_{t}Ac)

_{3}(μ

_{2}-H)

_{6}], [(H

_{t}Th)

_{3}(μ

_{2}-H)

_{6}],

^{+}, and [(H

_{t}Pa)

_{3}(μ

_{2}-H)

_{6}] clusters

^{1,2,a)}, Leonor Alvarado-Soto

^{1}, Ramiro Arratia-Perez

^{1,2}, Radovan Bast

^{3}and Luis Alvarez-Thon

^{4}

### Abstract

In this study we report about the aromaticity of the prototypical [(H_{t}Ac)_{3}(μ_{2}-H)_{6}], [(H_{t}Th)_{3}(μ_{2}-H)_{6}]^{+}, and [(H_{t}Pa)_{3}(μ_{2}-H)_{6}] clusters *via* two magnetic criteria: nucleus-independent chemical shifts (NICS) and the magnetically induced current density. All-electron density functional theory calculations were carried out using the two-component zeroth-order regular approach and the four-component Dirac-Coulomb Hamiltonian, including scalar and spin-orbit relativistic effects. Four-component current density maps and the integration of induced ring-current susceptibilities clearly show that the clusters [(H_{t}Ac)_{3}(μ_{2}-H)_{6}] and [(H_{t}Th)_{3}(μ_{2}-H)_{6}]^{+} are non-aromatic whereas [(H_{t}Pa)_{3}(μ_{2}-H)_{6}] is anti-aromatic. However, for the thorium cluster we find a discrepancy between the current density plots and the classification through the NICS index. Our results also demonstrate the increasing influence of *f* orbitals, on bonding and magnetic properties, with increasing atomic number in these clusters. We think that the enhanced electron mobility in [(H_{t}Pa)_{3}(μ_{2}-H)_{6}] is due the significant 5*f* character of its valence shell. Also the participation of *f* orbitals in bonding is the reason why the protactinium cluster has the shortest bond lengths of the three clusters. This study provides another example showing that the magnetically induced current density approach can give more reliable results than the NICS index.

This research used resources of the National Energy Research Scientific Computing Center, which is supported by the Office of Science of the U.S. Department of Energy under Contract No. DE-AC02-05CH11231. The authors are grateful for the financial support of the Grants: FONDECYT 3100048, 1110758, and 11100446, UNAB-DI-17-11/R, UNAB-DI-06-10/R, and NUCLEUS MILLENNIUM No. P07-006-F. R.B. kindly acknowledges grant FONDECYT 11100446 which funded his visit to the Universidad Andres Bello.

I. INTRODUCTION

II. COMPUTATIONAL DETAILS

A. ADF code

B. DIRAC code

III. RESULTS AND DISCUSSION

A. Geometry and electronic structure

B. Nucleus independent chemical shift

C. Induced current density maps

D. Integrated ring-current susceptibilities

E. Vertical excitation energies

F. Gauge invariance

IV. CONCLUSIONS

### Key Topics

- Current density
- 33.0
- Laser Doppler velocimetry
- 15.0
- Protactinium
- 15.0
- Actinides
- 12.0
- Paramagnetism
- 11.0

## Figures

Perspective view of the structure of [(H_{t}Ac)_{3}(μ_{2}-H)_{6}], [(H_{t}Th)_{3}(μ_{2}-H)_{6}]^{+}, and [(H_{t}Pa)_{3}(μ_{2}-H)_{6}] (H_{t} = terminal H atoms, H_{μ} = bridging H atoms) clusters.

Perspective view of the structure of [(H_{t}Ac)_{3}(μ_{2}-H)_{6}], [(H_{t}Th)_{3}(μ_{2}-H)_{6}]^{+}, and [(H_{t}Pa)_{3}(μ_{2}-H)_{6}] (H_{t} = terminal H atoms, H_{μ} = bridging H atoms) clusters.

Induced LDA total probability current density for [(H_{t}Ac)_{3}(μ_{2}-H)_{6}] (top), [(H_{t}Th)_{3}(μ_{2}-H)_{6}]^{+} (middle), and [(H_{t}Pa)_{3}(μ_{2}-H)_{6}] (bottom), plotted in the molecular plane. The dimensions are in Bohr atomic units. The magnetic field vector points towards the reader. Line intensity is proportional to the norm of the probability current density vector. The atomic centers are labeled and represented by small circles.

Induced LDA total probability current density for [(H_{t}Ac)_{3}(μ_{2}-H)_{6}] (top), [(H_{t}Th)_{3}(μ_{2}-H)_{6}]^{+} (middle), and [(H_{t}Pa)_{3}(μ_{2}-H)_{6}] (bottom), plotted in the molecular plane. The dimensions are in Bohr atomic units. The magnetic field vector points towards the reader. Line intensity is proportional to the norm of the probability current density vector. The atomic centers are labeled and represented by small circles.

Induced LDA paramagnetic (left) and diamagnetic (right) probability current density for [(H_{t}Pa)_{3}(μ_{2}-H)_{6}], plotted in the molecular plane. Same conventions are used as in Figure 2.

Induced LDA paramagnetic (left) and diamagnetic (right) probability current density for [(H_{t}Pa)_{3}(μ_{2}-H)_{6}], plotted in the molecular plane. Same conventions are used as in Figure 2.

Perspective view of the divergence of the induced current density (div **J**(**r**)) in [(H_{t}Pa)_{3}(μ_{2}-H)_{6}] at the iso-surface values of 0.010, 0.015, 0.020, and 0.050. The radii of the atomic centers correspond to their covalent radii. Each iso-surface encloses divergence values larger than the iso-surface value.

Perspective view of the divergence of the induced current density (div **J**(**r**)) in [(H_{t}Pa)_{3}(μ_{2}-H)_{6}] at the iso-surface values of 0.010, 0.015, 0.020, and 0.050. The radii of the atomic centers correspond to their covalent radii. Each iso-surface encloses divergence values larger than the iso-surface value.

## Tables

Calculated ADF-spin-orbit-ZORA energetic and structural properties of [(H_{t}Ac)_{3}(μ_{2}-H)_{6}], [(H_{t}Th)_{3}(μ_{2}-H)_{6}]^{+}, and [(H_{t}Pa)_{3}(μ_{2}-H)_{6}] (H_{t} = terminal H atoms, H_{μ} = bridging H atoms) clusters.

Calculated ADF-spin-orbit-ZORA energetic and structural properties of [(H_{t}Ac)_{3}(μ_{2}-H)_{6}], [(H_{t}Th)_{3}(μ_{2}-H)_{6}]^{+}, and [(H_{t}Pa)_{3}(μ_{2}-H)_{6}] (H_{t} = terminal H atoms, H_{μ} = bridging H atoms) clusters.

Calculated Dirac-Coulomb LDA electronic, and energetic properties of[(H_{t}Ac)_{3}(μ_{2}-H)_{6}], [(H_{t}Th)_{3}(μ_{2}-H)_{6}]^{+} and [(H_{t}Pa)_{3}(μ_{2}-H)_{6}] (H_{t} = terminal H atoms, H_{μ} = bridging H atoms) clusters.

Calculated Dirac-Coulomb LDA electronic, and energetic properties of[(H_{t}Ac)_{3}(μ_{2}-H)_{6}], [(H_{t}Th)_{3}(μ_{2}-H)_{6}]^{+} and [(H_{t}Pa)_{3}(μ_{2}-H)_{6}] (H_{t} = terminal H atoms, H_{μ} = bridging H atoms) clusters.

NICSs values (in ppm) considering scalar plus spin-orbit (ZORA + SO) effects. NICS_{zz} is the out-of-plane (zz) component of the shielding tensor and NICS_{iso} is the isotropic value.

NICSs values (in ppm) considering scalar plus spin-orbit (ZORA + SO) effects. NICS_{zz} is the out-of-plane (zz) component of the shielding tensor and NICS_{iso} is the isotropic value.

Induced ring current susceptibility (in nAT^{−1}) in [(H_{t}Ac)_{3}(μ_{2}-H)_{6}], [(H_{t}Th)_{3}(μ_{2}-H)_{6}]^{+}, and [(H_{t}Pa)_{3}(μ_{2}-H)_{6}].

Induced ring current susceptibility (in nAT^{−1}) in [(H_{t}Ac)_{3}(μ_{2}-H)_{6}], [(H_{t}Th)_{3}(μ_{2}-H)_{6}]^{+}, and [(H_{t}Pa)_{3}(μ_{2}-H)_{6}].

TD-DFT + SO excitation energies calculations for frontier orbitals in [(H_{t}Ac)_{3}(μ_{2}-H)_{6}], [(H_{t}Th)_{3}(μ_{2}-H)_{6}]^{+}, and [(H_{t}Pa)_{3}(μ_{2}-H)_{6}].

TD-DFT + SO excitation energies calculations for frontier orbitals in [(H_{t}Ac)_{3}(μ_{2}-H)_{6}], [(H_{t}Th)_{3}(μ_{2}-H)_{6}]^{+}, and [(H_{t}Pa)_{3}(μ_{2}-H)_{6}].

Article metrics loading...

Full text loading...

Commenting has been disabled for this content