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The projector augmented-wave ͑PAW͒ method was developed by Blöchl 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 Blöchl 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 ͑LAPW͒ 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, CaF 2 , fcc Ca, and bcc V. With the exception of 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. ͓S0163-1829͑97͒00404-9͔

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Several types of defect structures in PbWO 4 and CaMoO 4 are studied within the framework of density functional theory. While PbWO 4 is currently of greater technological interest, we were able to carry out more extensive calculations for CaMoO 4 , including lattice relaxation, large simulation cells, and more complicated defects. The structural and chemical similarity of the two materials suggests that their defect properties may also be similar. The electronic structure of isolated oxygen vacancies, oxygen and Pb or Ca double vacancies, and substitutional Y are modeled using a supercell approximation. We find that the main effect of oxygen vacancies in PbWO 4 and CaMoO 4 is the introduction of states of W or Mo d character into the band gap. The energies of these defect states are very sensitive to their occupancy. An isolated O vacancy produces a doubly occupied defect state below the conduction band. Removing charge from this defect state lowers its energy and causes additional states of W or Mo d character to move into the band gap. Large supercell simulations for the Ca and O double vacancy in an unrelaxed or slightly relaxed structure produce an unstable electronic structure suggesting the possibility of more extensive lattice distortion. In addition, we also present preliminary results of simulations of interstitial oxygen atoms in CaMoO 4 , finding a relatively stable configuration with the interstitial O forming a weak bond between two MoO 4 clusters.

Calculations of the stopping power (SP) of ion beams in solids have been based on a homogeneous electron gas scattering off a static atom and entail at least one free parameter. Here we report dynamical simulations of ions channeled in silicon. Time-dependent density-functional theory (TDDFT) is used. The calculated SPs are in excellent agreement with the observed oscillatory dependence on atomic number. TDDFT calculations for a homogeneous electron gas demonstrate that both dynamical response and nonuniformities in the electron density are essential to reproduce the data without free parameters.

A variational principle is not generally satisfied in steady-state quantum transport as opposed to the case of ground-state problems. We show that for a short-range potential, a functional for the scattering amplitude can be introduced that is stationary for arbitrary variations about the exact scattering wave function. However, except for the special case of spherically symmetric potentials, the functional does not satisfy any minimum principle even in linear response and for single-channel scattering. The absence of a minimum principle puts severe limitations on the choice of trial wave functions in transport calculations. Examples of electronic transport in selected quantum wires will be presented to illustrate the problem. DOI: 10.1103/PhysRevB.66.041405 PACS number͑s͒: 73.40.Jn, 73.40.Cg, 73.40.Gk, 85.65.ϩh The variational method is a powerful tool to estimate the ground-state energy of a particle with Hamiltonian H. 1 The method relies on the use of a trial wave function ͑or a family of trial wave functions͒ which reproduces as closely as possible the actual ground-state wave function GS . The functionalhas then the property that ͑2͒If the trial wave function depends on certain parameters, then due to Eq. ͑2͒, the best estimate for the ground-state wave function and consequently the ground-state energy can be obtained by minimizing the functional ͓Eq. ͑1͔͒ with respect to these parameters. Total-energy calculations in condensed-matter physics, for instance, are based on such a principle. 2 The families of trial wave functions used in actual calculations vary from linear combinations of atomic orbitals to plane waves, and the choice of one family with respect to another depends mainly on numerical convenience. 2 In all choices, however, confidence in the convergence of the results with respect to the best estimate of the ground-state wave function is guaranteed by the existence of the variational principle ͓Eq. ͑2͔͒. Electronic transport in a given sample connected to external reservoirs is neither an equilibrium nor a ground-state problem. The physical observable that one needs to calculate in this case is the electric current across the sample. In general, therefore, one should not expect to have a minimum principle from which the best estimate of the scattering amplitudes can be obtained. Note that the absence of such a principle puts severe limitations on the choice of trial wave functions in transport calculations since a minimum principle is necessary to uniquely determine the best estimate from a family of trial wave functions. 3 This problem was recognized a long time ago. 4 It was demonstrated 4 that a minimum principle still applies to the scattering amplitudes for a spherically symmetric potential at zero energy for the very special case when ͑i͒ a single s-wave channel contributes to scattering at that energy and (ii) the potential does not support bound states or, if it does, the radial part of the Hamiltonian has a negative expectation value on the bound states-trial wave functions. 4 In r...

The projector augmented wave ͑PAW͒ method for electronic structure calculations developed by Blöchl ͓Phys. Rev. B 50, 17 953 ͑1994͔͒ has been very successfully used for density functional studies. It has the numerical advantages of pseudopotential techniques while retaining the physics of all-electron formalisms. We describe a method for generating the set of atom-centered projector and basis functions that are needed for the PAW method. This scheme chooses the shapes of the projector functions from a set of orthogonal polynomials multiplied by a localizing weight factor. Numerical benefits of the scheme result from having direct control of the shape of the projector functions and from the use of a simple repulsive local potential term to eliminate ''ghost state'' problems, which can plague calculations of this kind. Electronic density of states results are presented for the mineral powellite (CaMoO 4). ͓S0163-1829͑98͒03416-X͔

We present a method for calculating some select eigenvalues and corresponding eigenvectors of a given Hamiltonian. We show that it is possible to target the eigenvalues and eigenvectors of interest without diagonalizing the full Hamiltonian, by using any arbitrary physical property of the eigenvectors. This allows us to target, for example, the eigenvectors based on their localization properties ͑e.g., states localized at a given surface or interface͒. We also show that the method scales linearly with system size.