  Owing to ring-strain, cyclic ketones exhibit complex excited-state dynamics
with multiple competing photochemical channels active on the ultrafast
timescale. While the excited-state dynamics of cyclobutanone after
$\pi^{\ast}\leftarrow n$ excitation into the lowest-energy excited singlet
state (S$_1$) has been extensively studied, the dynamics following
3$s\leftarrow n$ excitation into the higher-lying singlet Rydberg (S$_2$) state
are less well understood. Herein, we couple quantum and excited-state
trajectory surface-hopping molecular dynamics simulations to study the
relaxation of cyclobutanone following 3s$\leftarrow n$ excitation and to
predict the ultrafast electron diffraction scattering signal that we anticipate
to arise from the relaxation dynamics that we observe. Our simulations indicate
that relaxation from the initially-populated singlet Rydberg state occurs on
the hundreds-of-femtosecond to picosecond timescale consistent with the
symmetry-forbidden nature of the state-to-state transition involved. Once
cyclobutanone has relaxed non-radiatively to the electronic ground state
(S$_0$), the vibrationally hot molecules have sufficient energy to form
multiple fragmentory products on the electronic ground-state surface including
C$_2$H$_4$ + CH$_2$CO (C2; 20%), and C$_3$H$_6$ + CO (C3; 2.5%). We discuss the
limitations of our simulations, how these may influence the outcome of the
excited-state dynamics we observe, and -- ultimately -- the predictive power of
the simulated experimental observable.
