  The production of $^7$Be and $^7$Li nuclei plays an important role in
primordial nucleosynthesis, nuclear astrophysics, and fusion energy generation.
The $^3\mathrm{He}(\alpha , \gamma) ^7\mathrm{Be}$ and $^3\mathrm{H}(\alpha ,
\gamma) ^7\mathrm{Li}$ radiative-capture processes are important to determine
the $^7$Li abundance in the early universe and to predict the correct fraction
of pp-chain branches resulting in $^7$Be versus $^8$B neutrinos. In this work
we study the properties of $^7$Be and $^7$Li within the no-core shell model
with continuum (NCSMC) method, using chiral nucleon-nucleon interactions as the
only input, and analyze all the binary mass partitions involved in the
formation of these systems. The NCSMC is an ab initio method applicable to
light nuclei that provides a unified description of bound and scattering states
and thus is well suited to investigate systems with many resonances and
pronounced clustering like $^7$Be and $^7$Li. Our calculations reproduce all
the experimentally known states of the two systems and provide predictions for
several new resonances of both parities. Some of these new possible resonances
are built on the ground states of $^6$Li and $^6$He, and thus represent a
robust prediction. We do not find any resonance in the p${+}^6$Li mass
partition near the threshold. On the other hand, in the p${+}^6$He mass
partition of $^7$Li we observe an $S$-wave resonance near the threshold
producing a very pronounced peak in the calculated S factor of the
$^6\mathrm{He} (\mathrm{p},\gamma) ^7\mathrm{Li}$ radiative-capture reaction,
which could be relevant for astrophysics and its implications should be
investigated.
