CCL: Proper scaling of HF exchange for hybrid functionals
- From: Kjell Jorner <kjell.jorner++gmail.com>
- Subject: CCL: Proper scaling of HF exchange for hybrid
- Date: Wed, 26 Jun 2019 11:10:22 +0100
I have a question about the best way to scale HF
exchange in a hybrid functional. For example, B3LYP features three sources of
1. Exact HF exchange
2. Slater exchange
3. GGA correction to
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
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
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