[CP2K-user] [CP2K:13264] Benefit of contracted basis?
Nicholas Winner
nwi... at berkeley.edu
Sat May 9 19:34:05 UTC 2020
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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