The generalized Debye-Waller factor for atoms in a twisted environment. I. Sites at the core of a double helix

Lattice sites which have a proper or improper subgroup of 222 as the site group may exhibit an anharmonic twisted local potential. The generalized Debye-Waller factor for atoms occupying such sites is derived. If the twist axis is fixed by symmetry considerations the approximation used needs, in addition to three harmonic parameters, one anharmonicity parameter, essentially the local pitch. In the most general case with no symmetry restrictions three Eulerian angles are needed in addition to the pitch.