34
votes
How big should a supercell be in phonon calculations?
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 ...
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31
votes
Accepted
How should one choose the time step in a molecular dynamics integration?
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 ...
- 7,957
17
votes
How should one choose the time step in a molecular dynamics integration?
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,...
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17
votes
How big should a supercell be in phonon calculations?
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 ...
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15
votes
How big should a supercell be in phonon calculations?
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-...
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14
votes
Accepted
What are the physical reasons if the SCF doesn't converge?
I have written a section in the BDF user manual on this issue. It is in Chinese but I'll roughly translate the key parts to English as below.
Common reasons for the SCF procedure to fail to converge ...
- 9,076
13
votes
Difficult cases for converging Kohn-Sham SCF calculations
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 ...
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12
votes
Accepted
Are there examples of ab initio predictions on small molecules without the "major approximations"?
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 $\...
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12
votes
Accepted
DFT Knowledge Check for Posed Problem
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 ...
- 10.8k
12
votes
What is the mathematical condition that ensure that the self-consistent field (SCF) procedure must converge?
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: ...
- 17.9k
11
votes
What are the advantages of the Davidson diagonalization method over other sparse matrix diagonalization methods?
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 ...
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10
votes
Standard values for level of convergence
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 ...
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10
votes
Difficult cases for converging Kohn-Sham SCF calculations
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 ...
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10
votes
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How does charge mixing work?
Density mixing is a type of self-consistent field (SCF) method, which tries to find the closest density to the Kohn-Sham (or Hartree-Fock etc) ground state density by mixing previous densities and ...
- 6,567
9
votes
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Is it possible to get complex numbers as solutions for a secular determinant in simple Hückel method (SHM)?
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 ...
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9
votes
How should one choose the time step in a molecular dynamics integration?
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 ...
- 2,027
9
votes
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What are the advantages of the Davidson diagonalization method over other sparse matrix diagonalization methods?
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 ...
- 7,957
8
votes
What is the mathematical condition that ensure that the self-consistent field (SCF) procedure must converge?
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 ...
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8
votes
Calculating diffusion coefficient from Mean Squared Displacement
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 ...
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8
votes
How should one choose the time step in a molecular dynamics integration?
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 ...
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8
votes
What are the advantages of the Davidson diagonalization method over other sparse matrix diagonalization methods?
To supplement Cody's excellent answer, Davidson diagonalization originates from quantum chemistry, where solving configuration interaction problems requires diagonalizing the Hamiltonian in the space ...
- 17.9k
8
votes
What are the physical reasons if the SCF doesn't converge?
There are several good answers. One concern that's not currently mentioned in the other answers is when the initial guess is poor.
While most programs have several methods to perform an initial guess, ...
- 9,035
8
votes
Accepted
SCF energy keeps on fluctuating between two values, instead of converging, why?
The cause of the oscillations in the SCF energies is probably a "sloshing instability"; the two most common types are "charge sloshing" and "occupancy sloshing".
Sloshing ...
- 6,567
7
votes
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Convergence by energy and/or density?
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 ...
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7
votes
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Charge density convergence within VASP using spin polarized DFT+U
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 ...
- 106
7
votes
How to make SCF converge in SIESTA?
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 ...
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7
votes
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Use of higher-order integrators in molecular dynamics?
Higher-order integrators are used, but usually the way they perform the calculation is not through directly calculating higher order derivatives, but essentially through multiple force calculations. ...
- 2,027
7
votes
Accepted
The relationship between average eigenvalue and convergence performance in VASP?
In general, the difficulty of an optimisation problem depends on how widely spread the eigenvalues of the Hessian are. To see why this is, consider a minimisation problem where we wish to find the ...
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7
votes
What are the limitations of FCI?
Assuming that you have $N$ electrons and $K$ spatial orbitals, the total number of electron configurations that can be built is $$ N_{\rm confs} = {K \choose N_\alpha} {K \choose N_\beta} \approx {K ...
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6
votes
Why does the VASP electronic step not stop after getting converged?
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 ...
- 10.8k
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