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 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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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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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 ...
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What do we physically mean by smearing in condensed matter?

What do we physically mean by term smearing in DFT based codes like VASP or generally in condensed matter?
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Calculate total number of electrons from density of states? [closed]

Can someone tell me how to calculate the total number of electrons from partial density of states (projected on each atom)? Thanks
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Linear force vs. displacement relationship for crystalline solid

I did a series of density functional theory (DFT) calculations on crystalline silicon. These consisted of 50 total displacements of one atom from equilibrium in the x-direction until the displacement ...
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Casida equation, excited states and response theory

I have several doubts about the characterization of excited states within the framework of TD-DFT (Time dependent Density Functional Theory) / Response Theory. Just to give some context and fix ...
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Transient simulation of a Gaussian wave packet using time dependent Liouville-von Neumann equation in center mass coordinates?

I am working on a transient simulation of a Gaussian wave packet using time dependent Liouville-von Neumann equation in center mass coordinates. For discretization of diffusion term, I have used Crank ...
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679 views

Literature recommendation for classical density functional theory (DFT) and fundamental measure theory (FMT)

I'm very much interested in properly learning about density functional theory calculations (DFT) in classical settings, for example as used in the theory of liquids. Apart from the success of DFT ...
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how can DFT calculate band structure

I am trying to understand DFT, and so far i realized that DFT is really concerned with the ground state properties. My question is how can we calculate the band structure of a material using DFT ? I'...
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101 views

The exchange potential in Kohn-Sham equations for harmonic interactions

Is there an analytic formula for the exchange potential part in the effective potential of the Kohn-Sham equations for a system of N Bosons in a harmonic trap with mutual harmonic interactions or a ...
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163 views

Number of ionic steps in plane wave DFT

What is the significance of increasing (and decreasing) the number of ionic relaxation steps in a plane wave DFT calculation?
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(Solved) Is Kohn-Sham approach in DFT compatiable with Hohenberg-Kohn theorem?

From DFT theory, the Euler equation of an interacting system is: $$\begin{align*} \frac{\delta E_{v}[\rho]}{\delta \rho(\vec{r})} &= \frac{\delta}{\delta \rho} \left[T_{s}[\rho]+\int \rho(\vec{r})...
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projector augmented waves

I am starting out with density functional theory from an engineering perspective. Could anyone help me understand what the difference is between USPP (ultra-soft pseudopotential) and PAW (projector ...
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Can one always take a single-particle picture (i.e. DFT) irrespective of the strength of correlations?

Most textbooks on Kohn-Sham density functional theory will assert that it is exact assuming that one has the 'appropriate' exchange-correlation functional. To my mind, this is completely astounding ...
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Decomposition of N-representable density into determinantal wavefunction

My textbook "Density Functional Theory of Atoms and Molecules" by Parr and Yang says that any N-representable density is derivable from a single determinantal wavefunction. A density $\rho$ is N-...
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348 views

Hamiltonian with ext. vector potential - complex kinetic energy

in a given (TD)DFT code with an atomic basis set, i.e. $$ \psi(\mathbf{r},t) = \sum_i c_i(t) \phi_i(\mathbf{r}) $$ (where the non-on-site basis functions $\phi_i$ aren't necessarily orthogonal), the ...
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687 views

Many body Schrodinger equation - DFT / Exchange-Correlation term question

In principle if you solve the many body Schrodinger equation you will get the whole physics and nature of the problem. With the hamiltonian, in the most general case (without Born-Oppenheimer ...
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Question on the Proof of Hohenberg -Kohn Theorem

Between Equation (5) and Equation (6) of the the original paper titled as "Inhomogeneous Electron Gas" by P. Hohenberg and W. Kohn, there is a sentence stating that: " Now clearly (unless $v'(\...
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On the Full scope of Hohenberg-Kohn Theorem

The Hohenberg-Kohn Theorem (HK Theorem) tells us that, knowing the electronic density in the ground state of a system of electrons, we can reconstruct the external potential up to an additive constant ...
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Dependence of electron density functional on the number of electrons

The Hohenberg-Kohn theorem, the foundation of DFT, is based on the energy functional of electron density $n(\mathbf{r})$ for a system of Coulomb-interacting electrons, placed in in the external ...
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322 views

How to compute Coulomb repulsion from electron density numerically [closed]

The energy due to mutual repulsion of electrons (Hartree potential) is usually formulated similar to $$U_{ee}=\frac{e^2}{2}\int\frac{n(r)n(r')}{|r-r'|}\mathrm{d^3}r~ \mathrm{d^3}r'$$ I'm not a ...
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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. ...
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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 ...
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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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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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223 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 ...
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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 ...
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597 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 ...
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513 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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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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875 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?
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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 ...
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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....
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154 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 $N$ ...
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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 ...
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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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Understanding electronic band structure diagrams

Currently I'm trying to understand electronic band structures such as depicted below: band structure http://ej.iop.org/images/1367-2630/14/3/033045/Full/nj413738f1_online.jpg And following questions ...
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Why does Density Functional Theory (DFT) underestimate bandgaps?

Density Functional Theory (DFT) is formulated to obtain ground state properties of atoms, molecules and condensed matter. However, why is DFT not able to predict the exact band gaps of semiconductors ...
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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 ...
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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 ...
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Is density functional theory a mean-field theory?

Is density functional theory exact or just a mean-field theory?
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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 ...
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536 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 "...
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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 ...
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854 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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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 ...
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Computer coding of Perdew Burke and Ernzerhof (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?
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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 \...
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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 \...