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The Rule The timestep should be less than the period of the fastest vibration by at least 2. In signal processing this is known as Nyquist's theorem. If a function ${\displaystyle x(t)}$ contains no frequencies higher than B hertz, it is completely determined by giving its ordinates at a series of points spaced ${\displaystyle 1/(2B)}$ seconds apart. The ...


28

Quick Summary: There's no way around performing a convergence test. However, it is possible to obtain convergence much faster than the Phonopy approach by using nondiagonal supercells [1]. The basic quantity you build when performing a phonon calculation is the matrix of force constants, given by: $$ D_{i\alpha,i^{\prime}\alpha^{\prime}}(\mathbf{R}_p,\...


15

The Nyquist sampling theorem states that the time step must be half or less of the period of the quickest dynamics. This is the absolute maximum time step that can capture the quickest dynamics at all, and it is usually recommended to choose a much smaller time step (often chosen to be between 0.1 and 0.2 of the shortest period). Typical time steps range ...


14

Ideally, a convergence test would be the best way to decide the required size of the supercell, but it can get expensive. When phonopy (or any similar calculation technique) finds displacements in the cell based on symmetry, the idea is to see how the displacement of certain ions affects the forces on every ion within the cell. We must then take care that ...


13

Considering this in terms of a 2x2x2 supercell matrix is the wrong way to think about this, as choice depends on the cell length and bonding type. Given that rigorous convergence testing is near-impossible (see ProfM's answer), what saves the method is the rapid fall-off with distance of the force constant matrix $\Phi$. This "nearsigtedness" ...


13

A few materials/simulation boxes I've had some proper trouble with: HSE06 + noncollinear magnetism + antiferromagnetism, Vasp noncollinear: This was a strongly antiferro material (4 Fe atoms, in an up-down-up-down configuration). HSE06 is apparently difficult to converge anyway. Noncollinear magnetism/antiferromagnetism apparently creates problems for any ...


12

This question is a bit ill-defined: what do you mean by "the self-consistent field procedure"? If you mean the original Roothaan procedure, then the question makes sense, but it is uninteresting: nobody uses the Roothaan procedure, since it usually doesn't converge, and you need to do something smarter like use damping or other convergence acceleration ...


12

I agree with Camps that your best bet is to look at a potential advisor and see what they study. Your given example might be a bit of a stretch for some computational materials science advisors, due to its very fundamental nature of solving the problem rather than applying the problem. This could be exactly what one advisor works on though so you should ...


10

I wrote an answer to a similar question in the past, but focused in that question only on the state-of-the-art ultra-high precision calculations on atoms and the three most common isotopologues of $\ce{H_2}$. I will first repeat those here: Atomization energy of the H$_2$ molecule: 35999.582834(11) cm^-1 (present most accurate experiment) 35999.582820(26) cm^...


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This will be a long answer, so I will divide it in parts. Woods paper A significant limitation of the Woods et al paper is that it excludes atomic-basis set calculations where convergence acceleration is much more powerful than in plane wave codes. Namely, the update schemes discussed in the article talk about just the input and output densities, whereas ...


9

This is an excellent question! The reality is complicated even in LCAO calculations: every code has different defaults, which also depend on the run type. It seems that older LCAO codes simultaneously look at the convergence of the energy, and of the density matrix. Looking only at the change in energy is really bad behavior, since it doesn't tell you ...


9

The Davidson-Method is the best algorithm when you want a comparatively small number of eigenvectors/eigenvalues from a sparse, diagonally dominant matrix. MKL doesn’t have a sparse matrix diagonalization method, but it’s a good idea to use it for the Linear Algebra operations used when implementing Davidson. If you want ALL the eigenvectors then you ...


9

Following Nike Dattani's suggestion, I now add some comparisons of the Davidson method with methods that are more "modern" than it, to supplement the existing answers which compared the Davidson method with methods that predates it. However my answer will be more or less off-topic because I will mainly talk about disadvantages of the Davidson ...


8

In the Huckel method, you are just generating a very simplified version of the molecular Hamiltonian and determining it's eigenvalues. The molecular Hamiltonian will always be a Hermitian matrix (for the Huckel method, we can be more specific and say it's a real symmetric matrix by construction). Hermitian matrices are guaranteed to have all real eigenvalues ...


7

Approaching the fixed-point problem an SCF solves from the direct minimisation (DM) point of view (for the relation of DM to SCF, see my previous post, the key quantities to check for convergence are actually the total energy and it's derivative, i.e. the occupied-virtual block of the Fock / Kohn-Sham matrix. The latter is after all the gradient and that's ...


7

If by "the SCF method" you mean the simple SCF, the answer is: no, usually it does not converge (unless the problem is very simple; basically the gap is huge, so that the system does not respond very much to potentials). The damped SCF problem on the other hand does converge, for damping parameters small enough (unless you run into fractional occupations). ...


7

As with all MD simulations, you have to assume (often wrongly) convergence with finite time. This is fairly easy to do with autocorrelation functions though, because you know that once they become negative, you are already in the random fluctuation (i.e. uncorrelated noise) zone and this is the point where you can stop. This is slightly trickier in some ...


7

To supplement Cody's excellent answer, Davidson diagonalization originates from quantum chemistry, where solving configuration interaction problems requires diagonalizing the Hamiltonian in the space of electron configurations. The Davidson algorithm and refinements thereof enabled full configuration interaction calculations with matrix sizes of $10^9 \times ...


6

Judging by your initial energies, it looks like you're starting a calculation from scratch. I've had good luck so far converging spin-polarized calculations by first doing a non-spin-polarized calculation, writing the CHG, CHGCAR, and WAVECAR files, and using those to start a spin-polarized calculation. This is the recommended method if such calculations ...


6

In sisl one can create a Monkhorst-Pack grid with zooming capabilities. Here is a small Python snippet which creates the k-points for the zoomed in region. import numpy as np import sisl # time-reversal-symmetry trs = True # first argument is the lattice vectors (in case you want them in 1/Ang) # in this case it is just a square box of side-lengths 1 Ang ...


6

It is not converged, it needs to hit |-1E-5| on the fourth and fifth column. It gets close on the fifth column, but never quite makes it there. The lowest I see is about |-1.7E-5|. It seems to be struggling, if this isn't an optimized structure then you could lower EDIFF to 1E-4 or even 5E-4 for some initial steps...Or simply do not worry about it and ...


6

The best strategy when performing convergence tests is to directly converge the quantity you are interested in. This "quantity" can be a straight-forward physical property, like the band gap of a material, or a composite (for lack of a better word) property. In your case, you are interested in comparing the electronic density of states (DOS) ...


6

Other answers explaining Nyquist's Sampling Theorem are completely correct. Read those before mine. I'd like to add some information about how details of how you run your simulation can affect the Nyquist frequency, and therefore, in practice, affect the fundamental question of how to choose your time step. As one can easily imagine, tricks that let you ...


6

Having read the above answers I think it's important to point out why you generally use a time step below the upper limit provided by Nyquist's Theorem. The theorem itself describes the maximum number of signals it's possible to send through a telegraph cable and still have them be discernable from one another. That makes the limiting case a sampling ...


6

It is well-established that it can be quite difficult to converge the SCF for certain (hybrid) meta-GGA functionals compared to their (hybrid) GGA counterparts. This is especially true for plane-wave periodic DFT and is most often the case with many of the popular Minnesota functionals. In large part because of this reason, a revised version of M06-L ...


5

Here's some calculations I had some problems with: LaFeO$_3$ on LaAlO$_3$ with an adsorbed O atom. $\sqrt{2}\times\sqrt{2}$ perovskite cell in the x-y direction. 5 layers of LaAlO$_3$ (alternating LaO - AlO$_2$ - LaO etc.) with 3 layers of LaFeO$_3$ on top. The bottom 3 layers of LaAlO$_3$ are fixed. Anti-ferromagnetic order on the Fe atoms. Around 450 ...


5

My suggestion is that you first get an SCF calculation to converge for this structure before you try relaxing, especially if you aren't sure what you're going to get. Then you can proceed to converging the numerical settings like the cutoff energies for your properties of interest. I was able to get an SCF calculation to converge using your input file by ...


4

To compare calculations, it’s best to have all the calculation parameters possible the same, including the k-mesh spacing, plane wave energy cut-off, and the Brillouin zone integration method (with the same smearing width, if applicable). The settings must also be sufficiently converged for each case. In your example, if the B2 case a tighter k-point spacing ...


4

A mixing weight of 0.25 is pretty high, if not excessively high in this case. Did you try, say 0.02, or something like that? Also, kicks are only necessary when you have problems with stalls in convergence. If you stall after 50 SCF, you should have a kick at that point, but definitely not at every 3rd SCF, that may worsen your convergence. Generally one ...


3

Note that Q-Chem and Psi4 are not actually measuring the change in the density, but rather the orbital gradient. There is a subtle difference: no change in the density does not mean the energy has been minimized, but if the orbital gradient is zero you're mathematically certain to be at an extremal point, which can be either a local minimum or a saddle-point ...


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