previous quantum calculations [@Pogrebnya02; @Lee06; @Forrey01; @Otto08] and available experimental results [@Audibert75; @Bauer76; @Mate05]. We employ the BMKP PES and the full-dimensional TwoBC - quantum scattering program developed by Krems [@Roman06] implemented in our previous study [@Quemener08a]. The paper is organized as follows: In section II, we give an overview of the TIQM scattering theory of two $^1\Sigma$ diatomic molecules. In section III, we present state-to-state and initial state-selected cross sections and rate coefficients for the H$_2(v=1,j=0)$ + H$_2(v=0,j=0)$ and H$_2(v=0,j=0)$ + H$_2(v=0,j=0)$ collisions. Conclusions are given in section IV.

Molecule - molecule scattering theory
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The TIQM formalism for scattering of two $^1\Sigma$ diatomic molecules has been described by Takayanagi [@Takayanagi65], Green [@Green75], Alexander and DePristo [@Alexander77], and Zarur and Rabitz [@Zarur74], using the close-coupling (CC) formalism of Arthurs and Dalgarno [@Arthurs60]. A brief account of the theoretical formalism with particular emphasis on distinguishable versus indistinguishable molecule collisions is given here. For more details we refer to the original papers.

Figure \[JacCord-FIG\] shows the Jacobi vectors employed in the calculations where $\vec{r}_1(r_1,\hat{r}_1)$ and $\vec{r}_2(r_2,\hat{r}_2)$ describe the vectors joining the two atoms of the two H$_2$ molecules and $\vec{R}(R,\hat{R})$ denote the vector joining the centers of mass of the two 