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

Matt W mattwa... at gmail.com
Fri May 8 21:40:21 UTC 2020

```I think Nick is talking about the Auxiliary Density Matrix Method, where
the primary basis set is projected onto a smaller auxiliary basis to
facilitate the hybrid functional part of the Kohn-Sham build. In this case
there is no diagonalization involving the auxiliary basis as it gets merged
back into the main KS matrix before diagonalisation / OT. There are a bunch
of linear algebra operatations involved in the 'projections' from primary
to auxiliary basis and back that can be more efficient with contracted
functions but I am not sure there is a major advantage to using the
contracted versions, I've never benchmarked.

Matt

On Friday, May 8, 2020 at 8:32:49 PM UTC+1, Lucas Lodeiro wrote:
>
> 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 (<n... at berkeley.edu
> <javascript:>>) 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?
>>
>>
>> -Nick
>>
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