CAM functional

In DIRAC, you can calculate with the CAMB3LYP functional using:

.DFT
 CAMB3LYP

It is also possible to change the default parameters. The following line will reproduce the above functional:

.DFT
 CAM p:alpha=0.19 p:beta=0.46 p:mu=0.33 x:slater=1 x:becke=1 c:lyp=0.81 c:vwn5=0.19

but it will give you complete freedom over the parameters. As always, please verify your results carefully when changing these parameters.

Approaching the B3LYP limit

CAM uses the following partitioning of the two-electron interaction:

\begin{equation*} \frac{1}{r_{12}} = \frac{1 - [\alpha + \beta erf (\mu r_{12})}{r_{12}} + \frac{ [\alpha + \beta erf (\mu r_{12})}{r_{12}} \end{equation*}

For testing purposes we can try to approach the B3LYP limit using the CAM code, in order to check that the alpha/beta limits work well.

In B3LYP, “HF” admixture is 0.2 so in CAM this can be obtained with alpha=0.2 and beta=0.0.

So this is B3LYP:

.DFT
 GGAKEY Slater=0.8 Becke=0.72 HF=0.2 LYP=0.81 VWN=0.19

Now naively we could try to obtain B3LYP results like this (this is wrong):

.DFT
 CAM p:alpha=0.2 p:beta=0.0 p:mu=0.0 x:slater=0.8 x:becke=0.72 c:lyp=0.81 c:vwn5=0.19

This does not work in DIRAC and the correct B3LYP expressed using CAM in DIRAC can be obtained like this:

.DFT
 CAM p:alpha=0.2 p:beta=0.0 p:mu=0.0 x:slater=1.0 x:becke=0.9 c:lyp=0.81 c:vwn5=0.19

This is because x:slater and x:becke get scaled inside fun-cam.c by (1-alpha). The x:becke=0.9 can be surprising if you read the paper by Yanai et al. [Chem. Phys. Lett. 393 (2004) 51] and follow their examples.