Coupled cluster calculations of mean excitation energies of the noble gas atoms He, Ne and Ar and of the H₂ molecule

Abstract

Using an asymmetric Lanczos chain algorithm for the calculation of the coupled cluster linear response functions at the coupled cluster singles and doubles (CCSD) and coupled cluster singles and approximate iterative doubles (CC2) levels of approximation, we have calculated the mean excitation energies of the noble gases He, Ne and Ar, and of the hydrogen molecule (H₂). Convergence with respect to the one-electron basis set was investigated in detail for families of correlation-consistent basis sets including both augmentation and core-valence functions. We find that the electron correlation effects at the CCSD level change the mean excitation energies obtained at the uncorrelated Hartree–Fock level by about 1%. For the two-electron systems He and H₂, our CCSD results (for a Lanczos chain length equal to the full excitation space), I₀ = 42.28 eV (helium) and I₀ = 19.62 eV (H₂), correspond to full configuration interaction results and are therefore the exact, non-relativistic theoretical values for the mean excitation energy of these two systems within the Bethe theory for the chosen basis set and, in the case of H₂, at the experimental equilibrium geometry.

Keywords:

• mean excitation energy
• coupled cluster
• full configuration interaction
• helium
• neon
• argon
• hydrogen molecule
• asymmetric Lanczos chain algorithm

Acknowledgements

It is a pleasure to dedicate this contribution to Professor R.J. Bartlett. It is also thanks to his seminal contributions towards the development of correlated methods in general, and of coupled cluster methods in particular, that this study has been possible.

Additional information

Funding

S.P.A. Sauer acknowledges support by grants from the Danish Center for Scientific Computing (DCSC), the Danish Natural Science Research Council/Danish Councils for Independent Research [grant number 272-08-0486]; the Carlsberg foundation. O. Christiansen acknowledges support from the DCSC. S. Coriani acknowledges support from the Marie Curie FP7-PEOPLE-2009-IEF funding scheme [project number 254326], from the Italian Ministero dell’Istruzione, dell’Università e della Ricerca within PRIN2009 funding scheme [grant number 2009C28YBF_001, ‘Modelli teorici per processi di fotoassorbimento e fotoemissione’]; from the University of Trieste [grant CHIM02-Ricerca].