[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.


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?
>> Thanks for your help.
>> -Nick
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