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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Density functional matrix for network analysis
I am an archeologist just beginning to venture into the study of crystalline materials, specifically ceramics, to understand how their spatial distribution and formation process can be studied using ...
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Where to find model parameters of a simple Weyl semimetal?
A famous continuum model of Dirac semimetal is essentially two copies of the following Hamiltonian (up to some chirality reversal)
$$h=\begin{pmatrix}
M(k) & Ak_+ \\
Ak_- & -M(k)
\end{pmatrix}$...
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Where is the kinetic energy functional error in the exchange-correlation functional of DFT?
The Kohn-Sham DFT energy functional is:
$$E[\rho]=T^S[{\varphi_i}]+J[\rho]+M[\rho]+E^{xc}[\rho]$$
with the kinetic energy functional of non-interacting electrons $T^S$, the Hartree functional $J$, the ...
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In solid state physics and Density Functional Theory, how are Van Der Waals forces modelled?
Given a material, I'd like to know how to treat VdW interactions among layers. Specifically I'm using Quantum Espresso, an open-source suite based on Density Functional Theory, and I'd like to know ...
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How to induce the Phonon Effective mode mass?
i don't know the phonon effective mode formula. Who knows why effective mode mass formula have the following form?
https://doi.org/10.1103/PhysRevB.104.L060103 PDF
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Exchange correlation functional for harmonic oscillators
Is it possible to construct the exchange correlation functional in DFT for some exactly solvable system? My proposal is to look at a system of Harmonic oscillators. Consider two electrons moving in ...
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Why do IR spectra of calculation and experiment differ?
Recently I was simulating the IR spectra ( 400-3500 $cm^{-1}$ ) of an aromatic-like molecule with DFT. Then I did a comparison to the available experimental data.
Most data fitted well together: ...
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Electric field from DFT calculations in Vasp
This is a naive question. I am studying the surface-adsorbate systems using DFT calculations implemented in VASP. By setting LVHAR = True, I obtain LOCPOT which contains information about the ionic ...
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Some questions about the derivation process of many-body Green's functions (specifically, the Hedin equations)
The response of the Green's function under the action of an external field can be represented by the density correlation function L:
$$L_{s_1 s'_{1} , s_2 s_{2'} }(12) = - i \hbar \frac{ \delta G_{s_1 ...
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Significance of Self-Interaction in Hartree Potential
According to DFT (and correct me if I'm incorrect) the terms of Hartree potential and exchange correlation potential are introduced to simulate the particle (fermion-fermion) interaction in our system ...
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Coulombic Interaction in Condensed Matter
I am reading introductory DFT (Density Functional Theory) and I came across this,
Can someone explain why the system needs to be neutral for energy to be finite? and What does organising in neutral ...
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Density functional theory: logical steps from Hohenberg-Kohn theorems to Kohn-Sham equations
I'm trying to learn density functional theory (DFT), using Engel & Dreisler, Sholl & Steckel, and Wikipedia as 3 different sources of information. Although I have made some progress, I am ...
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Rewriting two-body operator in second-quantized form
I would like to understand the following identity for fermion field operators:
$$\psi^\dagger(x) \psi^\dagger(y) \psi(y) \psi(x) = \psi^\dagger(x) \psi(x) \psi^\dagger(y) \psi(y) - \delta(x - y) \psi^\...
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How to derive the following equation in DFT?
Recently, I have read a paper (J.Chem.Phys,99,1993 by Kais and others: download here) which uses Harmonium model to inverse Kohn-Sham equation and obtain exchange-correlation potential. Without going ...
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I'm trying to solve the expression for Dirac exchange, but I'm not understanding the variables change employed. How can I perform it? [closed]
I'm trying to perform the variables change employed in the book "Density Functional Theory of Atoms and Molecules", by Parr and Weitao - page 108. But, from the expression of \rho_{1} given ...
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Lagrangian of KS system under gauge field
Do you know how to derive this Lagrangian quantity?
It came from:
Bertsch, G. F., Iwata, J.-I., Rubio, A. & Yabana, K. Real-space, real-time method for the dielectric function. Phys Rev B 62, ...
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Gibbs energy calculations for compounds
I am studying machine learning during my master's degree and have a simple task. I am using the FactSage Pure Substance Database (https://www.crct.polymtl.ca), which provides a list of phases for a ...
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Hartree-Fock exchange energy: can $i = j$?
I am trying to understand the Hartree-Fock exchange energy used in a paper by Becke and Roussel [1], where it's defined as:
$$\begin{align}
E_X &= \sum\limits_{\sigma} E_{X\sigma} \tag{1}\\
&= ...
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Commutator in the derivation of the Runge-Gross Theorem
In the derivation of the Runge-Gross theorem, a theorem that states a one-to-one correspondence between potential and density in an evolving system, a commutator appears that I seem to have trouble ...
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Resources covering material of Cohen and Louie Condensed matter book (specifically with regards to computational physics)
I need to study the contents of Fundamentals of Condensed Matter Physics by Cohen & Louie for grad school, but it's not very well written with regards to pedagogically or even logically motivating ...
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Germanium bandgap with DFT+U calculations
DFT calculations with GGA functionals result in bulk germanium being metallic. Has anybody ever tried to correct this result by computing the bandgap with DFT+U in Quantum ESPRESSO?
I tried but failed....
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Atoms or molecules as strongly correlated systems
Electrons in atoms or molecules are of course correlated, in the sense that the many-electron wave function is not a Slater determinant. However, in my personal impression, the Hartree-Fock ...
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How is the band gap really defined and calculated?
When I look into literature I am quite confused on how the band gap of a semiconductor is defined. One statement I often read goes something like that:
The band gap of a semiconductor is the energy ...
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Is Thomas-Fermi screening the result of a Thomas-Fermi model in an external field?
On the one hand, the theory of Thomas-Fermi screening describes the response of an ideal metal (or electron gas) in the presence of an external field. In this theory, one assumes that you have a Fermi ...
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Hohenberg-Kohn Hamiltonian Expression
In Hohenberg and Kohn's paper on the inhomogeneous electron gas they express the Hamiltonian for "a collection of an arbitrary number of electrons moving under the influence of an external ...
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Do different Hamiltonians result in different ground states?
I'm learning density functional theory. In the proof of Hohenberg–Kohn theorem I, we assume that different Hamiltonians result in different ground states. Is it true?
In general, for example, we can ...
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From molecular orbitals to band diagram
Let’s say we have a periodic crystal structure. We could, in theory, treat this system as if it were a large molecule. Therefore, we could use Hartree Fock theory or other methods to get the molecular ...
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Why is the commensurate charge density wave for 1T-$\rm TaSe_2$ based on non-integer dimensions?
I have read several papers that have stated that the commensurate charge density wave (CDW) for 1T-$\rm TaSe_2$ comes from a $ \sqrt{13}a_0$ x $\sqrt{13}a_0$ periodic lattice distortion where $a_0$ ...
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Why is there no exchange interaction when there is no coulomb interaction?
The Hartree-Fock energy may be written as
$$
E_{HF}= \langle\Psi| H |\Psi\rangle = \sum_{a} \langle a| h |a \rangle + \frac{1}{2}\sum_{ab} \big( [aa |bb] - [ab|ba] \big),$$
with the exchange term
$$[...
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DFT Hartree Potential with Periodic Boundary Conditions
Suppose we have a periodic crystal. Let $\rho(r)$ be the electronic density, and let $a$ be the lattice vectors. Due to the periodicity, the Hartree potential can be written as
\begin{align}
V_H(r)&...
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Mixed second functional derivative not symmetrical with respect to order of differentiation
I have a functional $E$, which is a functional of two different functions and their gradients:
$$ E[\psi_1,\psi_2] = \int d^3\mathbf{x} ~ \varepsilon\{\mathbf{x}\}$$
where I'm using $\varepsilon\{\...
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When do we need to consider Quantum electrodynamic density functional theory?
We know well quantum electrodynamics (QED) and density functional theory (DFT). The former describes the quantum nature of electromagnetic field, and the latter typically concerns the quantum and many-...
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What is the mechanism behind the spectral property change in voltage sensitive dyes?
As far as I understand the change in spectral properties of voltage sensitive dyes is partially derived from the Stark Effect. However, even if this is the underlying physical phenomena, it is still ...
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How to derive the expression for the effective potential in Kohn-Sham operator in Kohn-Sham density functional theory?
In density functional theory the Kohn-Sham method provides a systematic way to approaching the correct electron density of a given system. Kohn-Sham method uses a non-interacting reference system ...
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How to calculate the orbital character for fatbands in Quantum Espresso?
we are calculating a fatbands structure using QE pw.x. When We get the projections by weight. There are orbitals missing in the projection file. Is there a way to get contribution about outermost ...
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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.
Which one is more accurate?
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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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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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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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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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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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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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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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