[CP2K-user] [CP2K:13262] Benefit of contracted basis?

[Lucas Lodeiro]

Hi Nick,
I am not an expert on CP2K, but this question is more general than CP2K
implementation.
When you have a set of primitives, you can use each of them by itself, then
you have one constant for each primitive to apply the variational
principle, and they are independent between them (obviously they have the
orthonormal restriction for the solutions).
If you contract some primitives, you have the "same" number of primitives
in the set, but your variational constant are less, this is, when you
contract some primitives, you constrain the constant of these primitives to
be in a given proportion, and this primitive mix have only one variational
constant, making more simple the "diagonalization" or solution for these
basis set, but with a lower variational convergence.
In simple, if you have 3 primitives for a particular orbital, you can mix
them with the constants a1,a2,a3 in any proportion, but if you constrain
the second and the third, you only have now 2 constants for the variation,
this is, a1 and a23.

Regards

El vie., 8 may. 2020 a las 14:05, Nicholas Winner (<nwi... at berkeley.edu>)
escribió:

> Hello all, a quick question:
>
> When employing an auxiliary basis for a system, we have a choice of many
> such as FITx, cFITx, cpFITx... I understand that the "x" refers to the
> number of Gaussian exponents, and that the prefix indicates whether you are
> using uncontracted, contracted, or contracted with additional polarization
> functions, respectively. What I don't know is why you would choose
> contracted/uncontracted. Both end up having the same number of primitive
> basis functions in your calculation if I understand correctly. So what is
> the use of having one over the other?
>
> Thanks for your help.
>
> -Nick
>
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