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By using the usual instanton method, we obtain the energy splitting due to quantum tunneling through the triple-well barrier. It is shown that the term related to the midpoint of the energy splitting in propagator is quite different from that of double-well case, in that it is proportional to the algebraic average of the frequencies of the left and central wells. The result of the energy splitting is consistent with the known variational calculation.

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Electronic states for two possible high-pressure phases (with the ThSi 2 structure and with the AlB 2 structure) of CaSi 2 are determined by means of a local density approximation band-structure calculation. We confirm that these polymorphs can be regarded as doped sp 2 networks of Si. However, a simple picture in terms of π-orbitals is not adequate for explaining the conduction bands, because (i) an s-like band, which is anti-bonding in sp 2 connections but bonding between segments of the network, appears and (ii) there is π -d hybridization between Si and Ca.