A first-principles method for polymers

Ultimately, our goal is to include the effects of the external fields in a parameter-free ground-state calculation of the properties of an infinite, periodic polymer. To this end we apply our own density-functional method that has been described in detail elsewhere [2,31] and, therefore, shall be only briefly discussed here. 

In our implementation of the method we consider infinite, periodic, isolated polymer chains. The periodicity is utilized in constructing Bloch functions from the basis functions of different unit cells. 

The method has been applied to a number of conjugated polymers over the last almost two decades (see, e.g.. Ref. [32]), and as a special application we also studied the case of chains exposed to an external electrostatic field perpendicular to the chain direction. Thereby, the periodicity was not destroyed and, accordingly, the basics of our approach could be kept unchanged. 

As one example we show in Fig. 4 results for polycarbonitrile exposed to an external field perpendicular to the chain direction. Polycarbonitrile, (CHN)jo resembles frans-polyacetylene but has every second CH group replaced by an N atom. In tbe figure we show both the band structures and 

We shall approximate the scalar potential of the electrostatic field by the sawtooth curve of Fig. 5 that has the periodicity of the Bom von Karman zone, i.e., of the length of one unit cell times the number of k points that is used in a calculation. We have here assumed that the potential takes both positive and negative values. By doing so, the average potential from the field vanishes and we have therefore an optimal starting point for eliminating effects that are linear in the number of k points of the calculation (i.e., in the length of the Bom von Karman zone). 

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