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Questions tagged [density-functional-theory]

Density functional theory (DFT) is a quantum mechanical model used to estimate the electronic structure of molecules and condensed matter. In broad terms, DFT works by treating all the electrons in the system as a single electron density, and computing physical quantities of interest as functionals of that electron density.

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Solution of KS equations - DFT

I know in DFT the real system is mapped onto a fictitious non-interacting system under an effective KS potential. My question is: When the Schrodinger equation is being solved (in each iteration of ...
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12 views

Why can a materials properties be determined with the gs - DFT

Can someone provide me with a text book or explanation as to why in DFT it is sufficient to obtain the ground state at $T=0$ to know a material's properties beyond $T=0$. I quoting from here ...
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22 views

Electron density in DFT (*ρ*(r)) and probability density (wave function squared)

Are the electron density in density functional theory, ρ(r), and probability density, defined as wave function squared, the same quantities?
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28 views

What does the “equilibrium” mean in DFT?

In DFT, we usually call the "equilibrium position" as the ion positions that corresponds to the global minimum of the (ground-state) Born-Oppenheimer potential energy surface (PES). Let's consider a ...
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51 views

What does the “lowest order adiabatic approximation” mean?

I came across a concept "lowest order adiabatic approximation" in solid-state physics. I searched and found dozens of "lowest order adiabatic approximation". I think the "lowest order adiabatic ...
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2answers
66 views

What are the differences of two electron current?

I often see two definition of current in the book and literature, and I am a little bit confused. The current density $$\textbf{J}_1(\textbf{r})=\frac{-ie\hbar}{2m_e}\sum\limits_{n\textbf{k}}\{\psi^*...
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1answer
23 views

Bloch functions and single-electron equation

The single electron equation is $[\frac{\hat{\textbf{p}}^2}{2m_e}+v^{KS}(\textbf{r})]\psi_{n\textbf{k}}(\textbf{r})=\varepsilon_{n}(\textbf{k})\psi_{n\textbf{k}}(\textbf{r})~~~~~$ (1) where $\hat{\...
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1answer
60 views

How is atomic position expressed in QM?

I am trying to understand how DFT works. I understand how to express the position of an atom or molecule in terms of the positions of the nuclei and electrons by setting up a Hamiltonian expressed in ...
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12 views

Spectrum of Dielectric Function along Energy

What do the peaks and troughs in the spectrum of the dielectric function (real and imaginary parts) along energy indicate? I understand that the real part represents the polarization and the imaginary ...
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124 views

Putting high symmetry points labels to a band structure plot [closed]

So far I've got this plot using Quantum Espresso. I want to put gamma, X, L, etc labels to the k-path. Quantum Espresso's ouput states the following: ...
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28 views

Quantum Nuclear Corrections

I am interested in calculating quantum nuclear corrections to energy profiles or free energy profiles. For example, say I perform a DFT simulation for some molecules, and I the energetic profile in ...
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2answers
52 views

Solid foundation for obtaining the band gap from density functional theory

Looking around a lot of solid calculations, the band gap is usually estimated by DFT. But I have some doubts of that within my knowledge, so I'm asking the question. The usual process to generate ...
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46 views

What is the difference between density functional theory and ab initio molecular dynamics?

I feel like I should know the answer to this question. But in standard implementations of (say) plane-wave DFT in softwares like VASP, the atomic positions are moved based on the Hellman-Feynman ...
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2answers
80 views

Orbitals without overlaps in band structures of solids

We know every band in the band structure of solids is the result of overlaps of an orbital type. My question is that when there is not any overlap between a type of orbitals(which may be the lowerest ...
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1answer
43 views

Why does using deuterium mass for hydrogen improve convergence of molecular dynamics simulations of water?

I've come across many papers performing ab initio MD (Carr-Parinello or Born-Oppenheimmer) simulations of water that use the deuterium mass for hydrogen. And they state that this helps improve ...
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2answers
88 views

In phonon theory, what is the physical significance of the force constants tensors?

I want to compute phase equilibria of crystalline solids using First-principle methods (DFT in particular). The methodology for this computation is described in this chapter. In order to calculate ...
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1answer
103 views

Functional derivative

I am not able to derive Eq. 21 of this paper F. Zahariev, S. S. Leang, and Mark S. Gordon, "Functional derivatives of meta-generalized gradient approximation (meta-GGA) type exchange-correlation ...
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66 views

Density Matrix approach in Density Functional Theory - interpretation

In a paper describing a Kohn-Sham Density Functional Theory implementation, the authors describe the use of the density matrix for e.g. the calculation of the electronic density and for efficiency ...
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43 views

How to evaluate individual Kohn-Sham orbital energies?

I have been able to calculate the electron densities in position and momentum space for arbitrary crystals, allowing calculation of the Hartree/Coulomb energy $E_{H}[\rho]$ and exchange-correlation ...
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35 views

How to minimize energy with the LDA functional?

I'm very new to DFT and have not been able to minimize the LDA functional to by varying electron density, $\rho$, or the Wigner-Seitz parameter, $r_s = (\frac{3}{4 \pi \rho})^{1/3}$. From what I've ...
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99 views

Band structure and Density of states (DOS)

Can someone explain how these two plots are related? How are the peaks in the right are associated with the left figure?
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34 views

DFT of a non-continuous discrete time series

I am looking for a periodic signal in a time series $x_i, \quad i=1, \, ...,\, N-1 , \, N , \, N+P , \, N+P+1 , \, ... , \, N+P+M$ where $P$ is an unkwnown gap in time, for which I have no ...
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156 views

kinetic energy of plane wave

I want to ask you about the relation between the kinetic energy of a planwave of the valences electrons and of the core electrons. because in the Plane Wave Basis Sets approximation that used in ...
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1answer
88 views

Inverse Green's Function identity in derivation of Hedin's equations

I'm trying to work through a derivation of Hedin's Equations in Effect of Interaction on One-Electron States by Hedin and Lundqvist (1969) and I've come across an identity that is given without much ...
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1answer
94 views

Symmetric part of hamilton matrix and eigenvalues

I'm working with a Density Functional Theory package and I am not sure with a procedure in the code. At some point, after the Hamilton matrix $H_{ij}=\langle\phi_i|\hat{H}|\phi_j\rangle\in\mathbb{R}$ (...
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1answer
107 views

Pseudopotential in VASP

I am a beginner in learning VASP (Vienna Ab-initio Simulation Package) and quite interested in the PAW (projector augmented wave) method implemented in VASP. As far as I knew, PAW is an all-electron ...
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91 views

How do you calculate effective mass exactly?

I know about the equation m*/me=hbar^2[(d2E(K)/dK2)]^-1. You need to get the second derivative of the E-K diagram at the point of interest. For electron effective mass, that's the lowest point in the ...
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97 views

Attractive exchange energy and correlation energy of different spin in DFT

In DFT, why do most texts ignore/don't mention the attractive exchange "force" between two antiparallel spins electrons? The repulsive "exchange" force of two same spins electrons are always ...
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1answer
132 views

Why does exchange lower energy with increasing electron density in Hartree-Fock

The Hartree-Fock equations include a term for the exchange interaction, which is usually explained as a repulsive force due to the Pauli exclusion principle. (It says so right in the description for ...
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1answer
117 views

What are sigma and pi bonds in physics language?

Chemists often discuss sigma and pi bonds. To a physicist, it's not easy to figure out what these actually are, as discussions tend to be full of lots of chemistry jargon about "antibonding", "...
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1answer
149 views

Density Functional Theory for Quantum Field Theory vs fixed-particle-number Quantum Mechanics

Introductions to Density Functional Theory (DFT) usually discuss the Hohenberg–Kohn theorems which prove that there exist universal functionals of density that can be used to determine ground state ...
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1answer
162 views

How can density functional theory (DFT) be understood in many body perturbation theory (MBPT) language?

Many body interacting fermions problems are formulated in the many body perturbation theory language using Feynman diagrams and imaginary time formalism. To the best of my knowledge the kinetic energy ...
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238 views

Vector potential and intensity units

In a code where the time-dependent (Kohn-Sham) hamiltonian is coupled to an electric field via a vector potential of the form $$ \vec{A}(t) = \frac{\vec{A}_0}{\sigma\sqrt{2\pi}} e^{-(t-t_0)^2/2\sigma^...
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174 views

What's the relationship between Density Functional Theory (DFT) and Kohn-Sham equations?

It seems Kohn-Sham equations are approximate methods to solve many body Schrodinger's equation. They directly split a multi-electron Schrodinger equation into many single-electron Schrodinger ...
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249 views

What do we physically mean by smearing in condensed matter?

What do we physically mean by term smearing in DFT based codes like VASP or generally in condensed matter?
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64 views

Calculate total number of electrons from density of states? [closed]

Can someone tell me how to calculate the total number of electrons from partial density of states (projected on each atom)? Thanks
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31 views

Linear force vs. displacement relationship for crystalline solid

I did a series of density functional theory (DFT) calculations on crystalline silicon. These consisted of 50 total displacements of one atom from equilibrium in the x-direction until the displacement ...
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1answer
450 views

Casida equation, excited states and response theory

I have several doubts about the characterization of excited states within the framework of TD-DFT (Time dependent Density Functional Theory) / Response Theory. Just to give some context and fix ...
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40 views

Transient simulation of a Gaussian wave packet using time dependent Liouville-von Neumann equation in center mass coordinates?

I am working on a transient simulation of a Gaussian wave packet using time dependent Liouville-von Neumann equation in center mass coordinates. For discretization of diffusion term, I have used Crank ...
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1answer
429 views

Literature recommendation for classical density functional theory (DFT) and fundamental measure theory (FMT)

I'm very much interested in properly learning about density functional theory calculations (DFT) in classical settings, for example as used in the theory of liquids. Apart from the success of DFT ...
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483 views

how can DFT calculate band structure

I am trying to understand DFT, and so far i realized that DFT is really concerned with the ground state properties. My question is how can we calculate the band structure of a material using DFT ? I'...
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88 views

The exchange potential in Kohn-Sham equations for harmonic interactions

Is there an analytic formula for the exchange potential part in the effective potential of the Kohn-Sham equations for a system of N Bosons in a harmonic trap with mutual harmonic interactions or a ...
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1answer
78 views

Number of ionic steps in plane wave DFT

What is the significance of increasing (and decreasing) the number of ionic relaxation steps in a plane wave DFT calculation?
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4answers
310 views

(Solved) Is Kohn-Sham approach in DFT compatiable with Hohenberg-Kohn theorem?

From DFT theory, the Euler equation of an interacting system is: $$\begin{align*} \frac{\delta E_{v}[\rho]}{\delta \rho(\vec{r})} &= \frac{\delta}{\delta \rho} \left[T_{s}[\rho]+\int \rho(\vec{r})...
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27 views

projector augmented waves

I am starting out with density functional theory from an engineering perspective. Could anyone help me understand what the difference is between USPP (ultra-soft pseudopotential) and PAW (projector ...
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1answer
202 views

Can one always take a single-particle picture (i.e. DFT) irrespective of the strength of correlations?

Most textbooks on Kohn-Sham density functional theory will assert that it is exact assuming that one has the 'appropriate' exchange-correlation functional. To my mind, this is completely astounding ...
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41 views

Decomposition of N-representable density into determinantal wavefunction

My textbook "Density Functional Theory of Atoms and Molecules" by Parr and Yang says that any N-representable density is derivable from a single determinantal wavefunction. A density $\rho$ is N-...
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2answers
205 views

Hamiltonian with ext. vector potential - complex kinetic energy

in a given (TD)DFT code with an atomic basis set, i.e. $$ \psi(\mathbf{r},t) = \sum_i c_i(t) \phi_i(\mathbf{r}) $$ (where the non-on-site basis functions $\phi_i$ aren't necessarily orthogonal), the ...
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1answer
434 views

Many body Schrodinger equation - DFT / Exchange-Correlation term question

In principle if you solve the many body Schrodinger equation you will get the whole physics and nature of the problem. With the hamiltonian, in the most general case (without Born-Oppenheimer ...
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1answer
340 views

Question on the Proof of Hohenberg -Kohn Theorem

Between Equation (5) and Equation (6) of the the original paper titled as "Inhomogeneous Electron Gas" by P. Hohenberg and W. Kohn, there is a sentence stating that: " Now clearly (unless $v'(\...