Relativistic coupled-cluster-based linear response theory for ionization potentials of alkali-metal and alkaline-earth-metal atoms

We have developed and applied the relativistic coupled-cluster-based linear response theory (RCCLRT) for computing the principal as well as the shake-up ionization potentials (IP’s) of Li, Be, Na, and Mg where the single-particle orbitals are generated by solving the relativistic Hartree-Fock-Roothaan equations using the Gaussian basis functions on a grid. The computed principal and shake-up ionization energies by the RCCLRT approach are in favorable agreement with the experimental results. Since for the (one-valence) IP problem, there is a formal equivalence between the principal IP values as obtained from the CCLRT and those obtained as eigenvalues of the multireference coupled-cluster theory, the computed quantities are fully size extensive. The approach via the RCCLRT has the additional advantage of providing the shake-up IP’s as well. These are, however, not fully size extensive, but the error scales as the number of valence excitations $\mathrm{}(2h-1p)\mathrm{}$, so the inextensivity error is rather small.