EPS_DEFAULT Meaning

[Robert Molt]

Good morning,

Can someone clarify the EPS_DEFAULT keyword? The manual is unclear. It states:

"Try setting all EPS_xxx to values leading to an energy correct up to EPS_DEFAULT"

[Krack Matthias]

Hi

 

Open the CP2K input reference

https://manual.cp2k.org/trunk/CP2K_INPUT/FORCE_EVAL/DFT/QS.html#CP2K_INPUT.FORCE_EVAL.DFT.QS.EPS_DEFAULT

in your browser and search/find all occurrences of “EPS_DEFAULT”. EPS_DEFAULT defines the default values for all EPS_xxx keywords referring to EPS_DEFAULT in their description.

 

Alternatively, you can consult the source code:

https://github.com/cp2k/cp2k/blob/master/src/cp_control_utils.F - L837-L858

 

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[Robert Molt]

I already cited the manual in my question. I do not know what "eps" is. The manual does not seem to say it, as far as I can see. I want to guess that this is referring to the eigenvalues of the Fock matrix, but this is not directly stated. Can this be defined relative to somehting in SCF theory? I want to guess that this puts a tolerance on eigenvalues, but then this would seemingly be redundant to having an EPS_SCF keyword? If this is different than EPS_SCF, can the definition be given?

[Krack Matthias]

“eps” is a short for “epsilon” and refers to a threshold value which controls the numerical accuracy.

 

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[Robert Molt]

I believe you are invoking that "epsilon" is often used as a symbol for a tolerance in numerical work. That is not my question. I am asking for the mathematical definition being invoked here; it is a control parameter for what? I am guessing that this is a control parameter for the SCF energy?

EPS_SCF appears in a different CP2K manual and has the definition "Target accuracy for the SCF convergence" This is a somewhat unclear definition, but given that it has a default threshold of 10**-5, I will assume it is stating that the largest matrix element difference between iterations must be no bigger than the threshold, since that is the usual criterion (as opposed to converged energy or converged eigenvalues).

Is EPS_DEFAULT overriding EPS_SCF values to govern convergence? Assuming that "epsilon" here is a numerical tolerance for an SCF, what specific element of the SCF process is it managing?

[Marcella Iannuzzi]

Dear ?

As you might have noticed, the EPS_DEFAULT is in a section of the input, the QS section, where several other EPS_* are present.  

Some of these can be controlled all at once by setting EPS_DEFAULT. Setting them individually overwrites the eps_default derived value.

Some more details on the meaning of each of them can be revealed by their description. 

If you have still doubts on what they refer to, you might have a look at the original QS papers.

Using default values for all of them is in  general a good choice, if you do not have a reason for doing otherwise. 

EPS_SCF,  as other  "accuracy control parameters", is  instead not controlled by EPS_DEFAULT

The exact meaning of EPS_SCF depends on the optimisation method in use, but it is not the energy convergence, 

With OT it can be considered as the maximin gradient.

Regards

Marcella

[Robert Molt]

Thank you so much! This answer is very helpful and appreciated, Marcella.