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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Functional derivatives in density functional theory

I am studying density functional theory and I am currently dealing with manipulating the intrinsic free energy, $\mathcal{F}$, which is defined as $$\mathcal{F} = F - \int dr \rho ^{(1)}(r)\phi (r) $$...
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Unit Cell of Twisted Bilayer Graphene

Would anyone please tell me how to build up the unit cell of twisted bilayer graphene? I know how to rotate the coordinate of atom with a certain angle through the multiplication of a rotation matrix, ...
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One large energy barrier vs. two small energy barriers

I am studying the reaction pathway of oxygen evolution reaction (OER) on a PtNi alloy catalyst using density functional theory (DFT). What I found is that, for different intermediates, the most ...
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Ionization potential for surfaces

For an isolated structure, like a molecule, the ionization potential can be computed using total energies obtained from DFT: $$IP = E(N) - E(N-1).$$ But what if I have a structure finite in one ...
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Looking for input to a simple transformative Ab initio molecular dynamics (AIMD) trajectory simulation

I'm looking for a simple Ab initio molecular dynamics (AIMD) simulation of some small molecular system that I can run myself on a desktop computer. I want a molecular system that actually changes ...
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Normalization of phonon density of states

Analogous to electronic structure calculations, we can solve for dispersion band structure of phonons for lattices using harmonic lattice approx. And we can find the so-called phonon density of states ...
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GUI for DFT calculations

I am a beginner in DFT. Can someone suggest a good DFT software with a GUI for simulating dipole moment directions and optical absorption spectra in an organic crystal? I have tried Burai. But it ...
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55 views

Invariance of spin-polarized Kohn-Sham Hamiltonian with respect to spin rotations

In collinear density functional theory, Kohn-Sham equation for spin-dependent wave functions is $$ \left[\left(-\frac{\hbar^{2}}{2 m} \nabla^{2}+\int \frac{n\left(\mathbf{r}^{\prime}\right)}{\left|\...
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Are electron dipolar spin-spin interactions included in DFT calculations?

I am studying point defects in hBN using Quantum Espresso. It is not clear if electron spin-spin interactions are typically/can be included in DFT calculations. I understand that spin-orbit ...
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Broken symmetry in presence of external confining field

Suppose, there is a many particle system confined by an externally applied field. I have found in books that the system doesn't remain translationally invariant. Can anybody explain why?
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Grand canonical ensemble in describing inhomogeneous fluids

I have seen that in the theories of inhomogeneous fluids classical Density Functional Theory is used, but the treatment is preferably done in Grand Canonical Ensemble. What is the reason for choosing ...
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Expectation Value of an Operator in the Projector Augmented Wave Method

I'm starting on DFT and came across this technique called PAW Wave Method for multi atoms system wave function. It is a widely employed method in DFT calculations. From the attached picture, I'm ...
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68 views

Power of electron density in Bloch's exchange term

Exchange term introduced by Felix Bloch is given by $$ E_x = c_2 \int n(\vec{r})^{4 / 3} d\vec{r} $$ In the example 1.6.7 of the attached reference, the power of $n(\vec{r})$ is derived as following $$...
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Does Density Functional Theory (DFT) underestimate the conduction band level only?

Based on the detailed answers provided for the reasons for the underestimation of bandgaps in DFT calculations, can we deduce that it is based on an underestimation of the conduction band level but ...
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Electronic polarizability in Hohenber and Kohn DFT paper

I try to reproduce Eq.(31) in Hohenberg and Kohn's paper Inhomogeneous Electron Gas (Phys. Rev. 136, B864 (1964)). My understanding to this model is that the external positive charge background(Eq.(27)...
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Calculation of elastic constants - when do we need to account for Poisson?

I try to calculate the elastic constant tensor for some organic molecular crystals. There are plenty of accounts in the literature where people do that, using atomic resolution models and DFT, EAM, or ...
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101 views

Energy dependence in density functional theory

According to the Kohn-Sham first theorem, the ground state energy of an electron system could be written as a function of the electron density $$E = E[n]$$ And we know that according to the Kohn-Sham ...
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164 views

How to choose Pseudopotential for DFT calculation?

I am beginner and newly started running DFT calculations to find out electronic band structure of certain materials in Quantum Espresso.But we have to select the pseudopotential for running scf loop. ...
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How should one systematically optimize various solar cell device parameters to achieve highest possible efficiency in a solar cell simulation? [closed]

I am confused as to which parameter I should start off with in order to optimizing the best performing solar cell. There are parameters like Thickness, Bandgap, Electron Affinity, relative Dielectric ...
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Any suggestion for a DFT software package for a beginner?

I would like to do start doing some basic calculations using DFT. I am interested in solid state physics of strongly correlated materials in 3d or 2d. I prefer free software (no license) which is easy ...
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51 views

Magnitude of band gap on including higher Fourier components

It is commonly shown that the magnitude of the band gap at the edge of the 1st Brillouin Zone is equal to twice the Fourier component of the potential energy for a one dimensional crystal. Also, the ...
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191 views

Step-by-step proof of the First Hohenberg-Kohn Theorem in DFT

I'm trying to proof the first Hohenberg-Kohn theorem using the Reductio ad absurdum, but I'm stucked in the last point. First, I know that the eletronic density is: $${ρ(r)=∑_{i=1}^n|χ_i(r)|²}$$ And, $...
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115 views

In the electron density, what exactly do you mean by $\sigma$ mathematically?

Suppose there is a many-body eigenvalue problem $$ H(r_1,\cdots,r_n) = - \frac{1}{2} \nabla^2|_{r_1\cdots,r_n} + V(r_1,\cdots,r_n). $$ This potential is symmetric and the hamiltonian does not depend ...
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Degree of kinetic energy component in Hamiltonian for any molecule

In reading "Density functional theory of atoms and molecules" by Parr and Yang, I was not sure what is meant by this sentence when the Virial theorem was introduced. Suppose I have a ...
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How to find density of states (DOS) for a nanoribbon (NR)?

I have a nanoribbon (NR) which is constructed of $N$ 1D chains. The Hamiltonian is written as the following:(for only N=3) $$ H= \begin{bmatrix} H_0&H_{12}&0\\ H_{21}&H_0&H_{23}\\ 0&...
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How can I easily generate $\rm GaAs$ band structure?

Is there a program where I can easily generate $\rm GaAs$ band structure that shows lowest conduction band valleys?
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The Hund's J - Why can this be quantified?

I was reading on the the implementation of Hubbard 'U' in Density Functional Theory. The Hubbard 'U' can be thought of as a parameter that accounts for the on-site electron-electron interactions in ...
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Mathematical expression of SCAN (Strongly Constrained and Appropriately Normed) constraints in DFT [closed]

Moved to materials stackexchange. I'm compiling the mathematical expression of SCAN (Strongly Constrained and Appropriately Normed) functionals' constraints, but apparently they are not very obvious ...
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Struggling to converge the potential of a binary alloy system using the Coherent Potential Approximation. Stuck with the troubleshooting

I'm trying to converge a dilute fcc alloy consisting of Cu and U, with the Uranium concentration at 0.01%, using Hubert Ebert's SPR-KKR program (https://www.ebert.cup.uni-muenchen.de/old/index.php?...
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95 views

Initial guess for electron density in density functional theory

I found a recursive scheme to solve the Kohn-Sham equation. However, I have a misunderstanding: how to choose the electron density for the initial step? There are two ways to calculate the electron ...
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93 views

Solving the Kohn-Sham equation

Consider the Kohn-Sham equation \begin{align} \left( - \frac{\hbar^2}{2m} \nabla^2 + \nu_\mathrm{eff}(\mathbf{r}) \right) \varphi_j(\mathbf{r}) &= \varepsilon_j\varphi_j(\mathbf{r}...
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How do you calculate the "true" chemical potential in classical density functional theory?

In classical density functional theory, one traditionally calculates the chemical potential by taking the variational derivative, \begin{equation} \mu_{i} = \frac{\delta F}{\delta \rho_{i}} \end{...
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How is Time-reversal symmetry important in Computational methods like Density Functional Theory (DFT)?

It's well known that symmetries help reduce the computational load in ab-initio calculations. These symmetries could involve rotation, inversion etc. I can understand how these symmetries make the ...
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Why are the bands in unit cell Density Functional Theory (DFT) calculations continuous?

The Bloch theorem states that a non-interacting electronic state of a confined system with periodic boundary conditions (and a periodic potential) is represented as $\psi_{\mathbf{k}}(\mathbf{r}) = u_{...
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Spin-Polarized calculation in density functional theorem

I am a beginner in DFT calculations. I want to know what is spin-polarization and is it necessary to choose it always while doing DFT calculations ? I do not understand what spin-polarization ...
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A query on density functional theory (DFT)?

I know this is not the best forum to ask this question (but I think it is a pretty good one). I have a fundamental confusion regarding DFT. In DFT all the calculations are performed using crystal ...
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221 views

Does the Schrodinger Equation yield a unique wave function and density?

I am learning DFT and the Hohenberg Kohn Theorem of Existence. And it says that there is a one-to-one correspondence between the external potential and the density. However the proofs that I have seen ...
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Why is the Fermi surface of a metal irregular at 0 K? And how does 'smearing' remedy the situation in DFT calculations?

I'm getting familiarized with DFT and was wondering why the Fermi surface of a metal is irregular at 0 K? It is for the same reason I believe, some 'smearing' needs to be done if the material in ...
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Why kinetic energy in Kohn-Sham equation is the major part of real many-body kinetic energy?

In deriving the Kohn-Sham equation, it is a main step to extract the 'major' part of the true kinetic energy exactly by using the fictitious non-interacting system and calculating its kinetic energy. ...
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Question of Linear Resonse TDDFT

In the LR-TDDFT, from my unserstanding, it is based on the perturbation theory and there seems no time propagation involved, why it is called TDDFT?
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What is electrical conductivity divided by scattering time in DFT calculations?

In DFT calculations, I see many graphs showing electrical conductivity divided by scattering time $\sigma/\tau$. But it is treated as electrical conductivity in the papers. What does this mean and why ...
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Direct & Indirect (Kohn-Sham) band gap for $\rm MgS$

I recently performed a groundstate calculation for $\rm MgS$ using the self-consistent Kohn-Sham equation with LDA exchange-correlation. $\rm MgS$ has an FCC crystal structure with two atoms per (non-...
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Exchange-correlation potential for one electron system

For classical ion, the DFT solution of the ground-state electronic system is given by $$ \left[-\frac{1}{2}\nabla^2 + V_H(\mathbf{r}) + V_{ei}(\mathbf{r}) + V_{xc}(\mathbf{r})\right]\psi(\mathbf{r}) = ...
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967 views

Density Functional Theory DFT-D, DFT-D2 and DFT-D3

I was looking for a reasonable explanation of the Grimme's dispersion correction methods but his papers are written in a very difficult language. Does anyone could explain me the differences between ...
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243 views

Interpretation of electronic band structure diagram

I want to understand the electronic band structure diagram of the following image, corresponding to $\text{MoS}_2$ (TMD): I read about DFT (density functional theory). DFT is based on solving the ...
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Why is density functional theory unreliable for prediction of band gap [closed]

Why is density functional theory unreliable for calculation of band gap?
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How to add spin-polarization to an atomic DFT calculation?

I wrote a simple program to calculate the ground state total energy of isolated atoms with a density-functional theory approach. I took a similar approach as can be found here: certik/dftatom ...
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The form of electronic density in DFT

I started to study density functional theory, and I saw that in general the eletronic density for a system of $N$ electrons is written as $$\rho(\textbf{r}) = \langle \psi | \sum_{i=1}^{N} \delta(\...
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Exchange has closed form also in DFT?

I have heard from my lecturer that in the context of DFT, the exact exchange energy has a known closed form, even though it is not a functional of the density. I have been trying to figure out what ...
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Can you explain DFT and TDDFT functioning (math aside)?

I have been recently reading a lot on the quantum mechanical theory regarding Density Functional Theory, DFT and Time-Dependent Density Functional Theory, TDDFT (Oscillatory and Rotatory Strengths in ...