Electronic Structure and Chemistry of the Heaviest Elements

Experimental and Theoretical Evidence for Relativistic Catalytic Activity in C-H Activation of N-Phenylbenzamide Using a Cationic Iridium Complex

This study elucidates that relativistic effect plays a key role in catalytic C-H activation using a cationic Ir complex. Experiments show that the cationic Ir(I)-diphosphine catalyst can be used for the deuterium substitution of N-phenylbenzamide, whereas a cationic Rh(I)-diphosphine catalyst is scarcely effective. Density functional theory calculations, including the relativistic effect, demonstrate a large difference in the reaction energy diagrams for the C-H activation of N-phenylbenzamide between the cationic Ir and Rh catalysts. In particular, the relatively low reaction barrier and considerably stabilized product obtained for the Ir catalysts are rationalized by strong Ir-C and Ir-H interactions, which originate from the relativistic self-consistent d-orbital expansion of Ir.

Assessing MP2 frozen natural orbitals in relativistic correlated electronic structure calculations

The high computational scaling with the basis set size and the number of correlated electrons is a bottleneck limiting applications of coupled cluster algorithms, in particular for calculations based on two- or four-component relativistic Hamiltonians, which often employ uncontracted basis sets. This problem may be alleviated by replacing canonical Hartree-Fock virtual orbitals by natural orbitals (NOs). In this paper, we describe the implementation of a module for generating NOs for correlated wavefunctions and, in particular, second order Møller-Plesset perturbation frozen natural orbitals (MP2FNOs) as a component of our novel implementation of relativistic coupled cluster theory for massively parallel architectures [Pototschnig et al. J. Chem. Theory Comput. 17, 5509, (2021)]. Our implementation can manipulate complex or quaternion density matrices, thus allowing for the generation of both Kramers-restricted and Kramers-unrestricted MP2FNOs. Furthermore, NOs are re-expressed in the parent atomic orbital (AO) basis, allowing for generating coupled cluster singles and doubles NOs in the AO basis for further analysis. By investigating the truncation errors of MP2FNOs for both the correlation energy and molecular properties-electric field gradients at the nuclei, electric dipole and quadrupole moments for hydrogen halides HX (X = F-Ts), and parity-violating energy differences for H₂Z₂ (Z = O-Se)-we find MP2FNOs accelerate the convergence of the correlation energy in a roughly uniform manner across the Periodic Table. It is possible to obtain reliable estimates for both energies and the molecular properties considered with virtual molecular orbital spaces truncated to about half the size of the full spaces.

Relativity in the electronic structure of the heaviest elements and its influence on periodicities in properties

Theoretical chemical studies demonstrated crucial importance of relativistic effects in the physics and chemistry of superheavy elements (SHEs). Performed, with many of them, in a close link to the experimental research, those investigations have shown that relativistic effects determine periodicities in physical and chemical properties of the elements in the chemical groups and rows of the Periodic Table beyond the 6th one. They could, however, also lead to some deviations from the established trends, so that the predictive power of the Periodic Table in this area may be lost. Results of those studies are overviewed here, with comparison to the recent experimental investigations.

Chemistry of the superheavy elements

The quest for superheavy elements (SHEs) is driven by the desire to find and explore one of the extreme limits of existence of matter. These elements exist solely due to their nuclear shell stabilization. All 15 presently 'known' SHEs (11 are officially 'discovered' and named) up to element 118 are short-lived and are man-made atom-at-a-time in heavy ion induced nuclear reactions. They are identical to the transactinide elements located in the seventh period of the periodic table beginning with rutherfordium (element 104), dubnium (element 105) and seaborgium (element 106) in groups 4, 5 and 6, respectively. Their chemical properties are often surprising and unexpected from simple extrapolations. After hassium (element 108), chemistry has now reached copernicium (element 112) and flerovium (element 114). For the later ones, the focus is on questions of their metallic or possibly noble gas-like character originating from interplay of most pronounced relativistic effects and electron-shell effects. SHEs provide unique opportunities to get insights into the influence of strong relativistic effects on the atomic electrons and to probe 'relativistically' influenced chemical properties and the architecture of the periodic table at its farthest reach. In addition, they establish a test bench to challenge the validity and predictive power of modern fully relativistic quantum chemical models.

Theoretical predictions of properties and volatility of chlorides and oxychlorides of group-4 elements. I. Electronic structures and properties of MCl₄ and MOCl₂ (M = Ti, Zr, Hf, and Rf)

Relativistic, infinite order exact two-component, density functional theory electronic structure calculations were performed for MCl4 and MOCl2 of group-4 elements Ti, Zr, Hf, and element 104, Rf, with the aim to predict their behaviour in gas-phase chromatography experiments. RfCl4 and RfOCl2 were shown to be less stable than their lighter homologs in the group, tetrachlorides and oxychlorides of Zr and Hf, respectively. The oxychlorides turned out to be stable as a bent structure, though the stabilization energy with respect to the flat one (C(2v)) is very small. The trend in the formation of the tetrachlorides from the oxychlorides in group 4 is shown to be Zr < Hf < Rf, while the one in the formation of the oxychlorides from the chlorides is opposite. All the calculated properties are used to estimate adsorption energy of these species on various surfaces in order to interpret results of gas-phase chromatography experiments, as is shown in Paper II.

Theoretical predictions of properties and volatility of chlorides and oxychlorides of group-4 elements. II. Adsorption of tetrachlorides and oxydichlorides of Zr, Hf, and Rf on neutral and modified surfaces

With the aim to interpret results of gas-phase chromatography experiments on volatility of group-4 tetrachlorides and oxychlorides including those of Rf, adsorption enthalpies of these species on neutral, and modified quartz surfaces were estimated on the basis of relativistic, two-component Density Functional Theory calculations of MCl4, MOCl2, MCl6(-), and MOCl4(2) with the use of adsorption models. Several mechanisms of adsorption were considered. In the case of physisorption of MCl4, the trend in the adsorption energy in the group should be Zr > Hf > Rf, so that the volatility should change in the opposite direction. The latter trend complies with the one in the sublimation enthalpies, ΔH(sub), of the Zr and Hf tetrachlorides, i.e., Zr < Hf. On the basis of a correlation between these quantities, ΔH(sub)(RfCl4) was predicted as 104.2 kJ/mol. The energy of physisorption of MOCl2 on quartz should increase in the group, Zr < Hf < Rf, as defined by increasing dipole moments of these molecules along the series. In the case of adsorption of MCl4 on quartz by chemical forces, formation of the MOCl2 or MOCl4(2-) complexes on the surface can take place, so that the sequence in the adsorption energy should be Zr > Hf > Rf, as defined by the complex formation energies. In the case of adsorption of MCl4 on a chlorinated quartz surface, formation of the MCl6(2-) surface complexes can occur, so that the trend in the adsorption strength should be Zr ≤ Hf < Rf. All the predicted sequences, showing a smooth change of the adsorption energy in the group, are in disagreement with the reversed trend Zr ≈ Rf < Hf, observed in the "one-atom-at-a-time" gas-phase chromatography experiments. Thus, currently no theoretical explanation can be found for the experimental observations.