In this paper, we have made a systematic study of partial fourth order perturbative schemes due to triples to compute the ionization potential within Fock-space multi-reference coupled-cluster theory. In particular, we have obtained computationally less expensive correlation schemes due to fourth order triples. Prototype examples have been considered to explore the efficacy of the approximate methods mentioned, while the bondonic formalism supporting the bonding phenomenology is also respectively for the first time here advanced.

Aug-cc-pVTZ basis 'box.1266' u 2:3 'box.1166' u 2:3 'box.1066

The negative ion resonance states, which are electronmolecule metastable compound states, play the most important role in free-electron controlled molecular reactions and low-energy free-electroninduced DNA damage. Their electronic structure is often only poorly described but crucial to an understanding of their reaction dynamics. One of the most important challenges to current electronic structure theory is the computation of negative ion resonance states. As a major step forward, coupled-cluster theories, which are well-known for their ability to produce the best approximate bound state electronic eigen solutions, are upgraded to offer the most accurate and effective approximations for negative ion resonance states. The existing Fock-space coupled-cluster (FSCC) and the equation-ofmotion coupled-cluster (EOM-CC) approaches that compute bound states are redesigned for the direct and simultaneous determination of both the kinetic energy of the free electron at which the electron-molecule compound states are resonantly formed and the corresponding autodetachment decay rate of the electron from the metastable compound state. This Feature Article reviews the computation of negative ion resonances using the FSCC approach and, in passing, provides the highlights of the equivalent EOM-CC approach.

Resonances are metastable states with finite lifetime. They play important role in physics, chemistry and biology. The theoretical calculation of resonance state is a challenging problem. In this paper we have studied the shape resonance of Be, Mg, N 2 and CO. We have used correlated independent particle approximation to the Fock space multi-reference coupled cluster singles-doubles with third-order triples (CAP-CIP-FSMRCCSD(T)) method augmented by complex absorption potential. The resonance energy and decay widths are obtained by solving a non-Hermitian eigen-value problem within FSMRCC framework. The effects of the lowest order triples on the resonance energy and decay are studied.

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.