Designed nonlocal pseudopotentials for enhanced transferability

Abstract

A new pseudopotential generation method is presented which significantly improves transferability. The method exploits the flexibility contained in the separable Kleinman-Bylander form of the nonlocal pseudopotential [Phys. Rev. Lett. 48, 1425(1982]. By adjusting the functional form of the local potential, we are able to improve the agreement with all-electron calculations. Results are presented for the Ca atomic pseudopotential. Configuration testing, logarithmic derivatives and chemical hardness all confirm the accuracy of these new pseudopotentials.The pseudopotential (PS) approximation, or the separation of electrons into core and valence based on their level of participation in chemical bonding, lies at the heart of most modern electronic structure calculations. The original PS formalism 1 grew out of the orthogonalized plane-wave approach. 2 The atomic PS replaces the nuclear Coulomb potential plus core electrons, thus simplifying the original system of differential equations. Adopting the PS approximation may introduce some unphysical results if the PSs are not constructed judiciously. The accuracy of the PS, or its transferability, may be gauged by its ability to reproduce the results of allelectron (AE) calculations in a variety of atomic environments. Most transferability testing has centered on configuration testing, characterization of the scattering properties using logarithmic derivatives, and, more recently, chemical hardness. 3 The earliest PSs generated for use in density-functional theory calculations replaced the strongly attractive Coulombic potential near the origin with a weaker local potential, and core electrons were eliminated from the calculations. 4 In this approach, approximate agreement between PS and AE eigenvalues and logarithmic derivatives was achieved for many elements. However, first row non-metals and first-row transition metals could not be accurately described by these PSs.To improve PS transferability, more complicated (and more flexible) semilocal (SL) PSs were designed 5 with a different spherically symmetric potential for each angular momentum. This added flexibility permits the enforcement of the norm-conservation condition at the reference energy, ε i , for R greater than the core radius, r c d dεwhere φ AE i ( r ) and φ PS i ( r ) are the AE and PS KohnSham eigenstates for the state i. Including this criterion into PS generation greatly improves transferability.Incorporating norm-conservation makes it possible to have exact agreement between the AE and PS eigenvalues and wave functions outside r c for one electronic reference state (RS). 5 However, the corresponding singleparticle differential equation for a PS constructed with this method is more complicated because of the angular momentum projection. Expressing the SL PSs within a plane-wave basis requires the computation of V ( G, G ′ ) instead of just V ( G − G ′ ) where G is a reciprocal lattice vector. This results in a huge memory expense.The fully separable nonlocal (NL) Kleinman-Bylander PS form 6 dramaticall...

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