Single reference coupled cluster calculations for weakly bound alkaline-earth metal dimers in the ground state: a useful perturbative scheme for an iterative triples correction

Abstract

We apply here a new iterative triples correction for the single reference coupled-cluster method with singles and doubles scheme (termed as CCSDT-1a+d). All diagonal terms in have been included in the T ₃ determining equation, in addition to . This minor change in the CCSDT-1a approximation (includes the primary effects of connected triples excitations iteratively) shows a dramatic change in the study of correlation of weakly bonded systems as discussed here. To achieve a general assessment of the potentiality of the CCSDT-1a + d calculations, the ground state potential energy surfaces (PESs) of alkaline-earth dimers, including Mg₂, Ca₂ and the challenging Be₂ are considered. The systems considered here are treated as four-electron systems, keeping other electrons frozen in the correlation calculations. Generation of PESs for these dimers is very sensitive to the level of theory employed for the electron correlation. Basic spectroscopic constants including dissociation energy extracted from the calculated ground state PES are also reported. For all systems under study, the overall performance of CCSDT-1a+d is very competitive with that of the CCSD(T)/CCSDT method, and better than that of CCSDT-1a indicating that the former approach is more effective in handling dynamic correlation effects in comparison to the latter one in the presence of quasi-degeneracy to different extents. To calibrate our results we also report frozen-core FCI calculations.

Keywords:

• CCSDT
• PES
• alkaline-earth dimers
• spectroscopic constants
• frozen-core FCI

Acknowledgements

This publication has emanated from research conducted with the financial support of Department of Science and Technology, India [Grant No. SR/S1/PC-61/2009]. S.C. acknowledges the facilities developed in the Department of Chemistry, BESU through UGC-SAP program.

Notes

1. Like all ab initio methods it is systematically improvable to the exact result in the basis set, correlation limit. This feature is very different from the density functional methods.

2. Since the SRCC approach depends on the choice of a particular reference determinant or function, it can incur problems when the reference determinant or function is not the leading contribution to the wave function.

3. It is worth noting that the adequate treatment of ground- and excited-state PESs along bond breaking coordinates and other cases of electronic quasi-degeneracies has been the domain of expert multi-reference methods. The generalization of the SRCC theory to the MR case is not straightforward, or even unambiguous. Although the past two decades have witnessed a significant progress in the development of different MRCC theories, much remains to be done in order to achieve a universal applicability of these formalisms due to a number of practical problems, such as the intruder states, the requirement of a model space completeness, and the multiplicity and genealogy of solutions, not to mention the complexity of the resulting algorithms and the implied computational demands (for an excellent brief overview of these methods and the relevant literature, see 7). In SRCC calculations, all nondynamic correlation effects due to the MR nature of the electronic state of interest can be treated dynamically. Therefore, the SRCC calculations do not suffer from the convergence and intruder-state problems that often plague genuine MRCC computations.

4. The performance of CCSD(T) invariably goes down when breaking chemical bonds, especially the double and triple bonds, or when handling various open-shell systems, such as diradicals.

5. Noga and Bartlett 11 analysed the CCSDT-n methods by transferring the CCSDT amplitude equations into an operator form based on the expansion of the effective CC Hamiltonian in orders of perturbation theory. They clarified what level in the CCSDT-n hierarchy a given cluster operator term is introduced and at which order of perturbation theory this term starts to contribute.

6. The importance of various cluster contributions to the wave function and to the energy is best judged in terms of the order of perturbation theory in which they first enter.

7. A significant progress in calculations for small molecules has become possible after the introduction of the so-called correlation-consistent (cc) basis sets.

8. As no new energy terms enter at the CCSDT-1a level, CCSDT-1a and CCSDT-1b are so close that they should lead to almost identical results.