Abstract
The Korringa-Kohn-Rostoker (KKR) Green function (GF) method is a technique for all-electron full-potential density-functional calculations. Similar to the historical Wigner-Seitz cellular method, the KKR-GF method uses a partitioning of space into atomic Wigner-Seitz cells. However, the numerically demanding wave-function matching at the cell boundaries is avoided by use of an integral equation formalism based on the concept of reference Green functions. The advantage of this formalism will be illustrated by the recent progress made for very large systems with thousands of inequivalent atoms and for very accurate calculations of atomic forces and total energies.
Highlights
Since the early days of quantum mechanics it has been recognized that the quantum mechanical laws could be used to describe ”a large part of physics and the whole of chemistry” as, for instance, Paul Dirac [1] argues in his paper on ”Quantum Mechanics of Many-Electron Systems” in 1929
Within Hohenberg-Kohn-Sham density-functional theory the approximation consists in the expressions chosen for the unknown exchange-correlation functional and the simplification that arises is the use of the electronic density as the fundamental quantity instead of many-electron wave function
The one-electron Schrödinger equation is solved by dividing the periodic crystal into non-overlapping cells centred at each atom, by determining single-cell solutions and putting them together with appropriate boundary conditions. It is the aim of the present contribution to relate this historical Wigner-Seitz approach to the modern KKR-Green function (GF) method and to illustrate the capabilities of this approach by showing that very large systems with thousands atoms can be studied and that very accurate forces and total energies can be calculated
Summary
Since the early days of quantum mechanics it has been recognized that the quantum mechanical laws could be used to describe ”a large part of physics and the whole of chemistry” as, for instance, Paul Dirac [1] argues in his paper on ”Quantum Mechanics of Many-Electron Systems” in 1929. The one-electron Schrödinger equation is solved by dividing the periodic crystal into non-overlapping cells centred at each atom, by determining single-cell solutions and putting them together with appropriate boundary conditions It is the aim of the present contribution to relate this historical Wigner-Seitz approach to the modern KKR-GF method and to illustrate the capabilities of this approach by showing that very large systems with thousands atoms can be studied and that very accurate forces and total energies can be calculated.
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