Elsevier

Chemical Physics Letters

Volume 662, 1 October 2016, Pages 169-175
Chemical Physics Letters

Research paper
4-Component correlated all-electron study on Eka-actinium Fluoride (E121F) including Gaunt interaction: Accurate analytical form, bonding and influence on rovibrational spectra

https://doi.org/10.1016/j.cplett.2016.09.025Get rights and content

Highlights

  • Prolapse free Gaussian basis set suitable for molecular calculations for Eka-actinium.

  • Numerical atomic calculations for Eka-actinium (E121).

  • Correlated four-component calculations on E121F with inclusion of Gaunt interaction.

  • Accurate analytical function describing the potential energy curve of E121F molecule.

  • Rovibrational spectra of E121F with inclusion of Gaunt interaction.

Abstract

A prolapse-free basis set for Eka-Actinium (E121, Z = 121), numerical atomic calculations on E121, spectroscopic constants and accurate analytical form for the potential energy curve of diatomic E121F obtained at 4-component all-electron CCSD(T) level including Gaunt interaction are presented. The results show a strong and polarized bond (≈181 kcal/mol in strength) between E121 and F, the outermost frontier molecular orbitals from E121F should be fairly similar to the ones from AcF and there is no evidence of break of periodic trends. Moreover, the Gaunt interaction, although small, is expected to influence considerably the overall rovibrational spectra.

Graphical abstract

Electron density for eka-actinium fluorine (E121F) obtained at 4-component B3LYP level (density isovalue of 0.005) with Gaunt interaction in the distance of equilibrium (4.10 bohr). It can be observed that the bond is covalent and polarized, as expected between fluorine and a IIIB element.

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Introduction

The Periodic Table has 15 superheavy elements (SHE) known [1] and it is now completed up to its seventh period with the discovery of elements Og [2] (Z = 118) and Ts [3] (Z = 117). The SHE are artificially produced elements with Z > 103, that usually have short half-lives and low production rates that makes their experimental studies limited to just a few isotopes that can be investigated by atom-at-time techniques [4].

As a consequence, theoretical studies on SHE are of relevance since in most cases they are the only way to obtain reliable chemical, physical or spectroscopic properties on molecules containing SHE. This importance is especially true for SHE from eka-francium (Z = 119) onwards, where no element has been synthetized or discovered so far: attempts to produce eka-francium and eka-radium, as well the confirmation of the existence [5] in nature of a long lived isotope of element eka-thorium (Z = 122) have failed.

Little is known about the chemistry and spectroscopic properties of SHE form the 8th period. There are relatively few theoretical studies in the literature about molecules with these elements [6], [7], [8], [9] perhaps due to the high level methods involved in the description of their electronic structure. Besides a good treatment of electron correlation effects, not only the inclusion of scalar relativistic and spin orbit coupling are mandatory, but also Gaunt, Breit or even higher level Quantum Electrodynamics effects (QED) may also be important [10], [11].

Regarding the element E121, there are only atomic studies to the best of our knowledge: it seems based on these studies [12], [13], [14] that the ground state of the E121 (eka-actinium) should be [Uuo] 8s28p1/21 in contrast with the7s26d3/21 of Actinium. In addition, Eliav [12] et al. found that the Breit term on most transitions are rather small (0.01–0.02 eV) but goes up to 0.1 eV for transitions involving f electrons.

In this contribution we present a basis set suitable for 4-component molecular calculations, relativistic numerical calculations for E121 atom, as well as molecular relativistic calculations at 4-Component CCSD(T) and B3LYP levels with (and without) inclusion of Gaunt interaction. Besides the generation of the basis set for E121, the aim is twofold: to obtain an accurate analytical form for the potential energy curve for E121F and to investigate the influence of Gaunt interaction on spectroscopic constants, rotational spectra and bonding. Further discussion on bonding is also presented, showing similarities with E121F and AcF.

Section snippets

Method and computational details

All atomic basis set expansion calculations for generating the gaussian basis set for E121 were performed using the DFRATOM program [15] with a protocol employed previously [16] on development of basis sets for SHE, so it will be briefly described:

  • (a)

    The polynomial version of the Generator Coordinate Dirac-Fock (pGCDF) method was adopted [17];

  • (b)

    The pGCDF parameters were optimized by employing the Downhill Simplex Algorithm;

  • (c)

    The value of the speed of light used was c = 137.0359895 in atomic units;

  • (d)

    The

Results and discussion

The basis set generated in this work is prolapse free, so some comments about the prolapse are appropriate. The prolapse was first described by Faegri [34] when he found that some of his basis had total energy below the numerical values of reference. The prolapse occurs due to basis set deficiency at the innermost atomic region and it has been discussed [35] as a consequence of neglecting the minimax theorem. The drawbacks regarding prolapse are that it may lead to wrong results such as the

Conclusion

A 4-component basis set suitable for molecular for E121 and numerical results for the E121 atom to assess the basis set is reliable are presented. The analytical form of q-Rydberg of order 10 proposed in this work succeeded in fitting the ground state PEC of E121F with the low root mean square deviation of 2.2369 × 10−5 Hartree (≈0.014 kcal/mol). This value represents less than 0.008% of the value of the dissociation energy of E121F. The quality of the fit is highlighted by the close agreement of

Acknowledgments

LGMM acknowledges CNPq (Conselho Nacional de Desenvolvimento Científico e Tecnológico, Brazilian Agency) for his postdoctoral scholarship (Grant number 157843/2015-7). DHTA Acknowledges CAPES (Coordenação de Aperfeiçoamento de Pessoal de Nível Superior) for his doctoral scholarship. The authors thank FINATEC (Fundação de Empreendimentos Científicos e Tecnológicos), FAPDF (Fundação de Apoio à Pesquisa do Distrito Federal) and FAPESP (2013/19289-0, 2016/07476-9) for financial support. The authors

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