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

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.

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).