I am doing DFT calculations in dmol3 and would like to conceptually understand the convergence threshold parameters and how changing them affects my calculations. Thanks
Dear Valeria Armendariz,
The need for "convergence" and "convergence threshold" runs deep into the numerical calculations. The point is computers cannot perform an infinite number of operations in a finite time. Thus, you need to introduce truncations. For example, in the numerical evaluation of an integral you need to define a finite mesh with a finite spacing. The quality of your results depends on how fine the mesh is. However, after a certain point increasing the number of point does not increase the accuracy or you reach a moment when you decide the result is accurate enough.
The same applies with DFT calculation. For example, you need to reduce the basis set to a finite set. The number of elements in the basis define the level of you accuracy. However, by convention, "chemical accuracy" is set at around 20-50 meV for the exchange and correlation functionals. Any numerical accuracy below that threshold will be unnecessary and a waste of numerical resources. Because there are other approximations, outside of the numerical code, that establish an effective threshold. Another threshold is the numerical power at your disposal. Increasing accuracy might increase the numerical demand thus you need to stop when you maxed out your resources.
There are in general many parameters to converge and they do depend on the code you are using. I am not an expert of dmol3 so on this I cannot really help.
I hope this helps,
Roberto
Dear Valeria, here two examples of convergence.
Energy convergence: This criterion involves monitoring the change in total energy between successive iterations of the calculation. Once the energy change falls below a certain threshold, typically a small value like 10^-6 to 10^-8 atomic units (a.u.), the calculation is considered converged.
Force convergence: When studying molecular dynamics or optimizing molecular structures, forces acting on atoms are minimized. Force convergence criteria involve comparing the magnitudes of atomic forces between iterations, and convergence is achieved when the forces fall below a certain threshold, usually a small value like 10^-4 to 10^-5 a.u. / Å.
And finally, DO NOT increase the threshold, or the calculated energy or geometry will not be a true minimum. Use the default threshold or smaller.
Best, Pablo
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