All-electron triple zeta basis sets for the actinides

The curious case of the crystalline tri-thorium cluster: cyclic delocalization without aromatic stabilization?

Actinides have been known to form extremely weak homonuclear bonds with their d-type orbitals, and one should therefore expect the superposition of cyclic resonance forms containing such bonds to bring rather marginal aromatic stabilization to the system, if any. It is for this very reason that the discovery of the cyclically delocalized Th3 σ-bonding in the crystalline cluster isolated by Liddle and co-workers has sparked such vigorous discussion on the actual role of molecular aromaticity on the periphery of the periodic table. It has recently been argued that the tri-thorium ring at the heart of the cluster features considerable aromatic stabilization energy comparable to the heterocyclic π-aromatic rings such as thiophene. However, previous investigations involved highly ionized model clusters like Th3Cl64+ or Th310+ in which aromatic stabilization associated with the cyclic delocalization of charge is dramatically exaggerated. In this work we investigate the model tri-thorium clusters at different geometries and ionization states to show that cyclic delocalization of electrons in the isolated crystalline cluster may be associated with rather marginal σ-aromatic stabilization energy thus strongly suggesting its non-aromatic character.

Paramagnetic NMR Shielding Tensors and Ring Currents: Efficient Implementation and Application to Heavy Element Compounds

We present an efficient implementation of paramagnetic NMR shielding tensors and shifts in a nonrelativistic and scalar-relativistic density functional theory framework. For the latter, we make use of the scalar exact two-component Hamiltonian in its local approximation, and generally we apply the well established (multipole-accelerated) resolution of the identity approximation and the seminumerical exchange approximation. The perturbed density matrix of a paramagnetic NMR shielding calculation is further used to study the magnetically induced current density and ring currents of open-shell systems as illustrated for [U@Bi₁₂]^3-. [U@Bi₁₂]^3- features delocalized highest occupied molecular orbitals and sustains a net diatropic ring current of ca. 18 nA/T through the Bi₁₂ torus similar to the all-metal aromatic heavy-element cluster [Th@Bi₁₂]^4-.

Norm-Conserving Pseudopotentials and Basis Sets to Explore Actinide Chemistry in Complex Environments

We have developed a new set of norm-conserving pseudopotentials and companion Gaussian basis sets for the actinide (An) series (Ac-Lr) using the Goedecker, Teter, and Hutter (GTH) formalism with the Perdew, Burke, and Ernzerhof (PBE) exchange-correlation functional of generalized gradient approximation. To test the accuracy and reliability of the newly parameterized An-GTH pseudopotentials and basis sets, a variety of benchmarks on actinide-containing molecules were carried out and compared to all-electron and available experimental results. The new pseudopotentials include both medium- ([Xe]4f¹⁴) and large-core ([Xe]4f¹⁴5d¹⁰) options that successfully reproduce the structures and energetics, particularly redox processes. The medium-core size set, in particular, reproduces all-electron calculations over multiple oxidation states from 0 to VII, whereas the large-core set is suitable only for the early series elements and low oxidation states. The underlying reason for these transferability issues is discussed in detail. This work fills a critical void in the literature for studying the chemistry of 5f-block elements in the condensed phase.

Assessing the Accuracy of Local Hybrid Density Functional Approximations for Molecular Response Properties

A comprehensive overview of the performance of local hybrid functionals for molecular properties like excited states, ionization potentials within the GW framework, polarizabilities, magnetizabilities, NMR chemical shifts, and NMR spin-spin coupling constants is presented. We apply the generalization of the kinetic energy, τ, with the paramagnetic current density to all magnetic properties and the excitation energies from time-dependent density functional theory. This restores gauge invariance for these properties. Different ansätze for local mixing functions such as the iso-orbital indicator, the correlation length, the Görling-Levy second-order limit, and the spin polarization are compared. For the latter, we propose a modified version of the corresponding hyper-generalized gradient approximation functional of Perdew, Staroverov, Tao, and Scuseria (PSTS) [Phys. Rev. A 2008, 78, 052513] to allow for a numerically stable evaluation of the exchange-correlation kernel and hyperkernel. The PSTS functional leads to a very consistent improvement compared to the related TPSSh functional. It is further shown that the "best" choice of the local mixing function depends on the studied property and molecular class. While functionals based on the iso-orbital indicator lead to rather accurate excitation energies and ionization energies, the results are less impressive for NMR properties, for which a considerable dependence on the considered molecular test set and nuclei is observed. Johnson's local hybrid functional based on the correlation length yields remarkable results for NMR shifts of compounds featuring heavy elements and also for the excitation energies of organic compounds.

Chemical bonding between thorium atoms and a carbon hexagon in carbon nanomaterials

We explore the unusual nature of chemical bonding of thorium atoms with a ring of six carbon atoms (hexagon) in novel carbon materials. Our ab initio calculations of Th-based metallofullerenes (Th@C60 and Th@C20) and Th bound to benzene or coronene at the Hartree-Fock level with the second order perturbation (MP2) correction accounting for the van der Waals interactions demonstrate that the optimal position of the thorium atom is where it faces the center of a hexagon and is located at a distance of 2.01-2.07 Å from the center. For Th encapsulated in C60 it is found at 2.01 Å, whereas the other local energy minima are shifted to larger energies (0.22 eV and higher). Inside C60 the highest local minimum at 1.17 eV is observed when Th faces the center of the five member carbon ring (pentagon). Based on our calculations for Th with benzene and coronene where the global minimum for Th corresponds to its position at 2.05 Å (benzene) or 2.02 Å (coronene) from the hexagon center, we conclude that a well pronounced minimum is likely to be present in graphene and in a single wall carbon nanotube. The ground state of Th is singlet, and other high spin states (triplet and quintet) lie higher in energy (>1.62 eV). We discuss a potential use of carbon nanomaterials with the 229Th isotope having its nuclear transition in the optical range, for metrological purposes.