A Simplified Approach to the Density Functional Theory of Molecules

A simplified molecular orbital (MO) formalism based on density functional theory is developed. Starting from the same energy expression as Kohn-Sham theory the electronic density is expanded in terms of atomic mono-center densities. Application of the variational principle leads to a secular matrix with a particularly transparent structure which allows the definition of a resonance integral taking into account the effect of interference in a natural way. The construction of the secular matrix scales formally as N2 instead of N3 in the Kohn-Sham formalism with N being the dimension of the atomic orbital (AO) basis set.

The Green Function Cellular Method and Its Relation to Multiple Scattering Theory

ABSTRACTWe investigate techniques for solving the wave equation which are based on the idea of obtaining exact local solutions within each potential cell, which are then joined to form a global solution. We derive full potential multiple scattering theory (MST) from the Lippmann-Schwinger equation and show that it as well as a closely related cellular method are techniques of this type. This cellular method appears to have all of the advantages of MST and the added advantage of having a secular matrix with only nearest neighbor interactions. Since this cellular method is easily linearized one can rigorously reduce electronic structure calculations to the problem of solving a nearest neighbor tight-binding problem.