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