  We present two new methods for performing ab initio calculations of excited
states for closed-shell systems within the in-medium similarity renormalization
group (IMSRG) framework. Both are based on combining the IMSRG with simple
many-body methods commonly used to target excited states, such as the
Tamm-Dancoff approximation (TDA) and equations-of-motion (EOM) techniques. In
the first approach, a two-step sequential IMSRG transformation is used to drive
the Hamiltonian to a form where a simple TDA calculation (i.e., diagonalization
in the space of $1$p$1$h excitations) becomes exact for a subset of
eigenvalues. In the second approach, equations-of-motion (EOM) techniques are
applied to the ground-state-decoupled IMSRG Hamiltonian to access excited
states. We perform proof-of-principle calculations for parabolic quantum dots
in two-dimensions and the closed shell nuclei $^{16}$O and $^{22}$O. We find
that the TDA-IMSRG approach gives better accuracy than the EOM-IMSRG when
calculations converge, but is otherwise lacking the versatility and numerical
stability of the latter. Our calculated spectra are in reasonable agreement
with analogous EOM-coupled-cluster (EOM-CC) calculations, which paves the way
for more interesting applications of the EOM-IMSRG to calculations of
consistently evolved observables such as electromagnetic strength functions and
nuclear matrix elements, and extensions to nuclei within 1-2 nucleons of a
closed shell by generalizing the EOM ladder operator to include particle-number
nonconserving terms.
