  The extension of least-squares tensor hypercontracted second- and third-order
M{\o}ller-Plessett perturbation theory (LS-THC-MP2 and LS-THC-MP3) to
open-shell systems is an important development due to the scaling reduction
afforded by THC and the ubiquity of molecular ions, radicals, and other
open-shell reactive species. The complexity of wavefunction-based quantum
chemical methods such as M{\o}ller-Plessett and coupled cluster theory is
reflected in the steep scaling of the computational costs with the molecular
size. The least-squares tensor hypercontraction (LS-THC) method is an
efficient, single-step factorization for the two-electron integral tensor, but
can also be used to factorize the double excitation amplitudes, leading to
significant scaling reduction. Here, we extend this promising method to
open-shell variants of LS-THC-MP2 and -MP3 using diagrammatic techniques and
explicit spin-summation. The accuracy of the resulting methods for open-shell
species is benchmarked on standard tests systems such as regular alkanes, as
well as realistic systems involving bond breaking, radical stabilization, and
other effects. We find that open-shell LS-THC-MP$n$ methods exhibit errors
highly comparable to those produced by closed-shell LS-THC-MP$n$, and are
highly insensitive to particular chemical interactions, geometries, or even to
moderate spin contamination.
