The inverse sandwich Ca-C8H8-Ca is predicted to be an open-shell singlet state. Since the C8H8 ligand prevents the spin-up and spin-down electrons of different calcium atoms from forming Ca-Ca bonds, the spin-coupling electrons lead to a singlet diradical character. The metal-ligand interaction contributes to the stability of Ca-C8H8-Ca against dissociation and isomerization. For the coordination complex (DME)3Ca-C8H8-Ca(DME)3, the open-shell singlet state is unavailable, while the closed-shell singlet state with direct Ca-Ca bonds is more favorable, because dimethyl ether molecules could push the spin-paired electrons of different calcium atoms to migrate towards the direction of Ca-Ca bonding. For Ca-C4H4-Ca, the ground state is an open-shell singlet state, of which the diradical character is very similar to that of Ca-C8H8-Ca. For (DME)3Ca-C4H4-Ca(DME)3, the lowest energy is the triplet state.
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