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The eigenstates of the hydrogen molecule ion have been determined by a variational calculation without resorting to the Born–Oppenheimer or adiabatic approximations. A Slater-type orbital basis in terms of perimetric coordinates was used and the eigenvalues were obtained by diagonalizing a 300×300 matrix. Computational techniques and numerical stability tests are described. Because of the relatively small basis and the large number of bound states, most of the eigenvalues were sensitive to the basis set. With a basis which favored the upper states, 18 bound states were obtained in a single diagonalization vs 20 bound states in the adiabatic approximation. With the best basis for the ground state, the eigenvalues of the six lowest levels were 1 to 3×10-6 a.u. lower than adiabatic calculations and the differences appear to increase with increasing vibrational quantum number. [ABSTRACT FROM AUTHOR]