From the gas phase to the solid state: The chemical bonding in the superheavy element flerovium.

As early as 1975, Pitzer suggested that copernicium, flerovium, and oganesson are volatile substances behaving like noble gas because of their closed-shell configurations and accompanying relativistic effects. It is, however, precarious to predict the chemical bonding and physical behavior of a solid by knowledge of its atomic or molecular properties only. Copernicium and oganesson have been analyzed very recently by our group. Both are predicted to be semiconductors and volatile substances with rather low melting and boiling points, which may justify a comparison with the noble gas elements. Here, we study closed-shell flerovium in detail to predict its solid-state properties, including the melting point, by decomposing the total energy into many-body forces derived from relativistic coupled-cluster theory and from density functional theory. The convergence of such a decomposition for flerovium is critically analyzed, and the problem of using density functional theory is highlighted. We predict that flerovium in many ways does not behave like a typical noble gas element despite its closed-shell 7p1/2 2 configuration and resulting weak interactions. Unlike the case of noble gases, the many-body expansion in terms of the interaction energy does not converge smoothly. This makes the accurate prediction of phase transitions very difficult. Nevertheless, a first prediction by Monte Carlo simulation estimates the melting point at 284 ± 50 K. Furthermore, calculations for the electronic bandgap suggests that flerovium is a semiconductor similar to copernicium.

The Lennard-Jones Potential Revisited: Analytical Expressions for Vibrational Effects in Cubic and Hexagonal Close-Packed Lattices.

Analytical formulas are derived for the zero-point vibrational energy and anharmonicity corrections of the cohesive energy and the mode Grüneisen parameter within the Einstein model for the cubic lattices (sc, bcc, and fcc) and for the hexagonal close-packed structure. This extends the work done by Lennard-Jones and Ingham in 1924, Corner in 1939, and Wallace in 1965. The formulas are based on the description of two-body energy contributions by an inverse power expansion (extended Lennard-Jones potential). These make use of three-dimensional lattice sums, which can be transformed to fast converging series and accurately determined by various expansion techniques. We apply these new lattice sum expressions to the rare gas solids and discuss associated critical points. The derived formulas give qualitative but nevertheless deep insight into vibrational effects in solids from the lightest (helium) to the heaviest rare gas element (oganesson), both presenting special cases because of strong quantum effects for the former and strong relativistic effects for the latter.

Accurate elemental boiling points from first principles.

The normal boiling point (NBP) is a fundamental property of liquids and marks the intersection of the Gibbs energies of the liquid and the gas-phase at ambient pressure. This work provides the first comprehensive demonstration of the calculation of boiling points of atomic liquids through first-principles molecular-dynamics simulations. To this end, thermodynamic integration (TDI) and perturbation theory (TPT) are combined with a density-functional theory (DFT) Hamiltonian, which provides absolute Gibbs energies, internal energies, and entropies of atomic liquids with an accuracy of a few meV/atom. Linear extrapolation to the intersection with the Gibbs energy of a non-interacting gas-phase eventually pins-down the NBPs. While these direct results can already be quite accurate, they are susceptible to a systematic over or underbinding of the employed density functional. It is shown how this dependency can be strongly reduced and the robustness of the method increased through a simple linear correction termed λ-scaling. Eventually, by carefully tuning of the technical parameters of the approach, the walltime per element is reduced from weeks to about a day (10-20k core-hours), enabling extensive testing for B, Al, Na, K, Ca, Sr, Ba, Mn, Cu, Xe, and Hg. This comprehensive benchmark demonstrates the excellent performance and robustness of the approach with a mean absolute deviation (MAD) of less than 2% from experimental NBPs and very similar accuracy for liquid entropies (MAD 2.3 J (mol K)-1, 2% relative). In some cases, the uncertainties in the predictions are several times smaller than the variation between literature values, allowing us to clear out long-standing ambiguities in the NBPs of B and Ba.

Oganesson: A Noble Gas Element That Is Neither Noble Nor a Gas.

Oganesson (Og) is the last entry into the Periodic Table completing the seventh period of elements and group 18 of the noble gases. Only five atoms of Og have been successfully produced in nuclear collision experiments, with an estimate half-life for 294 118 Og of 0. 69 + 0 . 64 - 0 . 22  ms.[1] With such a short lifetime, chemical and physical properties inevitably have to come from accurate relativistic quantum theory. Here, we employ two complementary computational approaches, namely parallel tempering Monte-Carlo (PTMC) simulations and first-principles thermodynamic integration (TI), both calibrated against a highly accurate coupled-cluster reference to pin-down the melting and boiling points of this super-heavy element. In excellent agreement, these approaches show Og to be a solid at ambient conditions with a melting point of ≈325 K. In contrast, calculations in the nonrelativistic limit reveal a melting point for Og of 220 K, suggesting a gaseous state as expected for a typical noble gas element. Accordingly, relativistic effects shift the solid-to-liquid phase transition by about 100 K.

The periodic table and the physics that drives it.

Mendeleev's introduction of the periodic table of elements is one of the most important milestones in the history of chemistry, as it brought order into the known chemical and physical behaviour of the elements. The periodic table can be seen as parallel to the Standard Model in particle physics, in which the elementary particles known today can be ordered according to their intrinsic properties. The underlying fundamental theory to describe the interactions between particles comes from quantum theory or, more specifically, from quantum field theory and its inherent symmetries. In the periodic table, the elements are placed into a certain period and group based on electronic configurations that originate from the Pauli and Aufbau principles for the electrons surrounding a positively charged nucleus. This order enables us to approximately predict the chemical and physical properties of elements. Apparent anomalies can arise from relativistic effects, partial-screening phenomena (of type lanthanide contraction) and the compact size of the first shell of every l-value. Further, ambiguities in electron configurations and the breakdown of assigning a dominant configuration, owing to configuration mixing and dense spectra for the heaviest elements in the periodic table. For the short-lived transactinides, the nuclear stability becomes an important factor in chemical studies. Nuclear stability, decay rates, spectra and reaction cross sections are also important for predicting the astrophysical origin of the elements, including the production of the heavy elements beyond iron in supernova explosions or neutron-star mergers. In this Perspective, we critically analyse the periodic table of elements and the current status of theoretical predictions and origins for the heaviest elements, which combine both quantum chemistry and physics.

Copernicium: A Relativistic Noble Liquid.

The chemical nature and aggregate state of superheavy copernicium (Cn) have been subject of speculation for many years. While strong relativistic effects render Cn chemically inert, which led Pitzer to suggest a noble-gas-like behavior in 1975, Eichler and co-workers in 2008 reported substantial interactions with a gold surface in atom-at-a-time experiments, suggesting a metallic character and a solid aggregate state. Herein, we explore the physicochemical properties of Cn by means of first-principles free-energy calculations, which confirm Pitzer's original hypothesis: With predicted melting and boiling points of 283±11 K and 340±10 K, Cn is indeed a volatile liquid and exhibits a density very similar to that of mercury. However, in stark contrast to mercury and the lighter Group 12 metals, we find bulk Cn to be bound by dispersion and to exhibit a large band gap of 6.4 eV, which is consistent with a noble-gas-like character. This non-group-conforming behavior is eventually traced back to strong scalar-relativistic effects, and in the non-relativistic limit, Cn appears as a common Group 12 metal.

Oganesson Is a Semiconductor: On the Relativistic Band-Gap Narrowing in the Heaviest Noble-Gas Solids.

Oganesson (Og) is the most recent addition to Group 18. Investigations of its atomic electronic structure have unraveled a tremendous impact of relativistic effects, raising the question whether the heaviest noble gas lives up to its position in the periodic table. To address the issue, we explore the electronic structure of bulk Og by means of relativistic Kohn-Sham density functional theory and many-body perturbation theory in the form of the GW method. Calculating the band structure of the noble-gas solids from Ne to Og, we demonstrate excellent agreement for the band gaps of the experimentally known solids from Ne to Xe and provide values of 7.1 eV and 1.5 eV for the unknown solids of Rn and Og. While this is in line with periodic trends for Rn, the band gap of Og completely breaks with these trends. The surprisingly small band gap of Og moreover means that, in stark contrast to all other noble-gas solids, the solid form of Og is a semiconductor.

Solid Oganesson via a Many-Body Interaction Expansion Based on Relativistic Coupled-Cluster Theory and from Plane-Wave Relativistic Density Functional Theory.

Many-body potentials up to fourth order are constructed using nonrelativistic, scalar-relativistic, and relativistic coupled-cluster theory to accurately describe the interaction between superheavy oganesson atoms. The obtained distance-dependent energy values were fitted to extended two-body Lennard-Jones and three-body Axilrod-Teller-Muto potentials, with the fourth-order term treated through a classical long-range Drude dipole interaction model. From these interaction potentials, spectroscopic constants for the oganesson dimer and solid-state properties were obtained. Furthermore, these high-level results are compared to scalar-relativistic and two-component plane-wave DFT calculations based on a tailor-made projector augmented wave pseudopotential (PAW-PP) and newly derived parameters for Grimme's dispersion correction. It is shown that the functionals PBE-D3(BJ), PBEsol, and in particular SCAN provide excellent agreement with the many-body reference for solid oganesson. Finally, the results for oganesson are compared and related to the lighter rare gas elements, and periodic trends are discussed.

A Hundred-Year-Old Experiment Re-evaluated: Accurate Ab†Initio Monte†Carlo Simulations of the Melting of Radon.

State-of-the-art relativistic coupled-cluster theory is used to construct many-body potentials for the noble-gas element radon to determine its bulk properties including the solid-to-liquid phase transition from parallel tempering Monte Carlo simulations through either direct sampling of the bulk or from a finite cluster approach. The calculated melting temperature are 200(3) K and 200(6) K from bulk simulations and from extrapolation of finite cluster values, respectively. This is in excellent agreement with the often debated (but widely cited) and only available value of 202 K, dating back to measurements by Gray and Ramsay in 1909.