Meaning of E symbol (left superscript) from Psi4 documnetation


#1

The psi4 documentation on SAPT has SAPT2 defined as a sum of SAPT0 and some additional interaction energies. In those equations there are two terms at the end with

E_ind and a left superscript t

I do not get the meaning of this term. Attaching a link to the page

http://www.psicode.org/psi4manual/1.2/sapt.html


#2

This is getting into the weeds of the definition of the SAPT terms. From my understanding, the induction energy E_ind^(2k) (where the superscript indicates that this term treats the intermolecular perturbation to second order and the intramonomer perturbation to k th order) can be decomposed into two contributions called the apparent (a) and true (t) contributions.

E_ind^(2k) = ^a E_ind^(2k) + ^t E_ind^(2k)

In practice, the apparent contributions are more important (i.e. numerically larger) than the true contributions, and so they are included in the SAPT0 energy. The term E_ind,resp^(20), the third term in the definition of SAPT0, contains the apparent contributions for all orders of the intramonomer perturbation.

E_ind,resp^(20) = sum_{k=0}^infinity ^a E_ind^(2k)

In order to account for the rest of the intramonomer correction to the second-order induction energy, i.e. E_ind^(22), SAPT2 adds the missing true contributions ^t E_ind^(22). Again, these true contributions are smaller than the apparent contributions ^a E_ind^(22) that are already included in the SAPT0 term E_ind,resp^(20).

If you want to know more, you can read about these terms in the section on the induction energy in this 1994 SAPT review or in this 1980 research article.