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The ``projector augmented-wave'' (PAW) method was developed by Blochl as a new 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 wavefunctions 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 Blochl 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, CaF2, fcc Ca, and bcc V. With the exception of CaF2, for which core electron polarization effects are important, the structural properties of these materials are well represented equally well by the PAW, LAPW, and pseudopotential formalisms.