Questions tagged [kohn-sham]

Questions related to the Kohn-Sham approach to DFT.

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6 votes
2 answers
181 views

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 ...
5 votes
1 answer
96 views

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 ...
5 votes
0 answers
56 views

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 ...
8 votes
2 answers
223 views

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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7 votes
0 answers
101 views

Scaling and speedup of Real-space based DFT calculations using Finite Elements approach

I have recently encountered paper where the authors have formulated Kohn-Sham equations using the finite-element package deal.II. It stated in paper DFT-FE was significantly faster than QE for all ...
  • 3,267
10 votes
1 answer
106 views

Orthonormality of Kohn-Sham orbitals

I was wondering if Kohn-Sham orbitals corresponding to a different Bloch wavevector should be orthogonal? I know that we should have $$\int d \boldsymbol{r}\phi_i(\boldsymbol{r}) \phi_j^*(\boldsymbol{...
8 votes
1 answer
288 views

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 ...
  • 1,647
5 votes
2 answers
223 views

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 ...
  • 1,647
8 votes
1 answer
187 views

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 $\rho$ ...
  • 1,647
7 votes
2 answers
228 views

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 ...
10 votes
1 answer
192 views

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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13 votes
1 answer
960 views

What does occupations='tetrahedra' mean in Quantum ESPRESSO?

I am trying to understand Quantum ESPRESSO input file, line by line. So far everything seems pretty easy to understand. However, I do not know what ...
  • 335
12 votes
2 answers
540 views

How can we say that the KS equation is describing a noninteracting many-electron system?

Based on HK's two theorems, the density functional theory was built. Because one can't find the universal energy functional $F_{HK}[n(r)]$, Kohn and Sham further proposed the Kohn-Sham ansatz: mapping ...
  • 14k
12 votes
2 answers
142 views

Procedure to classify errors in Kohn-Sham DFT

I was reading this paper which basically outlines the two main types of errors that one encounters in Kohn-Sham DFT : Density-based errors and Functional-based errors. I understand the practical ...
  • 2,336
12 votes
3 answers
723 views

Total energy from KS-DFT: How reliable is it and why?

As the title suggests, my question is fundamental - How reliable are the total energy values from Kohn-Sham Density Functional Theory, and why. I acknowledge that absolute values of energies are ...
  • 2,336
9 votes
1 answer
308 views

'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-...
  • 2,336
11 votes
2 answers
759 views

What's the relationship between the first HK theorem and the second HK theorem?

The first Hohenberg-Kohn (HK) theorem: The external potential $v(\vec{r})$ is determined, within a trivial additive constant, by the ground-state electron density $\rho(\vec{r})$. From basic quantum ...
  • 14k
13 votes
3 answers
497 views

Ion-ion interaction potential in Kohn-Sham DFT

The Kohn-Sham equation as described in "Density Functional Theory: A Practical Introduction" by Dr David Sholl is: $$\tag{1}\left[-\frac{\hbar^2}{2m}\nabla^2+V({\bf r})+V_H({\bf r})+V_{XC}({\...
17 votes
1 answer
754 views

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 ...
  • 14k
8 votes
3 answers
490 views

Does Kohn-Sham DFT use Slater determinants?

In the Hartree method, it is known that the wavefunction of the system does not obey the antisymmetry principle of fermions - that is when you swap two particles, they don't up a negative sign. ...
  • 2,336
16 votes
1 answer
495 views

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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12 votes
1 answer
195 views

What's the physics contained in the exchange-correlation functional in the framework of KS-DFT?

This question is inspired by this post. In the Kohn-Sham framework of density functional theory, the total energy is expressed as: $$E=E_{kin}^{non}+E_{ext}+E_{H}+E_{xc}$$ in which The first term is ...
  • 14k
16 votes
3 answers
1k views

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 ...
  • 14k
7 votes
1 answer
77 views

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?
  • 936
15 votes
2 answers
644 views

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 ...
  • 936
25 votes
3 answers
1k views

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 ...
  • 2,336
16 votes
2 answers
348 views

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 ...
  • 2,336
16 votes
1 answer
922 views

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 ...
  • 2,336
12 votes
3 answers
150 views

Physically motivated double hybrid DFT?

This question came to mind while writing another question here Extended Hybrid Methods, but I felt it was distinct enough to ask separately. In double hybrids DFT methods, you essentially perform a ...
  • 14.3k
9 votes
1 answer
58 views

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 ...
  • 14.3k
16 votes
4 answers
238 views

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?
  • 936
18 votes
2 answers
181 views

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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