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[Abstract = "Calculations of the Born-Oppenheimer (BO) potential energy curves and adiabatic corrections for three lowest 3IIg and three lowest 3IIu, states of the hydrogen molecule have been performed using explicitly correlated wavefunctions in elliptic coordinates. The accuracy of the results obtained has been discussed. The adiabatic corrections as functions of R possess complex structure with one or more maxima illustrating changes in the character of the wavefunctions. It is shown that for the k state the adiabatic curve has huge maximum of the order of 50 000 cm- 1 ."]