Static Dipole Polarizability for the $1S\sigma$ electronic state of the   $H^+_2$ molecular ion
  The static dipole polarizabibility for the $1s\sigma$ electron state of the $\mathrm{H}_{2}^{+}$ hydrogen molecular ion is calculated within Born-Oppenheimer approximation. The variational expansion with randomly chosen exponents has been used for numerical studies. The results obtained for the dipole polarizability are accurate to the nine digits. 
Ts.Tsogbayar