Application of First Principles Density Functional Theory DFT to Polymers

4 Application of First Principles Density Functional Theory (DFT) to Polymers 

The DFT has been successfully applied in different levels of approximation to the ground state properties of 3D solids and of molecules. Though there are a few DFT calculations for polymers in the literature,80,81 these calculations have not included a systematic investigation of the dependence of their total energy per unit cell on their conformation and of their valence electron structure (photoelectron spectra). 

1 Methods. - The program used in our calculations was developed by Mintmire for polymeric chains82-84 and for 2D periodic systems85 based on LDA molecular programs using a linear combination of Gaussians.86,87 

The chain program was developed to be able to take into account simple translation as well as helical symmetry. In the case of a helical polymer we can define a screw operator S(a, 0)88 with a translation along the z-axis (the long axis of the polymer) and with a right-handed rotation about the z-axis. Applying this operator to the position vector r one obtains 

Since the symmetry generated by the screw operator S is isomorphic with the one-dimensional translational group, Bloch s theorem is valid also in this case. Therefore, the one-electron wave functions will transform under S as 

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