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Quartic scaling second-order approximate coupled cluster singles and doubles via tensor hypercontraction: THC-CC2
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10.1063/1.4795514
/content/aip/journal/jcp/138/12/10.1063/1.4795514
http://aip.metastore.ingenta.com/content/aip/journal/jcp/138/12/10.1063/1.4795514

Figures

Image of FIG. 1.
FIG. 1.

A test set of 21 molecules representative of typical applications for CC2.

Image of FIG. 2.
FIG. 2.

Errors in millihartrees of THC-CC2 relative to DF-CC2 (THC error), THC-CC2 relative to CC2 (total error), and DF-CC2 relative to CC2 (DF error) for a set of 20 water clusters. All correlation energies are computed using the cc-pVDZ basis.

Image of FIG. 3.
FIG. 3.

Errors in millihartrees of THC-CC2 relative to DF-CC2 (THC error), THC-CC2 relative to CC2 (total error), and DF-CC2 relative to CC2 (DF error) for linear alkanes of increasing length. All correlation energies are computed using the cc-pVDZ basis.

Image of FIG. 4.
FIG. 4.

Errors in millihartrees of THC-CC2 relative to DF-CC2 (THC error), THC-CC2 relative to CC2 (total error), and DF-CC2 relative to CC2 (DF error) for alkenes of increasing length. All correlation energies are computed using the cc-pVDZ basis.

Image of FIG. 5.
FIG. 5.

Timings of 10 THC-CC2 iterations using a cc-pVDZ basis for water clusters containing up to 40 water molecules. LS-THC refers to the formation of the THC integrals, Eq. (20) . T1, T2-J, and T2-K refer to the evaluation of the terms contained in Algorithms 1–3 , respectively. THC-CC2 refers to the total computation time (everything excepting the solution of the Hartree-Fock equations). Both axes use a logarithmic scale.

Tables

Generic image for table

An algorithm for evaluating contributions to the CC2 singles amplitudes from Eq. (35) and contributions to the CC2 energy from .

Generic image for table

An algorithm for evaluating Coulomb-like contributions to the CC2 energy and singles amplitudes from Eqs. (38) and (39) .

Generic image for table

An algorithm for evaluating exchange-like contributions to the CC2 energy and singles amplitudes from Eqs. (41) and (42) .

Generic image for table

A general schematic for an THC-CC2 algorithm.

Generic image for table
Table I.

Errors in the correlation energy of THC-CC2/cc-pVDZ relative to DF-CC2/cc-pVDZ for a representitive set of 21 molecules. The molecules are shown in Figure 1 . The number of basis functions and grid points used for each computation are also listed.

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/content/aip/journal/jcp/138/12/10.1063/1.4795514
2013-03-28
2014-04-19
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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Quartic scaling second-order approximate coupled cluster singles and doubles via tensor hypercontraction: THC-CC2
http://aip.metastore.ingenta.com/content/aip/journal/jcp/138/12/10.1063/1.4795514
10.1063/1.4795514
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