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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 definition of size-extensivity, so I had to look deeper into the reference that they provided. They say that size-extensivity was introduced by Bartlett, and they ...


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 ...


14

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 ...


13

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 (...


12

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 ...


12

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 ...


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 ...


11

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

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 ...


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\,...


10

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 "bioelectronics" which one might say was more physics and biology than chemistry). I was much more interested in physics and biology (and math) than chemistry, so I ...


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

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

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

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 ...


8

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, ...


7

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 ...


7

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),(...


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

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 gathered at CERN. I had some much earlier experience working in a condensed matter lab, yet gained very little (to no) chemistry experience. To date, I have never ...


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

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},\...


6

Constraints #9, #10, #12: Uniform and non-uniform density scaling limit The uniform density scaling constraint is obtained by substituting the density into $n(\mathbf{r}) \rightarrow n_\gamma (\mathbf{r})$ which is defined by $$ n_\gamma(\mathbf{r}) = \gamma^3 n(\gamma\mathbf{r}). $$ While the non-uniform density scaling is given as $$ \begin{align} n^x_\...


5

"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 from spectroscopic experiments, such that a Hamiltonian using this potential, when fed through the Schroedinger equation, will give eigenvalue differences that ...


5

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 ...


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

Answering "How does a beginner condensed matter theorist working on real materials, get up to speed?" is not as easy as it could appear. From my own experience, if you are a condensed matter theory PhD student and only focus on condensed matter, you will (should?) grow faster. In my case, I am a physicist and also made my PhD in theoretical ...


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 ...


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