The LSMS method has been implemented on various distributed memory massively parallel message passing platforms including Intel Paragons and CRAY T3Es, as well as on heterogeneous computing systems using PVM as the communication tool. Its ideal linear O[N]-scaling has been observed for system sizes up to 1024 atoms. This is the first time that O[N] scaling of a first principles method has been observed on a massively parallel computer for systems of this size. Continued O[N] scaling is expected for even larger systems as more powerful MPP’s become available or multiple parallel machines are coupled together.
The LSMS method has been applied to very large cell (256<N<1024) simulations of disordered alloys, bulk amorphous metals, and magnetic inhomogeneities in disordered alloys. It has been used to understand the nature of charge correlation and magnetic moment correlation in random alloys. In the former case a new relationship has been discovered between charge transfer and the Madelung contribution to the total energy of random alloys, clarifying some area of recent controversy. The large cell spin-polarized calculation of disordered NiCu alloys has been used to understand the nature of magnetic moment inhomogeneities in these alloys and to provide the first quantitative theory of the results of neutron scattering experiments of the magnetic scattering cross-section.
A major problem with the LSMS method is the assumption that the one-electron potential and charge density are spherically symmetric around each atom. This will pose serious limits on the application of the current LSMS code. In cases like allowing the atomic positions to relax and calculating the force on individual atoms, it is required to solve the quantum mechanical equation for one-electron potentials of general form (full potential). As the fundamental problems with full-potential multiple scattering theory have been solved in the early 90's, this restriction is readily to be removed. Nevertheless, the computational efforts involved in full-potential approach can be very intensive, which is part of the historical reason that electronic structure calculations using full-potential multiple scattering method are rarely seen in the literature. Fortunately, the new generation of MPP systems like CRAY-T3E offer significant improvement over the previous generation of MPP systems in terms of both hardware and software performance. The new version of the LSMS code will be able to perform electronic structure calculations for both spherical and non-spherical symmetric potentials, and will allow us to deal with such complex problems as electronic structures of amorphous alloys, grain boundaries and dislocation cores.
Researchers at PSC and Oak Ridge National Laboratory are joining their efforts in developing full-potential LSMS method. Some progress has been made recently and has been presented at American Physical Society (APS) March meeting at Los Angeles. The modules written in FORTRAN 90 for calculating full-potential multiple scattering matrices have been developed and are ready to use. These modules have been tested by the empty lattice band structure calculation. In the empty lattice test, electron is assumed to move under the influence of a constant potential in the 3-d space. The electronic states are sought that have periodic characteristics associated with a 3-d lattice. The empty lattice band structure calculation is a typical full-potential problem. The analytical solution to the electronic states of the problem is however trivial and has long been used to check the accuracy of the full-potential multiple scattering band structure calculation. We have developed a new algorithm to calculate the scattering matrices that avoids the expansion of the Voronoi cell truncation function, a procedure that introduces error and has been used by others. The result for the electronic structure indicates the error of our calculation is less than 0.01eV for a constant potential chosen to be -7.0eV.