Band structure calculations are used to analyze the structures of one-dimensional (BeCl2)" and (BeMe2)" polymers. The distortion away from the ideal tetrahedral angle at the beryllium atom, 98.2°in (BeCl2)" and 114°in (BeMe2)", is related to the existence of a lone pair on the bridging group or atom available for bonding with the Be centers. The analysis accounts correctly for the structures of other one-dimensional polymers such as (SiS2)", (SiSe2)", and fibrous (Si02)". The stability of these polymers is discussed in terms of the number of valence electrons per unit cell. It is demonstrated that 32 electrons per unit cell is the optimal number, which is in good agreement with the experimental evidence. New one-dimensional (MX2)" polymers are proposed on the basis of this 32-electron rule.In this paper we present a theoretical analysis of edgesharing tetrahedral (MX2)" periodic systems ( = main group metal, X = halide, alkyl, alkoxide, hydride) by means of band structure calculations. Our purpose is a better understanding of the structures and stabilities of these systems.One-dimensional polymeric chains of MX2 are commonly found for M = Be1-5 and Mg6"8 with various bridging X's. The best known examples are (BeCl2)"* and (BeMe2)".2 The simplest compound (BeH2)"3 has been synthesized, although its structure could not be determined. With M = Be, X can also be an alkoxy group48 or a dissimilar pair (H, alkyl).* Grignard reagents are believed to be polymeric.8 (MgMe2)"6 and (MgEt2)",7 which are also related to Grignard reagents, are well-characterized polymers.The basic motif of these polymers is an edge-sharing tetrahedron as shown in 1. A similar arrangement is known for the silicon derivatives9 (SiS2)", (SiSe2)", and fibrous (Si02)".A small-size polymer made of gallium and selenium (Ga6Se14)10™ has been recently characterized.10 An interesting pattern emerges from the examination of the geometrical parameters of 1. Although M is said to be tetrahedrally coordinated, the angle at the M center, ZXMX, departs noticeably from the usual value of 109.47°. In (Be-Cl2)" the /ClBeCl angle is 98.2°1 while in (BeMe2)" the