From owner-chemistry@ccl.net Wed Jun 26 14:10:00 2019 From: "Kjell Jorner kjell.jorner/a\gmail.com" To: CCL Subject: CCL: Proper scaling of HF exchange for hybrid functionals Message-Id: <-53770-190626061045-23851-PiUtB0nmu9GwcB6mPcZufw+/-server.ccl.net> X-Original-From: Kjell Jorner Content-Type: multipart/alternative; boundary="0000000000007fd087058c3741f3" Date: Wed, 26 Jun 2019 11:10:22 +0100 MIME-Version: 1.0 Sent to CCL by: Kjell Jorner [kjell.jorner : gmail.com] --0000000000007fd087058c3741f3 Content-Type: text/plain; charset="UTF-8" Hello, I have a question about the best way to scale HF exchange in a hybrid functional. For example, B3LYP features three sources of exchange: 1. Exact HF exchange 2. Slater exchange 3. GGA correction to Slater exchange The approach taken by Becke in his original B3-paper from 1993 is to have one parameter that scales HF and Slater exchange so that the total is unity. A second parameter controls the amount of GGA exchange correction. My interpretation is that in this way, the GGA correction is optimized in a semiempirical manner together with the admixture of HF exchange. He writes "Clearly, the coefficient a_x has value less than unity, since the presence of the E_x_exact term reduces the need for the gradient correction Delta_E_X_B88." In the literature, there are two approaches two scaling the HF exchange in B3LYP: 1. Adjusting only the balance between HF and Slater exchange, keeping the GGA exchange correction fixed. This is exemplified by the B3LYP* functional which uses 15% HF exchange with an unchanged 72% GGA correction (Hess, 2002). 2. Adjusting the balance between HF and Slater exchange, as well as scaling the GGA exchange correction accordingly (Kulik, 2015). > From my intuition, it does not make sense to have a GGA correction in the limit 100% HF exchange. Method 2 would therefore be preferred when one wants to assess the effect of HF exchange over a large range. Does anyone have any comments or are aware of any literature on this topic? Best, Kjell Jorner References: Becke, 1993: https://doi.org/10.1063/1.464913 Hess, 2002: https://doi.org/10.1063/1.1493179 Kulik, 2015: https://doi.org/10.1063/1.4926836 --0000000000007fd087058c3741f3 Content-Type: text/html; charset="UTF-8" Content-Transfer-Encoding: quoted-printable
Hello,

I have a question about the best way to sca= le HF exchange in a hybrid functional. For example, B3LYP features three so= urces of exchange:
1. Exact HF exchange
2. Slater exchange
3. GGA = correction to Slater exchange

The approach taken by Becke in his ori= ginal B3-paper from 1993 is to have one parameter that scales HF and Slater= exchange so that the total is unity. A second parameter controls the amoun= t of GGA exchange correction. My interpretation is that in this way, the GG= A correction is optimized in a semiempirical manner together with the admix= ture of HF exchange. He writes "Clearly, the coefficient a_x has value= less than unity, since the presence of the E_x_exact term reduces the need= for the gradient correction Delta_E_X_B88."

In the literature,= there are two approaches two scaling the HF exchange in B3LYP:
1. Adjus= ting only the balance between HF and Slater exchange, keeping the GGA excha= nge correction fixed. This is exemplified by the B3LYP* functional which us= es 15% HF exchange with an unchanged 72% GGA correction (Hess, 2002).
2.= Adjusting the balance between HF and Slater exchange, as well as scaling t= he GGA exchange correction accordingly (Kulik, 2015).

From my intuit= ion, it does not make sense to have a GGA correction in the limit 100% HF e= xchange. Method 2 would therefore be preferred when one wants to assess the= effect of HF exchange over a large range. Does anyone have any comments or= are aware of any literature on this topic?

Best,
Kjell Jorner
References:
Becke, 1993: https://doi.org/10.1063/1.464913
Hess, 2002: https://doi.org/10.1063/1.1493179
Kulik, 2= 015: https://doi.org/10.1063/= 1.4926836
--0000000000007fd087058c3741f3-- From owner-chemistry@ccl.net Wed Jun 26 16:51:01 2019 From: "Marcel Swart marcel.swart+*+gmail.com" To: CCL Subject: CCL: Proper scaling of HF exchange for hybrid functionals Message-Id: <-53771-190626164904-8411-CZNu40/VMEDk61CqikxQPA%x%server.ccl.net> X-Original-From: Marcel Swart Content-Transfer-Encoding: 7bit Content-Type: multipart/alternative; boundary=Apple-Mail-63FB81F2-E780-4E61-BF6F-4352247E1EE0 Date: Wed, 26 Jun 2019 22:48:53 +0200 Mime-Version: 1.0 (1.0) Sent to CCL by: Marcel Swart [marcel.swart^-^gmail.com] --Apple-Mail-63FB81F2-E780-4E61-BF6F-4352247E1EE0 Content-Type: text/plain; charset=utf-8 Content-Transfer-Encoding: quoted-printable Markus Reiher=E2=80=99s original paper from 2001, yes. And last year in the E= COSTBio ChemEurJ issue there was a paper by Harvey and de Proft that is rele= vant for it. And many many more in between, which are hopefully highlighted in that latte= r one, or in one of the reviews/perspectives listed on the DFTPoll page: http://www.marcelswart.eu/dft-poll/reviews.html Marcel Marcel Swart FRSC FYAE, Prof. Dr. ICREA Research Professor at University of Girona Director of Institut de Qu=C3=ADmica Computacional i Cat=C3=A0lisi Univ. Girona, Campus Montilivi (Ci=C3=A8ncies) c/ Maria Aur=C3=A8lia Capmany i Farn=C3=A9s, 69 17003 Girona, Spain www.marcelswart.eu marcel.swart%x%gmail.com vCard addressbook://www.marcelswart.eu/MSwart.vcf > On 26 Jun 2019, at 12:10, Kjell Jorner kjell.jorner/agmail.com wrote: >=20 > Hello,=20 >=20 > I have a question about the best way to scale HF exchange in a hybrid func= tional. For example, B3LYP features three sources of exchange: > 1. Exact HF exchange > 2. Slater exchange > 3. GGA correction to Slater exchange >=20 > The approach taken by Becke in his original B3-paper from 1993 is to have o= ne parameter that scales HF and Slater exchange so that the total is unity. A= second parameter controls the amount of GGA exchange correction. My interpr= etation is that in this way, the GGA correction is optimized in a semiempiri= cal manner together with the admixture of HF exchange. He writes "Clearly, t= he coefficient a_x has value less than unity, since the presence of the E_x_= exact term reduces the need for the gradient correction Delta_E_X_B88." >=20 > In the literature, there are two approaches two scaling the HF exchange in= B3LYP: > 1. Adjusting only the balance between HF and Slater exchange, keeping the G= GA exchange correction fixed. This is exemplified by the B3LYP* functional w= hich uses 15% HF exchange with an unchanged 72% GGA correction (Hess, 2002).= > 2. Adjusting the balance between HF and Slater exchange, as well as scalin= g the GGA exchange correction accordingly (Kulik, 2015). >=20 > =46rom my intuition, it does not make sense to have a GGA correction in th= e limit 100% HF exchange. Method 2 would therefore be preferred when one wan= ts to assess the effect of HF exchange over a large range. Does anyone have a= ny comments or are aware of any literature on this topic? >=20 > Best, > Kjell Jorner >=20 > References: > Becke, 1993: https://doi.org/10.1063/1.464913 > Hess, 2002: https://doi.org/10.1063/1.1493179 > Kulik, 2015: https://doi.org/10.1063/1.4926836 --Apple-Mail-63FB81F2-E780-4E61-BF6F-4352247E1EE0 Content-Type: text/html; charset=utf-8 Content-Transfer-Encoding: quoted-printable Markus Reiher=E2=80=99s original paper from= 2001, yes. And last year in the ECOSTBio ChemEurJ issue there was a paper b= y Harvey and de Proft that is relevant for it.
And many many more in bet= ween, which are hopefully highlighted in that latter one, or in one of the r= eviews/perspectives listed on the DFTPoll page:

Marcel


<= b class=3D"">Marcel Swart FRSC FYAE, Prof. Dr.
ICREA Research Professor at University of Girona<= /font>
Director of Institut de Qu=C3=ADmi= ca Computacional i Cat=C3=A0lisi

Univ. Girona, C= ampus Montilivi (Ci=C3=A8ncies)
c/ M= aria Aur=C3=A8lia Capmany i Farn=C3=A9s, 69
1= 7003 Girona, Spain

www.marcelswart.eu
marcel.swart%x%g= mail.com

vCard
= addressbook://www.marcelswart.eu/MSwart.vcf
<= div class=3D"" style=3D"font-family: Arial; font-size: 12px; -webkit-text-si= ze-adjust: auto; font-variant-ligatures: normal; font-variant-position: norm= al; font-variant-numeric: normal; font-variant-alternates: normal; font-vari= ant-east-asian: normal; word-wrap: break-word; -webkit-nbsp-mode: space; lin= e-break: after-white-space;"><= br class=3D"">

On 26 Jun 2019, a= t 12:10, Kjell Jorner kjell.jorner/agmail.com<= /a> <owner-chemistry%x%ccl.net> wrote:

Hello,

I have a question about the best way to scale HF e= xchange in a hybrid functional. For example, B3LYP features three sources of= exchange:
1. Exact HF exchange
2. Slater exchange
3. GGA correctio= n to Slater exchange

The approach taken by Becke in his original B3-p= aper from 1993 is to have one parameter that scales HF and Slater exchange s= o that the total is unity. A second parameter controls the amount of GGA exc= hange correction. My interpretation is that in this way, the GGA correction i= s optimized in a semiempirical manner together with the admixture of HF exch= ange. He writes "Clearly, the coefficient a_x has value less than unity, sin= ce the presence of the E_x_exact term reduces the need for the gradient corr= ection Delta_E_X_B88."

In the literature, there are two approaches tw= o scaling the HF exchange in B3LYP:
1. Adjusting only the balance between= HF and Slater exchange, keeping the GGA exchange correction fixed. This is e= xemplified by the B3LYP* functional which uses 15% HF exchange with an uncha= nged 72% GGA correction (Hess, 2002).
2. Adjusting the balance between HF= and Slater exchange, as well as scaling the GGA exchange correction accordi= ngly (Kulik, 2015).

=46rom my intuition, it does not make sense to ha= ve a GGA correction in the limit 100% HF exchange. Method 2 would therefore b= e preferred when one wants to assess the effect of HF exchange over a large r= ange. Does anyone have any comments or are aware of any literature on this t= opic?

Best,
Kjell Jorner

References:
Becke, 1993: https://doi.org/10.1063/1.464913<= br>Hess, 2002: https://doi.org= /10.1063/1.1493179
Kulik, 2015: https://doi.org/10.1063/1.4926836
= --Apple-Mail-63FB81F2-E780-4E61-BF6F-4352247E1EE0--