Maximally Efficient Symmetry Group Founded Diagonalization of Biophysical and Quantum Chemical Hamiltonians

We show that modified Wigner projector technique and generalized Bloch theorem approach yield maximally 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. Key–Words: Deoxyribonucleic Acid (DNA), Symmetry, Wigner Group Projectors, Modified Group Projector Technique, Generalized Bloch Theorem, Electronic Bands, Eigenproblem, Inductive Spaces, Tight-binding Approximation