  In this work we investigate the performance of a recently proposed
transcorrelated (TC) approach based on a single-parameter correlation factor
[JCP, 154, 8, 2021] for systems involving more than two electrons. The benefit
of such an approach relies on its simplicity as efficient numerical-analytical
schemes can be set up to compute the two- and three-body integrals occuring in
the effective TC Hamiltonian. To obtain accurate ground state energies within a
given basis set, the present TC scheme is coupled to the recently proposed
TC-full configuration interaction quantum Monte Carlo method [JCP, 151, 6,
2019]. We report ground state total energies on the Li-Ne series, together with
their first cations, computed in increasing large basis sets and compare to
more elaborate correlation factors involving electron-electron-nucleus
coordinates. Numerical results on the Li-Ne ionization potentials show that the
use of the single-parameter correlation factor brings on average only a
slightly lower accuracy (1.2 mH) in a triple-zeta quality basis set with
respect to a more sophisticated correlation factor. However, already using a
quadruple-zeta quality basis set yields results within chemical accuracy to
complete basis set limit results when using this novel single-parameter
correlation factor.
