From owner-chemistry@ccl.net Thu Jun 27 04:01:00 2019 From: "Susi Lehtola susi.lehtola#%#alumni.helsinki.fi" To: CCL Subject: CCL: Proper scaling of HF exchange for hybrid functionals Message-Id: <-53772-190627034935-4095-MViIdhx4uG6AFGQWrhHVkw,,server.ccl.net> X-Original-From: Susi Lehtola Content-Language: en-US Content-Transfer-Encoding: 7bit Content-Type: text/plain; charset=utf-8; format=flowed Date: Thu, 27 Jun 2019 10:49:24 +0300 MIME-Version: 1.0 Sent to CCL by: Susi Lehtola [susi.lehtola|,|alumni.helsinki.fi] On 6/26/19 1:10 PM, Kjell Jorner kjell.jorner/agmail.com wrote: > 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? B3LYP is old, as has been established many times on this list. Instead of fixing the functional form beforehand (what you are repeating above), the proper way to optimize is to adjust everything simultaneously - including the funtional form - see e.g. the papers on combinatorially optimized functionals (wB97X-V, B97M-V, wB97M-V) by Mardirossian and Head-Gordon. For a more usual, limited use case, one just scales between full DFT exchange and exact exchange, possibly in a range-separated manner (e.g. long-range only); this may give you information on e.g. self-interaction errors. -- ------------------------------------------------------------------ Mr. Susi Lehtola, PhD Junior Fellow, Adjunct Professor susi.lehtola===alumni.helsinki.fi University of Helsinki http://susilehtola.github.io/ Finland ------------------------------------------------------------------ Susi Lehtola, dosentti, FT tutkijatohtori susi.lehtola===alumni.helsinki.fi Helsingin yliopisto http://susilehtola.github.io/ ------------------------------------------------------------------ From owner-chemistry@ccl.net Thu Jun 27 11:31:00 2019 From: "Martin Kaupp martin.kaupp() tu-berlin.de" To: CCL Subject: CCL: Proper scaling of HF exchange for hybrid functionals Message-Id: <-53773-190627065752-8198-Zay2eQ5fXC72GWGpVUTeMA:+:server.ccl.net> X-Original-From: Martin Kaupp Content-Type: multipart/alternative; boundary="------------BD7D4955E144A7C8965B6B4F" Date: Thu, 27 Jun 2019 13:03:07 +0200 MIME-Version: 1.0 Sent to CCL by: Martin Kaupp [martin.kaupp[-]tu-berlin.de] --------------BD7D4955E144A7C8965B6B4F Content-Type: text/plain; charset="utf-8"; format=flowed Content-Transfer-Encoding: 8bit Hi all, In addition to the mentioned constant HF exchange admixture ("global hybrids") and range-separated functionals ("RS hybrids"), where the admixture depends on the interelectronic distance, let me mention a third possibility that has so far received less attention: in "local hybrid functionals" the HF exchange admixture is different at each point in (real) space, governed by a so-called "local mixing function" (LMF). Most of the additional implementation challenges for such local hybrids have been overcome, and a set of "first-generation" local hybrids are available in Turbomole since version 7.3  (in the upcoming version 7.4, parallelization and some more possibilities have been enabled), which for example provide outstanding performance for triplet excitations in TDDFT but also give remarkably good thermochemistry and barriers. We are continuing to work on improved LMFs and functionals, on excited-state gradients, NMR shifts and spin-spin coupling constants, on a relativistic two-component implementation of many properties, and a comprehensive review has appeared recently: /Local Hybrid Functionals: Theory, Implementation, and Performance of an Emerging New Tool in Quantum Chemistry and Beyond /T. M. Maier, A. V. Arbuznikov, M. Kaupp /WIREs Comp. Mol. Sci./ *2019*, /9/, e1378. DOI: 10.1002/wcms.1378. Many regards, Martin Kaupp Am 27.06.2019 um 09:49 schrieb Susi Lehtola susi.lehtola#%#alumni.helsinki.fi: > > Sent to CCL by: Susi Lehtola [susi.lehtola|,|alumni.helsinki.fi] > On 6/26/19 1:10 PM, Kjell Jorner kjell.jorner/agmail.com wrote: >> 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? > > B3LYP is old, as has been established many times on this list. Instead > of fixing the functional form beforehand (what you are repeating > above), the proper way to optimize is to adjust everything > simultaneously - including the funtional form - see e.g. the papers on > combinatorially optimized functionals (wB97X-V, B97M-V, wB97M-V) by > Mardirossian and Head-Gordon. > > For a more usual, limited use case, one just scales between full DFT > exchange and exact exchange, possibly in a range-separated manner > (e.g. long-range only); this may give you information on e.g. > self-interaction errors. -- Prof. Dr. Martin Kaupp Technische Universität Berlin Institut für Chemie Theoretische Chemie Sekr. C 7 Strasse des 17. Juni 135 D-10623 Berlin Gebäude C, Ostflügel, EG, Raum C 78 Telefon +49 30 314 79682 Telefax +49 30 314 21075 email: martin.kaupp#tu-berlin.de www: http://www.quantenchemie.tu-berlin.de/ --------------BD7D4955E144A7C8965B6B4F Content-Type: text/html; charset="utf-8" Content-Transfer-Encoding: 8bit

Hi all,

In addition to the mentioned constant HF exchange admixture ("global hybrids") and range-separated functionals ("RS hybrids"), where the admixture depends on the interelectronic distance, let me mention a third possibility that has so far received less attention: in "local hybrid functionals" the HF exchange admixture is different at each point in (real) space, governed by a so-called "local mixing function" (LMF). Most of the additional implementation challenges for such local hybrids have been overcome, and a set of "first-generation" local hybrids are available in Turbomole since version 7.3  (in the upcoming version 7.4, parallelization and some more possibilities have been enabled), which for example provide outstanding performance for triplet excitations in TDDFT but also give remarkably good thermochemistry and barriers. We are continuing to work on improved LMFs and functionals, on excited-state gradients, NMR shifts and spin-spin coupling constants, on a relativistic two-component implementation of many properties, and a comprehensive review has appeared recently: 

Local Hybrid Functionals: Theory, Implementation, and Performance of an Emerging New Tool in Quantum Chemistry and Beyond T. M. Maier, A. V. Arbuznikov, M. Kaupp WIREs Comp. Mol. Sci. 2019, 9, e1378. DOI: 10.1002/wcms.1378.

Many regards,

Martin Kaupp

Am 27.06.2019 um 09:49 schrieb Susi Lehtola susi.lehtola#%#alumni.helsinki.fi:

Sent to CCL by: Susi Lehtola [susi.lehtola|,|alumni.helsinki.fi]
On 6/26/19 1:10 PM, Kjell Jorner kjell.jorner/agmail.com wrote:
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?

B3LYP is old, as has been established many times on this list. Instead of fixing the functional form beforehand (what you are repeating above), the proper way to optimize is to adjust everything simultaneously - including the funtional form - see e.g. the papers on combinatorially optimized functionals (wB97X-V, B97M-V, wB97M-V) by Mardirossian and Head-Gordon.

For a more usual, limited use case, one just scales between full DFT exchange and exact exchange, possibly in a range-separated manner (e.g. long-range only); this may give you information on e.g. self-interaction errors. 
-- 
Prof. Dr. Martin Kaupp
Technische Universität Berlin 
Institut für Chemie 
Theoretische Chemie 
Sekr. C 7 
Strasse des 17. Juni 135 
D-10623 Berlin 

Gebäude C, Ostflügel, EG, Raum C 78
Telefon  +49 30 314 79682
Telefax +49 30 314 21075
email: martin.kaupp#tu-berlin.de
www: http://www.quantenchemie.tu-berlin.de/
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