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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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