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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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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Hirshfeld partitioning of the electron density

What is the theoretical background of the Hirshfeld partitioning of the electron density in simple terms? I checked many sources but could not find any good explanation.
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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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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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66 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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42 views

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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What are the meaning of the $s$, $p$, $d$ orbital contributions in partial density of states?

Lets say I have pDOS of Na, K or Al. Integrating total DOS for the last energy interval until Fermi level gives number of valence electrons for corresponding metal. That's also okay. My question is, ...
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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 ...
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Is there an anisotropy factor (g factor) for TDDFT Abs and CD calculations?

Experimentally, anisotropy factor is calculated by dividing the CD spectra by the absorbance spectra multiplying by a factor of 32980 (in order to get a nondimensional quantity) Theoretical ...
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Double zeta polarised, triple zeta double polarized. What is the definition?

I understand that a single zeta basis contains the hydrogen stationary states $\psi_{nlm_l}$ for a particular selection of quantum numbers $(n,l,m_l)$. You can decide the quantum numbers that will be ...
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43 views

Can you calculate the static lattice/potential energy given a phonon dispersion curve?

Let's say I determine a material's dispersion relation from experiments. Would it then be possible to use the information contained within the dispersion relation to calculate the material's static ...
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Lagrange multiplier associated with the requirement of constant particle number

I am following Jones and Gunnarsson (1989). In their paper, readers find the following equation that is often used in many-body quantum physics, in particular density functional theory: $$ \frac{\...
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Functional form for pseudopotential

I have found this resource quite good for a brief summary of pseudopotentials, of which I am trying to learn more about. The author shows that, once a functional form for the pseudo-wavefunctions has ...
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Is correlation in electronic structure theory ‘a bin’ that accounts for all the behaviour that we do not understand?

I have been trying to learn about exchange and correlation. I have a vague understanding of exchange. It is a repulsion due to equal direction spins, that Hartree-Fock captures exactly. But what ...
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Local density approximation: How do I get an expression for exchange and correlation for an atom?

I want to make a DFT program for an atom in the local density approximation. The user specifies the proton number and electron quantum numbers $n,l$, and the program returns the ground state energy by ...
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67 views

High DFT error for HOMO-LUMO calculation

In a paper by Zhang and Musgrave it is stated that Unfortunately, although molecular orbital (MO) theory is of immense utility, commonly used DFT functionals that can economically calculate the ...
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Density functional theory: How do I derive potentials $V[n]$ from expressions for the energy $E[n]$?

In the following, suppose $n$ is the electron density and $n^\uparrow$ and $n^\downarrow$ denote the density of spin up and spin down electrons respectively. Therefore $n = n^\uparrow + n^\downarrow$. ...
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DFT: When would one use a LDA over a GGA method?

Computationally using Density Functional Theory (DFT), is there any examples where Local Density Approximation (LDA) would be preferred over using Gradient Generalized Approximation (GGA) methods for ...
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Good introductory book to computational physics [duplicate]

First time asking a question here. As per the title I'm trying to find a decent book that serves as an introduction to computational methods used in physics. A little background on myself will help ...
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Vacancy formation energy and chemical potential

TLDR: What exactly is the difference between vacancy formation energy and chemical potential? Does the vacancy formation energy include, e.g., the energetic cost of bond-breaking, or is this ...
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Can we invert Density Functional Theory through sufficiently accurate experiment?

The famous Hohenberg-Kohn theorems say that there is a one-to-one mapping between the many-body Hamiltonian, $\mathcal{H}$, of a solid and its ground-state electron density $\rho(\mathbf{r})$. As far ...
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Flattened band in band structure

What does a flattened band in a band structure plot imply? I've been reading this paper https://doi.org/10.1016/j.apsusc.2012.06.092 and one of the primary results is the flattening of bands however ...
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Deriving the expression for one body density

My textbook (Richard M. Martin - Electronic structure) has the following equation for the one body density of a system of $N$ electrons: $$ \langle \Psi | \Psi \rangle n(r) = \langle \Psi | \hat n(r) |...
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Constructing many-body densities from Kohn-Sham orbitals

In many electronic structure methods, one solves "effective" one-particle Schrödinger equations for one-particle wavefunctions. In my case, I have Kohn-Sham orbitals from a DFT calculation. The ...
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Transition Dipole Moments and Quantum Yield

I'm using some DFT calculations to compute Transition Dipole Moments between the HOMO and LUMO of a molecule in different geometries. Intuitively, this is closely related to the relative probability (...
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115 views

Definition of electron density in DFT

I read that the electron density used for density functional theory in a system of $N$ electrons with wavefunction $\psi$ is defined as $$\rho(r)=N\int d^3r_2\dots d^3r_N \psi^*(r,r_2,\dots r_N)\psi(...
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Finding mathematically the ground state density in DFT

I've posted this question in the chemistry exchange, but it did not get any answer; maybe it is better suited here? To find the ground state density in DFT, you set the following Lagrangian: $$L = E[...
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Sinkhorn Algorithm Normalization Issue

I was reading the Sinkhorn algorithm, from the following link: https://mindcodec.ai/2018/10/01/an-intuitive-guide-to-optimal-transport-part-iii-entropic-regularization-and-the-sinkhorn-iterations/ The ...
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What is a pseudo wave and how to calculate it?

In a description of the density of states in https://wiki.fysik.dtu.dk/gpaw/documentation/pdos/pdos.html I find the term pseudo (partial) wave (in the section Molecular Orbital PDOS). What is it and ...
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DFT vs spin polarized DFT

What is the difference between DFT and spin polarized DFT? Will it matter which one I use if I am only after the band structure and not the magnetic properties?
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Combined effects of strain and doping on the electronic structure of semiconductors

I've read papers in DFT studies on band gap tuning in semiconductors and the usually studied methods are either through doping or application of external strain. But its always just one or the other. ...
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What are possible causes that can lead a self consistent calculation to diverge in DFT?

I am extending a code written to do self consistent Density Functional Theory calculations to the case of spin polarized systems. Due to the modifications, the calculations are leading to diverging ...
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How can I obtain by hand the molecular orbital expression for the H2 system, using the Self Consistent Field (SCF) Cycle in DFT calculations?

After doing some energy calculations for the H2 system in Gaussian, using wb97xd/STO-3G basis, and generating a .wfn file, I wanted to understand better how the computer does the calculations. I ...
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56 views

Can the “external” field in DFT be that of an electron?

In my experience with (Kohn-Sham) density functional theory, the external potential is due to a massive particle like a nucleus or ion. I have never seen an electron be the source of the potential, ...
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Will inclusion of spin polarized states have any effect in DFT calculations in atoms in absence of any Electric or Magnetic Fields?

I am working on understanding the Spin Polarized Density Functional Theory Calculations. In my understanding as of now, in absence of any external electromagnetic fields, the only parts of the total ...
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Which basis set on NIST CCCDBD should I compare my DFT results using plane-wave basis set?

I'm attempting to benchmark some water monomer and dipole calculations against the NIST CCCBDB (https://cccbdb.nist.gov/dipole2x.asp), and I'm not certain with which basis set I should compare. As ...
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Why am I getting substantially different energy values when I include core electrons in this VASP calculation?

I am investigating the potential energy map of a periodic array of water molecules as a function of rotation. As part of that, I am attempting to determine the partial charges (to determine the dipole)...
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Are there any techniques for calculating decomposition barriers for a set of crystals?

For a hypothetical crystal system ABO3, let's say there are two competing phases AO and BO2, which come from the decomposition of ABO3. Using DFT, I can calculate the energetic difference between ABO3,...
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Expected value of the current density operator

In Ullrich's TD-DFT book, the paramagnetic current-density operator is defined as $$\hat{\mathbf{j}}(\mathbf{r})=\frac{1}{2i}\sum_{a=1}^{N}\left[\nabla_a\delta(\mathbf{r}-\mathbf{r}_a)+\delta(\mathbf{...
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DFT_NL van der Waals Integral $\int (r_1-r_2)^-6$

I am trying to implement a vdW interaction on my grid for DFT calculations with quadrature. But it does not work because of the singularity at $r_1=r_2$. Is there an algorithm to overcome this?
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$z$-polarized laser pulse and conserved $L_z$

I am currently reading a book "Time-Dependent Density Functional Theory: Concepts and Applications". This book says as follows: In its ground state, the valence electrons of $\rm Na_9^+$ form a ...
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Total electronic energy as the sum of single particle energies

In Hartree-Fock / Kohn-Sham theory, the total energy of a system of electrons is the sum of single electron energies $\varepsilon_k$ plus some correction $C[\rho]$ depending on the electron density $\...
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Wigner-Seitz radius and Spin-polarized Density Functional Theory (DFT) calculations

The density functional theory (DFT) is widely used to predict the electronic structure of materials. The electron density is the fundamental variable in DFT. However, some DFT codes (eg. VASP) use ...
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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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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 ...