D. R. Hamann

A very simple procedure to extract pseudopotentials from ab initio atomic calculations is presented. The pseudopotentials yield exact eigenvalues and nodeless eigenfunctions which agree with atomic wave functions beyond a chosen radius ${\mathcal{r}}_{c}$. Moreover, logarithmic derivatives of real and pseudo wave functions and their first energy derivatives agree for $\mathcal{r}>{\mathcal{r}}_{c}$ guaranteeing excellent transferability of the pseudopotentials.

We present a theory for tunneling between a real surface and a model probe tip, applicable to the recently developed ``scanning tunneling microscope.'' The tunneling current is found to be proportional to the local density of states of the surface, at the position of the tip. The effective lateral resolution is related to the tip radius R and the vacuum gap distance d approximately as [(2 \AA{})(R+d${)]}^{1/2}$. The theory is applied to the 2\ifmmode\times\else\texttimes\fi{}1 and 3\ifmmode\times\else\texttimes\fi{}1 reconstructions of Au(110); results for the respective corrugation amplitudes and for the gap distance are all in excellent agreement with experimental results of Binnig et al. if a 9-\AA{} tip radius is assumed. In addition, a convenient approximate calculational method based on atom superposition is tested; it gives reasonable agreement with the self-consistent calculation and with experiment for Au(110). This method is used to test the structure sensitivity of the microscope. We conclude that for the Au(110) measurements the experimental ``image'' is relatively insensitive to the positions of atoms beyond the first atomic layer. Finally, tunneling to semiconductor surfaces is considered. Calculations for GaAs(110) illustrate interesting qualitative differences from tunneling to metal surfaces.

Recent developments have enabled pseudopotential methods to reproduce accurately the results of all-electron calculations for the self-consistent electronic structure of atoms, molecules, and solids. The properties of these potentials are discussed in the context of earlier approaches, and their numerous recent successful applications are summarized. While the generation of these pseudopotentials from all-electron atom calculations is straightforward in principle, detailed consideration of the differences in physics of various groups of atoms is necessary to achieve pseudopotentials with the most desirable attributes. One important attribute developed here is optimum transferability to various systems. Another is the ability to be fitted with a small set of analytic functions useful with a variety of wave-function representations. On the basis of these considerations, a consistent set of pseudopotentials has been developed for the entire Periodic Table. Relativistic effects are included in a way that enables the potentials to be used in nonrelativistic formulations. The scheme used to generate the numerical potentials, the fitting procedure, and the testing of the fit are discussed. Representative examples of potentials are shown that display attributes spanning the set. A complete tabulation of the fitted potentials is given along with a guide to its use.

Fully nonlocal two-projector norm-conserving pseudopotentials are shown to be compatible with a systematic approach to the optimization of convergence with the size of the plane-wave basis. A reformulation of the optimization is developed, including the ability to apply it to positive-energy atomic scattering states and to enforce greater continuity in the pseudopotential. The generalization of norm conservation to multiple projectors is reviewed and recast for the present purposes. Comparisons among the results of all-electron and one- and two-projector norm-conserving pseudopotential calculations of lattice constants and bulk moduli are made for a group of solids chosen to represent a variety of types of bonding and a sampling of the periodic table.