Source-linked AI summary
Generation of Projector Augmented-Wave atomic data: a 71 elements validated table in the XML format
François Jollet, Marc Torrent, Natalie Holzwarth
TL;DR
PAW atomic datasets require generation procedures that balance accuracy, transferability, and efficiency across elements and bulk solids. The paper reviews these procedures, creates and validates a 71-element XML table, and proposes a rescaled delta-factor criterion to improve cross-element comparisons.
Problem
PAW atomic-data generation involves diverse schemes and known difficulty in achieving efficient, transferable datasets, while the delta factor can depend strongly on element properties and fitted equation-of-state values.
Method
The paper reviews PAW generation schemes, uses ATOMPAW to build a 71-element JTH table, and evaluates it with the delta and rescaled delta_1 factors.
Results
The JTH table has a mean delta value of 0.4 meV, and gives smaller delta and delta_1 values than PAW 0.9 and GBRV-v1 at all tested cutoffs.
Takeaways & Limitations
The JTH table provides a validated PAW dataset with reported accuracy, transferability, and bulk-solid efficiency across its tested elements and cutoffs.
Takeaways & Limitations
The modified RRKJ scheme was not used because it required further testing, and the delta factor is sensitive to fitted V0, B, and B’ values for some elements.
Abstract
from arXiv · showhide
A Projector Augmented Wave (PAW) atomic data file is needed to be generated for each element, and plays in the PAW method the role of the pseudopotential file for norm-conserving (NC) or ultra-soft (US) plane wave calculations. In this paper, we present a review on how to obtain these data as well as results concerning their accuracy, their transferability and their efficiency for bulk solids. Following \cite{Lejaeghere}, we propose a new criterium to test PAW atomic data and we provide a new table written in a XML format potentially readable by every PAW electronic structure code.
1. Introduction
PAW atomic data extend pseudopotential files with partial waves and projectors, making their generation a diverse and technically demanding task. The paper reviews generation schemes, introduces a 71-element XML table, and evaluates its accuracy, transferability, and bulk-solid efficiency.
- PAW uses a linear transformation to express all-electron wavefunctions through plane-wave pseudo-wavefunctions, atomic partial waves, and projectors.The PAW atomic data file must provide both all-electron and pseudo partial waves together with associated projectors.
- The diversity of PAW generation schemes and the difficulty of obtaining efficient, transferable atomic data make dataset generation tedious.Existing approaches include Blöchl, Vanderbilt, RRKJ, and implementations with compensation charges.
- The paper reviews available PAW atomic-data generation schemes and presents a new table covering 71 elements.The table is written in XML format and is intended to be potentially readable by every PAW electronic-structure code.
- The new table is assessed for accuracy, transferability, and efficiency in bulk solids.Validation uses the delta factor and a modified delta factor described in the paper.
2. General background and formalism
PAW data generation combines all-electron atomic calculations, pseudization of potentials and partial waves, projector construction, and treatment of core densities. Different schemes impose distinct numerical and physical choices, while compensation charges and implementation details affect the resulting formalism.
- 2. General background and formalism: PAW links all-electron and pseudo wavefunctions through a linear transformation involving partial waves and dual projector functions.Partial waves are equal outside augmentation spheres, while projectors provide the corresponding dual representation.
- 2. General background and formalism: The PAW Hamiltonian combines an effective local potential with a non-local projector term, and the atomic data file supplies the associated atomic quantities.These include partial waves, projectors, compensation charge, pseudo core density, and the pseudized nuclear-core Coulomb contribution.
- 2.1. All electron atomic calculations: Generation begins with an all-electron atomic calculation, partitions core and valence densities, and selects a finite partial-wave basis.The core density is treated as frozen, and two partial waves per angular momentum are usually chosen for ground-state calculations.
- 2.2. Potential pseudization: The local potential is pseudized so that the resulting potential matches the all-electron potential smoothly at a cutoff radius.Troullier–Martins, ultrasoft, and Bessel-based schemes are available; scheme choice can affect scattering properties and ghost-state formation.
- 2.3.1. The Vanderbilt scheme: The Vanderbilt scheme constructs pseudized partial waves and projectors from polynomial or RRKJ forms, with localized auxiliary functions determining the projector combinations.The construction is designed so the smooth functions satisfy the atomic PAW Hamiltonian conditions.
- 2.3.1. The Vanderbilt scheme: The modified RRKJ scheme targets continuous projector derivatives and controlled node counts but was not used because it required further testing.This marks a scope boundary of the current study’s Vanderbilt-type generation choices.
- 2.3.2. The Blöchl scheme: Blöchl’s scheme generates pseudo-basis functions using a shape function and matches logarithmic derivatives before forming and orthogonalizing projectors.The final basis and projector functions are obtained through Gram–Schmidt orthogonalization.
- 2.4. Core densities and unscrened potential: Core-density treatment pseudizes the core charge and unscreens the local potential, with compensation charges used to reproduce the all-electron charge multipole moments.Blöchl and Kresse–Joubert formulations differ in compensation-charge definitions and exchange-correlation treatment; including the compensation charge there can change physical results under some conditions.
3. PAW atomic data generation
PAW atomic data generation follows established pseudopotential steps, including functional and wave-equation selection, valence-state choice, basis construction, pseudization, and validation against atomic behavior and stability criteria.
- Each element begins with choosing an exchange-correlation functional and a scalar-relativistic wave equation.
- Semi-core states are generally included for transition metals and rare-earth materials, and may prevent ghost states even when physical conditions do not require them.
- A logarithmic all-electron grid accurately resolves the near-nucleus region, while cutoff radii are crucial for PAW efficiency.
- The partial-wave basis commonly uses two partial waves per angular momentum, increasing to three when conduction-band accuracy is important.
- Blöchl, Vanderbilt-polynomial, and RRKJ schemes can pseudize wavefunctions; RRKJ generally provides the best performance, while Blöchl may be accurate but inefficient.
- Accuracy and transferability are assessed through comparable amplitudes of partial waves, pseudized waves, and projectors, plus agreement of logarithmic derivatives with the all-electron problem.
- For local potentials, changing the pseudopotential scheme is often the effective cure for ghost states, with bessel choices requiring smaller matching radii and validation against AE valence energies.
4. PAW atomic data validation and efficiency
The authors validate ABINIT and a new 71-element JTH PAW table against all-electron reference calculations, using the delta factor and a renormalized delta1 factor to assess accuracy and efficiency. JTH achieves lower delta and delta1 values than PAW 0.9 and GBRV-v1, with good convergence at 20 Ha and useful performance at 15 Ha.
- Validation methodology: PAW accuracy is assessed by comparing equilibrium volumes and bulk moduli from solid-state calculations with all-electron reference results.The delta factor summarizes these equation-of-state differences across elements, while the reference data include equilibrium volume, bulk modulus, and its derivative.
- Validation methodology: A mean delta of 1.6 meV for 68 PAW 0.9 elements at 20 Ha and 40 Ha closely matches GPAW’s 1.8 meV, validating ABINIT and the Delta process.The comparison used the recommended k-point sampling, Fermi-Dirac broadening, and crystallographic data from the Delta package.
- JTH table: The new JTH table contains 71 PAW datasets for elements from H to Rn, excluding At and lanthanides except Lu.The datasets were generated with ATOMPAW from existing or newly prepared input files.
- JTH table: 0.4 meV is the JTH table’s mean delta, compared with 1.6–1.8 meV reported for other codes or PAW packages.The delta factor provides both element-wise accuracy measures and a mean value characterizing an entire atomic dataset.
- Delta1 factor: The delta factor can weight elements unevenly because equilibrium volumes and bulk moduli vary widely across the periodic table.A 0.76% volume deviation gives delta values of 0.39 meV for Cs and 9.14 meV for Os in PAW 0.9 calculations.
- Delta1 factor: Delta1 rescales delta to common reference values Vref = 30 Bohrs^3 and Bref = 100 GPa, enabling more balanced cross-element comparisons.The authors evaluate delta and delta1 at 12, 15, 20, and 40 Ha for JTH, PAW 0.9, and GBRV-v1.
- Comparative efficiency: JTH has lower delta and delta1 values than PAW 0.9 and GBRV-v1 at all tested cutoffs, with all three packages well converged at 20 Ha.The authors also report that JTH’s low values at 15 Ha are important for high-throughput calculations.
- Comparative efficiency: Excluding N and O, GBRV-v1 has delta = 1.484 meV; excluding H, N, and O, it has delta1 = 2.944 meV.The delta1 comparison treats elements with low and high equilibrium volumes and bulk moduli on an equal footing, highlighting questionable elements.
5. Conclusions
The study delivers a validated 71-element JTH PAW dataset with good accuracy and efficiency, distributed in XML for broad PAW-code readability and high-throughput use.
- The JTH table contains PAW atomic data for 71 elements and was validated against all-electron calculations using the ∆ and modified ∆1 factors.
- Its accuracy and efficiency compared with other packages make the JTH table a candidate for high-throughput calculations.
- The dataset is provided as XML files designed to be easily readable by all PAW codes and distributed through the ABINIT website.
Appendix A.
The appendix analyzes how the ∆ factor scales with material properties, including bulk modulus and equilibrium volume, under simplifying proportionality assumptions.
- The ∆ factor scales with the bulk modulus: if B_A = αB_C, then ∆_B ≃ α∆_C under the stated assumption.
- For equilibrium-volume dependence, the appendix considers elements with proportional reference volumes and equal bulk moduli and derivatives.
- Under these assumptions, each of the seven terms contributing to F is proportional to α^3.
- The appendix gives an example contribution to F_A(V_f) for n = 4 within this proportional-scaling analysis.