Efficient self-consistency for magnetic tight binding

Tight binding can be extended to magnetic systems by including an exchange interaction on an atomic site that favours net spin polarisation. We have used a published model, extended to include long-ranged Coulomb interactions, to study defects in iron. We have found that achieving self-consistency using conventional techniques was either unstable or very slow. By formulating the problem of achieving charge and spin self-consistency as a search for stationary points of a Harris–Foulkes functional, extended to include spin, we have derived a much more efficient scheme based on a Newton–Raphson procedure. We demonstrate the capabilities of our method by looking at vacancies and self-interstitials in iron. Self-consistency can indeed be achieved in a more efficient and stable manner, but care needs to be taken to manage this. The algorithm is implemented in the code plato.Program summaryProgram title:platoCatalogue identifier: AEFC_v2_0Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEFC_v2_0.htmlProgram obtainable from: CPC Program Library, Queenʼs University, Belfast, N. IrelandLicensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.htmlNo. of lines in distributed program, including test data, etc.: 228 747No. of bytes in distributed program, including test data, etc.: 1 880 369Distribution format: tar.gzProgramming language: C and PERLComputer: Apple Macintosh, PC, Unix machinesOperating system: Unix, Linux, Mac OS X, Windows XPHas the code been vectorised or parallelised?: Yes. Up to 256 processors testedRAM: Up to 2 Gbytes per processorClassification: 7.3External routines: LAPACK, BLAS and optionally ScaLAPACK, BLACS, PBLAS, FFTWCatalogue identifier of previous version: AEFC_v1_0Journal reference of previous version: Comput. Phys. Comm. 180 (2009) 2616Does the new version supersede the previous version?: YesNature of problem: Achieving charge and spin self-consistency in magnetic tight binding can be very difficult. Our existing schemes failed altogether, or were very slow.Solution method: A new scheme for achieving self-consistency in orthogonal tight binding has been introduced that explicitly evaluates the first and second derivatives of the energy with respect to input charge and spin, and then uses these to search for stationary values of the energy.Reasons for new version: Bug fixes and new functionality.Summary of revisions: New charge and spin mixing scheme for orthogonal tight binding. Numerous small bug fixes.Restrictions: The new mixing scheme scales poorly with system size. In particular the memory usage scales as number of atoms to the power 4. It is restricted to systems with about 200 atoms or less.Running time: Test cases will run in a few minutes, large calculations may run for several days.