Symmetry-adapted modeling for molecules and crystals

We have developed a symmetry-adapted modeling procedure for molecules and crystals. By using the completeness of multipoles to express spatial and time-reversal parity-specific anisotropic distributions, we can generate systematically the complete symmetry-adapted multipole basis set to describe any of electronic degrees of freedom in isolated cluster systems and periodic crystals. The symmetry-adapted modeling is then achieved by expressing the Hamiltonian in terms of the linear combination of these bases belonging to the identity irreducible representation, and the model parameters (linear coefficients) in the Hamiltonian can be determined so as to reproduce the electronic structures given by the density-functional computation. We demonstrate our method for the modeling of graphene and emphasize usefulness of the symmetry-adapted basis to analyze and predict physical phenomena and spontaneous symmetry breaking in a phase transition. The present method is complementary to de facto standard Wannier tight-binding modeling, and it provides us with a fundamental basis to develop a symmetry-based analysis for materials science.