Muffin-tin orbitals and molecular calculations: General formalism

Abstract

An account is given of a new formalism for calculating energy levels in molecules using techniques that derive from the band theory of metals. After showing how the molecular potential may be transformed into a cellular potential we define the basis set of muffin-tin orbitals and discuss some of their properties. The relationship between the scattered wave formulation of Johnson, which is restricted to muffin-tin potentials, and our more general approach based on the use of a linear combination of muffin-tin orbitals (L.C.M.T.O.) is explicitly indicated. We then show how the properties of the muffin-tin orbitals, together with the technique of cellular integration, give rise to a hamiltonian matrix. This matrix is as general as, but simpler than that obtained by the use of atomic orbitals, and it is linear in energy and therefore computationally faster than the secular matrix of the scattered wave method.