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Questions tagged [kohn-sham]

Questions related to the Kohn-Sham approach to DFT.

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8 votes
2 answers
111 views

How do DFT software packages enforce spin multiplicity?

New to matter modeling In KS-DFT software packages (I particularly have Gaussian in mind although I know they are ultimately not open-source), how is finding a ground state with a certain spin ...
21 votes
2 answers
876 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 (...
8 votes
2 answers
120 views

What is the Hamiltonian in the adiabatic connection?

I am trying to understand the adiabatic connection as motivation for hybrid functionals that include Hartree-Fock like exchange. While it sounds intuitive that the exchange of the noninteracting Kohn-...
9 votes
3 answers
115 views

Which expectation values can be determined with KS orbitals?

Suppose $A$ is some hermitian operator and $\Psi$ is a many body state function of a many-body hamiltonian $H = T + U + V$, where $U$ is electron-electron interaction and V is electron-nuclear ...
3 votes
1 answer
91 views

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 ...
7 votes
0 answers
159 views

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 ...
1 vote
0 answers
51 views

Question on known expression (see post) of exact XC functional in analytic (but not closed) form [closed]

This paper analytically solves the "inverse DFT problem" of mapping the ground-state density to the exact XC functional. And the exact density, i.e. the FCC/FCI density, can be expressed as ...
2 votes
1 answer
92 views

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 ...
7 votes
1 answer
129 views

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 &...
3 votes
1 answer
165 views

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....
3 votes
0 answers
32 views

Is this method of obtaining only the exact "first excited state" density correct, under select conditions that makes it mathematically non-ambiguous? [closed]

(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) ...
3 votes
1 answer
187 views

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 ...
6 votes
2 answers
214 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
155 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 ...
9 votes
2 answers
565 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}}...
5 votes
0 answers
83 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 ...
10 votes
1 answer
201 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
372 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 ...
10 votes
1 answer
526 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 ...
5 votes
2 answers
331 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 ...
7 votes
2 answers
283 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 ...
8 votes
1 answer
397 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 $\rho$ ...
13 votes
1 answer
2k 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 ...
13 votes
2 answers
1k 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 ...
12 votes
3 answers
1k 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 ...
18 votes
3 answers
3k 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 ...
12 votes
2 answers
205 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 ...
10 votes
1 answer
996 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-...
11 votes
2 answers
989 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 ...
13 votes
3 answers
670 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}({\...
18 votes
1 answer
832 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 ...
11 votes
3 answers
1k 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. ...
12 votes
1 answer
342 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 ...
9 votes
1 answer
76 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 ...
7 votes
1 answer
106 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?
13 votes
3 answers
205 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 ...
28 votes
3 answers
3k 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 ...
17 votes
2 answers
2k 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 ...
16 votes
2 answers
708 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 ...
16 votes
4 answers
424 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?
18 votes
1 answer
2k 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 ...
18 votes
2 answers
245 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?