Developing the MTO Formalism
نویسنده
چکیده
The TB-LMTO-ASA method is reviewed and generalized to an accurate and robust TB-NMTO minimal-basis method, which solves Schrödinger’s equation to Nth order in the energy expansion for an overlapping MT-potential, and which may include any degree of downfolding. For N = 1, the simple TBLMTO-ASA formalism is preserved. For a discrete energy mesh, the NMTO basis set may be given as: χ (r) = ∑ n φ (εn, r)L (N) n in terms of kinked partial waves, φ (ε, r) , evaluated on the mesh, ε0, ..., εN . This basis solves Schrödinger’s equation for the MT-potential to within an error ∝ (ε− ε0) ... (ε− εN ) . The Lagrange matrix-coefficients, L (N) n , as well as the Hamiltonian and overlap matrices for the NMTO set, have simple expressions in terms of energy derivatives on the mesh of the Green matrix, defined as the inverse of the screened KKR matrix. The variationally determined single-electron energies have errors ∝ (ε− ε0) 2 ... (ε− εN) 2 . A method for obtaining orthonormal NMTO sets is given and several applications are presented.
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