Density-functional exchange correlation through coordinate scaling in adiabatic connection and correlation hole

1991 ◽  
Vol 43 (9) ◽  
pp. 4637-4646 ◽  
Author(s):  
Mel Levy
Keyword(s):  
Density Functional ◽  
Exchange Correlation ◽  
Correlation Hole ◽  
Coordinate Scaling

scholarly journals Coordinate Scaling in Time-Independent Excited-State Density Functional Theory for Coulomb Systems

Computation ◽  
2019 ◽  
Vol 7 (4) ◽  
pp. 59
Author(s):  
Ágnes Nagy
Keyword(s):  
Density Functional Theory ◽  
Excited State ◽  
Excited States ◽  
Density Functional ◽  
Coulomb Systems ◽  
State Theory ◽  
State Density ◽  
Functional Theory ◽  
Exchange Correlation ◽  
Coordinate Scaling

A time-independent density functional theory for excited states of Coulomb systems has recently been proposed in a series of papers. It has been revealed that the Coulomb density determines not only its Hamiltonian, but the degree of excitation as well. A universal functional valid for any excited state has been constructed. The excited-state Kohn–Sham equations bear resemblance to those of the ground-state theory. In this paper, it is studied how the excited-state functionals behave under coordinate scaling. A few relations for the scaled exchange, correlation, exchange-correlation, and kinetic functionals are presented. These relations are expected to be advantageous for designing approximate functionals.

DENSITY FUNCTIONALS AND SMALL INTERPARTICLE SEPARATIONS IN ELECTRONIC SYSTEMS

1995 ◽  
Vol 09 (14) ◽  
pp. 829-838 ◽  
Author(s):  
KIERON BURKE ◽  
JOHN P. PERDEW
Keyword(s):  
Spin Density ◽  
Density Functional ◽  
Electronic System ◽  
Electronic Systems ◽  
Hole Density ◽  
Density Functionals ◽  
Sum Rule ◽  
Exchange Correlation ◽  
Strongly Interacting ◽  
Correlation Hole

We review some recent results concerning the probability that two electrons will be found close together in any interacting electronic system, and why this probability is usually well approximated by local (LSD) and semilocal spin density functional theories. The success of these approximations for the energy in "normal" systems is explained by the usual sum rule arguments on the system- and spherically-averaged exchange-correlation hole density <n xc (u)>, coupled with the nearly correct, but not exact, behavior of these approximations as the interelectronic separation u → 0. We argue that the accuracy of the LSD on-top hole density in "normal" systems is due to its accuracy in the noninteracting, weakly-interacting, and strongly-interacting limits.

Exchange-Correlation Energy Densities and Response Potentials: Connection Between Two Definitions and Analytical Model for the Strong-Coupling Limit of a Stretched Bond

2019 ◽  
Author(s):  
S. Giarrusso ◽  
Paola Gori-Giorgi
Keyword(s):  
Density Functional Theory ◽  
Strong Coupling ◽  
Density Functional ◽  
Correlation Energy ◽  
Order Term ◽  
Strong Coupling Limit ◽  
Local Form ◽  
Coupling Constant ◽  
Functional Theory ◽  
Exchange Correlation

We analyze in depth two widely used definitions (from the theory of conditional probablity amplitudes and from the adiabatic connection formalism) of the exchange-correlation energy density and of the response potential of Kohn-Sham density functional theory. We introduce a local form of the coupling-constant-dependent Hohenberg-Kohn functional, showing that the difference between the two definitions is due to a corresponding local first-order term in the coupling constant, which disappears globally (when integrated over all space), but not locally. We also design an analytic representation for the response potential in the strong-coupling limit of density functional theory for a model single stretched bond.<br>

Evaluating Transition Metal Barrier Heights with the Latest DFT Exchange–Correlation Functionals – the MOBH35 Benchmark Dataset

2019 ◽  
Author(s):  
Mark Iron ◽  
Trevor Janes
Keyword(s):  
Transition Metal ◽  
Density Functional ◽  
Computational Cost ◽  
Basis Set ◽  
Functional Theory ◽  
Exchange Correlation ◽  
Barrier Heights ◽  
Complete Basis Set ◽  
Complete Basis Set Limit ◽  
Hybrid Functionals

A new database of transition metal reaction barrier heights – MOBH35 – is presented. Benchmark energies (forward and reverse barriers and reaction energy) are calculated using DLPNO-CCSD(T) extrapolated to the complete basis set limit using a Weizmann1-like scheme. Using these benchmark energies, the performance of a wide selection of density functional theory (DFT) exchange–correlation functionals, including the latest from the Truhlar and Head-Gordon groups, is evaluated. It was found, using the def2-TZVPP basis set, that the ωB97M-V (MAD 1.8 kcal/mol), ωB97X-V (MAD 2.1 kcal/mol) and SCAN0 (MAD 2.1 kcal/mol) hybrid functionals are recommended. The double-hybrid functionals PWPB95 (MAD 1.6 kcal/mol) and B2K-PLYP (MAD 1.8 kcal/mol) did perform slightly better but this has to be balanced by their increased computational cost.

scholarly journals Application of time-dependent current-density-functional theory to nonlocal exchange-correlation effects in polymers

2003 ◽  
Vol 118 (3) ◽  
pp. 1044-1053 ◽  
Author(s):  
M. van Faassen ◽  
P. L. de Boeij ◽  
R. van Leeuwen ◽  
J. A. Berger ◽  
J. G. Snijders
Keyword(s):  
Density Functional Theory ◽  
Current Density ◽  
Density Functional ◽  
Time Dependent ◽  
Correlation Effects ◽  
Functional Theory ◽  
Exchange Correlation
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