Many-core acceleration of the first-principles all-electron quantum perturbation calculations

Abstract The first-principles quantum perturbation theory, also called density-functional perturbation theory (DFPT), is the state-of-the-art formalism to directly link the experimental response properties of the materials with the quantum modeling of the electrons. Here in this work, we present an implementation of all-electron DFPT for massively parallel Sunway many-core architectures to accelerate DFPT calculation. We have paid special attention to the calculation of the response density matrix, the real-space integration of the response density as well as the response Hamiltonian matrix. We also employ the fast and massively parallel linear scaling scheme together with the load balance algorithm for the DFPT calculations to improve the scalability. Using the above approaches, the accurate first-principles quantum perturbation calculations can be extended over millions of cores.

[1]  Meng Zhang,et al.  Redesigning LAMMPS for Peta-Scale and Hundred-Billion-Atom Simulation on Sunway TaihuLight , 2018, SC18: International Conference for High Performance Computing, Networking, Storage and Analysis.

[2]  Matthias Scheffler,et al.  Lattice dynamics calculations based on density-functional perturbation theory in real space , 2016, Comput. Phys. Commun..

[3]  Mariana Rossi,et al.  All-electron, real-space perturbation theory for homogeneous electric fields: theory, implementation, and application within DFT , 2018, New Journal of Physics.

[4]  Superconductivity in diamond, electron–phonon interaction and the zero-point renormalization of semiconducting gaps , 2006 .

[5]  A. Zunger,et al.  Self-interaction correction to density-functional approximations for many-electron systems , 1981 .

[6]  R. Sternheimer,et al.  ELECTRONIC POLARIZABILITIES OF IONS FROM THE HARTREE-FOCK WAVE FUNCTIONS , 1954 .

[7]  Yu.,et al.  Linear-response calculations within the linearized augmented plane-wave method. , 1994, Physical review. B, Condensed matter.

[8]  David R. Bowler,et al.  Recent progress with large‐scale ab initio calculations: the CONQUEST code , 2006 .

[9]  Xavier Gonze,et al.  First-principles responses of solids to atomic displacements and homogeneous electric fields: Implementation of a conjugate-gradient algorithm , 1997 .

[10]  J. S. Binkley,et al.  Derivative studies in hartree-fock and møller-plesset theories , 2009 .

[11]  G. Kresse,et al.  Ab initio molecular dynamics for liquid metals. , 1993 .

[12]  Michael J. Frisch,et al.  Direct analytic SCF second derivatives and electric field properties , 1990 .

[13]  Bernard Delley,et al.  High order integration schemes on the unit sphere , 1996, J. Comput. Chem..

[14]  B. Delley,et al.  Analytic energy derivatives in the numerical local‐density‐functional approach , 1991 .

[15]  G. Scuseria,et al.  Efficient evaluation of analytic vibrational frequencies in Hartree-Fock and density functional theory for periodic nonconducting systems. , 2007, The Journal of chemical physics.

[16]  Xavier Gonze,et al.  Dynamical matrices, born effective charges, dielectric permittivity tensors, and interatomic force constants from density-functional perturbation theory , 1997 .

[17]  Stefano de Gironcoli,et al.  QUANTUM ESPRESSO: a modular and open-source software project for quantum simulations of materials , 2009, Journal of physics. Condensed matter : an Institute of Physics journal.

[18]  P. Pulay.  Convergence acceleration of iterative sequences. the case of scf iteration , 1980 .

[19]  Anders M.N. Niklasson.  Expansion algorithm for the density matrix , 2002 .

[20]  Takahito Nakajima,et al.  Massively parallel sparse matrix function calculations with NTPoly , 2017, Comput. Phys. Commun..

[21]  Jon Baker,et al.  The effect of grid quality and weight derivatives in density functional calculations , 1994 .

[22]  Rodríguez,et al.  Fast full-potential calculations with a converged basis of atom-centered linear muffin-tin orbitals: Structural and dynamic properties of silicon. , 1989, Physical review. B, Condensed matter.

[23]  Stefan Goedecker,et al.  Daubechies wavelets for linear scaling density functional theory. , 2014, The Journal of chemical physics.

[24]  Valéry Weber,et al.  Ab initio linear scaling response theory: electric polarizability by perturbed projection. , 2004, Physical review letters.

[25]  B. Johansson,et al.  Phonons and electron-phonon interaction by linear-response theory within the LAPW method , 2001 .

[26]  Matthias Scheffler,et al.  Efficient O(N) integration for all-electron electronic structure calculation using numeric basis functions , 2009, J. Comput. Phys..

[27]  Elisabeth Sjöstedt,et al.  Efficient linearization of the augmented plane-wave method , 2001 .

[28]  Peng Zhang,et al.  Towards Highly Efficient DGEMM on the Emerging SW26010 Many-Core Processor , 2017, 2017 46th International Conference on Parallel Processing (ICPP).

[29]  Chris-Kriton Skylaris,et al.  Introducing ONETEP: linear-scaling density functional simulations on parallel computers. , 2005, The Journal of chemical physics.

[30]  Matthias Scheffler,et al.  Ab initio molecular simulations with numeric atom-centered orbitals , 2009, Comput. Phys. Commun..

[31]  Stefano de Gironcoli,et al.  Phonons and related crystal properties from density-functional perturbation theory , 2000, cond-mat/0012092.

[32]  Strongly Correlated Impurity Band Superconductivity in Diamond: X-ray Spectroscopic evidence for upper Hubbard and mid-gap bands , 2004, cond-mat/0410296.

[33]  A. Tkatchenko,et al.  Resolution-of-identity approach to Hartree–Fock, hybrid density functionals, RPA, MP2 and GW with numeric atom-centered orbital basis functions , 2012, 1201.0655.

[34]  Xavier Andrade,et al.  Real-space grids and the Octopus code as tools for the development of new simulation approaches for electronic systems. , 2015, Physical chemistry chemical physics : PCCP.

[35]  R. Orlando,et al.  Ab initio analytical infrared intensities for periodic systems through a coupled perturbed Hartree-Fock/Kohn-Sham method. , 2012, The Journal of chemical physics.

[36]  Savrasov,et al.  Electron-phonon interactions and related physical properties of metals from linear-response theory. , 1996, Physical review. B, Condensed matter.

[37]  A. Becke.  A multicenter numerical integration scheme for polyatomic molecules , 1988 .

[38]  Stefano de Gironcoli,et al.  Reproducibility in density functional theory calculations of solids , 2016, Science.

[39]  Stefano de Gironcoli,et al.  Ab initio calculation of phonon dispersions in semiconductors. , 1991, Physical review. B, Condensed matter.

[40]  Samuel Williams,et al.  Exploiting Multiple Levels of Parallelism in Sparse Matrix-Matrix Multiplication , 2015, SIAM J. Sci. Comput..

[41]  B. Delley.  An all‐electron numerical method for solving the local density functional for polyatomic molecules , 1990 .

[42]  Nathaniel Raimbault,et al.  Anharmonic effects in the low-frequency vibrational modes of aspirin and paracetamol crystals , 2019, Physical Review Materials.

[43]  Robert A. van de Geijn,et al.  Anatomy of high-performance matrix multiplication , 2008, TOMS.