Intermediate Hamiltonian coupled cluster methods: meV accuracy for alkaline earth transition energies

The Fock-space coupled cluster method is a multireference approach, which partitions the function space into a relatively small P, comprising the most important functions, and the complementary Q=1−P. The effect of Q is included approximately, by 'dressing' the effective Hamiltonian matrix elements in the P space; the latter is then diagonalized, to yield a large number of transition energies in a single calculation. The method has been applied to many atomic systems, both light and heavy, yielding transition energies in excellent agreement with experiment in most cases. The quality of results improves with the size of P, but the problem of converging the coupled cluster iterations places severe limitations on P. This bottleneck has been overcome by the recent intermediate Hamiltonian Fock-space coupled cluster method. Three variants of the method are presented here and applied to transition energies of alkaline earth atoms. The best performance is exhibited by the extrapolated intermediate Hamiltonian (XIH) approach, which allows the use of very large P spaces (many thousands of configuration state functions) and extrapolates the results to those of the full FSCC, which cannot be obtained directly for these large spaces. The average absolute error of the alkaline earth (Be-Ra) ionization potentials obtained by XIH is 4 meV, and the largest error is 10 meV. The average XIH absolute error for 30 excitation energies of Be is 2 meV, and 23 energies of Mg come out with an average absolute error of 1 meV.