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
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