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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

### Abstract

Accurate extrapolation to the complete basis set (CBS) limit of valence correlationenergies calculated with explicitly correlated MP2-F12 and CCSD(T)-F12b methods have been investigated using a Schwenke-style approach for molecules containing both first and second row atoms. Extrapolation coefficients that are optimal for molecular systems containing first row elements differ from those optimized for second row analogs, hence values optimized for a combined set of first and second row systems are also presented. The new coefficients are shown to produce excellent results in both Schwenke-style and equivalent power-law-based two-point CBS extrapolations, with the MP2-F12/cc-pV(D,T)Z-F12 extrapolations producing an average error of just with a maximum error of 0.49 for a collection of 23 small molecules. The use of larger basis sets, i.e., cc-pV(T,Q)Z-F12 and aug-cc-pV(Q,5)Z, in extrapolations of the MP2-F12 correlationenergy leads to average errors that are smaller than the degree of confidence in the reference data . The latter were obtained through use of very large basis sets in MP2-F12 calculations on small molecules containing both first and second row elements. CBS limits obtained from optimized coefficients for conventional MP2 are only comparable to the accuracy of the MP2-F12/cc-pV(D,T)Z-F12 extrapolation when the and basis sets are used. The CCSD(T)-F12b correlationenergy is extrapolated as two distinct parts: CCSD-F12b and (T). While the CCSD-F12b extrapolations with smaller basis sets are statistically less accurate than those of the MP2-F12 correlationenergies, this is presumably due to the slower basis set convergence of the CCSD-F12b method compared to MP2-F12. The use of larger basis sets in the CCSD-F12b extrapolations produces correlationenergies with accuracies exceeding the confidence in the reference data (also obtained in large basis set F12 calculations). It is demonstrated that the use of the 3C(D) *Ansatz* is preferred for MP2-F12 CBS extrapolations. Optimal values of the geminal Slater exponent are presented for the diagonal, fixed amplitude *Ansatz* in MP2-F12 calculations, and these are also recommended for CCSD-F12b calculations.

© 2009 American Institute of Physics

Received 16 September 2009
Accepted 29 October 2009
Published online 20 November 2009

Acknowledgments: J.G.H. and K.A.P. acknowledge the support of the National Science Foundation (Grant No. CHE-0723997). G.K. and H.J.W. were supported by the Deutsche Forschungsgemeinschaft (DFG) with the priority program 1145 and by Grant No. DFG WE 984/16-1.

Article outline:

I. INTRODUCTION

II. COMPUTATIONAL PROCEDURE

III. RESULTS AND DISCUSSION

A. Calculation of reference correlationenergies

B. Selection of DF auxiliary basis sets for MP2-F12 and CCSD(T)-F12b

C. Choice of geminal Slater exponent for the fixed amplitude *Ansatz*

D. Extrapolation of correlationenergies using series of and basis sets

1. MP2 and MP2-F12

2. CCSD-F12b and CCSD(T)-F12b

IV. CONCLUSIONS

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2009-11-20

2014-04-21

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