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+T*(3). We present two approximate fourth-order schemes, MRCCSD+T*−a(4) and MRCCSD+T*(4). 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 Li2 molecule, using four different basis sets, as well as BeO and CH+. We have calculated the vertical electron affinities of Li2 at the geometry of the neutral Li2 molecule. We also present the vertical ionization potentials of the Li2 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.
Highlights
Many electron systems often require improved electron correlation, for a quality description of the wave function, in order to understand the structure and properties of these systems
It is clear that each such formal scheme of quantum electronic affinity, based on bondonic formalism, may be considered with the above general scheme of fourth-order bondonic expansion, giving rise to the actual specializations, which are conceptually equivalent with the Fock-space multi-reference coupled-cluster singles doubles and triplets (MRCCSD+T) methods for the interacting clusters of electrons, in an iteratively composed way
In the smallest basis-A, which is of just DZVP quality, using one active particle, we observe that the FSMRCCSD calculation underestimates the electron affinity
Summary
Many electron systems often require improved electron correlation, for a quality description of the wave function, in order to understand the structure and properties of these systems. The FSCC, in its singles and doubles model (FSCCSD), has been well developed and studied for direct difference energies [40,41,42], as well as for energy derivatives, by Pal and co-workers [47,48,49] They have formulated a linear response approach [47], followed by the evolution of a Z-vector-type approach [48], with the idea of Lagrange multipliers [49], within FSMRCC method, in order to get a satisfactory result for the calculation of energy derivatives, including properties such as the dipole moments and polarizabilities of molecules. We report the development of a computer code of perturbative approximation to a FSCCSDT model, using a primarily non-iterative or single-iteration approach for the inclusion of triples up to third and fourth order.
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