A new method for generating and using first-principles pseudopotentials is developed to treat explicitly the nonlinear exchange and correlation interaction between the core and the valence charge densities. Compared to existing potentials, the new scheme leads to significant improvement in the transferability of the potential. In particular, the spinpolarized configurations are well described with a single potential. The need for separate spin-up and spin-down ionic pesudopotentials is, thus, eliminated. The method can easily be implemented with minimal increase in computational effort. Results for both atoms and solids are demonstrated.

The zinc-blende (ZB) and wurtzite (W) structures are the most common crystal forms of binary octet semiconductors. In this work we have developed a simple scaling that systematizes the T=O energy difference bE~z a between W and ZB for all simple binary semiconductors. We have first calculated the energy difference hE "za( AB) for A1N, GaN, InN, A1P, A1As, GaP, GaAs, ZnS, ZnSe, ZnTe, CdS, C, and Si using a numerically precise implementation of the first-principles local-density formalism (LDF), including structural relaxations. We then find a linear scaling between AE~"za(AB) and an atomistic orbital-radii coordinate R( A, B) that depends only on the properties of the free atoms A and B making up the binary compound AB. Unlike classical structural coordinates (electronegativity, atomic sizes, electron count), R is an orbital-dependent quantity; it is calculated from atomic pseudopotentials.The good linear fit found between hE za and R {rms error of -3 meV/atom) permits predictions of the W -ZB energy difference for many more AB compounds than the 13 used in establishing this fit. We use this model to identify chemical trends in hE~z a in the IV-IV, III-V, II-VI, and I-VII octet compounds as either the anion or the cation are varied. W'e further find that the ground state of Mg Te is the NiAs structure and that CdSe and HgSe are stable in the ZB form. These compounds were previously thought to be stable in the W structures.

We demonstrate a cluster expansion technique that is capable of accurately predicting formation energies in binary substitutional systems "ven for those with large atomic relaxations. Conventional cluster expansions converge rapidly only in the absence of atomic relaxations, and they fail for 1ongperiod lattice-mismatched superlattices. When combined with first-principles total-energy methods, our method allows for very fast calculations for structures containing hundreds or thousands of atoms. The convergence and effectiveness of the cluster expansion are enhanced in two ways. First, the expansion is recast into reciprocal space, which allows for the inclusion of all important pair interactions. Second, a reciprocal-space formulation for elastic strain energy is introduced, allowing accurate predictions for both long-and short-period superlattices. We illustrate the power of the method by performing a cluster expansion that requires total-energy calculations for only 12 simple input structures, with at most eight atoms per unit cell. We then correctly predict the formation energies of relaxed long-period superlattices, low-symmetry intermixed superlattices, structures with varied compositions, substitutional impurities, and a~1000 atom/cell simulation of the random alloy. For a lattice with N sites, the problem of finding the energies of the 2+ possible configurations can be exactly mapped into a Ising Hamiltonian: E(o) = Jp+ ) J;S,(o) + ) J;,S;(o)S~(cr) j&i + ) J, , I,S,(rr)S, (o)SI,(o) + for configuration o, where the J's are "interaction energies, " and the first summation is over all sites in the lattice, the second over all pairs of sites, the third over all triplets, and so on. The primary advantage of thecluster expansion is that the interaction energies J are the same for all configurations o. Thus, once the J's are known, the energy E(o) of any configuration can be calculated almost immediately by simply calculating the spin products and summing Eq. (1). Because the Ising representation of the energy can be calculated rapidly, and is also a linear function of the spin products, one can readily (i) apply linear programming techniques to find ground-state structures P, (ii) use statistical-mechanics techniques (Monte Carlo and cluster variation methods) to calculate phase diagrams, ii i~a nd (iii) calculate the energy of an arbitrarily complex configuration.

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