The simplest way of approaching the limit of the infinite chain is to perform computations on finite systems of increasing number M of atoms and then extrapolate to M— oo. This is also the most physical in the sense that the finite systems are often real molecules. We will refer to this case as open chain. A second, more formal way is to impose periodic boundary conditions to the finite system of M atoms and then let M oo. This choice allows for faster convergence to the limit and it is often preferred in practice. Consider a cyclic polyacetylene molecule (annulene) composed of M = 2N -CH- units, disposed on a ring in the jc,y plane. After dimerization the molecule is composed of N monomers -CH=CH- this is the elementary cell of our system. We number the C atoms (or sites) by a cyclic index i = 0,. ..,2A — 1 indexes 2A, 2A + 1,... coincide with 0,1,... respectively. Two families of orbital energies are obtained [7] [Pg.350]

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