[CP2K-user] [CP2K:13264] Benefit of contracted basis?

[Nicholas Winner]

Thank you Jurg, so the contracted basis functions take up less memory 
footprint? Even though there are the same number of them?

On Saturday, May 9, 2020 at 2:38:09 AM UTC-7, jgh wrote:
>
> Hi 
>
> there are some gains in the linear algebra parts (density matrix 
> contractions), but the big difference is memory. You gain because 
> of the n^4 scaling of the number of integrals to store. 
>
> Juerg 
> -------------------------------------------------------------- 
> Juerg Hutter                         Phone : ++41 44 635 4491 
> Institut für Chemie C                FAX   : ++41 44 635 6838 
> Universität Zürich                   E-mail: h... at chem.uzh.ch 
> Winterthurerstrasse 190 
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> --------------------------------------------------------------- 
>
> -----c... at googlegroups.com wrote: ----- 
> To: "cp2k" <c... at googlegroups.com> 
> From: "Matt W" 
> Sent by: c... at googlegroups.com 
> Date: 05/08/2020 11:40PM 
> Subject: Re: [CP2K:13264] Benefit of contracted basis? 
>
> 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>) 
> 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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