Approximating the basis set dependence of coupled cluster calculations: Evaluation of perturbation theory approximations for stable molecules

The coupled cluster CCSD(T) method provides a theoretically sound, accurate description of the electronic structure of a wide range of molecules. To obtain accurate results, however, very large basis sets must be used. Since the computational cost of CCSD(T) calculations formally increases with the seventh power of the number of basis functions (N7), the CCSD(T) method can only be applied to a restricted range of molecules. In this work we show that the basis set dependence of the CCSD(T) method is well described by perturbation theory. Starting with CCSD(T)/aug-cc-pVTZ calculations, use of the MP3 method to simulate the effect of increasing the basis set to aug-cc-pV5Z leads to average absolute errors, relative to the full CCSD(T)/aug-cc-pV5Z calculations, of less than ±0.4 kcal/mol (De), ±0.0002 Å (re), ±2 cm−1 (ωe), 0.1 kcal/mol (IPe), and 0.2 kcal/mol (EAe) for the test set of diatomic molecules considered here. Although the corresponding MP2 approximation does not provide this high level of accuracy, it also should be useful for many molecular studies. When properly implemented, the savings in computer time should be significant since the MP3 method formally scales as N6, while the MP2 method scales as only N5.