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Computational Details of Magnesium Dimer

Potentials dissociating to the 1S + 1P and 1S + 3P asymptotes

The multiconfiguration basis set for the calculation of the excited Mg2 molecule is based on the Dirac-Fock atomic orbitals the [1s2 2s2] 2p6 3s2 configuration with additional Dirac-Fock 3p and 4s orbitals and Sturmian orbitals labeled 3d and 4p. The closed shells 1s22s2 + 1s22s2 form the core of the molecule and no excitations from these shells will be allowed. The 2p6, 3s2, 3p, and 4s orbitals are valence orbitals and single and double occupation and excitation from these orbitals occur. Covalent and ionic configurations are constructed by distributing electrons from the valence orbitals in all allowed ways over the orbitals. There are 393 nonrelativistic molecular configurations and 2290 relativistic configurations. The potential curves are calculated based on the relativistic Hamiltonian in order to take into account the spin-orbit splittings of the excited states. There are sixteen Omegag/u± relativistic potentials dissociating to the 1S + 1P and 1S + 3P asymptotes. Twelve of these potentials dissociate to the 1S + 3P asymptotes. Non relativistic labels are indicated in parenthesis. The zero of energy is located at the dissociation limit of the ground state of Mg2. The symbols on the curves belong to different fine structure levels with the same nonrelativistic symmetry.

Potentials dissociating to the 3P + 3P asymptotes

The multiconfiguration basis set for the calculation of the highly excited state potentials dissociating to the 3P + 3P asymptotes of the Mg2 molecule is based on the Dirac-Fock atomic orbitals belonging to the [1s2 2s2] 2p6 3s3p configuration with an additional Dirac-Fock 4s orbital and Sturmian orbitals labeled 3d and 4p. The closed shells 1s2 2s2 + 1s2 2s2 form the core of the molecule and no excitations from these shells will be allowed. The 2p6, 3s, 3p, and 4s orbitals are valence orbitals and single and double occupation and excitation from these orbitals occur. Covalent and ionic configurations are constructed by distributing electrons from the valence orbitals in all allowed ways over the orbitals. This leads to the same number of molecular configuration as in the calculation for the lower lying excited states. Again the potential curves are calculated based on the relativistic Hamiltonian in order to take into account the spin-orbit splittings of the excited states.

The number of relativistic potentials Omegag/u± = 0, 1, 2, 3, 4 dissociating to the 3P + 3P asymptotes is now significantly larger. The zero of energy is again at the dissociation limit of the ground state of Mg2. Some of the 0+ and 0- curves are degenerate on the scale of the figures. Lines with filled circles indicate nearly degenerate potentials.

The 3s2 + 3s4s limits lie just below those of the 3P + 3P states. Curves correlating to the 3s2 + 3s4s limits only appear for Omega = 0 and 1 and are shown as red dotted lines in the figures. Only the 1Sigmag+ curve can couple by exchange to the two 1Sigmag+ curves dissociating to 3P + 3P. However, the 3s2 + 3s4s 1Sigmag+ curve is attractive while the 3P + 3P curves have a repulsive dispersion. Thus it can be expected that mixing is minimal.

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