On the validity of formal electron counting rules in lithium silicides

The validity of widely used electron counting rules (i.e. (8-N) rule) is investigated in two of the four stable crystalline lithium silicides (Li₁₂Si₇ and Li₂₁Si₅) by means of semiempirical MO calculations of the INDO-type on the stage of localized orbitals which are derived from the canonical one-particle set by a unitary transformation. This representation allows for a transparent interpretation of the nature of the chemical bond in the employed systems. Finite cluster models are used in both cases. The system Li₁₂Si₇ is approximated by [Li₂₁Si₄]⁹⁺ units, the latter one by [Li₂₂Si₄]⁴⁺ fragments. It is demonstrated that the extension of the octet configuration is only pretended in these systems. The close cage of Li atoms allows for the formation of an additional bonding one-electron state formed by the 2s AO's at the metal centers. This cage orbital is highly independent from the Si subspace. It can be occupied by two electrons that are not considered in formal counting rules. The geometric condition supporting the formation of such a function is a close cage of Li atoms. This solid-state effect has a molecular counter part in hyperlithiated molecules (i.e. [CLi₄]²⁻, [CLi₅]⁻, CLi₆). It is shown that other crystalline lithium silicides are stabilized by Li 2s cage orbitals too.