  We propose a simple gradient-dependent bound for the exchange-correlation
energy (sLL), based on the recent non-local bound derived by Lewin and Lieb. We
show that sLL is equivalent to the original Lieb-Oxford bound in
rapidly-varying density cases but it is tighter for slowly-varying density
systems. To show the utility of the sLL bound we apply it to the construction
of simple semilocal and non-local exchange and correlation functionals. In both
cases improved results, with respect to the use of Lieb-Oxford bound, are
obtained showing the power of the sLL bound.
