文档介绍：Developing the MTO Formalism
O. K. Andersen, T. Saha-Dasgupta, R. W. Tank, C. Arcangeli, O. Jepsen, and
G. Krier
Max-Planck-Institut FKF, D-70569 Stuttgart, FRG,
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Abstract. The TB-LMTO-ASA method is reviewed and generalized to an accurate
and robust TB-NMTO minimal-basis method, which solves Schr¨odinger’s equation to
Nth order in the energy expansion for an overlapping MT-potential, and which may
include any degree of N =1, the simple TB-LMTO-ASA formalism is
χ(N)
a discrete energy mesh, the NMTO basis set may be given as: (r)=
φε, L(N) φε, ,
n ( n r) n in terms of kinked partial waves, ( r) evaluated on the mesh,
ε0, ..., εN . This basis solves Schr¨odinger’s equation for the MT-potential to within an
(N)
error ∝(ε−ε0) ... (ε−εN ) . The Lagrange matrix-coefficients, Ln , 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 variationally determined single-electron energies have errors
2 2
∝(ε−ε0) ... (ε−εN ) . A method for obtaining orthonormal NMTO sets is given and
several applications are presented.
1 Overview
Muffin-tin orbitals (MTOs) have been used for a long time in ab initio calcu-
lations of the electronic structure of condensed matter. Over the years, several
MTO-based methods have been devised and further developed. The ultimate aim
is tofind a generally applicable electronic-structuremethodwhich is accurate
and robust, as well as intelligible.
In order to be intelligible, such a method must employ a small, single-electron
basis of atom-centered, short-ranged orbitals. Moreover, the single-electron Ha-
miltonian must have a simple, analytical form, which relates to a two-center,
orthogonal, tight-binding (TB) Hamiltonian.
In this sense, the conventional linear muffin-tin-orbitals meth