Abstract
We present two algorithms to compute system-specific polarizabilities and dispersion coefficients such that required memory and computational time scale linearly with increasing number of atoms in the unit cell for large systems. The first algorithm computes the atom-in-material (AIM) static polarizability tensors, force-field polarizabilities, and C6, C8, C9, C10 dispersion coefficients using the MCLF method. The second algorithm computes the AIM polarizability tensors and C6 coefficients using the TS-SCS method. Linear-scaling computational cost is achieved using a dipole interaction cutoff length function combined with iterative methods that avoid large dense matrix multiplies and large matrix inversions. For MCLF, Richardson extrapolation of the screening increments is used. For TS-SCS, a failproof conjugate residual (FCR) algorithm is introduced that solves any linear equation system having Hermitian coefficients matrix. These algorithms have mathematically provable stable convergence that resists round-off errors. We parallelized these methods to provide rapid computation on multi-core computers. Excellent parallelization efficiencies were obtained, and adding parallel processors does not significantly increase memory requirements. This enables system-specific polarizabilities and dispersion coefficients to be readily computed for materials containing millions of atoms in the unit cell. The largest example studied herein is an ice crystal containing >2 million atoms in the unit cell. For this material, the FCR algorithm solved a linear equation system containing >6 million rows, 7.57 billion interacting atom pairs, 45.4 billion stored non-negligible matrix components used in each large matrix-vector multiplication, and ∼19 million unknowns per frequency point (>300 million total unknowns).
Highlights
In the rst part of this series, we introduced the MCLF method to compute atom-inmaterial (AIM) polarizabilities and dispersion coefficients.[1]
We developed computationally efficient algorithms to compute atom-in-material polarizabilities and dispersion coefficients using MCLF and Tkatchenko–Scheffler method with self-consistent screening (TS-SCS) analysis
Our TSSCS algorithm uses a special conjugate residual algorithm that resists round-off errors
Summary
In the rst part of this series, we introduced the MCLF method (acronym from authors' last initials) to compute atom-inmaterial (AIM) polarizabilities and dispersion coefficients.[1]. Both our linear-scaling MCLF and linearscaling TS-SCS algorithms avoid large dense matrix multiplications and large matrix inversions. DDEC6 and many other stockholder partitioning methods can be made strictly linearscaling by using a cutoff radius around each atom in a material.[12] The electron and spin densities assigned to an atom in the material are zero outside this cutoff radius This yields linear-scaling computational time and memory, because the number of integration points per atom does not increase as Natoms increases.[12] Natoms is the number of atoms in the unit cell. This strategy would make sense, because DDEC6 analysis is more localized (i.e., cutoff radius 1⁄4 5 A) compared to MCLF (or TS-SCS) analysis (e.g., dipole interaction cutoff length 1⁄4 50 bohr).[1,13]
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.