Comparison of the projector augmented-wave, pseudopotential, and linearized augmented-plane-wave formalisms for density-functional calculations of solids

The projector augmented-wave (PAW) method was developed by Bl\"ochl as a method to accurately and efficiently calculate the electronic structure of materials within the framework of density-functional theory. It contains the numerical advantages of pseudopotential calculations while retaining the physics of all-electron calculations, including the correct nodal behavior of the valence-electron wave functions and the ability to include upper core states in addition to valence states in the self-consistent iterations. It uses many of the same ideas developed by Vanderbilt in his ``soft pseudopotential'' formalism and in earlier work by Bl\"ochl in his ``generalized separable potentials,'' and has been successfully demonstrated for several interesting materials. We have developed a version of the PAW formalism for general use in structural and dynamical studies of materials. In the present paper, we investigate the accuracy of this implementation in comparison with corresponding results obtained using pseudopotential and linearized augmented-plane-wave (LAPW) codes. We present results of calculations for the cohesive energy, equilibrium lattice constant, and bulk modulus for several representative covalent, ionic, and metallic materials including diamond, silicon, SiC, ${\mathrm{CaF}}_{2}$, fcc Ca, and bcc V. With the exception of ${\mathrm{CaF}}_{2}$, for which core-electron polarization effects are important, the structural properties of these materials are represented equally well by the PAW, LAPW, and pseudopotential formalisms.