- Q: What does convergence mean?
- A: Any property may be converged, including total energy, some energy difference, lattice parameter, etc. The important thing to note is that convergence is always defined with respect to your "most accurate" calculation. Convergence is not necessarily reached when the difference in desired property between the n-1st calculation and the nth calculation falls below some threshold! If you look at things that way, you run the risk of prematurely declaring a calculation converged. See the below example.
In this figure, if you were to only consider the current calculation and the one before it, you would call an energy cutoff of 300eV converged, as the difference in what we're calculating between cutoff=350eV and cutoff=300eV just happens to be zero. Clearly, though, we are not yet converged at cutoff=300eV. Instead, if we compare everything to cutoff=600eV (which we take as our most accurate answer), we see that cutoff=500eV is the correct convergence threshold.
- Q: Where can I learn more about quantum mechanics?
- General introductions to Quantum Mechanics: http://walet.phy.umist.ac.uk/QM/LectureNotes/QM.html. In particular look at Chapters 1, 2, 3, 8, 11.
- Operators, expectation values, bra-kets: Paragraphs 1.1 and 1.2 of http://www-keeler.ch.cam.ac.uk/lectures/quant_letter.pdf. Or, more complete: http://www.math.utah.edu/~gold/doc/quantum.pdf. Very simple primer: http://www.chem1.com/acad/webtut/atomic/. Note, it is not always important to know every detail of quantum mechanics to run a quantum mechanics code.
- Q: How precisely do I need to get the lattice parameter?
- A: Lattice parameters are typically listed to within 0.01 Angstroms. There are applications when higher precision is required; this is not one of them.
- Q: The energies when you move an atom (the force calculations) are higher than when you don't?
- A: This is correct. Remember equilibrium has the lowest energy. Equilibrium for this structure has C at 0 0 0 and at .25 .25 .25. As a side note the forces will give you an idea of how far you are from equilibrium (they tell you which direction the atoms "want" to move). The stresses tell you which direction the cell parameters "want" to change to reach equilibrium.
- Q: Why is my E vs. lattice constant plot jagged?
- A: There are a number of solutions to this; the easiest is to raise the energy cutoff.
- Q: Why do the weights of the k-points add up to 2, not 1?
- A: This is a “feature” of the code. Don’t worry about it.
- Q: I don’t understand convergence of energy and forces. It seems that, as a percentage of the absolute value, energies converge much faster.
- A: Sometimes you are interested in an absolute value, rather than a percentage value. For instance, let’s say you can measure length to within 1mm. If you measure the length of an ant, in terms of percentage error, you may be off by 50% or more. If you measure the length of an elephant, in terms of absolute error, you may be off by 0.01%. But usually you don’t care as long as you are to within 1mm. Errors on forces are the same. Don’t worry about the percentage errors so much. You could always arbitrarily decrease the percentage errors on the forces by taking a bigger displacement. From experience, we know that a good error on energy differences is ~5 meV/atom. From experience, we also know that a good error on forces is 10 meV/Angstrom. These are just values that we know, because we have done many first-principles calculations in the past. This is what you should look for.
- Q: Does PWSCF use LDA or GGA? DFT or Hartree Fock?
- A: PWSCF uses DFT. It has both LDA and GGA, but in this lab we only use LDA.
- Q: My energies are really different from lab 1. What is the ‘correct’ scale I should be looking for?
- A: Remember that absolute energies do not usually mean very much. We are mostly interested in energy differences. Also, the reference energies are different. In lab 1, the reference energies (when atoms are infinitely far apart) is 0. In lab 2, this is not the case. The absolute energies can shift a lot, depending on which reference energies you take.
- Q: Why do I take symmetric k-point grids? Can I take asymmetric k-point grids?
- A: For this material, we take a symmetric k-point grid because it is the same in all three lattice directions. This is not always true. The ‘best’ k-point meshes arethose that sample k-space evenly in all directions. Thus, for a tetragonal cell (with a=b, c=2a, and all angles 90 degrees) we might take a 8x8x4 mesh. Think about why this is (Note that if a lattice vector is longer in real space, it is shorter in k-space).
Discussion of some parts of the Problem 2 input file:
- When you are asked to relax the atoms in BaTiO3, instead of a single self-consistent field calculation ('scf'), we will be doing a 'relax' calculation which includes a series of SCF calculations. Here, the ions are allowed to move in order to reduce the total system energy. This setting is very much like setting the 'opti' flag in GULP.
- Since we will be using ion “dynamics”, we now need the new IONS section. We are not, however, using real dynamics (i.e. there is no time coordinate used in the relaxations), but just searching for the minimum energy relaxations. This section should be omitted for the scf calculations of part (a).