  The perturbatively selected configuration interaction scheme (CIPSI) is
particularly effective in constructing determinantal expansions for quantum
Monte Carlo (QMC) simulations with Jastrow-Slater wave functions: fast and
smooth convergence of ground-state properties, as well as balanced descriptions
of ground- and excited-states of different symmetries have been reported. In
particular, accurate excitation energies have been obtained by the pivotal
requirement of using CIPSI expansions with similar second-order perturbation
corrections for each state, that is, similar estimated errors with respect to
the full configuration interaction limit. Here we elaborate on the CIPSI
selection criterion for excited states of the same symmetry as the ground
state, generating expansions from a common orbital set. Using these expansions
in QMC as determinantal components of Jastrow-Slater wave functions, we compute
the lowest, bright excited state of thiophene, which is challenging due to its
significant multireference character. The resulting vertical excitation
energies are within 0.05~eV of the best theoretical estimates, already with
expansions of only a few thousand determinants. Furthermore, we relax the
ground- and excited-state structures following the corresponding root in
variational Monte Carlo and obtain bond lengths which are accurate to better
than 0.01~\AA. Therefore, while the full treatment at the CIPSI level of this
system would be quite demanding, in QMC we can compute high-quality excitation
energies and excited-state structural parameters building on affordable CIPSI
expansions with relatively few, well chosen determinants.
