A brief introduction to the projector augmented wave method is given and recent developments are reviewed. The projector augmented wave method is an all-electron method for efficient ab-initio molecular dynamics simulations with full wave functions. It extends and combines the traditions of existing augmented wave methods and the pseudopotential approach. Without sacrificing efficiency, the PAW method avoids transferability problems of the pseudopotential approach and it has been valuable to predict properties that depend on the full wave functions.

Several improvements of the tetrahedron method for Brillouin-zone integrations are presented. (1) A translational grid of k points and tetrahedra is suggested that renders the results for insulators identical to those obtained with special-point methods with the same number of k points. (2) A simple correction formula goes beyond the linear approximation of matrix elements within the tetrahedra and also improves the results for metals significantly.For a required accuracy this reduces the number of k points by orders of magnitude. (3) Irreducible k points and tetrahedra are selected by a fully automated procedure, requiring as input only the space-group operations. (4) The integration is formulated as a weighted sum over irreducible k points with integration weights calculated using the tetrahedron method once for a given band structure. This allows an e%cient use of the tetrahedron method also in plane-wave-based electronic-structure methods.

The so-called local density approximation plus the multi-orbital mean-field Hubbard model (LDA+U) has been implemented within the all-electron projector augmented-wave method (PAW), and then used to compute the insulating antiferromagnetic ground state of NiO and its optical properties. The electronic and optical properties have been investigated as a function of the Coulomb repulsion parameter U . We find that the value obtained from constrained LDA (U = 8 eV) is not the best possible choice, whereas an intermediate value (U = 5 eV) reproduces the experimental magnetic moment and optical properties satisfactorily. At intermediate U , the nature of the band gap is a mixture of charge transfer and Mott-Hubbard type, and becomes almost purely of the charge-transfer type at higher values of U . This is due to the enhancement of the oxygen 2p states near the top of the valence states with increasing U value.

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A brief introduction to the projector augmented wave method is given and recent developments are reviewed. The projector augmented wave method is an all-electron method for efficient ab initio molecular dynamics simulations with full wave functions. It extends and combines the traditions of existing augmented wave methods and the pseudopotential approach. Without sacrificing efficiency, the PAW method avoids transferability problems of the pseudopotential approach and it has been valuable to predict properties that depend on the full wave functions. Keywords. Electronic structure calculations; ab initio molecular dynamics; pseudopotentials; augmented wave methods.