It is shown that in the framework of the improved Bardeen-Cooper-Schrieffer (IBCS) theory the correlation energy per unit cell of a periodic polymer can be computed. Furthermore, a new concept of effective correlated pairs is introduced and the coefficient kappa modifies now the correlated term in the occupation number arised. The occupation numbers are expressed by means of quantities, which satisfy a trigonometric relation to warrant the nonidempontent condition. As a consequence a variational method can be introduced, which involves only an unconstrained minimization which may be performed using a conjugated gradient technique. Some results of calculations on nucleotide bases and the corresponding periodic polymers are presented.