27
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Given that Kohn-Sham DFT is strictly a ground-state method (at 0 K), how is it sufficient to describe materials in real-life applications?
These are a few extra points to complement Andrew Rosen's comprehensive response:
To be absolutely clear, typical DFT calculations are not performed at 0K, a better description of what happens is ...
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Given that Kohn-Sham DFT is strictly a ground-state method (at 0 K), how is it sufficient to describe materials in real-life applications?
You are correct that KS-DFT, strictly speaking, involves calculations of a potential energy surface at 0 K. However, if you accept that the density functional approximation you are using is ...
- 7,281
20
votes
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Difference between Van der Waals (DFT-D and DFT-D3) corrections in ab-initio calculations
As you mention, there are many empirical dispersion corrections for density functional theory.
Generally, the term "DFT-D" refers to a generic dispersion-corrected density functional calculation, ...
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votes
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What's the difference between spin-unpolarized, spin-polarized and non-colinear calculation?
Noncollinear magnetism means that the orientation of the magnetization varies in space. Examples for such structures are magnetic domain walls, spin spirals, or magnetic skyrmions. To describe these ...
- 1,426
14
votes
Hartree-Fock density vs Kohn-Sham density
Kieron Burke and co-workers have shown that in many cases one can get better results by using the HF density as input to a DFT-XC evaluation of the energy, as opposed to using the DFT-XC to generate a ...
- 1,311
14
votes
Do eigenvalues in DFT mean anything?
This is a very interesting question and to the best of my knowledge there is not yet a conclusive answer. As the chemistry stackexchange threads linked by @Tyberius already state Kohn-Sham orbital ...
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Is there any relevant DFT formalism apart from the Kohn-Sham approach?
At least I was able to find three other forms of DFT listed as:
Lattice density-functional theory: It's suitable for modeling the lattice gas, binary liquid solutions, order-disorder phase ...
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13
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Why is CPHF/CPKS necessary for calculating second derivatives?
It comes down to the fact that HF and KS both are variational methods. This short article by Julien Toulouse gives a great description of ways to compute static/dynamic response properties. I'll just ...
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Total energy from KS-DFT: How reliable is it and why?
The main issue here is that the calculated energy is a potential energy, that's why the absolute value is useless.
As potential energy always depends on a reference system, you can only use the ...
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12
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Deep Neural Networks: Are they able to provide insights for the many-electron problem or DFT?
"However, it is notorious due to the exponential wall"
That is completely true, though there's indeed some methods such as FCIQMC, SHCI, and DMRG that try to mitigate this:
How to overcome ...
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12
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Is there any relevant DFT formalism apart from the Kohn-Sham approach?
Orbital-Free Density Functional Theory (OFDFT) is, as the name suggests, an attempt to work with DFT without using the Kohn-Sham (KSDFT) approach of expressing the density as a sum of non-interacting ...
- 15.2k
12
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Given that Kohn-Sham DFT is strictly a ground-state method (at 0 K), how is it sufficient to describe materials in real-life applications?
Kohn-Sham DFT may only be rigorous at zero temperature, but at nonzero temperature,
Kohn-Sham-Mermin DFT is an equally rigorous replacement. There are two major differences
Rather than deriving the ...
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How can we say that the KS equation is describing a noninteracting many-electron system?
First of all, let me emphasize that it is more appropriate to speak of KS equations (plural), which you correctly denoted by an index $i$ in your post. This index goes over all KS orbitals (i.e. ...
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What does occupations='tetrahedra' mean in Quantum ESPRESSO?
For the "why" you should use the tetrahedron method when computing the density of states, check out this paper on exactly that topic! In short, other approaches (e.g. Gaussian smearing) will ...
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11
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Is the electronic band gap the only thing that is affected, when switching from standard KS-DFT to Hybrid functionals?
The band gap problem in DFT is not just due to approximate exchange-correlation functionals--it is a reflection of the fact that the Kohn-Sham (K-S) orbitals are a mathematical construction of a non-...
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Ion-ion interaction potential in Kohn-Sham DFT
If the ion-ion interaction contributes a constant term to the Hamiltonian $H$, then our new Hamiltonian is $H+C$. The eigenvalue of a constant is just itself, so we have:
$$
\tag{1}
(H + C )\psi = (\...
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What's the relationship between the first HK theorem and the second HK theorem?
Using your notation, the definition for the universal functional is
$$
F_{HK}[\rho] = \left< \psi_0[\rho] \right| \hat{T} + \hat{W} \left| \psi_0[\rho] \right>,
$$
where $\hat{T}$ and $\hat{W}$ ...
- 1,883
10
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What's the difference between spin-unpolarized, spin-polarized and non-colinear calculation?
Basically, this is the split between restricted, unrestricted, and generalized Hartree-Fock (or Kohn-Sham) theory.
In the restricted theory, both the spin-up and spin-down electrons occupy the same ...
- 18k
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Ion-ion interaction potential in Kohn-Sham DFT
Add more information to @Nike Dattani's answer:
The matter can be viewed as a set of ions and electrons. The Kohn-Sham equation listed in your post aims to solve the electronic part. As for the ionic ...
- 14.9k
10
votes
Physically motivated double hybrid DFT?
It's determined by fitting. You optimize the functional (i.e. the coefficients therein) to yield the lowest errors possible.
See e.g. the wB97M(2) functional for an example of a recent double hybrid.
- 18k
10
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Do eigenvalues in DFT mean anything?
A few more papers to add to Michael's answer:
What Do the Kohn-Sham Orbitals and Eigenvalues Mean
Relationship of Kohn–Sham eigenvalues to excitation energies
- 18k
10
votes
Total energy from KS-DFT: How reliable is it and why?
Your question is on absolute energies, but all of your physical examples are relative energies. One could also add properties to the list; however, these are again not determined by the total energy, ...
- 18k
9
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How can we say that the KS equation is describing a noninteracting many-electron system?
As you note, the interacting electrons and the Kohn-Sham non-interacting electrons have the same density. How is this possible when the Hamiltonians for the two systems are so different?
The answer is ...
- 1,883
9
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Replacement from minimizing the energy to solving the KS equation (or eigenvalue problem)
The trick is that, instead of solving $\frac{\delta E}{\delta \rho}=0$, we solve the equivalent set of equations $\frac{\delta E}{\delta \psi^*_n}=0, \forall n$ (plus the Lagrange multipliers required ...
- 9,076
8
votes
Hartree-Fock density vs Kohn-Sham density
I guess this will go in the answer slot, it is a bit long for a comment.
DFT typically has quite a bit less spin contamination than HF (attributed to the inclusion of correlation).
One issue however ...
- 4,306
8
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Ion-ion interaction potential in Kohn-Sham DFT
I would like to emphasise a few aspects that seem to be a little bit between the lines in the other answers.
Density functional theory is based on the fact that observables of an interacting-electron ...
- 1,426
8
votes
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A mapping between effective potential and non-interacting electrons moving on the potential
Roughly speaking and provided that the Hohenberg-Kohn theorem applies, if the $v$-representable ground state density of an interacting system $\rho$ is additionally non-interacting $v$-representable, ...
- 659
8
votes
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Orthonormality of Kohn-Sham orbitals
You are correct that orbitals from different $k$-points should be orthogonal. $k$-points are irreps of the translation group and, similar to the irreps of point groups for molecules, integrals of two ...
- 15.2k
7
votes
Does Kohn-Sham DFT use Slater determinants?
A couple of comments perhaps to clarify some points.
The first Hohenberg-Kohn theorem states that the one-electron density determines uniquely the energy, for a non-degenerate ground state. The second ...
- 1,311
7
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Does Kohn-Sham DFT use Slater determinants?
As Nike has already mentioned, Slater determinants occur in KS-DFT in much the same way that they do in Hartree-Fock as a way to combine a set of one-electron orbitals into an antisymmetric many-...
- 15.2k
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