Accurate construction of transition metal pseudopotentials for oxides

We generate a series of Zr pseudopotentials and use them to calculate the properties of PbZrOs, in order to examine the relationship between pseudo-atomic properties and solid-state oxide results. We find that lattice constants and bond lengths within the oxide unit cell are quite sensitive to pseudopotential construction errors, and clear correlations emerge. These trends motivate our identification of two criteria for accurate transition metal pseudopotentials for use in oxide calculations, which are similar to the criteria for metal use. We find that both the preservation of all-electron tail norm and the preservation of all-electron ionization energy are necessary to give good lattice constants for oxides. INTRODUCTION Perovskites (oxides with chemical formula ABO3) are an important class of materials; many common minerals are perovskites, and ferroelectric perovskites such as PbZixTii_xO^ (PZT) have many industrial applications including sonar. The phase diagram of PZT has been extensively studied experimentally and theoretically. Recently a virtual crystal method was used to predict theoretically a compositional phase transition in this material [1]. The changes in structure between the tetragonal and rhombohedral phases of PZT are subtle and are sensitive to temperature, composition and pressure. This makes it a good industrial material, but also presents challenging problems in modeling this material theoretically. Density functional theory [2,3] (DFT) calculations have been widely used to study PZT and other perovskites with both the local density approximation (LDA) and generalized gradient approximation (GGA) for the exchange-correlation functional. Within DFT, one has a choice of using either all-electron or pseudopotential (PSP) methods. While the former are more accurate, they are much more computationally expensive; therefore many DFT studies of perovskites in recent years have been done using PSPs. CP582, Fundamental Physics of Ferroelectrics 2001, edited by H. Krakauer © 2001 American Institute of Physics 0-7354-0021-0/017$ 18.00 211 Downloaded 02 May 2005 to 165.123.34.86. Redistribution subject to AIP license or copyright, see http://proceedings.aip.org/proceedings/cpcr.jsp The absence of core electrons in the calculation and the reduced-cutoff planewave expansion of the PSP greatly reduce the computational cost of the solidstate calculation as compared those employing all-electron potentials. Modern PSP construction methods insure that the PSP agrees with the all-electron potential outside a specified core radius (rc) for a given reference configuration. A perfect PSP would be completely transferable, i.e. it would mimic the behavior of the all-electron nucleus and core potential in various local chemical environments, producing solid-state results identical to those of an all-electron calculation. In practice, the transformation of a real, physical all-electron system into an artificial one consisting of PSPs and valence electrons will often introduce errors in the calculation. This can be due to either inaccuracies in the wave function and PSP in the valence region in atomic configurations other than reference or to the omission of the wave function oscillations in the core region. Methods capable of generating transferable PSPs with small plane-wave cutoffs have been developed over the course of the past twenty years [4-10]. PSP DFT calculations involving transition metal elements have become widespread. Nevertheless, some fundamental questions regarding PSP transferability remain unresolved. While it is axiomatic that a PSP must preserve certain all-electron properties to be considered transferable, it is unclear which all-electron properties are crucial. Various criteria for comparing to all-electron results have been proposed, such as agreement between all-electron and PSP eigenvalues along with total energy differences, norm-conservation at the reference configuration and preservation of logarithmic derivatives at rc [4], and the correct chemical hardness matrix [11]. The agreement between all-electron and PSP eigenvalues and total energy differences are the criteria which are most often used and are generally considered when determining if a given PSP is transferable. However, no clear correlation has been firmly established between these criteria and solid-state results. Recently, we have discovered that solid-state transition metal lattice constants and bulk moduli are very sensitive to PSP error, with variations in the solid-state DFT results directly correlated to errors in the atomic properties of the PSP [12]. Extending the norm conservation concept of Hamann, Schliiter and Chiang [4], we have shown that errors in the norm of the wave function beyond rc in configurations other than the reference as well as total energy difference and eigenvalue errors affect solid-state results. Therefore, both the energy differences and wave function norms must be preserved for configurations other than reference in order to obtain correct solid-state properties. In this work we will examine PbZrOa (PZ), as a test case to determine the relationship between solid-state results and PSP error for perovskite oxides.