A compact, few-parametric, physically adequate, 3-term variational trial function is used to calculate with high accuracy the energy of the ground state ${}^3Pi_u$ of the hydrogen molecule ${rm H}_2$ in strong magnetic field ${bf B}$ in the range $5times10^{10}, {rm G} leq B leq 10^{13},$G. The nuclei (protons) are assumed as infinitely massive (BO appproximation of zero order) and situated along the magnetic field line (parallel configuration).
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