15

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 uniqueness of solutions to the Schrödinger equation for specific classes of potentials and boundary conditions, but in general it is possible to come up with cases ...


13

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 the question what you need is Car-Parrinello or Born Oppenheimer MD. These essentially automate the idea of do a quantum electronic structure calculation, take ...


12

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 $\langle m,m'|V_{ee}|m',m\rangle$. Mathematically, each of these matrix elements is an integral involving wave functions in the system. If we know these wave functions or know how to approximate ...


12

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 the simulation. What you are describing is (essentially) what we call molecular-dynamics even though you're dealing with atoms rather than molecules. In MD (...


11

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 agree, but I'll begin with a disclaimer that looking up "molecular dynamics" probably won't turn up the kind of results you want. Since your comments ...


11

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 materials Not interested in learning details of DFT/software developing Since the OP is already aware of Quantum ESPRESSO and is interested only in calculating basic ...


10

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, suggestions to the post will be welcome! Using an approach I saw here, we can use a chain rule and obtain the following: $$\frac{\delta F[\rho(\boldsymbol{r})]}{\delta ...


10

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 all constituent dipole moments the system (red arrows in the figure below): In your case you have vectors such as: $26.78 \, \hat{x} -6.31\, \hat{y} + 27.17\,...


9

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, and for each distance, you calculate the system energy. The image below is the result of such calculation but between a metal atom and a carbon nanotube1. You ...


9

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, since the one-particle density matrix becomes non-diagonal. You can make the density diagonal like (2) by switching to natural orbitals, but then you have ...


8

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, I mean long time duration at room temperature) and it is used in any red (due to the gap) laser pointer. For electronic data, you can consult this page at the ...


8

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-order density matrices, and natural spin-orbitals and solution of the v-representability problem", PNAS 76 (12) 6062-6065 (1979); https://doi.org/10.1073/pnas....


8

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 dynamics simulations of molecules and solids. SIESTA's efficiency stems from the use of a basis set of strictly-localized atomic orbitals. A very important feature ...


8

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 can't be an inversion centre. In the bilayer the inversion centre is between the layers. Then the direction of the trigonal prism is reversed but it is also ...


7

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 Hamiltonian (in this case the kinetic energy operator) for a diatomic, which is often written as follows: $$\tag{1} \hat{H} = \hat{T} = \frac{J_x^2}{2I_x} + \frac{...


7

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 choose based on what you want to do. I wanted to take a different perspective. If you're familiar with writing code and want to program the simulation yourself, ...


6

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 has a built-in help system. The on-the-fly pseudopotential generation system makes calculations very easy to set up and avoids some common pitfalls. MPI ...


6

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 with the bra-ket notation, I recommend the discussion of variational methods in Sakurai's Modern Quantum Mechanics. The following will be based on Sakurai's ...


6

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)+ It's not clear to me what you write. In the first page of the Internationl Tables you find all the symmetry operations that are listed with Roman numerals (1),(...


6

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 mind when looking at such band structures are: If the system has time reversal symmetry, then if there is an electron with quantum numbers $(\mathbf{k},\...


4

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 $w(r) = \int Fdr$, not $w(r) = \int Frdr$, as you can see from dimensional analysis ($dr$ has the dimension of length, too). Therefore, you treat $r_1$ as constant, integrate ...


4

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 functional theory (DFT). While I am not aware of any examples of this, there are examples of reverse-engineering a computationally obtained density to say ...


3

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 implements a QSGW+DMFT module to that. When localized electronic orbitals ($d-$ or $f-$ type) participate in the states near the Fermi level, the effect of ...


2

I managed to get the converged U$_{0.01}$Cu$_{0.99}$ potential by converging a pure Uranium potential in a Cu lattice. Then by increasing the concentration of Cu and using the old converged potential as a starting potential you can increase the concentration of Cu in steps until finally reaching a converged U$_{0.01}$Cu$_{0.99}$ potential. This is a good ...


2

ProfM's argument is absolutely right. Here I support a more detailed explanation based on first-principles calculations. The spin-resolved band structure of monolayer MoS$_2$ with the consideration of spin-orbit coupling is shown below: You can first find the two split valence bands around $K$ and $-K$ valleys. In particular, spin-$z$ is a good quantum ...


1

I've never come across any paper where they investigated how simultaneously varying both the amount of doping and strain affects the electronic structure of materials. Why is this so? Doping and strain are viewed as effective methods to engineer the properties of materials. It is true that doping and strain can be applied at the same time. However, from the ...


1

I suspect the reason is due to the model. Often doping is performed in the dilute doping region where you do not relax the cell to optimize the strain induced by the adsorbate. This is because it is assumed the doping is done in a way that the bulk structure imposes its lattice constant on the dopant. The dopant actually does induce strain so they are not ...


1

Someone else can probably answer this in more detail, but most software packages allow for simulated spectra to be calculated just as you have said (not just the excitations). You can probably take the spectra and treat it the same as your experimental spectra. At the very least, I was able to find a recent paper that appears to have done exactly just that. ...


Only top voted, non community-wiki answers of a minimum length are eligible