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 ...

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833 views

What is the current state of research into $v$-representability?

In their proof, Hohenberg and Kohn (Phys Rev 136 (1964) B864) established that the ground state density, $\rho_\text{gs}$, uniquely determines the Hamiltonian. This had the effect of establishing an ...
8
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1answer
506 views

Understanding electronic band structure diagrams

Currently I'm trying to understand electronic band structures such as depicted below: And following questions were arisen. Why are there multiple lines in valence side and conduction side? Where ...
7
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2answers
498 views

Time-dependent Schrodinger equation from variational principle

In the paper, "Density-functional theory for time-dependent systems" Physical Review Letters 52 (12): 997 the authors mentioned that the action $$ A= \int_{t_0}^{t_1} \mathrm dt \langle \Phi(t) | i \...
5
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4answers
174 views

Interpretation of Orbital Magnetic Moment

The wavefunctions for atomic orbitals have always been described to me one of two ways: As a "smeared out" electron standing wave with integer number circumference of de Broglie wavelengths As a "...
5
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1answer
972 views

Implementing simple atom model using density functional theory (DFT)

I am trying to write computer code which will find the energy and density function for an atom with $Z$ protons and $N$ electrons. I am working in 1D for simplicity and would like to make the overall ...
5
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2answers
1k views

B3LYP vs PBE functionals for conjugated organic systems

Two of the most popular (exchange and correlation) functionals for density functional theory are B3LYP and PBE. Out of the people I've worked with / learned from, mostly the computational chemists ...
4
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1answer
322 views

Antisymmetric functions as Slater determinants

Can any antisymmetric function, i.e., a function of $N$ spatial-plus-spin variables $\{x_i\ | \ i= 1, \ldots, N\}$ satisfying $$ \psi(x_1,\ldots, x_i, \ldots, x_j, \ldots, x_N) = -\psi(x_1,\ldots, ...
3
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1answer
166 views

How does a unique electron probability distribution correspond to one wavefunction?

I'm reading the Wikipedia article on DFT, and it says that there is a one-to-one correspondence between the ground state particle density $$n_0(\vec{r}) = N \int \text{d}^3 r_2 \int \text{d}^3 r_3 \...
3
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1answer
427 views

How to calculate excluded volume in Onsager's hard-rod model?

Can somebody please provide a derivation of how to calculate excluded volume of two rods with angle of intersection being $\gamma$. rods are cylinders, capped with semi-spheres. Onsager theory of hard ...
2
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2answers
821 views

Coulomb potential energy functional derivative

I'm having problem understanding how to compute a functional derivative when it's involved more than one integral, such as the coulomb potential energy functional: $$ J[\rho] = \frac 12\int \frac{\...
2
votes
1answer
131 views

DFT breakdown for effects that depend on phase?

Given the Hohenberg-Kohn theorem, a given ground-state density uniquely defines all ground state properties, because in principle the external potential $V_{ext}$ can be understood as a functional of ...
2
votes
2answers
254 views

Why does GW-DFT give higher bandgaps in semiconductors

Usually the GW Density Functional Theory (DFT) gives larger band gaps in semiconductors compared to the LDA and GGA methods. This seems to be related to the screened potential in GW, but it is not ...
2
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1answer
665 views

Constrained-search formulation of DFT: by Levy or by Levy-Lieb

I'm a bit puzzled about how to give the right references for the constrained-search formulation of DFT. Till now, I only heard it being called "Levy constrained-search" but came about some papers and ...
1
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2answers
530 views

Which is the best DFT functional for band gap calculation?

Density Functional Theory (DFT) does not predict the correct band gap (E$_{g})$ of the materials. Which exchange and correlation functional predicts the E$_{g}$ value exactly? What about the HOMO-...
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2answers
187 views

why is DFT(Density Functional Theory) weak in evaluating semiconductor and insulator bandgaps?

we say that the DFT (Density Functional Theory) is to obtain the ground state properties of a quantum system and then we say: so, we can not use it to obtain the semiconductors and insulators band ...
1
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1answer
34 views

Nonzero stress on crystal at equilibrium volume?

Using a first principles computational method such as DFT, you can calculate the energy of a unit cell at different volumes to obtain a parabolic energy vs. volume curve. The minimum of this curve ...
1
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2answers
371 views

Is density functional theory a mean-field theory?

Is density functional theory exact or just a mean-field theory?
1
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1answer
436 views

Dopant Charge Transfer and Fermi Level shift

When a system has a dopant, how much does the Fermi level shift? For example, say a finite concentration of substitutional dopants replace some bulk atoms, and each has one extra electron. Ignore any ...
1
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1answer
178 views

Dyson Schwinger equation

given the Dyson equations $ \frac{\delta S}{\delta \phi(x)}\left[-i \frac{\delta}{\delta J}\right]Z[J]+J(x)Z[J]=0 $ is true that they are a solution or differential representation of the Generating ...
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1answer
55 views

why pseudo wave functions can be used to calculate berry connection

Berry connection plays a very important role in topological insulators. Berry connection $A(k)$ is defined to be $i\langle u(k)|\nabla_k|u(k)\rangle$, where $|u(k)\rangle$ is the periodic part of ...
1
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1answer
206 views

What exactly is a one particle density?

In Density Functional Theory (DFT) we derive the Grand Potential as a functional of a so-called one particle density (OPD). I have trouble imagining what exactly that is. Could someone help me with ...
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0answers
37 views

What approximation does Tamm-Dancoff approximation (CI singles) correspond to in real time Time-Dependent Density Functional Theory?

Starting from equations of motion for time-dependent density functional theory (in real time) $$ \frac{ {\rm d} \rho_{nn} }{ {\rm d} t} = i \left[ \rho_{nn}^{(1)}, h^{\rm KS} \right] \quad\text{...
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1answer
107 views

many body wavefunction and exchange correlation

Everywhere I ready about HF or DFT the term exchange correlation functional comes up. I have a couple of fundamental questions about these: 1) Books say that the correlation energy is the difference ...
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0answers
41 views

Non-Linear Behavior of Iterated Functional Maps

The universal behavior of certain iterated nonlinear function maps (ie period doubling bifurcation route to chaos): $$x_{i+1}=f(x_i)$$ have been known since Feigenbaum: (see http://...
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0answers
55 views

Definition of linear response kernel in terms of wavefunctions (Parr/Yang)

I'm trying to understand the derivation of the linear response kernel in Parr/Yang's "Density-functional theory of atoms and molecules". First some background information: We look at a system of $N$ ...
1
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1answer
206 views

Kohn-Sham equations from variational principle

I'm trying to understand how the Kohn-Sham equations arise from the variational principle, failing. I think my problem is the inability to apply the variational principle. Or, I lack some crucial ...
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0answers
44 views

Computer coding of Perdew Burke and Ernzerho (PBE) method

I have been assigned the task to write a computer code to implement the Perdew Burke and Ernzerhof (PBE) method. Does anyone know a good reference which can make the coding of this method easier?
0
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1answer
27 views

Electronic or excitonic band structure?

Usually, in the papers the electronic band structure for monolayers $WS_2$ is something like in the figure below: As you can see the direct bandgap is around ~2.0 eV. When we excite electrons at the ...
0
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2answers
152 views

Density Functional Theory (DFT) calculation for metals

Why is DFT not used in calculating electronic structures and properties of metals? I know DFT calculations are not accurate for metallic structures. Can someone explain why?
0
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2answers
158 views

Density Functional Theory (DFT) tutorial guide

I am going to start learning about DFT calculations. Could anyone advise me the best starting point for that? Simple example guiding tutorial with explanations would be great. Any input would be good....
0
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1answer
121 views

What do DFT band structure plots actually show?

In a lot of the literature, we see plots of the energy band structure from DFT simulations. How are these eigen-energies obtained as function of crystal momentum within the DFT framework? Are they the ...
0
votes
1answer
276 views

DFT Calculations, Atomic Ionization Potentials — Which Exchange-Correlation Functional to Use, to Preserve Koopmans' Theorem?

I have a program which can perform density-functional calculations for atoms, given a density functional. Of course the simplest form of exchange potential to use is one relevant for a uniform ...
0
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45 views

Why are the $d$- or $f$-orbitals considered localised?

Why is it said that the $d$ and $f$ orbitals are localized and the on-site electron correlations could be important? How should one understand this in the context of solid-state physics?
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31 views

Projected band structure plot - orbital characteristics plotted vs the K values?

I'm not understanding what is it that I have to plot for obtaining the orbital characteristics of a band in the band structure diagram. Usually we plot the energy eigenvalues for a given k point. ...
0
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0answers
11 views

Orthogonality condition between core and valence states (pseudopotentials)

In the paper "Pseudopotential methods in condensed matter applications" by W. E. Pickett the author comments the following in the introduction section (Page 4, 1st paragraph - introduction) "Although ...
0
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23 views

The d-orbital splittings in WS2 monolayer

According to this paper (and many others), the formely degenerate $d$ orbitals of the tungsten atoms in the $WS_2$ monolayer are split into three groups: (1) $d_{z^2}$, (2) $d_{x^2-y^2}, d_{xy}$ and (...
0
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0answers
13 views

Reference request: Generalized gradient approximation (GGA) exchange-correlation functionals

I find myself at a loss when it comes to trying to understand the details of exchange-correlation functionals beyond the Local Density Approximation (LDA). I tried to read some papers, like the ...
0
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0answers
27 views

Why is more difficult for a DFT to converge with non-periodic conditions?

I am simulating a cubic amorphous silica system. When all boundaries are periodic the SCF iteration converges rapidly. However, when the boundary is not periodic in the $x$ direction, the SCF ...
0
votes
1answer
33 views

Velocity matrix and non-local pseudo potentials

It is known that velocity of bloch wave functions are related to band energy derivatives: $$v(k)=\frac{1}{\hbar}\frac{\partial \epsilon}{\partial k}$$ However, in the following paper, it is given ...
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0answers
103 views

Why formation energy calculation is essential in DFT studies?

I use Density Functional Theory (DFT) to calculate the electronic properties of doped molecules/materials. By doping, I mean both substitutional doping and interstitial doping. At present, I optimize ...
0
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0answers
73 views

Implementing Hartree potential in DFT code

I am trying to write my own (localized orbital) density functional theory (DFT) code in order to understand the intrinsics of DFT. Initially, I calculated the electron-electron repulsion by evaluating ...
0
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0answers
36 views

Is the there a unique correspondence between the potential and bound state wave functions? [duplicate]

I'm asking specifically for the schrodinger equation. Is there a unique correspondence between the energy eigenfunctions $\phi_i(x)$ and the potential term $U(x) = V(x)\phi(x)$? Furthermore, is this ...
0
votes
1answer
71 views

At what densities the many-body approaches are valid?

Suppose we have a n-particle interacting system with a potential $V=a/(r1-r2)$, it is a pseudo-coulomb potential: you can choose it fermion or boson. Then, at what densities the many-body approaches ...
0
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0answers
75 views

Phase separation - density functional theory

I would like to get the equilibrium density profile $\rho(x)$ of a non ideal gas that has phase separated. I start by defining a simple free energy density. The total free energy $F[\rho]$ is a ...
0
votes
0answers
31 views

Couting the occupied states in band structure

I work with several dft codes and I have produced the band structures of some doped semiconductors with their plots. The problem I have is that I do not know how I can analyze the band structure and ...