scholarly journals Power Laws Used to Extrapolate the Coupled Cluster Correlation Energy to the Thermodynamic Limit

2021 ◽  
Author(s):  
Tina N. Mihm ◽  
Bingdi Yang ◽  
James J. Shepherd
Keyword(s):  
Thermodynamic Limit ◽  
Correlation Energy ◽  
Power Laws ◽  
Coupled Cluster ◽  
Cluster Correlation

Towards density functional approximations from coupled cluster correlation energy densities

2019 ◽  
Vol 150 (24) ◽  
pp. 244116 ◽  
Author(s):  
Johannes T. Margraf ◽  
Christian Kunkel ◽  
Karsten Reuter
Keyword(s):  
Density Functional ◽  
Correlation Energy ◽  
Coupled Cluster ◽  
Cluster Correlation

Towards Density Functional Approximations from Coupled Cluster Correlation Energy Densities

2019 ◽  
Author(s):  
Johannes T. Margraf ◽  
Christian Kunkel ◽  
Karsten Reuter
Keyword(s):  
Surface Science ◽  
Density Functional ◽  
Correlation Energy ◽  
Local Density ◽  
Coupled Cluster ◽  
Electron Systems ◽  
Condensed Matter Theory ◽  
Matter Theory ◽  
Helium Isoelectronic Series ◽  
Cluster Correlation

<div> <div> <div> <p>(Semi-)local density functional approximations (DFAs) are the workhorse electronic structure methods in condensed matter theory and surface science. The correlation energy density εc(r) (a spatial function that yields the correlation energy Ec upon integration) is central to defining such DFAs. Unlike Ec, εc(r) is not uniquely defined, however. Indeed, there are infinitely many functions that integrate to the correct Ec for a given electron density ρ. The challenge for constructing useful DFAs is thus to find a suitable connection between εc(r) and ρ. Herein, we present a new such approach by deriving εc(r) directly from the coupled- cluster (CC) energy expression. The corresponding energy densities are analyzed for prototypical two-electron systems. To explore their usefulness for designing DFAs, we construct a semilocal functional to approximate the numerical CC correlation energy densities. Importantly, the energy densities are not simply used as reference data, but guide the choice of the functional form, leading to a remarkably simple and accurate correlation functional for the Helium isoelectronic series. </p> </div> </div> </div>

Making the Coupled Cluster Correlation Energy Machine-Learnable

2018 ◽  
Vol 122 (30) ◽  
pp. 6343-6348 ◽  
Author(s):  
Johannes T. Margraf ◽  
Karsten Reuter
Keyword(s):  
Correlation Energy ◽  
Coupled Cluster ◽  
Cluster Correlation

Towards Density Functional Approximations from Coupled Cluster Correlation Energy Densities

2019 ◽  
Author(s):  
Johannes T. Margraf ◽  
Christian Kunkel ◽  
Karsten Reuter
Keyword(s):  
Surface Science ◽  
Density Functional ◽  
Correlation Energy ◽  
Local Density ◽  
Coupled Cluster ◽  
Electron Systems ◽  
Condensed Matter Theory ◽  
Matter Theory ◽  
Helium Isoelectronic Series ◽  
Cluster Correlation

<div> <div> <div> <p>(Semi-)local density functional approximations (DFAs) are the workhorse electronic structure methods in condensed matter theory and surface science. The correlation energy density εc(r) (a spatial function that yields the correlation energy Ec upon integration) is central to defining such DFAs. Unlike Ec, εc(r) is not uniquely defined, however. Indeed, there are infinitely many functions that integrate to the correct Ec for a given electron density ρ. The challenge for constructing useful DFAs is thus to find a suitable connection between εc(r) and ρ. Herein, we present a new such approach by deriving εc(r) directly from the coupled- cluster (CC) energy expression. The corresponding energy densities are analyzed for prototypical two-electron systems. To explore their usefulness for designing DFAs, we construct a semilocal functional to approximate the numerical CC correlation energy densities. Importantly, the energy densities are not simply used as reference data, but guide the choice of the functional form, leading to a remarkably simple and accurate correlation functional for the Helium isoelectronic series. </p> </div> </div> </div>

Towards Density Functional Approximations from Coupled Cluster Correlation Energy Densities

2019 ◽  
Author(s):  
Johannes T. Margraf ◽  
Christian Kunkel ◽  
Karsten Reuter
Keyword(s):  
Surface Science ◽  
Density Functional ◽  
Correlation Energy ◽  
Local Density ◽  
Coupled Cluster ◽  
Electron Systems ◽  
Condensed Matter Theory ◽  
Matter Theory ◽  
Helium Isoelectronic Series ◽  
Cluster Correlation

<div> <div> <div> <p>(Semi-)local density functional approximations (DFAs) are the workhorse electronic structure methods in condensed matter theory and surface science. The correlation energy density εc(r) (a spatial function that yields the correlation energy Ec upon integration) is central to defining such DFAs. Unlike Ec, εc(r) is not uniquely defined, however. Indeed, there are infinitely many functions that integrate to the correct Ec for a given electron density ρ. The challenge for constructing useful DFAs is thus to find a suitable connection between εc(r) and ρ. Herein, we present a new such approach by deriving εc(r) directly from the coupled- cluster (CC) energy expression. The corresponding energy densities are analyzed for prototypical two-electron systems. To explore their usefulness for designing DFAs, we construct a semilocal functional to approximate the numerical CC correlation energy densities. Importantly, the energy densities are not simply used as reference data, but guide the choice of the functional form, leading to a remarkably simple and accurate correlation functional for the Helium isoelectronic series. </p> </div> </div> </div>

Linear scaling coupled cluster method with correlation energy based error control

2010 ◽  
Vol 133 (1) ◽  
pp. 014107 ◽  
Author(s):  
Marcin Ziółkowski ◽  
Branislav Jansík ◽  
Thomas Kjærgaard ◽  
Poul Jørgensen
Keyword(s):  
Error Control ◽  
Correlation Energy ◽  
Cluster Method ◽  
Coupled Cluster ◽  
Linear Scaling ◽  
Coupled Cluster Method
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