
Theoretical Calculations ◽  
Density Functional Theory Calculations ◽  
State Density ◽  
Amino Acid Residues ◽  
Functional Theory ◽  
Solvent Interactions ◽  
Positively Charged

The low-wavenumber Raman spectra in combination with theoretical calculations via solid-state density functional theory (DFT)-D3 are displayed. The vibrational structures and interaction with solvent of poly-l-proline and the oligoproline P12 series are identified.

Terahertz spectroscopy and solid-state density functional theory calculations of structural isomers: Nicotinic acid, isonicotinic acid and 2-picolinic acid

2017 ◽  
Vol 31 (13) ◽  
pp. 1750149 ◽  
Author(s):  
Ling Ding ◽  
Wen-Hui Fan ◽  
Xu Chen ◽  
Ze-You Chen ◽  
Chao Song
Keyword(s):  
Density Functional Theory ◽  
Nicotinic Acid ◽  
Density Functional ◽  
Isonicotinic Acid ◽  
Picolinic Acid ◽  
Molecular Crystals ◽  
Density Functional Theory Calculations ◽  
State Density ◽  
Functional Theory ◽  
Absorption Features

We report, for the first time to our knowledge, the terahertz (THz) spectra of isonicotinic acid and 2-picolinic acid. The distinct THz spectral differences among these two isomers and nicotinic acid have also been observed, indicating that the THz vibrational modes are highly sensitive to the structural differences even in similar molecular crystals. Besides, solid-state density functional theory calculations reveal better qualitative agreement with the measured absorption features, which are related to the molecular vibrations of nicotinic acid and isonicotinic acid. As for 2-picolinic acid, the calculation based on the primitive cell reproduces the absorption features at 1.46, 1.82 and 2.46 THz originating from intermolecular vibrations. These results suggest that THz spectra can identify the complex intermolecular interactions even in similar molecular crystals, which shows potential applications in identifying isomers in food and pharmaceutical production.

Sign in / Sign up

Export Citation Format

Share Document