Equation of motion method has proven efficient for electronic structure calculations of very large systems, i.e. containing several million atoms. In this work, we redesign its previously published implementation and hereby release a revised software tool, EQMO, now capable of solving a crystalline TiO2 test sample of nearly a quarter of a billion atoms on NEC SX-Aurora TSUBASA vector computer. The legacy code has been rewritten in modern free-form Fortran, and the main developments include MPI support and optimisations for parallel execution.
Journal reference of previous version: Marek T. Michalewicz, Herbert B. Shore, N. Tit, J.W. Halley, Equation of motion method for the electronic structure of disordered transition metal oxides, Comput. Phys. Commun. 71 (1992) 222–234.
Does the new version supersede the previous version?: Yes
Reasons for the new version: Major revision
Summary of revisions: The legacy Fortran code has been rewritten in modern free-form Fortran. The OpenMP support has been replaced with OpenMPI suitable for NEC SX-Aurora TSUBASA architecture. The sequential and MPI versions can be built independently to produce two separate binary files for both x86_64 CPU and NEC vector computer. The program has been developed and tested with GNU Fortran and NEC Fortran compilers.
Nature of problem: Electronic structure calculation of a large system, i.e. containing several million atoms, is a computationally demanding task. The problem is to determine electronic properties of solid state systems in an efficient manner. The program, at its current development stage, is capable of calculating electronic properties (density of electronic states) of rutile TiO2 structure distorted by point defects, and is intended to be further developed towards treating a wide range of crystalline systems.
Solution method: EQMO software tool is an equation of motion implementation designed to determine electronic structure (density of electronic states) of large-scale crystalline systems. The solution method is based on solving the Schrödinger equation with a tight-binding Hamiltonian, and its physical and mathematical foundations remain unchanged with respect to the previous release. For an explicit formalism with elaborate description, the reader is referred to the literature referenced below [1,2,3,4,5,6,7,8,9,10], and in particular – to the journal reference of the previous implementation along with the supplemented dataset [5]. The program is able to perform a benchmark on a TiO2 sample of nearly a quarter of a billion atoms on NEC SX-Aurora TSUBASA vector computer, and its functionality can be further expanded.
References
[1]
J.W. Halley, Phys. Rev. B 36 (1987) 6640.
[2]
J.W. Halley, M.T. Michalewicz, N. Tit, Phys. Rev. B 41 (1990) 10165.
[3]
J.W. Halley, M. Kozlowski, M. Michalewicz, W. Smyrl, N. Tit, Surf. Sci. 256 (1991) 397–408.
Marek T. Michalewicz, Herbert B. Shore, N. Tit, J.W. Halley, Comput. Phys. Commun. 71 (1992) 222–234.
[6]
Nacir Tit, J.W. Halley, Marek T. Michalewicz, H. Shore, Appl. Surf. Sci. 65/66 (1993) 246–251.
[7]
Marek T. Michalewicz, Comput. Phys. Commun. 79 (1994) 13–23.
[8]
Marek T. Michalewicz, Mark Priebatsch, Parallel Comput. 21 (1995) 853–870.
[9]
M.T. Michalewicz, Roger Brown, in: Computational Chemistry and Chemical Engineering, World Scientific, ISBN 978-981-4545-80-8, 1996, pp. 301–313.
[10]
Marek T. Michalewicz, Per Nyberg, Aust. J. Phys. 52 (5) (1999) 919–927.
Section snippets
Acknowledgement
This work has been supported by Interdisciplinary Centre for Mathematical and Computational Modelling, University of Warsaw (ICM UW).
Declaration of Competing Interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
