Graphics Processing Unit acceleration of the Random Phase Approximation in the projector augmented wave method

Abstract

The Random Phase Approximation (RPA) for correlation energy in the gridbased projector augmented wave (gpaw) code is accelerated by porting to the Graphics Processing Unit (GPU) architecture. The acceleration is achieved by grouping independent vectors/matrices and transforming the implementation from being memory bound to being computation/latency bound. With this approach, both the CPU and GPU implementations have been enhanced. We tested the GPU implementation on a few representative systems: molecules (O 2 ), bulk solids (Li 2 O and MoO 3 ) and molecules adsorbed on metal surfaces (N 2 /Ru(0001) and CO/Ni(111)). Improvements from 10× to 40× have been achieved (8-GPUs versus 8-CPUs) . A realistic RPA calculation for CO/Ni(111) surface can be finished in 5.5 hours using 8 GPUs. It is thus promising to employ non-self-consistent RPA for routine surface chemistry simulations.

Random Phase Approximation for Periodic Systems Employing Direct Coulomb Lattice Summation

“…Published work evaluates RPA correlation energies in the space representation, eq , reciprocal space representation, , or using particle–hole representations. , Superoperators and their supermatrix representations have a long tradition in propagator theory. , The supermatrix formalism in terms of orbitals was also presented for related approaches, for example, for the RPA-renormalized many-body perturbation theory and the GW method …”

“…In terms of accuracy, major benefits of RPA are the parameter-free inclusion of dispersive long ranging interactions and the nondivergent behavior for small gap systems and metals. RPA has been extensively tested for small systems, ,− and unit cells − and RPA data of more complex systems − were published in the last years (see also the citations in refs , , and ). In summary, relative energies of conformers, molecular equilibrium structures, lattice constants, bulk moduli, and reaction energies improve in comparison to semilocal and hybrid DFT approximations though binding energies are underestimated compared to highly accurate reference data, and bond dissociation can exhibit nonphysical features, as often demonstrated for diatomics.…”

“…Contemporary work on ACFD-RPA methods based on plane waves can be found in refs − . RPA subject to periodic boundary conditions (PBC) is also part of implementations, which use projector augmented plane waves (PAW), grid-based PAW, and orbital basis sets of Gaussian-type functions (GTF) mixed with grid-based auxiliary plane waves or with a grid-free analytical Fourier-transform variant . These methods make use of RI in the plane wave basis and thus scale at most as in the number of FLOP.…”

Harnessing the Power of Multi-GPU Acceleration into the Quantum Interaction Computational Kernel Program

“…The power of using multiple GPUs has been harnessed into a range of traditional computational chemistry tools, − including a range of ab initio electronic structure software packages. − However, among these are only a few Gaussian function based quantum chemistry codes for mean-field Hartree–Fock (HF) and density functional theory (DFT) calculations. − ,,− …”

GPU acceleration of all-electron electronic structure theory using localized numeric atom-centered basis functions

“…The feasibility of GPU-accelerated electronic structure calculations was demonstrated in works by Ufimtsev and Martínez [40,41,42,43] which would form the basis for the TeraChem electronic structure package [44], as well as by Yasuda using the Gaussian package [45,46]. Since then, a number of electronic structure packages have incorporated GPU acceleration, including ABINIT [47], ADF [48], BigDFT [49,50], CP2K [51], GPAW [52,53,54], LS3DF [55], octopus [56,57,58], ONETEP [59], PEtot (now PWmat) [60,61,62,63], Q-Chem [64,65,15], Quantum ESPRESSO [66,67], RMG [68,69], VASP [70,71,72,73], and FHI-aims (this work). Development cost can be alleviated by using dropin GPU-accelerated libraries such as cuBLAS [74], cuFFT [75], Thrust [76], ELPA [77,78,79], and MAGMA [80,81,82]…”