scholarly journals Spin-state dependence of exchange–correlation holes

2020 ◽  
Vol 224 ◽  
pp. 56-78
Author(s):  
Julia Brüggemann ◽  
Christoph R. Jacob
Keyword(s):  
Spin State ◽  
Density Functional ◽  
State Dependence ◽  
Spin States ◽  
Exchange Correlation ◽  
State Dependent ◽  
Dependent Density

The exchange–correlation holes of different spin-states are analyzed, as a step towards explicitly spin-state dependent density-functional approximations.

scholarly journals Spin-State Dependence of Exchange-Correlation Holes

2020 ◽  
Author(s):  
Julia Brüggemann ◽  
Christoph R. Jacob
Keyword(s):  
Spin State ◽  
State Dependence ◽  
Open Shell ◽  
Model Systems ◽  
Triplet States ◽  
Exchange Correlation ◽  
Electron Density Matrix ◽  
State Dependent ◽  
Lithium Dimer ◽  
Singlet And Triplet States

<div>Applications of density functionaltheory (DFT) in computational chemistry rely on an approximate exchange-correlation (xc) functional. However, existing approximations can fail dramatically for open-shell molecules, in particular for transition-metal complexes or radicals. Most importantly, predicting energy-differences between different spin-states with approximate exchange-correlation functionals remains extremely challenging. Formally, it is known that the exact xc functional should be spin-state dependent, but none of the available approximations features such an explicit spin-state dependence [Ch.~R.~Jacob, M.~Reiher, \textit{Int. J. Quantum Chem.}, 2012, \textbf{112}, 3661–3684]. Thus, to find novel approximations for the xc functional for open-shell systems, the development of spin-state dependent xc functionals appears to be a promising avenue. Here, we set out to shed light on the spin-state dependence of the xc functional by investigating the underlying xc holes, which we extract from configuration interaction calculations for model systems. We analyze the similarities and differences between the xc holes of the lowest-energy singlet and triplet states of the dihydrogen molecule, the helium atom, and the lithium dimer. To shed further light on the spin-state dependence of these xc holes we also discuss exact conditions that can be derived from the spin structure of the reduced two-electron density matrix. Altogether, our results suggest several possible routes towards the construction of explicitly spin-state dependent approximations for the xc functional.<br></div><br>

scholarly journals Spin-State Dependence of Exchange-Correlation Holes

2020 ◽  
Author(s):  
Julia Brüggemann ◽  
Christoph R. Jacob
Keyword(s):  
Spin State ◽  
State Dependence ◽  
Open Shell ◽  
Model Systems ◽  
Triplet States ◽  
Exchange Correlation ◽  
Electron Density Matrix ◽  
State Dependent ◽  
Lithium Dimer ◽  
Singlet And Triplet States

<div>Applications of density functionaltheory (DFT) in computational chemistry rely on an approximate exchange-correlation (xc) functional. However, existing approximations can fail dramatically for open-shell molecules, in particular for transition-metal complexes or radicals. Most importantly, predicting energy-differences between different spin-states with approximate exchange-correlation functionals remains extremely challenging. Formally, it is known that the exact xc functional should be spin-state dependent, but none of the available approximations features such an explicit spin-state dependence [Ch.~R.~Jacob, M.~Reiher, \textit{Int. J. Quantum Chem.}, 2012, \textbf{112}, 3661–3684]. Thus, to find novel approximations for the xc functional for open-shell systems, the development of spin-state dependent xc functionals appears to be a promising avenue. Here, we set out to shed light on the spin-state dependence of the xc functional by investigating the underlying xc holes, which we extract from configuration interaction calculations for model systems. We analyze the similarities and differences between the xc holes of the lowest-energy singlet and triplet states of the dihydrogen molecule, the helium atom, and the lithium dimer. To shed further light on the spin-state dependence of these xc holes we also discuss exact conditions that can be derived from the spin structure of the reduced two-electron density matrix. Altogether, our results suggest several possible routes towards the construction of explicitly spin-state dependent approximations for the xc functional.<br></div><br>

scholarly journals Spin-State Dependence of Exchange-Correlation Holes

2020 ◽  
Author(s):  
Julia Brüggemann ◽  
Christoph R. Jacob
Keyword(s):  
Spin State ◽  
State Dependence ◽  
Open Shell ◽  
Model Systems ◽  
Triplet States ◽  
Exchange Correlation ◽  
Electron Density Matrix ◽  
State Dependent ◽  
Lithium Dimer ◽  
Singlet And Triplet States

<div>Applications of density functionaltheory (DFT) in computational chemistry rely on an approximate exchange-correlation (xc) functional. However, existing approximations can fail dramatically for open-shell molecules, in particular for transition-metal complexes or radicals. Most importantly, predicting energy-differences between different spin-states with approximate exchange-correlation functionals remains extremely challenging. Formally, it is known that the exact xc functional should be spin-state dependent, but none of the available approximations features such an explicit spin-state dependence [Ch.~R.~Jacob, M.~Reiher, \textit{Int. J. Quantum Chem.}, 2012, \textbf{112}, 3661–3684]. Thus, to find novel approximations for the xc functional for open-shell systems, the development of spin-state dependent xc functionals appears to be a promising avenue. Here, we set out to shed light on the spin-state dependence of the xc functional by investigating the underlying xc holes, which we extract from configuration interaction calculations for model systems. We analyze the similarities and differences between the xc holes of the lowest-energy singlet and triplet states of the dihydrogen molecule, the helium atom, and the lithium dimer. To shed further light on the spin-state dependence of these xc holes we also discuss exact conditions that can be derived from the spin structure of the reduced two-electron density matrix. Altogether, our results suggest several possible routes towards the construction of explicitly spin-state dependent approximations for the xc functional.<br></div><br>

scholarly journals Spin-State Dependence of Exchange-Correlation Holes

2020 ◽  
Author(s):  
Julia Brüggemann ◽  
Christoph R. Jacob
Keyword(s):  
Spin State ◽  
State Dependence ◽  
Open Shell ◽  
Model Systems ◽  
Triplet States ◽  
Exchange Correlation ◽  
Electron Density Matrix ◽  
State Dependent ◽  
Lithium Dimer ◽  
Singlet And Triplet States

<div>Applications of density functionaltheory (DFT) in computational chemistry rely on an approximate exchange-correlation (xc) functional. However, existing approximations can fail dramatically for open-shell molecules, in particular for transition-metal complexes or radicals. Most importantly, predicting energy-differences between different spin-states with approximate exchange-correlation functionals remains extremely challenging. Formally, it is known that the exact xc functional should be spin-state dependent, but none of the available approximations features such an explicit spin-state dependence [Ch.~R.~Jacob, M.~Reiher, \textit{Int. J. Quantum Chem.}, 2012, \textbf{112}, 3661–3684]. Thus, to find novel approximations for the xc functional for open-shell systems, the development of spin-state dependent xc functionals appears to be a promising avenue. Here, we set out to shed light on the spin-state dependence of the xc functional by investigating the underlying xc holes, which we extract from configuration interaction calculations for model systems. We analyze the similarities and differences between the xc holes of the lowest-energy singlet and triplet states of the dihydrogen molecule, the helium atom, and the lithium dimer. To shed further light on the spin-state dependence of these xc holes we also discuss exact conditions that can be derived from the spin structure of the reduced two-electron density matrix. Altogether, our results suggest several possible routes towards the construction of explicitly spin-state dependent approximations for the xc functional.<br></div><br>

EXCHANGE–CORRELATION KERNEL IN TIME-DEPENDENT DENSITY FUNCTIONAL THEORY DERIVED FROM MANY-BODY THEORY

2004 ◽  
Vol 18 (07) ◽  
pp. 1055-1067 ◽  
Author(s):  
K. KARLSSON ◽  
F. ARYASETIAWAN
Keyword(s):  
Density Functional Theory ◽  
Optical Absorption ◽  
Density Functional ◽  
Time Dependent ◽  
Many Body ◽  
Functional Theory ◽  
Correlation Kernel ◽  
Exchange Correlation ◽  
Many Body Theory ◽  
Dependent Density

We derive a simplified Bethe–Salpeter equation for calculating optical absorption based on the assumption of a local electron–hole interaction. The original four-point equation for the kernel is reduced to a two-point one. A connection to the exchange–correlation kernel in time-dependent density functional theory can be established. The resulting fxc is found to be -W/2 where W contains only the short-range (local) part of the Coulomb screened interaction. This simple approximation was successfully applied to optical absorption spectra of some excitonic crystals, reproducing not only the continuum excitons but also the bound ones.

scholarly journals Optical Properties of Silver-Mediated DNA from Molecular Dynamics and Time Dependent Density Functional Theory

2018 ◽  
Vol 19 (8) ◽  
pp. 2346 ◽  
Author(s):  
Esko Makkonen ◽  
Patrick Rinke ◽  
Olga Lopez-Acevedo ◽  
Xi Chen
Keyword(s):  
Molecular Dynamics ◽  
Density Functional ◽  
Time Dependent ◽  
Basis Set ◽  
Dna Nanostructures ◽  
Exchange Correlation ◽  
Hartree Fock ◽  
Spurious Peak ◽  
20 Nm ◽  
Dependent Density

We report a combined quantum mechanics/molecular mechanics (QM/MM) molecular dynamics and time-dependent density functional (TDDFT) study of metal-mediated deoxyribonucleic acid (M-DNA) nanostructures. For the Ag + -mediated guanine tetramer, we found the maug-cc-pvdz basis set to be sufficient for calculating electronic circular dichroism (ECD) spectra. Our calculations further show that the B3LYP, CAM-B3LYP, B3LYP*, and PBE exchange-correlation functionals are all able to predict negative peaks in the measured ECD spectra within a 20 nm range. However, a spurious positive peak is present in the CAM-B3LYP ECD spectra. We trace the origins of this spurious peak and find that is likely due to the sensitivity of silver atoms to the amount of Hartree–Fock exchange in the exchange-correlation functional. Our presented approach provides guidance for future computational investigations of other Ag + -mediated DNA species.

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