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Extrapolating MP2 and CCSD explicitly correlated correlation energies to the complete basis set limit with first and second row correlation consistent basis sets
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10.1063/1.3265857
/content/aip/journal/jcp/131/19/10.1063/1.3265857
http://aip.metastore.ingenta.com/content/aip/journal/jcp/131/19/10.1063/1.3265857

Figures

Image of FIG. 1.
FIG. 1.

Mean absolute errors of select CBS extrapolations and mean absolute basis set errors for a set of first and second row systems. The CBS extrapolations encompass the traditional fixed exponent power-law-based scheme (CBS MP2 ) and the Schwenke-style conventional MP2 (CBS MP2 Schwenke) and explicitly correlated MP2 (CBS MP2-F12 Schwenke) schemes. Basis sets are referred to by their cardinal number and basis set extrapolations by the cardinal number of the largest basis set used in the extrapolation.

Image of FIG. 2.
FIG. 2.

Mean absolute errors of CBS extrapolations and mean absolute basis set errors of the CCSD-F12b correlation energy with Ansatz 3C(FIX) for a set of fourteen systems containing first and second row elements. Basis sets are referred to by their cardinal number, , and CBS extrapolations by the cardinal number of the largest basis set used in the extrapolation.

Image of FIG. 3.
FIG. 3.

Mean absolute errors of CBS extrapolations and mean absolute basis set errors of the (T) component of the CCSD(T)-F12b correlation energy with Ansatz 3C(FIX) for a set of fourteen systems containing first and second row elements. Basis sets are referred to by their cardinal number, , and CBS extrapolations by the cardinal number of the largest basis set used in the extrapolation.

Tables

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Table I.

MP2-F12 frozen-core correlation energy contributions from each angular momentum quantum number for Ar, Ne, and . Values in parentheses indicate the incremental change in correlation energy with the addition of basis functions in each angular momenta.

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Table II.

CCSD-F12b frozen-core correlation energy contributions from each angular momentum quantum number for Ar, Ne, and . Values in parentheses indicate the incremental change in correlation energy with the addition of basis functions in each angular momenta.

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Table III.

Reference frozen-core MP2 correlation energies.

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Table IV.

Reference frozen-core CCSD and (T) correlation energies .

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Table V.

Recommended values of the geminal Slater exponent , using and basis sets with the MP2-F12 method and the 3C(FIX) Ansatz. Also reported are the mean signed errors per correlated electron (MSE) for using these values of (relative to the optimal value for the given molecule) and the standard deviation of that error (Std. dev.). See text for further details.

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Table VI.

CBS coefficients for extrapolation of MP2-F12/3C correlation energies using Eqs. (2) and (4) along with statistics of the error in the extrapolated energy relative to reference data .

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Table VII.

Optimized CBS extrapolation coefficients for MP2-F12/3C and error statistics for an enlarged test set of systems that includes group 13 elements and systems containing a mixture of first and second row elements (see text for further details). All errors reported in . These are the recommended values for this method.

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Table VIII.

Optimized CBS extrapolation coefficients for conventional MP2 using a combined set of 14 first and second row systems. (The systems are: Ne, , , , CO, HF, , Ar, , , , SiS, HCl, and .) All error statistics reported in .

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Table IX.

Optimized CBS extrapolation coefficients for MP2-F12 with Ansätze 3C(D) and 3C(FIX) using a combined set of fourteen first and second row systems. All error statistics reported in .

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Table X.

Optimized CBS coefficients for the extrapolation of CCSD-F12b correlation energies using the 3C(FIX) Ansatz for the systems presented in Table IV. Error statistics of the extrapolated energies relative to reference data are presented in .

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Table XI.

Optimized CBS coefficients for the extrapolation of the (T) contribution to the CCSD(T)-F12b/3C(FIX) correlation energy. Error statistics for the extrapolated energy are relative to the reference data in Table IV and are reported in .

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/content/aip/journal/jcp/131/19/10.1063/1.3265857
2009-11-20
2014-04-17
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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Extrapolating MP2 and CCSD explicitly correlated correlation energies to the complete basis set limit with first and second row correlation consistent basis sets
http://aip.metastore.ingenta.com/content/aip/journal/jcp/131/19/10.1063/1.3265857
10.1063/1.3265857
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