  Dynamical mean field theory (DMFT) combined with the local density
approximation (LDA) is widely used in solids to predict properties of
correlated systems. In this paper, its application to one of the simplest
strongly correlated systems, the hydrogen molecule H$_2$, is demonstrated to
develop a parameter-free LDA+DMFT framework. We propose a method to calculate
the exact intersection of LDA and DMFT that leads to highly accurate
subtraction of the doubly counted correlation in both methods. When the exact
double-counting treatment and a good projector to the correlated subspace are
used, LDA+DMFT yields very accurate total energy and excitation spectrum of the
H$_2$ molecule. We also discuss how this double-counting scheme can be extended
to solid state calculations.
