Electronic structure of crystalline polymers

Structural notations and conventions

Considered are only 1D-polymers aligned in one direction, with a single bond between monomers.
The coordinate system is oriented in such a way that polymer chains run along X axis and the π-system is directed along Z axis.
Each monomer has continuous set of atom indexes, and monomers with smaller X-coordinate have smaller indexes.
By default the origin is put at the middle point between the unit cell and its left replica.
Capping atoms (do not belong to monomers) are indexed at the very end of an oligomer and are ordered as left end, then right end.
A crystal or a bundle of polymer chains are defined by a list of five parameters per bundle: [ξ,y,z,φ,g], see figure. Here ξ=x/a] is the shift along the polymer in units of the translation period a, y,z are displacements in YZ-plane, φ is "setting angle" defining polymer rotation around X-axis in the right-hand rule, such that φ=0 corresponds to the polymer plane perpendicular to Z-axis, and g is a combination of X,Y,Z-reflections, This parameters are applied in the reverse order: the reference polymer [0,0,0,0,1] is transformed by g, then rotated by φ, and then displaced by (ξa,y,z).

All calculations and data processing are performed with the same set of computational protocols referenced below:

Initial geometry is generated from the list of [ξ,y,z,φ,g] for the unit cell. Initial guess for parameters y,z,φ can be derived from a cross-sectional model of polymer packing, whereas a scan is needed to determine optimal values of ξ,g. Also, all conformations of a single polymer chain should be considered. MD in a small supercell allows to get new structures. For two polymer chains per unt cell, the procedure is illustrated for P3HT system in Ref.[Zhugayevych18].
Molecular crystal geometry optimization
Electronic coarse-graining of insulators
Calculation of coarse-grained electronic Hamiltonian for molecular crystals