# Questions tagged [kohn-sham]

Questions related to the Kohn-Sham approach to DFT.

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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 appears to be so popular even though it is strictly a ground-state method - all calculations are done at 0 K. How then, is it so popular when describing materials that have real-life ...
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### Is there any relevant DFT formalism apart from the Kohn-Sham approach?

I wonder if all DFT codes are based on the Kohn-Sham formalism?. If other methods are available, what are their scopes?
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### Difference between Van der Waals (DFT-D and DFT-D3) corrections in ab-initio calculations

In Kohn-Sham DFT calculations, Van der Waals corrections are often implemented in the structure optimization calculations because the typical functionals such as LDA and GGA are found to not treat ...
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### What's the difference between spin-unpolarized, spin-polarized and non-colinear calculation?

The central goal of the first-principles simulation with DFT is to solve the Kohn-Sham equation: $$[-\dfrac{1}{2}\nabla^2+v_{\textit{eff}}(\vec{r})]\phi_n(\vec{r})=E_n\psi_n(\vec{r}) \tag{1}$$ Here ...
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### Why is CPHF/CPKS necessary for calculating second derivatives?

This question is coming from an answer to one of my previous questions. During optimizations, QM programs usually compute the gradient(first derivative) analytically, and take a guess of the hessian (...
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### Deep Neural Networks: Are they able to provide insights for the many-electron problem or DFT?

The solution of the many-electron Schrodinger equation is the key to understand the properties of matter. However, it is notorious due to the exponential wall (for example, see section II (C) of ...
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### Do eigenvalues in DFT mean anything?

My question is specifically related to the molecular energies of Kohn-Sham DFT: Do eigenvalues in KS-DFT mean anything?
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### Hartree-Fock density vs Kohn-Sham density

Hartree-Fock density is free of self-interaction but lacks electron correlation effects, while the density from KS-DFT (using an xc functional or potential, both which are explicitly density-dependent ...
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### Is the electronic band gap the only thing that is affected, when switching from standard KS-DFT to Hybrid functionals?

It is very well known that Kohn-Sham DFT underestimates bandgap. To get an accurate estimate of the bandgap, people often turn to Hybrid functionals (if they don't want to perform the actual ...
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### Quantum ESPRESSO ph.x output

I wanted to calculate the normal modes of some particular material using the Quantum ESPRESSO. Everything went fairly well, but there is a couple of lines in the output that I do not understand. In ...
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### 'Exchange' in Hartree-Fock and Kohn-Sham DFT

I am a bit confused about the notions of exchange in the Hartree-Fock and Kohn-Sham Density Functional Theory schemes. In Hartree-Fock, one just writes down the many-electron wavefunction as a hartree-...
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### Extended Hybrid Methods

Hybrid DFT methods, where the functional is supplemented with Hartree-Fock exchange, have become increasingly popular due to their low cost and decent accuracy. Double hybrids, which mix in an MP2 ...
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### Why Kohn-Sham equations are regarded as single-particle equations?

The Kohn-Sham equations are given by:  \left(-\frac{\hbar^2}{2m} \nabla_{i}^{2}+V_{s}\left(\hat{\boldsymbol{r}}_{i}\right)+V_{H}\left(\hat{\boldsymbol{r}}_{i}\right)+V_{X C}\left(\hat{\boldsymbol{r}}...
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### Replacement from minimizing the energy to solving the KS equation (or eigenvalue problem)

I am now reading the paper (or review for beginners), A bird's-eye view of density-functional theory, but I could not understand that the energy minimization problem, in which the derivative of the ...
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### A mapping between effective potential and non-interacting electrons moving on the potential

From this question and answer, I understood the Hohenberg-Kohn theorem and found that there is a one-to-one correspondence between the external potential $V_\text{ext}$ and the electron density $\rho$ ...
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### What is the real reason behind the minimization of the system at the beginning of a Car-Parrinello MD calculation?

I've been studying MD and more specifically about Car-Parrinello Molecular Dynamics and I'm not entirely sure if I understood the meaning behind the minimization. This is the way I understand it: The ...
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### Is there a relation between self-interaction errors and integer-discontinuities in Kohn-Sham-DFT?

I am wondering whether or not self-interaction error and integer-discontinuity in Kohn-Sham density functionals, are related to each other?
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### Is an "exact" double hybrid density the same as the "exact" DFT density?

Double hybrid approximate functionals have "unoccupied" Kohn-Sham orbitals in their formulations due to their MP2 component; however, the "exact functional" depends only on the &...
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### Scaling and speed-up of real-space DFT calculations using finite elements approach

I have recently encountered this paper in which the authors have formulated Kohn-Sham equations using the finite elements package deal.II, leading to an open-source software called DFT-FE. It stated ...
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### Closed-form expression for excitation energies, given the exact XC functional

In an answer to my question regarding the theoretical rigour in computing excitation energies using only the Kohn-Sham orbital energies, the rigour turned out to be nonexistent. After looking this ...
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### Relationship between functional derivative and potential value at a position

Thanks to very helpful and detailed answers for my previous question, I understand the functional derivative of the energy with respect to the density. In addition, this functional derivative is equal ...
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### Question on generalised Kohn-Sham "band gap"

It is often said that the optical band gap, i.e. the first excitation energy, of a species is exactly equal to the difference between the (Kohn-Sham) HOMO and LUMO. This would mean that the state of ...
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### Does a TD-DFT excitation from a closed-shell determinant only include the alpha electron part?

From an input in ORCA 5.0.3 ! PBE 6-31G* %TDDFT NROOTS 3 END * xyz 0 1 H 0. 0. 0. H 0. 0. 0.7414 * the output includes ...
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### Decay rate of DSD-PBEPBE-D3BJ

I gave up on the wB97X-2(TQZ) functional, which would have an exact decay rate of -1/r, re: my previous question and decided to use DSD-PBEPBE-D3BJ, which is available on vanilla Psi4. I then looked ...
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### Neural network as a customised XC functional in PySCF?

I've been trying to implement neural network as a customised exchange-correlation functional in PySCF but with no success. Below is the example code for customised XC functional. Anyone has any idea ...
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### Is this method of obtaining only the exact "other" densities, and no other properties w.l.o.g, correct?

In Kohn-Sham DFT, the exact density of the ground-state wavefunction is given by summing the squares of the filled K-S orbitals. Suppose now that one only needs the exact density (and nothing else w.l....
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### Is this method of obtaining only the exact "first excited state" density correct, under select conditions that makes it mathematically non-ambiguous?

(For context, see my other question here; this has been disproven (albeit contestedly), and is not even well-defined in the first place, so I'm going to ask a slightly different (and well-defined) ...
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### Is there an analogue of the K-S theorem for double hybrids

In my previous question, I was basically asking whether the results of the double hybrid using the exact XC functional are the same as those of just the exact XC functional. Even that sentence is hard ...
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