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Efficient distance-including integral screening in linear-scaling Møller-Plesset perturbation theory
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10.1063/1.4770502
/content/aip/journal/jcp/138/1/10.1063/1.4770502
http://aip.metastore.ingenta.com/content/aip/journal/jcp/138/1/10.1063/1.4770502

Figures

Image of FIG. 1.
FIG. 1.

Decay behavior of a (p F p F |p H p H ) integral shell block in a HF⋯HF dimer (6-31G** basis).

Image of FIG. 2.
FIG. 2.

Dependence of the error of the Coulomb-type term for the first Laplace point on the number of calculated HTI shell quartets in QQZZR4 and pure Schwarz (QQZZ) screening calculations for a linear alkane C40H82 (6-31G* basis) with external thresholds of ϑ = 10−6 (left point) and 10−7 (right point) as well as results based on a hypothetical exact screening with thresholds of ϑ = 10−8, 10−9, 10−10 (from left to right). The reference energy corresponds to a pure Schwarz calculation with ϑ = 10−10. The exact screening is simulated by neglecting all integral shell blocks whose largest actual value is smaller than the chosen threshold. The internal screening threshold was fixed to 10−10 in all calculations.

Image of FIG. 3.
FIG. 3.

Error in the opposite-spin MP2 term and speedup (via ratio of integrals) for QQZZR4 AO-MP2 calculations of the whole test set with the 6-31G* basis set (right endpoint: ϑ = 10−6, left endpoint: ϑ = 10−7) relative to the values of a pure Schwarz (QQZZ) calculation with ϑ = 10−6. The Schwarz reference is indicated as a black asterisk at the intersection of the horizontal and vertical line. Values to the right of this reference point indicate increased speed, while values below the reference indicate improved accuracy. The lines that end close to the reference point correspond to very compact or delocalized systems, where QQZZR4 essentially reverts to pure Schwarz screening. The underlying data to the plot can be found in Table II . System sizes in the test set range from 30 to 204 atoms and 250 to 1499 basis functions.

Image of FIG. 4.
FIG. 4.

CPU times for SOS-MO-MP2, RI-MP2, and SOS-RI-MP2 (both with aux-SVP auxiliary basis) as well as SOS-AO-MP2 (ϑ = 10−6) calculations on DNA systems with the 6-31G* basis. The number in brackets indicates the scaling behavior with respect to the previous point. Neither the common MO-MP2 nor any of the RI-MP2 versions are feasible for the largest systems due to their steep scaling with system size, so the data points (*) were extrapolated conservatively with the scaling behavior of the previous points (MO-MP2 4.41, RI-MP2 4.85, SOS-RI-MP2 3.94).

Image of FIG. 5.
FIG. 5.

Cutout of the X-ray structure of a DNA double strand with an 8-oxoguanine lesion in complex with the MutM repair protein. Calculations of two conformers were performed at the SOS-AO-MP2 level of theory. The cutout comprises 2025 atoms and 20 371 basis functions in a 6-31G** basis. The SOS-AO-MP2 calculation took 8.5 days on a cluster with 160 cores in parallel.

Tables

Generic image for table
Table I.

Errors in the opposite-spin MP2 term for DNA2 (128 atoms) and Amylose8 (171 atoms) in 6-31G* basis and hydrogen chains with 6-31G** basis. Pure Schwarz screening (QQZZ), a modified—not recommended—QQZZR4 screening using only untransformed extents (QQZZR4 untrf), and the usual QQZZR4 screening are compared for a screening threshold of ϑ = 10−7.

Generic image for table
Table II.

Total number of half-transformed integrals (HTIs) and error of the opposite-spin AO-MP2 energy with respect to MO-MP2 for calculations in the 6-31G* basis. The absolute energies as well as the canonical reference values are provided in the supplementary material. 76

Generic image for table
Table III.

Total number of half-transformed integrals (HTIs) and error of the opposite-spin AO-MP2/QQZZR4 energy with respect to MO-MP2 for calculations in the SV(P) basis. The absolute energies as well as the canonical reference values are provided in the supplementary material. 76

Generic image for table
Table IV.

The number of basis functions, the total number of half-transformed integrals (HTIs), the scaling with system size, and the error of the opposite-spin AO-MP2/QQZZR4 energy with respect to MO-MP2 for calculations on linear alkanes.

Generic image for table
Table V.

Counterpoise-corrected SOS-AO-MP2/QQZZR4 results for the S22 test set with a SVP basis. The root-mean-square deviation (RMSD) of the errors in the interaction energy with respect to full SOS-MO-MP2 are given.

Generic image for table
Table VI.

Number of basis functions and HTI products as well as the scaling behavior of the number of HTIs with respect to the next smaller system for DNA double-strands with a 6-31G* basis set (ϑ = 10−6).

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/content/aip/journal/jcp/138/1/10.1063/1.4770502
2013-01-02
2014-04-23
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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Efficient distance-including integral screening in linear-scaling Møller-Plesset perturbation theory
http://aip.metastore.ingenta.com/content/aip/journal/jcp/138/1/10.1063/1.4770502
10.1063/1.4770502
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