Open-Shell Tensor Hypercontraction

The extension of least-squares tensor
hypercontracted
second- and
third-order Møller–Plesset 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 Møller–Plesset
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 by using diagrammatic techniques and explicit spin summation.
The accuracy of the resulting methods for open-shell species is benchmarked
on standard test 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-MPn methods
exhibit errors highly comparable to those produced by closed-shell
LS-THC-MPn and are highly insensitive to particular
chemical interactions, geometries, or even moderate spin contamination.