During the SAPT2 calculation, Psi4 is showing an error that the 6-31+G(d,p) basis set is not defined for cobalt atom. However, in Gaussian same basis set is working for the cobalt-containing complexes during structure optimization. Is there any alternative way to do the SAPT2 calculation with the same basis set?

You’d need to add the basis set yourself. See here.

The developers want to interface Psi to the Basis Set Exchange so these kinds of problems don’t occur nearly as often, but that’s not a project under active development.

The Pople sets are a huge mess. For instance, there is no 6-311G set for transition metals and Gaussian actually will use a non-polarized Wachters-Hay basis set for transition metals, and the basis sets have huge errors.

Proper 6-31G basis sets do appear to have been optimized for the transition metals, as one can see from Gaussian’s basis set home page. However, I do not see any paper on diffuse functions on their list.

Moreover, it has been pointed out that the 6-31G basis by Rassolov and coworkers, which is used in Gaussian, has huge errors for transition metals; see Mitin et al in An improved 6-31G* basis set for first-row transition metals: The Journal of Chemical Physics: Vol 118, No 17. The Mitin et al basis, m6-31G* is available on the Basis Set Exchange.

However, this still leaves one huge issue. For historical reasons, the Pople sets employ cartesian D functions. However, the newer Pople sets also use spherical F functions. Like many other programs, as far as I am aware Psi4 does not support mixed-shell representations; instead, the basis set will be used with cartesian F functions, which is not the same as what you have in Gaussian.

In short, I would leave the Pople sets in history, and use modern basis set families, instead. The Karlsruhe def2 family uses only spherical functions, is available for almost the entire periodic table, uses ECPs for core potentials, and comes in a variety of levels of accuracy ranging from split valence to quadruple zeta. Jensen’s pcseg-n basis sets are another good option if you are working in the four first periods of the periodic table.