Three-Body Excitations in Fock-Space Coupled-Cluster: Fourth Order Perturbation Correction to Electron Affinity and Its Relation to Bondonic Formalism

Abstract

In this paper, we present a formulation of highly correlated Fock-space multi-reference coupled-cluster (FSMRCC) methods, including approximate triples on top of the FSMRCC with singles and doubles, which correct the electron affinities by at least at third and up to the fourth order in perturbation. We discuss various partial fourth-order schemes, which are reliable and yet computationally more efficient than the full fourth-order triples scheme. The third-order scheme is called MRCCSD+. We present two approximate fourth-order schemes, MRCCSD+ and MRCCSD+. The results that are presented allow one to choose an appropriate fourth-order scheme, which is less expensive and right for the problem. All these schemes are based on the effective Hamiltonian scheme, and provide a direct calculation of the vertical electron affinities. We apply these schemes to a prototype molecule, using four different basis sets, as well as BeO and CH+. We have calculated the vertical electron affinities of at the geometry of the neutral molecule. We also present the vertical ionization potentials of the anion at the geometry of the anion ground state. We have also shown how to calculate adiabatic electron affinity, though in that case we lose the advantages of direct calculation. BeO has been examined in two basis sets. For CH+, four different basis sets have been used. We have presented the partial fourth-order schemes to the EA in all the basis sets. The results are analyzed to illustrate the importance of triples, as well as highlight computationally efficient partial fourth-order schemes. The choice of the basis set on the electron affinity calculation is also emphasized. Comparisons with available experimental and theoretical results are presented. The general fourth-order schemes, which are conceptually equivalent with the Fock-space multi-reference coupled-cluster singles, doubles, and triplets (MRCCSD+T) methods, based on bondonic formalism, are also presented here in a composed way, for quantum electronic affinity.

Generalized relativistic small‐core pseudopotentials accounting for quantum electrodynamic effects: Construction and pilot applications

“…This method can be readily used in conjunction with various relativistic approximations to the many-electron Hamiltonian (the relativistic Fock space coupled cluster theory, FS-RCC) [51,52], including those involving QED terms [53][54][55]. The most widely used FS-RCC model which accounts for only single and double excitations in the cluster operator (FS-RCCSD) generally cannot be regarded as complete enough [12,33,56,57] (see also [58][59][60][61] for the non-relativistic case). The error arising from the neglect of higher excitations varies in a wide range for different systems; in general, the role of triples is especially important for electronic states with more than one valence quasiparticle.…”