# Confirmation for how CBS is computed

Hi,

I would like to verify how a complete basis set limit is computed. In my input I have the following line:

`energy(cbs, corl_wfn='mp2', corl_basis='aug-cc-pv[tq]z', scf_basis='aug-cc-pv[dtq]z', corl_scheme=corl_xtpl_helgaker_2, scf_scheme=scf_xtpl_helgaker_3)`

At the end of the run, the log file includes these lines:

`==> Stages <==`
`scf hf / aug-cc-pv[dtq]z 1 -193.21347417 scf_xtpl_helgaker_3`
`corl mp2 / aug-cc-pv[tq]z 1 -194.08699951 corl_xtpl_helgaker_2`
`corl hf / aug-cc-pv[tq]z -1 -193.21831488 corl_xtpl_helgaker_2`

It is clear that the scf limit, obtained from the use of three basis sets, was computed using Helgaker’s exponential equation (scf_xtpl_helgaker_3).

Now here is my desire for confirmation - for the correlation energy, was the Helgaker’s power equation (data from two basis sets, i.e. corl_xtpl_helgaker_2) used for computing both the MP2 total energy (-194.08699951) and the HF total energy (193.21831488)? The reason I ask is because there is another exponential extrapolation option in the manual for computing the scf component using the data from two basis sets, which is scf_xtpl_helgaker_2.

Another small question. The final extrapolated correlation energy reported to be:

`==> CBS <==`
`corl mp2 / aug-cc-pv[tq]z -0.86868463 corl_xtpl_helgaker_2`

In Psi4, is this final computed value obtained by taking the difference in the above total energies in the `==> Stages <==` section, or was the correlation energy here directly extrapolated (corl_xtpl_helgaker_2) using the reported `Correlation Energy` found in each of the individual basis set calculations?

Karl

Thanks for the careful question.

You’re quite right that an entity labeled `... hf / aug-cc-pv[tq]z ... corl_xtpl_helgaker_2` makes no sense in its own right. It’s purely computed as the analog of the `mp2` quantity so as to extract the `mp2 – hf` correlation energy. (The function used to work in correlation energies directly, which is more natural for CBS, but switched to this way when the `cbs()` procedure started supporting gradients, as a “CCSD correlation gradient” isn’t natural for derivatives coding.)

The final computed value is from the `==> Stages <==` section with “Energy” figures multiplied by “Wt” (weight) figures and summed. It should be completely equivalent to the figure extractable from the `==> Components <==` section and to the figure extractable from the individual calcs.

Please let me know if any of this doesn’t make sense or if you notice anything suspicious.

Hello Lori,

However, I can provide a little bit more feedback, which might be helpful for future folks who are curious about this. I took the time to manually confirm the line `hf / aug-cc-pv[tq]z ... corl_xtpl_helgaker_2` (i.e. the use of corl_xtpl_helgaker_2 equation). For 8 different conformations of propan-2-ol, I was able to reproduce the values shown in the `==> CBS <==` section. So nothing suspicious.