Polyethylene statistical weight matrix

For linear polyethylene, the first order interaction can be given by a diagonal statistical weight matrix... 

As an example, the statistical weight matrix for polyethylene with its three-fold rotational states (trans, gauche plus, gauche minus) is... 

For polyethylene, the first two points specify dimensions of 3 x 3 for U(. Assuming the order of indexing of rows and columns is f, if ", , the third point specifies the presence of a in all elements in the second and third columns. The fourth point specifies the appearance of in the 2,3 and 3,2 elements. Therefore the statistical weight matrix for polyethylene is the 3x3 matrix in equation (4) (12). 

TT. There is Xo increase of the energy at the inversion of the spiralization sense and the corresponding statistical weight may be taken as 1 (fig. 13). We can write now a simplified matrix of statistical weights analogous to (37), written for polyethylene, but relative to pairs of bonds. The compacted matrix has the form ... 

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