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Pre-selective screening for matrix elements in linear-scaling exact exchange calculations
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10.1063/1.4796441
/content/aip/journal/jcp/138/13/10.1063/1.4796441
http://aip.metastore.ingenta.com/content/aip/journal/jcp/138/13/10.1063/1.4796441

Figures

Image of FIG. 1.
FIG. 1.

Number of significant shell-pairs determined by using the screening matrix Q′ (red/circles) as compared to those by selecting exact elements in the exchange matrix K (blue/squares) for an amylose fragment containing 16 α-D-glucose units (HF/SVP). The black line depicts the total number of shell-pairs.

Image of FIG. 2.
FIG. 2.

Average wall-times (in seconds) for exchange-matrix calculations for a series of linear alkanes with HF/SV using 1, 2, and 4 GPUs. The largest system is C640H1282 comprising 1922 atoms and 8324 basis functions.

Image of FIG. 3.
FIG. 3.

Average wall-times (in seconds) for exchange- and Coulomb-matrix calculations for a series of linear alkanes with HF/SV and HF/SVP using 4 GPUs. Here, the largest system is C640H1282 comprising 1922 atoms and 8324 (SV) or 15 370 (SVP) basis functions, respectively.

Image of FIG. 4.
FIG. 4.

Average wall-times (in seconds) for exchange-correlation- and Coulomb-matrix calculations for a series of linear alkanes using S-VWN/SVP and PBE/SVP and two different grids on 4 GPUs.

Tables

Generic image for table
Generic image for table
Table I.

Effect of pre-selective screening on the final SCF energy, average wall-time for the exchange calculation, and total number of SCF iterations for the example of a DNA-fragment with four A-T base pairs (HF/SVP). Note that preLinK only selects significant elements in the final K matrix, while the number of integrals necessary is also controlled by the Schwarz screening threshold ϑint, set here conservatively to 10−10. The deviation from the reference value (ϑpre = 10−12) is given in 10−6 a.u. (μH).

Generic image for table
Table II.

Average wall-times (in seconds) using 4 GPUs for a single calculation of the exchange- and Coulomb-matrix, respectively. All calculations were performed with a convergence criterion of ϑconv = 10−7, a conservative integral-threshold of ϑint = 10−10, and a preselection threshold of ϑpre = 10−4. N A denotes the number of atoms, N Q the number of significant shell-quartets (× 103) after preselection, the scaling of N Q with respect to the next smaller system size. The largest systems listed are C640H1282, Amylose64, and DNA16, respectively.

Generic image for table
Table III.

Wall-times (in seconds) using 4 GPUs and scaling behavior for a single calculation of the exchange- and Coulomb-matrix, respectively, for a series of DNA-fragments using different exchange thresholds. The significant shell-pairs are determined with ϑ = 10−10, the Coulomb screening threshold is ϑint = 10−10. The error in the final SCF-energy (mhartree) is given with respect to the calculation with ϑint = 10−10 and ϑpre = 10−4 for the exchange calculation.

Generic image for table
Table IV.

Wall-times (in seconds) for a single Coulomb-, exchange-, and exchange-correlation matrix calculation using the PRISM-algorithm on CPUs as well as the GPU-algorithm on GPUs and CPUs, respectively, for an amylose fragment containing 16 α-D-glucose units (HF and PBE using SV and SVP basis sets, ϑint = 10−10, ϑpre = 10−4, grid: 75/302). DFT timings include grid generation.

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/content/aip/journal/jcp/138/13/10.1063/1.4796441
2013-04-04
2014-04-20
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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Pre-selective screening for matrix elements in linear-scaling exact exchange calculations
http://aip.metastore.ingenta.com/content/aip/journal/jcp/138/13/10.1063/1.4796441
10.1063/1.4796441
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