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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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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sizes of monolayer supercell used in density functional theory calculations

I want to save computational time in a DFT study on monolayer Mo$\textrm{S}_2$ so I'm looking to use a $2\times2$ or a $3\times2$ monolayer supercell so that the calculations would only involve 24 to ...
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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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34 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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59 views

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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18 views

Is the electrostatic potential also undetermined by a constant in 2d periodic boundary conditions?

In 3D periodic boundary conditions (PBC), the electrostatic potential is underdetermined by a constant. Is this also true for any other periodicity as 2D or 1D?
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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 ...
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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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31 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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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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70 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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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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64 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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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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225 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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30 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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64 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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91 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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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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77 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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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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123 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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167 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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74 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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214 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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206 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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129 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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127 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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136 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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121 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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182 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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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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183 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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195 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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255 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 ...