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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Confusion on FFT grid size used in ab initio calculations for periodic systems with planewave basis

Sorry it might be a long post, I'll try to write down all my thinking on this topic, and it is appreciated to point out whether and where I make mistakes. We are talking about algorithms used in ...
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Hartree-Fock vs. density functional theory

What is the relationship/difference between the Hartree-Fock method and the density functional theory? It seems the basic formulations of them are very similar.
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Understanding the derivation of the variational principle in classical density functional theory

I am trying to understand the derivation of the variational principle as presented in Bob Evan's 1979 work.[1]. The part that is tripping me up is when he presents the following result. He starts by ...
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How to use Density Functional Theory to get the correct energy spectrum

I'm having some trouble understanding how DFT can be used to obtain results for electronic structure calculations. We can assume that we're studying an $N$ electron atom with a fixed nucleus and want ...
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How to make sense of phonon dispersion curves and dynamic stability?

I've been working on this material that I've been doing DFT calculations on and I've managed to obtain the phonon dispersion curves for it. Calculation for it took quite a while, but here it is: Now ...
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What is the single active electron approximation?

I keep stumbling upon this approximation while reading papers on atomic physics, but I couldn't find a proper description of what it is in any textbook or pedagogical paper. The closest I could find ...
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How to fit Tight-Binding parameters to DFT results in a general situation?

I've been searching for an answer to this for several days and couldn't find what I need. I'm explaining myself: I got the Bandstructure of a MoS2 monolayer using DFT (PBE functionals) and I wanted to ...
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Computing functional derivative of exchange-correlation functional

Sakurai and Napolitano's chapter on density functional theory has claims that it is "straightforward" to find $\delta U_{\text{xc}}/\delta n$ for $$U_{\text{xc}}[n]=\int d^3 x n(\mathbf{x})\...
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Potential Energy of Electron - Nuclei Interaction as a Functional of Electron Density

In density functional theory (DFT), electron density is a central quantity. Because of this, we want to calculate electron - nuclei potential energy as functional of electron density. If we know how ...
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Why are kinetic energy of electrons and potential energy of electron - electron interaction universal operators?

Time indepedendent Schrödinger equation for a system (atom or molecule) consisting of N electrons can be written as (with applying Born - Oppenheimer approximation): $$ \left[\left(\sum_{i=1}^N - \...
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Probability more than 1 when integrating the Electron density in Density functional theory

The electron density used in density functional theory for a system of $N$ electrons with wavefunction $\psi$ is defined as $$\rho(r)=N\int \Psi^*(r,r_2,\dots r_N)\Psi(r,r_2,\dots r_N) d^3r_2\dots d^...
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How to derive specific heat of a crystalline material from phonon density of states?

I have done a simulation of a crystalline material using DFT and have extracted its normal modes and its phonon density of states. Does anyone have an algorithm/code or a detailed resource that can ...
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How to theoretically verify whether a new phase of matter having superconductivity? Any DFT code?

Is there any existing theory, formulation, index, or code that could indicate whether a new superconducting phase is found? If yes, how to further check if the new matter is a conventional or ...
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Kohn-Sham equations, Sakurai 3rd edition, possible typo?

In Sakurai's quantum mechanics book 3rd edition page 448, equation 7.88, the book writes "Kohn and Sham found a way to derive a self-consistent approximation scheme, based on single particle ...
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Brillouin zone integration and delta function

Many BZ integrals of interest are related to the spectral function $$ G(\omega) = \int_{BZ}\frac{F(\mathbf{k})d\mathbf{k}}{\omega - \omega(\mathbf{k}) + i\eta} \tag{1} $$ where $\omega(\mathbf{k})$ ...
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Is the tunnelling effect already naturally accounted for in the density functional theory?

Would it be correct to say the tunnelling effect is already naturally accounted for in the density functional theory or the Hartree-Fock formulation of the many-body problem to the Shrodinger equation?...
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Is there anyway to break the cubic harmonics in condensed matter

Since I started doing the calculation of condensed matters, the two $e_g $ orbitals or three $t_{2g }$ orbitals are assumed equivalent and I have never doubted this. From most books, this is also ...
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What is the difference between lattice models and tight-binding simulations?

In condensed-matter physics, people use different methods to solve the many-particle Schrödinger equation. I was wondering about two of those methods, the lattice model and tight-binding simulation. ...
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What does pair density integrate to for two distinct particles?

We know that pair density defined as follows for two electrons $$ \Gamma(x_1,x_2)=N(N-1)\int...\int \lvert \Psi (x_1,x_2,...,x_N)\rvert^2 dx_3...dx_N $$ where $N$ is the total number of electrons and $...
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Band structure of Group-IV crystals

Talking specifically about the $sp^3$ hybridized crystals, it can be seen that all the group-IV elements from carbon to germanium sport a band gap in the bulk of their crystals, but Sn and Pb. Also we ...
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What are Crystal Electric Field Parameters?

What does the following notation mean? $$A_{20}\left<r^2\right> = -100 \mathrm{K}$$ Where $A_{20}$ is termed a Crystal Electric Field Parameter. I often see this notation when reading papers on ...
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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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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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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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3 votes
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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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3 votes
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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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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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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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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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