Ab initio potential energy curves and vibrational levels for the C and D 1Πu states of the hydrogen molecule

Two lowest eigenvalues of the Hamiltonian for the hydrogen molecule corresponding to the ¹Π_u symmetry have been calculated in the Born-Oppenheimer approximation. They represent the C and D states, respectively. Different highly flexible wavefunctions were used for both states and the calculations were performed for a wide range of internuclear distances: 1 ≤ R ≤ 12 a.u. for the C state, and 1 ≤ R ≤ 25 a.u. for the D state. The calculated potential energy curves are more accurate than any previous ab initio results for the above states. The vibrational Schrödinger equation for both states has been solved for H₂, HD, and D₂ using the Numerov method. The resulting energies and rotational constants are compared with the experimental values.