Operator approach in the linearized augmented-plane-wave method: Efficient electronic-structure calculations including forces

The most efficient algorithms for the calculation of the electronic and structural properties of solids and molecules are based on iterative diagonalization methods or the Car-Parrinello molecular-dynamics approach. In these methods, the Hamiltonian is used as an operator and it is therefore not necessary to know the explicit form of the Hamiltonian matrix. We will show that the full-potential linearized augmented-plane-wave (LAPW) method can be formulated in operator form, and that this formulation allows very efficient electronic-structure calculations. We furthermore derive an approach for the calculation of forces in density-functional calculations, which eliminates complications arising from the self-consistency requirement. We then apply this approach to the LAPW method.