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