The Calculation of Effective Total Energy per Unit Cell

3 The Calculation of Effective Total Energy per Unit Cell. - The NFC method does not provide, however, an effective total energy per unit cell of a disordered chain. For this purpose one can apply either a cluster method22 or the so-called elongation method.23 

In the cluster method one starts for instance with the first ten units (from the left) of a disordered chain of say 100 units. In this way we obtain the total energy 2 i io We can then shift the cluster stepwise to the right by one unit until we reach the cluster of units 91-100, eliminating at the same time the furthest left unit, respectively. The cluster length remains in this way constant (10 units in our example). Adding all the cluster energies one can write 

Since in this way the energy of each unit is counted several times, one has to substract from (16) the sum of energies of the previous clusters reduced by one unit  

The difference of equations (16) and (17) gives the total energy of the complete finite disordered chain 

Dividing (18) by the number of units N one obtains an effective energy per unit cell for the disordered chain 

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