| Abstrakt: |
A theorem is proved stating that in atoms, molecules, and solids, only the set of the spherical parts of the density around each nucleus determines uniquely the external potential. Therefore, the induced Kohn and Sham (KS) potential has spherical symmetry around each nucleus, and furthermore, it has the symmetry of the external potential. In this way, the inconsistencies of standard density functional theory (DFT) concerning the asymmetry of the KS potential are remedied. As a result of the above, the ground state is uniquely determined by this set of spherical densities. In the case of a symmetry group G of a Hamiltonian H, the minimizing subspace of the Hamiltonian for each irreducible representation of G is uniquely determined by this set of spherical densities. Thus, the present theory opens the way for new density functionals and more accurate molecular calculations as it exploits local symmetries. Moreover, the theory of “Atoms in Molecules” formulated by Bader, by using the open quantum mechanics theory, can be explained in terms of DFT [R. F. W. Bader, Atoms in Molecules. A Quantum Theory (Oxford University Press, Oxford, 1990)]. [ABSTRACT FROM AUTHOR] |
