Efficient Computation of Hybrid and Screened Hybrid Functionals in Real-Space with Projection Operators*

The use of hybrid and screened hybrid functionals in Density Functional Theory (DFT) became popular as they allow to reduce the error between the calculated and experimentally measured properties. The calculation of the Fock exchange operator, required for those methods, is becoming a computationally prohibitive task with system size. An efficient approach, is to replace the explicit calculation of the Fock operator with its projection on the Hilbert sub-space that is spanned by the previous self-consistent field (SCF) occupied eigenvectors. It is possible to extend the method by projecting also on low lying empty eigenvectors to calculate also the empty eigenvalues. We have implemented this method¹ within the PARSEC^2,3 real-space code and combined it with efficient Poisson solvers⁴ and further hardware acceleration by Graphical Processing Units (GPUs) to achieve affordable hybrid calculations of atomistic structures with 1000 atoms on a single workstation⁵. We demonstrate the efficiency of this method by calculating the electronic properties of silicon quantum dots (QD) and graphene nano-ribbons with hybrid and screened hybrid functionals (e.g. PBE0 and HSE)⁵. We show how the formalism can be equally applied in real-space to 3D⁶ and 2D periodic systems.



References:

[1] Nicholas M. Boffi, Manish Jain, and Amir Natan, J. Chem. Theory Comput. 12, no. 8 (2016): 3614-3622.
[2] James R. Chelikowsky, N. Troullier, and Y. Saad, Phys. Rev. Lett. 72, no. 8 (1994): 1240.
[3] Leeor Kronik, Adi Makmal, Murilo L. Tiago, M. M. G. Alemany, Manish Jain, Xiangyang Huang, Yousef Saad, and James R. Chelikowsky, Phys. Status Solidi (b) 243, no. 5 (2006): 1063-1079.
[4] D. Gabay, A. Boag, and A. Natan, Comput. Phys. Comm. 215 (2017): 1-6.
[5] D. Gabay, X. Wang, V. Lomakin, A. Boag, M. Jain, and A. Natan, Comput. Phys. Comm. 221 (2017): 95-101.
[6] Amir Natan, Phys. Chem. Chem. Phys, 17, no. 47 (2015): 31510-31515.