Abstract: We show that modified Wigner projector technique and generalized Bloch theorem approach yield max- imally efficient diagonalization of the Hamiltonian of the large symmetrical systems. For the sake of illustration, we perform a case study of the simplified DNA molecule model and solve the energy eigenproblem analytically by using the unit symmetry cell (symcell) and the corresponding low-dimensional subspaces only. Relevant dynamical parameters are automatically obtained, enabling direct interpretation of the result. Effectiveness of the procedure is based on the two key points: (1) replacing infinite sums over the group elements by modified group projectors which are inherently determined by the group generators only; (2) reducing the dynamics of the system (from the infinite dimensional state space) to the low-dimensional symcell subspace, taking the benefit from the induced structure of the state space. Unlike the original Wigner projectors, the modified group projector technique is directly numerically applicable.

Keywords: Deoxyribonucleic Acid (DNA), Symmetry, Wigner Group Projectors, Modified Group Projector Technique, Generalized Bloch Theorem, Electronic Bands, Eigenproblem, Inductive Spaces, Tight-binding Approximation

Pages: 7-12