  The internal conversion from the optically bright S$_2$
($^1$B$_{2\mathrm{u}}$, $\pi\pi^*$) state to the dark S$_1$
($^1$B$_{3\mathrm{u}}$, n$\pi^*$) state in pyrazine is a standard benchmark for
experimental and theoretical studies on ultrafast radiationless decay. Since
2008 a few theoretical groups have suggested significant contributions of other
dark states S$_3$ ($^1$A$_\mathrm{u}$, n$\pi^*$) and S$_4$
($^1$B$_{2\mathrm{g}}$, n$\pi^*$) to the decay of S$_2$. We have previously
reported the results of nuclear wave packet simulations [Phys. Chem. Chem.
Phys. 17, 2012 (2015)] and photoelectron spectrum calculations [Chem. Phys.
515, 704 (2018)] that support the conventional two-state picture. In this
article, the two different approaches, i.e., wave packet simulation and
photoelectron spectrum calculation are combined: We computed the time-resolved
vacuum ultraviolet photoelectron spectrum and photoelectron angular
distribution for the ionization of the wave packet transferred from S$_2$ to
S$_1$. The present results reproduce almost all the characteristic features of
the corresponding experimental time-resolved spectrum [T. Horio et al., J.
Chem. Phys. 145, 044306 (2016)] such as a rapid change from a three-band to
two-band structure. This further supports the existence and character of the
widely accepted pathway (S$_2$ $\rightarrow$ S$_1$) of ultrafast internal
conversion in pyrazine.
