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.