  A novel parameterisation of a Hamiltonian based on chiral effective field
theory is introduced. Specifically, three-nucleon operators at
next-to-next-to-leading order are combined with an existing (and successful)
two-body interaction containing terms up to next-to-next-to-next-to-leading
order. The resulting potential is labelled $N\!N\!$+$3N\text{(lnl)}$. The
objective of the present work is to investigate the performance of this new
Hamiltonian across light and medium-mass nuclei. Binding energies, nuclear
radii and excitation spectra are computed using no-core shell model and
self-consistent Green's function approaches. Calculations with
$N\!N\!$+$3N\text{(lnl)}$ are compared to two other representative Hamiltonians
currently in use, namely NNLO$_{\text{sat}}$ and the older $N\!N\!$+$3N(400)$.
Overall, the performance of the novel interaction is very encouraging. In light
nuclei, total energies are generally in good agreement with experimental data.
Known spectra are also well reproduced with a few notable exceptions. The good
description of ground-state energies carries on to heavier nuclei, all the way
from oxygen to nickel isotopes. Except for those involving excitation processes
across the $N=20$ gap, which is overestimated by the new interaction, spectra
are of very good quality, in general superior to those obtained with
NNLO$_{\text{sat}}$. Although largely improving on $N\!N\!$+$3N(400)$ results,
charge radii calculated with $N\!N\!$+$3N\text{(lnl)}$ still underestimate
experimental values, as opposed to the ones computed with NNLO$_{\text{sat}}$
that successfully reproduce available data on nickel. On the whole, the new
two- plus three-nucleon Hamiltonian introduced in the present work represents a
promising alternative to existing nuclear interactions.
