  We derive a sufficient condition on a bounded pseudoconvex domain
$\Omega\subset\mathbb{C}^2$ with smooth boundary such that $-(-\rho)^\eta$ is
plurisubharmonic on $\Omega$ for $\eta>0$ arbitrarily close to $1$ (the
supremum of $\eta$ is called Diederich-Forn{\ae}ss index, see Definition (df)).
This condition (see Theorem prop) extends a theorem of Forn{\ae}ss and Herbig
in 2007 and only requires restriction on Levi-flat sets of the boundary
$\partial\Omega$. Since the condition is on Levi-flat sets, it contains more
geometric information. As an application of this new condition, we discuss how
the geometry of the Levi-flat sets affects the Diederich-Forn{\ae}ss index.
Among other results, we show that the Diederich-Forn{\ae}ss index is $1$ if
only the Levi-flat sets form a real curve transversal to the holomorphic
tangent vector fields on $\partial\Omega$ (see Theorem [main]). We also give a
specific example (see Theorem [example]) on the bounded pseudoconvex domains
which verify the application but are neither of finite type nor admit a
plurisubharmonic defining function on the boundary.
