16 votes

Mathematical expression of SCAN (Strongly Constrained and Appropriately Normed) constraints in DFT

Constraint #13: Size-Extensivity While the Wikipedia page for size-consistency and size-extensivity gives a clear formula for the definition of size-consistency, unfortunately they did not give a ...
  • 29.7k
15 votes
Accepted

Does the Schrödinger equation have unique solutions?

The solutions to the Schrödinger equation are not unique in general, and uniqueness depends on several things such as the form of the potential and boundary conditions. Many papers have discussed ...
  • 29.7k
14 votes

How do I simulate the interaction between two atoms?

EDIT Doing what you want is hard! You will need a full quantum mechanics based simulation. This is unlikely to be something you can build yourself at the current time. Based on your new additions to ...
  • 319
13 votes

How do I simulate the interaction between two atoms?

How to proceed depends on how accurate you want the outcome. Throughout my answer I will provide blue buttons which demonstrate that there's entire tags in our community to address certain aspects of ...
  • 29.7k
12 votes

DFT software package for a beginner?

QuantumVITAS As I understand, OP's requirements are Do basic calculations using DFT Prefer open source software which is easy to use Interested in DFT only as a tool to calculate properties of ...
  • 8,452
12 votes
Accepted

The Hund's J - Why can this be quantified?

When I first read your question, I found it somewhat puzzling. I have to admit, I still do in part. Why? Well, even your link defines $J$ as a sum of matrix elements $\langle m,m'|V_{ee}|m',m\rangle$. ...
  • 4,403
11 votes
Accepted

How do you calculate the "true" chemical potential in classical density functional theory?

Seeing that this question has gathered attention but no replies, I will give it a stab. Note that I am not an expert on DFT or functional calculus, so take this with a grain of salt. As usual, ...
  • 1,848
11 votes

How do I simulate the interaction between two atoms?

Generally speaking, most work in molecular dynamics tries to simulate how actual molecules behave (i.e. quantum mechanics) and it doesn't sound like you want to go down that rabbit hole. I completely ...
10 votes

How do I simulate the interaction between two atoms?

In order to simulate two atom interaction, you have different path to follow. One is to use Density Functional Theory (DFT) or ab initio, make a script where the distance of the atoms is decreasing, ...
  • 19.9k
9 votes
Accepted

Electron density arising from Slater determinant wave function

The proof that (2) is the density arising from a Slater determinant wave function can be found in basically any quantum chemistry textbook. (2) does NOT hold for multiconfigurational wave functions, ...
  • 15.7k
9 votes
Accepted

What is the right way to calculate <A><A>?

The dipole moment is typically a vector quantity, and the "total dipole moment" which is the $A$ in your question description and the black arrow in the figure below, is the vector sum of ...
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9 votes

How does a beginner condensed matter theorist working on real materials, get up to speed?

Welcome to the club of academic migrants! I didn't take any university-level chemistry courses during my undergrad years (except a special topics course for graduate students called "...
  • 29.7k
8 votes

Electron density arising from Slater determinant wave function

On the specific subject of the "EDIT", this was exactly the concern addressed by Mel Levy in the 1970s, e.g. M. Levy, "Universal variational functionals of electron densities, first-...
  • 4,527
8 votes

Is there any software that can generate the electronic DOS of GaAs?

The $\ce{GaAs}$ is one of the must studied semiconductors. One of its main application was as the active site of semiconductor laser, becoming the first stable material used on this devices (by stable,...
  • 19.9k
8 votes

DFT software package for a beginner?

SIESTA I strongly recommend SIESTA. From the site: SIESTA is both a method and its computer program implementation, to perform efficient electronic structure calculations and ab initio molecular ...
  • 19.9k
8 votes
Accepted

Inversion symmetry in 2D materials

Let's give it another go: In the monolayer you would place the inversion centre on the green atom. But this would reverse the direction of the trigonal prism formed by the yellow atoms. Hence, there ...
  • 1,411
7 votes

How do I simulate the interaction between two atoms?

The simplest possible atomic simulation: a noble gas As explained by Nike Dattani, what method you use depends on what you want to simulate and why. He gives you a good roadmap for what method to ...
7 votes

DFT software package for a beginner?

CASTEP I would recommend CASTEP. It is not open source but does have a cost-free academic license option. It is very easy to use and beginner-friendly, with sensible "default" parameters and ...
  • 661
7 votes

What does it mean to assign group operations to distinct sets for space groups?

When your lattice is primitive you have only the (0,0,0)+ set; when your lattice has some kind of centering (body- or face-centering) other sets are present, such as (1/2, 1/2, 1/2)+ or (1/2, 1/2, 0)+ ...
  • 601
7 votes
Accepted

How are molecular rotational states modeled within the Born Oppenheimer Approximation for polyatomic molecules?

The Hamiltonian Just as for vibrations we have the harmonic oscillator approximation, for rotations we often use the rigid rotor approximation, where bond lengths are fixed. Recall the rigid-rotor ...
  • 29.7k
7 votes

How does a beginner condensed matter theorist working on real materials, get up to speed?

I'm grad student about to finish their PhD, so you may find my perspective valuable. For reference, my undergrad degree was in physics and math, where I did big data analysis on high energy data ...
6 votes
Accepted

How is the error in a wavefunction related to the error in energy?

You can, in fact, do better as the answer to this Physics.SE question of yours indicates, assuming you're after an asymptotic expression. I haven't read the book you mention, but if you're familiar ...
  • 4,403
6 votes
Accepted

Separation of valence bands in transition metal dichalcogenides (TMDs)

I should start by saying that I am no expert in MoS$_2$, so this answer is my guess from looking at the reference you provide, and would be happy if someone corrects me. The general things to keep in ...
  • 10.6k
6 votes

Mathematical expression of SCAN (Strongly Constrained and Appropriately Normed) constraints in DFT

Constraints #9, #10, #12: Uniform and non-uniform density scaling limit The uniform density scaling constraint is obtained by substituting the density into $n(\mathbf{r}) \rightarrow n_\gamma (\mathbf{...
  • 883
5 votes
Accepted

Can we "invert" Density Functional Theory through sufficiently accurate experiment?

"Inversion" is common in wavefunction-based quantum mechanics, for example the RKR inversion method which constructs a potential energy function based on information that can be obtained ...
  • 29.7k
5 votes

Can we "invert" Density Functional Theory through sufficiently accurate experiment?

This is not a direct answer to your question, but I hope to get the ball rolling. In the question, you ask about reverse-engineering an experimentally obtained density to say something about density ...
  • 10.6k
4 votes

Wavefunction magnitudes being degenerate everywhere on parameter space even though energy degeneracies occur at isolated points?

This is a somewhat handwaving answer but I think it gets the main point across: We should start by pointing out that the two components of your eigenstates represent the wave function amplitudes on ...
4 votes

Simplifying double integrals of isotropic functions

The work is a single integral over $|r_1-r_2|$, not a double integral over $r_1$ and $r_2$. As you are fixing particle 1, you shouldn't integrate over particle 1. Moreover, the work is $w(r) = \int ...
  • 8,036
3 votes

DFT software package for a beginner?

Questaal Website: https://www.questaal.org/about/questaal/ Description: Questaal is the most advanced open-source DFT package to study strong correlation physics in 3D materials. In detail, Questaal ...
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Only top scored, non community-wiki answers of a minimum length are eligible