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

[Nicholas Winner]

Ah I see. Thank so much Matt, Jurg, and Lucas.

-Nick

On Saturday, May 9, 2020 at 12:17:09 PM UTC-7, Matt W wrote:
>
> You would have to calculate all the primitive integrals, but you would 
> only need to store their sum in memory as the contraction coeffs are fixed.
>
> On Saturday, May 9, 2020 at 7:28:01 PM UTC+1, Nicholas Winner wrote:
>>
>> 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 
>>> CH-8057 Zürich, Switzerland 
>>> --------------------------------------------------------------- 
>>>
>>> -----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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>>>
>>
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