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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 atoxnic wave functions beyond a chosen radius x,. Moreover, logarithmic derivatives of real and pseudo wave functions and their first energy derivatives agree for r &r, guaranteeing excellent transferability of the pseudopotentials. Pseudopotentials were originally introduced to simplify electronic structure calculations by eliminating the need to include atomic core states and the strong potentials responsible for binding them. ' Two roughly distinct lines of recent development are discernable: In one, ion pseudopotentials of enforced smoothness were empirically fitted to reproduce experimental energy bands. ' Consequently, wave functions were only approximately described. In the other, the orthogonalized-plane-wave (OPW) concept underlying the pseudopotential method was used to derive "first principles" pseudopotentials from atomic calculations. ' These latter potentials are generally "hard core" in character, that is, strongly repulsive at the origin. The resulting wave functions generally exhibit the correct shape outside the core region; however, they differ from the real wave functions by a normalization factor. 'It is the purpose of this Letter to demonstrate that the normalization and hard-core problems can be solved simultaneously, while also maximizing the range of systems in which a pseudopotential gives accurate results.The new family of energy-independent pseudopotentials introduced here have the following desirable properties:(1) Real and pseudo valence eigenvalues agree for a chosen "prototype" atomic configuration.(2) Real and pseudo atomic wave functions agree beyond a chosen "core radius" r,.(3) The integrals from 0 to r of the real and pseudo charge densities agree for r &r, for each valence state (norm conservation).(4) The logarithmic derivatives of the real and pseudo wave function and their first energy deriv atives agree for r &r,.Properties (3) and (4) are crucial for the pseudopotential to have optimum transferability among a variety of chemical environments in self-consistent calculations in which the pseudo charge density is treated as a real physical object. 'This approach starids in contrast to earlier OPW-like approaches" ' in which the normalized pseudo wave functions have to be orthogonalized to core states and renormalized in order to yield accurate charge densities outside the core region. ' Property (3) guarantees, through Gauss's theorem, that the electrostatic potential produced outside r, is identical for real and pseudo charge distributions. Property (4) guarantees that the scattering properties of the real ion cores are reproduced Mlitk rnininzum error as bonding or banding shifts eigenenergies away from the atomic levels. A central point of our approach is that these two aspects of transferability are related by a simple identity. The method permits the potentials to be intrinsically ...

A theory is presented for vacuum tunneling between a real solid surface and a model probe with a locally spherical tip, applicable to the recently developed "scanning tunneling microscope. " Calculations for 2&& 1 and 3& 1 reconstructions of Au(110) are in excellent agreement with recent experimental results, if an effective radius of curvature of 9 g is assumed for the tip.

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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 new formulation 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.2

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The widespread popularity of density functional theory has given rise to an extensive range of dedicated codes for predicting molecular and crystalline properties. However, each code implements the formalism in a different way, raising questions about the reproducibility of such predictions. We report the results of a community-wide effort that compared 15 solid-state codes, using 40 different potentials or basis set types, to assess the quality of the Perdew-Burke-Ernzerhof equations of state for 71 elemental crystals. We conclude that predictions from recent codes and pseudopotentials agree very well, with pairwise differences that are comparable to those between different high-precision experiments. Older methods, however, have less precise agreement. Our benchmark provides a framework for users and developers to document the precision of new applications and methodological improvements

First-principles calculations in crystalline structures are often performed with a planewave basis set. To make the number of basis functions tractable two approximations are usually introduced: core electrons are frozen and the diverging Coulomb potential near the nucleus is replaced by a smoother expression. The norm-conserving pseudopotential was the first successful method to apply these approximations in a fully ab initio way. Later on, more efficient and more exact approaches were developed based on the ultrasoft and the projector augmented wave formalisms. These formalisms are however more complex and developing new features in these frameworks is usually more difficult than in the norm-conserving framework. Most of the existing tables of normconserving pseudopotentials, generated long ago, do not include the latest developments, are not systematically tested or are not designed primarily for high accuracy. In this paper, we present our PseudoDojo framework for developing and testing full tables of pseudopotentials, and demonstrate it with a new table generated with the ONCVPSP approach. The PseudoDojo is an open source project, building on the AbiPy package, for developing and systematically testing pseudopotentials. At present it contains 7 different batteries of tests executed with ABINIT, which are performed as a function of the energy cutoff. The results of these tests are then used to provide hints for the energy cutoff for actual production calculations. Our final set contains 141 pseudopotentials split into a standard and a stringent accuracy table. In total around 70.000 calculations were performed to test the pseudopotentials. The process of developing the final table led to new insights into the effects of both the core-valence partitioning and the non-linear core corrections on the stability, convergence, and transferability of norm-conserving pseudopotentials. The PseudoDojo hence provides a set of pseudopotentials and general purpose tools for further testing and development, focusing of highly accurate calculations and their use in the development of ab initio packages. The pseudopotential files are available on the PseudoDojo web-interface www.pseudo-dojo.org in the psp8, UPF2, and PSML 1.1 formats.