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Register a new userThe PseudoDojo: Training and grading a 85 element optimized norm-conserving pseudopotential table
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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 norm- conserving 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. ...
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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.
We report Hartree-Fock (HF) based pseudopotentials suitable for plane-wave calculations. Unlike typical effective core potentials, the present pseudopotentials are finite at the origin and exhibit rapid convergence in a plane-wave basis; the optimized pseudopotential method [A. M. Rappe et. al, Phys. Rev. B 41 1227--30 (1990)] improves plane-wave convergence. Norm-conserving HF pseudopotentials are found to develop long-range non-Coulombic behavior which does not decay faster than 1/r, and is non-local. This behavior, which stems from the nonlocality of the exchange potential, is remedied using a recently developed self-consistent procedure [J. R. Trail and R. J. Needs, J. Chem. Phys. 122, 014112 (2005)]. The resulting pseudopotentials slightly violate the norm conservation of the core charge. We calculated several atomic properties using these pseudopotentials, and the results are in good agreement with all-electron HF values. The dissociation energies, equilibrium bond lengths, and frequency of vibrations of several dimers obtained with these HF pseudopotentials and plane waves are also in good agreement with all-electron results.
We show that efficient norm-conserving pseudopotentials for electronic structure calculations can be obtained from a polynomial Ansatz for the potential. Our pseudopotential is a polynomial of degree ten in the radial variable and fulfills the same smoothness conditions imposed by the Troullier-Martins method [Phys. Rev. B 43, 1993 (1991)] where pseudopotentials are represented by a polynomial of degree twenty-two. We compare our method to the Troullier-Martins approach in electronic structure calculations for diamond and iron in the bcc structure and find that the two methods perform equally well in calculations of the total energy. However, first and second derivatives of the total energy with respect to atomic coordinates converge significantly faster with the plane wave cutoff if the standard Troullier-Martins potentials are replaced by the pseudopotentials introduced here.
Norm-conserving pseudopotentials are used by a significant number of electronic-structure packages, but the practical differences among codes in the handling of the associated data hinder their interoperability and make it difficult to compare their results. At the same time, existing formats lack provenance data, which makes it difficult to track and document computational workflows. To address these problems, we first propose a file format (PSML) that maps the basic concepts of the norm-conserving pseudopotential domain in a flexible form and supports the inclusion of provenance information and other important metadata. Second, we provide a software library (libPSML) that can be used by electronic structure codes to transparently extract the information in the file and adapt it to their own data structures, or to create converters for other formats. Support for the new file format has been already implemented in several pseudopotential generator programs (including ATOM and ONCVPSP), and the library has been linked with Siesta and Abinit, allowing them to work with the same pseudopotential operator (with the same local part and fully non-local projectors) thus easing the comparison of their results for the structural and electronic properties, as shown for several example systems. This methodology can be easily transferred to any other package that uses norm-conserving pseudopotentials, and offers a proof-of-concept for a general approach to interoperability.
A new method is presented for obtaining all-electron results from a pseudopotential calculation. This is achieved by carrying out a localised calculation in the region of an atomic nucleus using the embedding potential method of Inglesfield [J.Phys. C {bf 14}, 3795 (1981)]. In this method the core region is emph{reconstructed}, and none of the simplifying approximations (such as spherical symmetry of the charge density/potential or frozen core electrons) that previous solutions to this problem have required are made. The embedding method requires an accurate real space Green function, and an analysis of the errors introduced in constructing this from a set of numerical eigenstates is given. Results are presented for an all-electron reconstruction of bulk aluminium, for both the charge density and the density of states.
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