  In this paper we prove an estimate for the total variation distance, in the
framework of the Breuer-Major theorem, using the Malliavin-Stein method,
assuming the underlying function $g$ to be once weakly differentiable with $g$
and $g'$ having finite moments of order four with respect to the standard
Gaussian density. This result is proved by a combination of Gebelein's
inequality and some novel estimates involving Malliavin operators.
