Recent developments in density functional theory (DFT) methods applicable to studies of large periodic systems are outlined. During the past three decades, DFT has become an essential part of computational materials science, addressing problems in materials design and processing. The theory allows us to interpret experimental data and to generate property data (such as binding energies of molecules on surfaces) for known materials, and also serves as an aid in the search for and design of novel materials and processes. A number of algorithmic implementations are currently being used, including ultrasoft pseudopotentials, efficient iterative schemes for solving the one-electron DFT equations, and computationally efficient codes for massively parallel computers. The first part of this article provides an overview of plane-wave pseudopotential DFT methods. Their capabilities are subsequently illustrated by examples including the prediction of crystal structures, the study of the compressibility of minerals, and applications to pressure-induced phase transitions. Future theoretical and computational developments are expected to lead to improved accuracy and to treatment of larger systems with a higher computational efficiency.

The application of gradient-corrected exchange-correlation functionals in total-energy calculations using a plane-wave basis set is discussed. The usual form of the exchange-correlation potential includes gradients whose calculation requires the use of a high-quality representation of the density which is computationally expensive in both memory and time. These problems may be overcome by defining an exchange-correlation potential for the discrete set of grid points consistent with the discretized form of the exchange-correlation energy that is used in Car-Parrinello-type total-energy calculations. This potential can be calculated exactly on the minimum fast-Fourier-transform grid and gives improved convergence and stability as well as computational efficiency.First-principles total-energy calculations based on density-functional theory' have become the major theoretical tool in solid-state physics, surface science, and molecular physics. Pseudopotential calculations using a planewave basis set and a Car-Parrinello approach to energy minimization ' have become increasingly important since this allows use to be made of the fast Fourier transform (FFT). Although the local-density approximation (LDA) to exchange and correlation gives a good description of many solid-state properties, for many applications it appears to be essential to go beyond the LDA by including gradient corrections. This is particularly important where accurate molecular bonding energies are required as in, for example, dissociative chemisorption. For bulk properties the need for gradient corrections is less clear although some improvements over LDA have been reported in calculations for semiconductors and transition metals. Unfortunately, the currently popular generalized gradient approximations (GGA) to the exchange-correlation energy functional (such as that of Perdew and Wang or Becke and Perdew ) give rise to potentials which are rapidly varying functions near to ion cores as has been noted previously in the context of pseudopotential generation. ' Because of this, and in order to calculate the required gradients accurately, a large number of plane waves are needed to represent these exchangecorrelation potentials accurately. In this paper it is pointed out that the exchange-correlation energy is, in practice, invariably approximated. It is shown that it is possible to construct an exchange-correlation potential which is consistent with this approximate form of the exchange-correlation energy and which can be calculated exactly much more efficiently than the conventional exchange-correlation potential.First recall the use of FFT's in Car-Parrinello-type totalenergy calculations. ' This makes use of the fact that the kinetic energy and Hartree energy/potential are easily calculated in reciprocal space (the Hartree potential, for example, becomes a simple product in reciprocal space) while the electron-ion potential energy is easily calculated in real space since the required integrals can be performed exactly as sums over the points of the m...

We have performed plane-wave pseudopotential density-functional theory calculations on the stoichiometric and reduced TiO 2 ͑110͒ surface, the 2ϫ1 and 1ϫ2 reconstructions of the surface formed by the removal of bridging-oxygen atoms, and on the oxygen vacancy in the bulk. The effect of including spin polarization is investigated, and it is found to give a qualitatively different electronic structure compared with a spin-paired description. In the spin-polarized solutions, the excess electrons generated by oxygen reduction occupy localized band-gap states formed from Ti (3d) orbitals, in agreement with experimental findings. In addition, the inclusion of spin polarization substantially lowers the energy of all the systems studied, when compared with spin-paired solutions. However, spin-polarization does not change the relative stability of the two reconstructions, which remain energetically equivalent. ͓S0163-1829͑97͒02724-0͔

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First-principles calculations based on density functional theory and the pseudopotential method have been used to investigate the influence of gradient corrections to the standard LDA technique on the equilibrium structure and energetics of rutile TiO 2 and SnO 2 perfect crystals and their (110) surfaces.We find that gradient corrections increase the calculated lattice parameters by roughly 3 %, as has been found for other types of material. Gradient corrections give only very minor changes to the equilibrium surface structure, but reduce the surface energies by about 30 %.

We show that plane wave ultrasoft pseudopotential methods readily extend to the calculation of the structural properties of lanthanide and actinide containing compounds. This is demonstrated through a series of calculations performed on UO, UO2, UO3, U3O8, UC2, alpha-CeC2, CeB6, CeSe, CeO2, NdB6, TmOI, LaBi, LaTiO3, YbO, and elemental Lu.

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