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/10.1063/1.464913Hess, 2002:
https://doi.org/10.1063/1.1493179Kulik, 2015:
https://doi.org/10.1063/1.4926836