Implementation of Spin-Orbit Couplings in Linear-Scaling Density Functional Theory

Key Personnel

PI/Co-Is: Dr. José María Escartín Esteban (University of Cambridge), Dr. Nicholas D.M. Hine (University of Warwick), Prof. Mike C. Payne (University of Cambridge)

Technical: Dr José María Escartín Esteban (University of Cambridge)

Project summary

Spin-Orbit Coupling (SOC) is a relativistic quantum-mechanical effect resulting from the interaction between the spin and orbital angular momentum of a particle. It has crucial effects on the electronic bandstructure of many technologically-relevant materials. While the underlying physics of how to implement it in calculations is well established, this functionality was not available in any linear-scaling, high-accuracy Density Functional Theory (DFT) package. In this project we implemented Spin-Orbit Couplings in a linear-scaling DFT code, ONETEP. This will significantly extend the range of materials that the linear-scaling code can describe accurately, and will lead to an enlargement of its user base.

Achievement of objectives

This project had four objectives:

1. Implementation of new capability to perform electronic structure calculations including Spin-Orbit Couplings (SOC) for energy and forces.
2. Validation of the parallel efficiency and scaling of Non-Collinear Magnetism (NCM)/SOC.
3. Dissemination activities
4. Integration of fully relativistic SOC with theoretical spectroscopy ('Advanced SOC')

The main objective of the project, after which it was named, was achieved. Thanks to this project, ONETEP can incorporate Spin-Orbit Couplings in the calculation of bandstructures. The project proposal described eight success metrics for this objective:

1. Implementation and documentation of scalar ZORA (Zeroth Order Regular Approximation to the Dirac equation).
2. Implementation and documentation of perturbative SOC on top of scalar ZORA.
3. Implementation of Non-Collinear Magnetism (NCM).
4. New code enabling the input and processing of fully relativistic pseudopotentials.
5. Creation and integration of a new module for fully relativistic, on-site spin-orbit coupling terms.
6. Benchmark vs CASTEP and Quantum Espresso of ZORA and spin-orbit splittings.
7. Production of new tests for the quality check suite covering all new functionality.
8. Documentation for new users on how to perform NCM and fully relativistic SOC calculations on ARCHER and elsewhere.

Of these metrics, the implementations (a) and (b) of SOC corrected by ZORA were completed, and this was benchmarked against the ABINIT software instead of the CASTEP and Quantum Espresso packages expected in metric (f). The rest of the metrics relate to a second, self-consistent implementation of SOC, based on NCM (c), which was not completed due to the sheer amount of work that it required. It should be noted that the SOC approach successfully implemented in ONETEP accurately describes SOC for most of the applications where its use is envisioned, and is expected to provide qualitatively correct descriptions even for the materials where the heaviest elements are present, where enhanced quantitative accuracy would require the self-consistent method.

Objectives (2) and (4) relied on the NCM-based method for computing SOC, and therefore could not be attained.

Objective (3), dissemination, was also left aside in order to focus on the implementation work required to complete (1). While we could have disseminated the implementation of perturbative SOC couplings, it made more sense to wait until the self-consistent SOC implementation was completed, since this second method will support simulations with SOC on a broader range of materials.

Summary of the software

ONETEP (Order-N Electronic Total Energy Package) is a state-of-the-art Density Functional Theory code specifically developed to simulate large physical systems in linear-scaling computational effort, while retaining the accuracy and systematic convergence with respect to basis size that have made traditional cubic-scaling plane wave codes so successful. The code is under active development by academics, researchers and research students from the universities of Cambridge, Southampton and Warwick, and Imperial College London.

ONETEP is widely used in the UK and internationally both by industry and by academics in a variety of research fields. It can be obtained by licence via Cambridge Enterprise or as part of the Materials Studio Package distributed by BIOVIA, a wholly owned subsidiary of Dassault Systèmes. See the ONETEP website, www.onetep.org, for details of licensing.

On ARCHER, multiple versions of ONETEP (including the last two stable releases) are available to licensed users as modules. Examples of job submission scripts and compilation details can be found at https://www.archer.ac.uk/documentation/software/onetep/. The code is already heavily used on ARCHER, where users run the code for applications ranging from biological systems such as proteins and DNA to inorganic nanomaterials such as amorphous nanoparticles and catalyst nanotubes.

Enhanced stability of the software

Before the start of this project, for some months, continuous integration runs of the development version of ONETEP had been showing some instability when ONETEP had been compiled with gfortran, with occasional unexplained crashes that were leaving traces evidencing failures during unidentified library calls.

As part of the eCSE project, an auxiliary module with interfaces to all BLAS/LAPACK and BLACS/ScaLAPACK procedures used in ONETEP was developed. This module was then systematically USEd in all the subprograms containing calls to those libraries. This led to the identification of a number of related bugs (wrong argument types, incompatible INTENTs, etc.), which were all fixed.

When these fixes were committed, ONETEP gfortran-compiled CI runs became stable, no longer showing any unidentified library crashes.

While these improvements did not bring an enhanced performance in terms of faster code for users, they did mean that users would no longer risk losing computational resources due to crashes.

Scientific Benefits

Spin-Orbit Coupling (SOC) plays a major role in the quantum-mechanical description of solids, since it is often the cause of the splitting of energy bands at or near points in k-space of high symmetry. Since SOC effects are particularly prevalent in heavier elements, it must be accounted for in the theoretical and computational studies of many materials that are currently the object of active research, ranging from CdSe nanoparticles to organometallic perovskites.

There is a growing interest in the theoretical and computational study of these materials, including transport calculations and theoretical spectroscopy, and leading to device modelling, a field in which electronic structure calculations are playing an ever-increasing role. These applications require accurate knowledge and understanding of the band structures of materials, for which SOC is essential.

To conclude, current experimental techniques are very powerful, but understanding their results is becoming increasingly difficult. SOC-enabled ONETEP will provide simulations that will go hand-in-hand with experiments in the above-mentioned fields, helping a range of scientific communities to interpret the physical phenomena they observe in materials containing heavier elements (third row and beyond of the Periodic Table). In particular, large-scale, realistic models of nanostructured forms of these materials can only be simulated on leadership HPC facilities such as ARCHER. To make optimal use of these facilities, simulation packages must include all relevant physical effects and display excellent scaling both in terms of simulated system size and number of parallel cores. ONETEP offers a unique opportunity to provide all these strengths in one package.