39
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Is there any DFT code or software that has the option to use this exact exchange-correlation energy functional?
Below is a summary of what I have found:
What is meant by "Exact exchange"$\,$?
The question mentions the following (in order of how they were presented in the question):
Exact exchange-correlation ...
12
votes
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How does libxc calculate the potential of GGA functionals?
Libxc does not compute the full potential. Instead, it provides necessary ingredients for the code that calls Libxc to compute the potential. This strategy allows the library to work with a variety of ...
- 1,913
11
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Is there any DFT code or software that has the option to use this exact exchange-correlation energy functional?
Whenever you see EXX, a warning flag should go up inside your head. It is never clear whether one means just using Hartree-Fock exchange in a DFT calculation, implying a generalized Kohn-Sham scheme ...
- 20.1k
10
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What is the physical meaning of the term "non-local interaction"?
The non-local operator in Hartree Fock is the Exchange operator. Locality is a mathematical property. Look at the Coulomb operator first which acts like this:
$$ \hat v_H\;\varphi_s(r) = \sum_i^{N_\...
- 605
9
votes
Non-Convergence of the XC functional in the sense of a Taylor series
I agree with the comment by @jheindel. One issue is that the derivatives in GGA and meta-GGA functionals are not used like a Taylor series. The derivatives are used to obey more known constraints and ...
- 1,738
9
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Where can I find BLYP pseudopotentials?
Try searching for BLYP pseudopotentials here - http://pseudopotentials.quantum-espresso.org/legacy_tables/hartwigesen-goedecker-hutter-pp
. One can generate BLYP and B3LYP pseudopotentials also.
- 1,542
8
votes
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Which strategy of improving the DFT band gap is the most effective?
It's a nice question, it will be difficult to compare their accuracy and efficiency in a single plot, because the band gap problem is mainly divided into two parts: the self-interaction and the ...
- 926
8
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DFT xc integration grid for periodic boundary conditions
Exactly the same grids as for molecules, i.e. Becke grids. You just need to take the periodic boundary conditions into account when building the grid weights.
edit: e.g. PySCF has both molecules and ...
- 20.1k
8
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Synergy of Exchange and Correlation, Why are they Combined in the Term "Exchange-Correlation" Energy
I guess the reason they are grouped together as XC, is that they are whatever is left when the Coulomb interactions and Slater determinant kinetic energy is accounted for, i.e. they are (by definition)...
- 1,886
7
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Parameterization in the generalised gradient approximation (GGA)
What role does the constant charge density play in GGA?
Most GGAs give out LDAs at the limit of zero gradient. This is, however, not always true.
Also, in literature, methods describe DFT ...
- 20.1k
7
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How can the GGA functionals in libxc be evaluated?
The xc energy is given by
$$ E_\text{xc} = \int n({\bf r}) \epsilon_\text{xc} ({\bf r}) {\rm d}^3r \equiv \int f_\text{xc} ({\bf r}) {\rm d}^3r $$
where $\epsilon_\text{xc}$ is the energy density per ...
- 20.1k
6
votes
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Self-interaction in density functional approximations for many-electron systems
No self-interaction in the exact functional
The electronic structure Hamiltonian in real space is
$$\tag{1}
H = T + V_{ee} + V_{\text{ext}} = -\frac12 \sum_i \nabla_i^2 + \sum_{i<j} \frac{1}{\lvert ...
- 1,116
6
votes
Non-Convergence of the XC functional in the sense of a Taylor series
It's somewhat ambiguous to talk about approximating the XC energy as a Taylor expansion. A Taylor expansion is a series involving a fixed number of variables, and contains successively higher (non-...
- 10.2k
6
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Why does the PBE XC functional not appear to be a sum of exchange and correlation energy?
The final equation you quoted merely serves to define $F_{XC}$, which is plotted in Fig. 1 of the article to succinctly illustrate the behavior of the PBE functional as a function of density and ...
- 10.2k
6
votes
What is the physical meaning of the term "non-local interaction"?
It's all hollow words if no proper definition is given. The definition I know is the following: For a one-body operator $A$, define
$$A(x,x^\prime):=\langle x|A|x^\prime\rangle \tag{1} \quad . $$
We ...
- 757
6
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Closed-form expression for excitation energies, given the exact XC functional
No, they cannot be obtained from a DFT calculation. As the first paper I linked in the previous response says, DFT is a ground state theory, and it should not be expected to get excited state ...
- 1,136
6
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'Exchange' in Hartree-Fock and Kohn-Sham DFT
In Hartree-Fock, one just writes down the many-electron wavefunction as a hartree-product. This does not capture any correlation effects since each electron is treated to be independent of each other.
...
- 20.1k
5
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What correlation effects are included in KS-DFT with LDA and GGA?
LDA only includes local density effects.
GGA also includes dependence on the gradient of the density.
Meta-GGAs include dependence on the Laplacian of the density and/or the local kinetic energy ...
- 20.1k
5
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What's the physics contained in the exchange-correlation functional in the framework of KS-DFT?
You have already detailed what the physics contained in the exchange-correlation functional is.
Self-interaction error is not physical; it is an artifact in density functional approximations that ...
- 20.1k
5
votes
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Closed-form expression for excitation energies, given the exact XC functional
Do you consider the exact frequency-dependent XC kernel as part of "the exact XC functional"? And do you allow the use of additional ingredients like two-electron integrals?
If both of your ...
- 10.2k
5
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Query on using the exchange-correlation functional GGA or LDA approximation in Quantum ESPRESSO for electronic and magnetic property calculations?
However, I am still unsure of how to specify that I want to run a calculation using GGA and LDA approximation in the input file.
Quantum ESPRESSO (QE) uses a plain-text input file and consists of the ...
5
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Synergy of Exchange and Correlation, Why are they Combined in the Term "Exchange-Correlation" Energy
This is pretty much a deliberate quirk of DFT.
You should, however, first take note that Exchange energy term is actually coming from the Coulomb interaction, albeit of course coming from the Slater ...
4
votes
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What is just "LDA" in GPAW?
According to GPAW's documentation, GPAW would use its own LDA implementation, but if I interpret the table correctly, that should correspond to libxc's LDA_X + LDA_C_PW:
Exchange-Correlation ...
- 4,891
4
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Obtaining data for plotting Fermi and Coulomb holes of a hydrogen molecule
I am not sure I fully understood your question, but I will give it a try.
The hydrogen molecule in its ground state only contains two electrons of opposite spin, which means that the exchange (Fermi) ...
4
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How to set different exchange correlational functionals in VASP?
How can I change this PBE to PW91 in INCAR to see the effect?
According to the element order of your POSCAR, concatenate the different ...
- 15.4k
4
votes
Self-interaction in density functional approximations for many-electron systems
The way I like to think about this is the Levy-Lieb functional. The universal functional takes the following form:
$F[\rho] = \underset{\substack{\Psi \mapsto \rho(\vec{r}) \\ \rho \in \mathcal{D}}}{...
- 520
3
votes
The projector augmented wave (PAW) method, pseudopotentials (PP), and exchange correlation functionals
PAW is proposed to deal with the interaction between electrons and ions. However, PBE or GGA (PBE just one kind of GGA) is just the exchange-correlation functional. You can think PAW and PBE are ...
- 15.4k
3
votes
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Is the pseudopotential designed for GGA also suited for meta-GGA?
In practice, you're likely to be okay. Borlido and coworkers (the article is open access) stuied just this for band gaps in 2020, concluding that the error based on the choice of functional is ...
- 1,116
3
votes
Is the pseudopotential designed for GGA also suited for meta-GGA?
In the case of an hybrid functional this is exactly what we do by using the GGA pseudopotentials, besides hybrid functionals are not often used for generating pseudopotentials from an all-electron ...
- 926
2
votes
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Dirac exchange energy and X_alpha LDA methods
How is LSDA exchange energy is derived?
LSDA exchange is computed from the homogeneous electron gas from the expression for exact exchange; see any standard textbook on electronic structure with ...
- 20.1k
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