  We evaluate the allowed $\beta^-$-decay properties of nuclei with $Z = 8 -
15$ systematically under the framework of the nuclear shell model with the use
of the valence space Hamiltonians derived from modern $ab~intio$ methods, such
as in-medium similarity renormalization group and coupled-cluster theory. For
comparison we also show results obtained with fitted interaction derived from
the chiral effective field theory and phenomenological USDB interaction. We
have performed calculations for O $\rightarrow$ F, F $\rightarrow$ Ne, Ne
$\rightarrow$ Na, Na $\rightarrow$ Mg, Mg $\rightarrow$ Al, Al $\rightarrow$
Si, Si $\rightarrow$ P and P $\rightarrow$ S transitions. Theoretical results
of $B(GT)$, log$ft$ values and half-lives, are discussed and compared with the
available experimental data.
