Article

# Is Eka‐Mercury (Element 112) a Group 12 Metal?

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## Abstract

(Graph Presented) Super heavy: According to relativistic Dirac-Kohn-Sham calculations, eka-mercury (element 112) is a semiconductor in the solid state (see band structure; red: filled bands, blue: empty bands). In the absence of relativistic effects, condensed eka-mercury would be a hexagonal close-packed metal similar to zinc and cadmium.

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... In recent years, experimental and theoretical investigations of super heavy element (SHE) Copernicium 'Cn' have gained some momentum [1,[3][4][5][6][7][8]. Experimental investigations though are not on physical and/or structural properties, as this element is synthesized via heavy ion fusion reactions in single-atom -at-a-time kind of experiments and is short lived. ...
... These relativistic effects are considered either via a perturbative method, which we will term as 'SO' calculations or by solving four component Dirac equation, called fully relativistic 'FR' calculations. Fully relativistic cal- culations, using first principles pseudopotential method on Cn by Gaston et al. [6] who have carried out the study under both scalar relativistic (SR) and fully relativistic (FR) cases using RFPLO and CRYSTAL03 code, predict it to be a semiconductor solid. Gaston et al. study has been carried out considering only two crystal structures namely, hcp and rhombohe- dral. ...
... In fact in our Type II computations the effect is much less pronounced, the SR equilibrium volume is 188.48 a.u. 3 which re- duces to 179.53a.u. 3 on inclusion of SO effects and hcp is the ground state crystal structure for both SR and SRþSO level of theory. One of the reason for their [6] extended volume and lower B 0 , though could be that they have used GGA for the exchange and correlation effects. Our bulk moduli values for the most stable crystal structure for the four cases are 58.73, ...
Article
First principles scalar relativistic (SR) calculations with and without including the spin orbit (SO) interactions have been performed for solid Copernicium (Cn) to determine its ground state equilibrium structure, volume, bulk modulus, pressure derivative of the bulk modulus, density of states and band structure. Both SR and SR+SO calculations have been performed with 6p levels treated as part of core electrons and also as part of valence electrons. These calculations have been performed for the rhombohedral, BCT, FCC, HCP, BCC and SC structures. Results have been compared with the results for Hg which is lighter homologue of Cn in the periodic table. We find hcp to be the stable crystal structure at SR level of theory and also at SR+SO level of theory when the 6p electrons are treated as part of core electrons. With 6p as part of valence electrons, SR+SO level of computations, however, yield bcc structure to be the most stable structure. Equilibrium volume (V0) of the most stable crystal structure at SR level of theory viz. hcp structure is 188.66 a.u.³whereas its value for the bcc structure, the equilibrium ground state structure at SR+SO level of theory is 165.71 a.u.³ i.e a large change due to relativistic effects is seen. The density of states at Fermi level is much smaller in Cn than in Hg, making it a poorer metal than mercury. In addition the cohesive energy of Cn is computed to be almost two times that of Hg for SR+SO case.
... Fortunately, for structures, vibrational frequencies, thermochemistry or kinetics, the predominant scalar (spin-free) relativistic effects may be included in a straightforward manner, and with excellent accuracy, by use of suitably parametrized relativistic pseudopotentials ("effective-core potentials", ECPs) [102][103][104][105]. Comparison with non-relativistically parametrized ECPs even allows the importance of relativity for a given reaction to be estimated. In the 5d (and 6d) series, the higher oxidation states are invariably stabilized by relativity (see Section 7 for a detailed discussion of the reasons) [20,77,100,[106][107][108]. ...
... Further interesting computational data are available for elements 111, 112, and 113 from the work of Seth et al. [106,108,349]. For group 11, i.e. ...
... Similar calculations for [112] F 4 indicate that the tetrafluoride of eka-mercury is also stabilized relative to HgF 4 by enhanced relativistic effects [108]. There is thus even more justification to classify element 112 as a transition metal element than for mercury [106]. This has led Seth et al. to also examine element 113 (eka-thallium) [107]. ...
Article
The highest accessible formal oxidation states of the d-block elements are scrutinized, both with respect to the available experimental evidence and quantum-chemical predictions. The focus is on fluoride, oxide, and oxyfluoride systems. The field has evolved significantly over the past 15 years due to the availability of quantitative computational predictions of thermochemical stabilities, and of spectroscopical parameters of a number of key molecules. The demands on the computational methodology used, as well as the experimental boundary conditions needed are reviewed, and reasons for the observed trends in oxidation states throughout the 3d, 4d, 5d, and 6d series are discussed.
... This is clearly a manifestation of strong many-body effects (beyond a simple 2-body interaction), which is known to be very important for mercury, and in fact for metallic systems in general143144145. Solid-state calculations for Cn put the cohesive energy of 1.13 eV above the value of Hg [146]. As the 7s orbital lies energetically and spatially within the 6d range, the higher oxidation state +IV becomes thermodynamically stable even more than in the case of Hg147148149. ...
... we have (113)F 3 → (113)F +F 2 +0.33 eV (+5.32 eV) [160] and FlF 4 → FlF 2 + F 2 − 0.16 eV (+6.06 eV) [161] using relativistic (nonrelativistic) levelFig. 6. Correlation between experimental adsorption enthalpies on gold surfaces of homologues of elements Cn through 118 and their respective sublimation enthalpies compared with recent data for Cn, Fl and 120 coming from oneatom-at-a-time experiments [150,155], experimental estimates [6], and computational (DFT) predictions [146,156,157]. Experimental data for Bi, Hg, Kr, Pb, Po, Rn, Tl, and Xe are taken from Ref. [158], and data for At taken from Ref. [159]. of theory. ...
... These values were obtained through an extrapolation, correlating the surface energies of elemental solids of groups 12 and 14 with their respective enthalpies of sublimation. However, most recent solid state calculations of cohesive energies predict E coh = 109 kJ/mol for Cn [16], and E coh = 48 kJ/mol for Fl [17]. In this case, the thermodynamic stability of the selenide formation in the solid state follows the trend Hg \ Cn \ Fl (see Fig. 1). ...
... 298 (Fl), leading to the extrapolated values DH blue and red arrows, respectively), are deduced from the empirical correlation reported in[5]. The extrapolated DH FlSe) values, based on the most recent solid state theoretical calculations of cohesive energies[16,17], are indicated (dashed blue and red arrows, respectively). (Colorfigure online) ...
Article
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The adsorption behavior of 197Hg and 183–185Hg on red amorphous selenium (red a-Se) and trigonal selenium (t-Se) was investigated experimentally by off-line and on-line gas chromatographic methods, in preparation of a sensitive chemical separation and characterization of the transactinides copernicium (Cn, Z = 112) and flerovium (Fl, Z = 114). Monte-Carlo simulations of a diffusion controlled deposition were in good agreement with the experimental results, assuming as interaction limits −ΔHadsred a-Se(Hg) > 85 kJ/mol, and −ΔHadst-Se(Hg) < 60 kJ/mol. Both Se allotropes can be used as stationary surfaces in comparative gas-chromatographic chemical investigations of Cn and Fl.
... Relativistic atomic calculations of Cn suggest an increased chemical stability of the elemental atomic state for Cn and some models predict even a noble-gas like inertness with exceptionally high promotion energies (E prom ) suggesting chemical properties similar to Rn [18]. Relativistic calculations of solid element 112 predicted a semiconductor-like band structure and hence, a non-noble-gas like behavior [98]. These strongly diverse predictions require experimental data, used as benchmark for the applied models. ...
... Thus, the macroscopic volatility expressed as its standard sublimation enthalpy can be deduced from this correlation using the − H Au ads (Cn) = 52 +4 −3 kJ mol −1 as H subl (Cn) = 36 ± 10 kJ mol −1 (68% c.i.). Recent solid state calculations of cohesive energies seem to underestimate the volatility of Cn and overestimate the solid state binding of Cn with E coh =1.13 eV (109 kJ mol −1 ) [98]. The trends established in the Periodic Table for group 12 are preserved (see Fig. 29, [3]) as already suggested in 1976 [97]. ...
Article
Chemical investigations of superheavy elements in the gas-phase, i.e. elements with Z≥104, allow assessing the influence of relativistic effects on their chemical properties. Furthermore, for some superheavy elements and their compounds quite unique gas-phase chemical properties were predicted. The experimental verification of these properties yields supporting evidence for a firm assignment of the atomic number. Prominent examples are the high volatility observed for HsO4 or the very weak interaction of Cn with gold surfaces. The unique properties of HsO4 were exploited to discover the doubly-magic even-even nucleus 270Hs and the new isotope 271Hs. The combination of kinematic pre-separation and gas-phase chemistry allowed gaining access to a new class of relatively fragile compounds, the carbonyl complexes of elements Sg through Mt. A not yet resolved issue concerns the interaction of Fl with gold surfaces. While competing experiments agree on the fact that Fl is a volatile element, there are discrepancies concerning its adsorption on gold surfaces with respect to its daughter Cn. The elucidation of these and other questions amounts to the fascination that gas-phase chemical investigations exert on current research at the extreme limits of chemistry today.
... The importance of the 6d electrons in Cn would indicate that the state of elemental Cn could well differ significantly from that of Hg. Relativistic band structure calculations [58] predict the binding energy of the solid to be 1.13 eV, which is double the value of 0.64 eV for Hg. This shows that the trend in the binding energies of elemental Hg and Cn does not follow the trend (table 15) of the reduction of the Cn polarizability when compared to that of Hg. ...
... The chemical activity of the 6d electrons coupled their ionization being preferred over that of the 7s electrons, when taken in conjunction with the result [58] that the predicted elemental binding energy of Cn is around 10 times greater than that of a noble gas solid, shows Cn does not resemble such a gas. This conclusion is not vitiated by the experimental result [59] that elemental Cn is somewhat volatile. ...
Article
The periodic table provides a deep unifying principle for understanding chemical behaviour by relating the properties of different elements. For those belonging to the fifth and earlier rows, the observations concerning these properties and their interrelationships acquired a sound theoretical basis by the understanding of electronic behaviour provided by non-relativistic quantum mechanics. However, for elements of high nuclear charge, such as occur in the sixth and higher rows of the periodic table, the systematic behaviour explained by non-relativistic quantum mechanics begins to fail. These problems are resolved by realizing that relativistic quantum mechanics is required in heavy elements where electrons velocities can reach significant fractions of the velocity of light. An essentially non-mathematical description of relativistic quantum mechanics explains how relativity modifies valence electron behaviour in heavy elements. The direct relativistic effect, arising from the relativistic increase of the electron mass with velocity, contracts orbitals of low angular momentum, increasing their binding energies. The indirect relativistic effect causes valence orbitals of high angular momentum to be more effectively screened as a result of the relativistic contraction of the core orbitals. In the alkali and alkaline earths, the s orbital contractions reverse the chemical trends on descending these groups, with heavy elements becoming less reactive. For valence d and f electrons, the indirect relativistic effect enhances the reductions in their binding energies on descending the periodic table. The d electrons in the heavier coinage metals thus become more chemically active, which causes these elements to exhibit higher oxidation states. The indirect effect on d orbitals causes the chemistries of the sixth-row transition elements to differ significantly from the very similar behaviours of the fourth and fifth-row transition series. The relativistic destabilization of f orbitals causes lanthanides to be chemically similar, forming mainly ionic compounds in oxidation state three, while allowing the earlier actinides to show a richer range of chemical behaviour with several higher oxidation states. For the 7p series of elements, relativity divides the non-relativistic p shell of three degenerate orbitals into one of much lower energy with the energies of the remaining two being substantially increased. These orbitals have angular shapes and spin distributions so different from those of the non-relativistic ones that the ability of the 7p elements to form covalent bonds is greatly inhibited. This article is part of the theme issue ‘Mendeleev and the periodic table’.
... [3][4][5] Concerning these trends, its lighter congener Hg is known to exhibit some very unusual behavior compared to both Zn and Cd, with reported low melting and boiling points (cf. Fig. 1) [6,7] -rendering Hg the only metallic liquid at room temperature and a superconductor with a transition temperature of 4.15 K. [8] These periodic anomalies can be traced back to strong relativistic effects within this group, [8][9][10][11][12][13][14] and, albeit to a far lesser extent, the lanthanide contraction originating from the poor nuclear shielding by the filled 4f -shell. [15] This renders it almost impossible to predict the physical and chemical behavior of Cn purely from periodic trends as originally proposed by Mendeleev. ...
Article
Full-text available
The chemical nature and aggregate state of 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 coworkers in 2008 reported substantial interactions with a gold surface and suggested a metallic character with a solid aggregate state based on atom‐at‐a‐time experiments. Here, we explore the physicochemical properties of Cn by means of first‐principles free‐energy calculations, confirming Pitzer's original hypothesis: With melting and boiling points of 283 ± 11 K and 340 ± 10 K, Cn is indeed a volatile liquid with a density very similar to mercury. Moreover, we show that bulk Cn is – in stark contrast to the lighter group 12 metals – dominated by dispersive interactions, and exhibits a large band gap of 6.4~eV, which is consistent with a noble‐gas‐like character. Eventually, the non‐group‐conforming behavior is traced back to strong scalar‐relativistic effects, and in the non‐relativistic limit, Cn appears as a common group 12 metal.
... [3][4][5] Concerning these trends, its lighter congener Hg is known to exhibit some very unusual behavior compared to both Zn and Cd, with reported low melting and boiling points (cf. Fig. 1) [6,7] -rendering Hg the only metallic liquid at room temperature and a superconductor with a transition temperature of 4.15 K. [8] These periodic anomalies can be traced back to strong relativistic effects within this group, [8][9][10][11][12][13][14] and, albeit to a far lesser extent, the lanthanide contraction originating from the poor nuclear shielding by the filled 4f -shell. [15] This renders it almost impossible to predict the physical and chemical behavior of Cn purely from periodic trends as originally proposed by Mendeleev. ...
Article
Full-text available
The chemical nature and aggregate state of 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 coworkers in 2008 reported substantial interactions with a gold surface and suggested a metallic character with a solid aggregate state based on atom‐at‐a‐time experiments. Here, we explore the physicochemical properties of Cn by means of first‐principles free‐energy calculations, confirming Pitzer's original hypothesis: With melting and boiling points of 283 ± 11 K and 340 ± 10 K, Cn is indeed a volatile liquid with a density very similar to mercury. Moreover, we show that bulk Cn is – in stark contrast to the lighter group 12 metals – dominated by dispersive interactions, and exhibits a large band gap of 6.4~eV, which is consistent with a noble‐gas‐like character. Eventually, the non‐group‐conforming behavior is traced back to strong scalar‐relativistic effects, and in the non‐relativistic limit, Cn appears as a common group 12 metal.
... Because of the strong relativistic 7s contraction, Cn is predicted to be a semiconductor or even an insulator in contrast to Hg 90,92 . The unusually high superconducting transition temperature of Hg, in comparison with that of Zn and Cd, is also attributed to relativistic effects 93 : without relativity, Heike Kamerlingh Onnes would not have discovered superconductivity. ...
Article
Full-text available
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.
... How volatile and reactive towards gold are Cn and Fl atoms in comparison with the lighter homologs and with Rn? The 4c-DFT calculations of the binding energies of group-12 homonuclear dimers [6,7] and the scalar relativistic (SR) DFT periodic ones of cohesive energies [22] have shown Cn-Cn and the bulk of Cn to be more bound than the corresponding Hg systems. Thus, a decrease in H sub in group 12 should not continue with Cn. ...
Article
Full-text available
Spectacular developments in the relativistic quantum theory and computational algorithms in the last few decades allowed for accurate calculations of properties of the superheavy elements (SHE) and their compounds. Often conducted in a close link to the experimental research, these investigations helped predict and interpret an outcome of sophisticated and expensive experiments with single atoms and to reveal the magnitude and importance of relativistic effects.
... The dissociation energies, D e , of the three species were found to increase in the order D e (Hg 2 ) < D e (Cn 2 ) < D e (Fl 2 ). Solid state investigations of Cn 38 and Fl 39 were also performed; however, as different computational methods were used for the two elements, direct comparison of their solid state properties is not possible. In this work, we investigate the trend in stability found earlier for the three M 2 dimers by performing consistent high quality relativistic CCSD(T) calculations for them. ...
Article
The structure and energetics of eight diatomic heavy-atom molecules are presented. These include the species MAu, M2, and MHg, with M standing for the Hg, Cn (element 112), and Fl (element 114) atoms. The infinite-order relativistic 2-component Hamiltonian, known to closely reproduce 4-component results at lower computational cost, is used as framework. High-accuracy treatment of correlation is achieved by using the coupled cluster scheme with single, double, and perturbative triple excitations in large converged basis sets. The calculated interatomic separation and bond energy of Hg2, the only compound with known experimental data, are in good agreement with measurements. The binding of Fl to Au is stronger than that of Cn, predicting stronger adsorption on gold surfaces. The bond in the M2 species is strongest for Fl2, being of chemical nature; weaker bonds appear in Cn2 and Hg2, which are bound by van der Waals interactions, with the former bound more strongly due to the smaller van der Waals radius. The same set of calculations was also performed using the relativistic density functional theory approach, in order to test the performance of the latter for these weakly bound systems with respect to the more accurate coupled cluster calculations. It was found that for the MAu species the B3LYP functional provides better agreement with the coupled cluster results than the B88/P86 functional. However, for the M2 and the MHg molecules, B3LYP tends to underestimate the binding energies.
... The investigation of the elemental state of SHEs with Z > 112 is of particular interest. Thermochemical predictions based on relativistic density functional theory [28][29][30][31][32] render all p 7 -elements as fairly volatile species. Nevertheless, addressing the chemical properties of these elements challenges a gas chromatographic system in a broad temperature range of roughly 100 − 1000 K. Thus, this clearly demonstrates the necessity of new detection techniques for future SHE chemistry experiments. ...
Article
Here, we present the fabrication details and functional tests of diamond-based α-spectroscopic sensors, dedicated for high-temperature experiments, targeting the chemistry of transactinide elements. Direct heating studies with this sensor material, revealed a current upper temperature threshold for a safe α-spectroscopic operation of . Up to this temperature, the diamond sensor could be operated in a stable manner over long time periods of the order of days. A satisfying resolution of FWHM was maintained throughout all conducted measurements. However, exceeding the mentioned temperature limit led to a pronounced spectroscopic degradation in the range of , thereby preventing any further α-spectroscopic application. These findings are in full agreement with available literature data. The presented detector development generally enables the chemical investigation of more short-lived and less volatile transactinide elements and their compounds, yet unreachable with the currently employed silicon-based solid state sensors. In a second part, the design, construction, and α-spectroscopic performance of a 4-segmented diamond detector, dedicated and used for transactinide element research, is given as an application example.
... And from group 12 onward, 10 of the valence electrons first become inactive in an inert d 10 shell. In the 7 th row, this may even happen only from group 13 (Nh) onward, [116][117][118]189] while Hg in row 6 is a border case [119,120]. ...
Article
Full-text available
The Periodic Law, one of the great discoveries in human history, is magnificent in the art of chemistry. Different arrangements of chemical elements in differently shaped Periodic Tables serve for different purposes. “Can this Periodic Table be derived from quantum chemistry or physics?” can only be answered positively, if the internal structure of the Periodic Table is explicitly connected to facts and data from chemistry. Quantum chemical rationalization of such a Periodic Tables is achieved by explaining the details of energies and radii of atomic core and valence orbitals in the leading electron configurations of chemically bonded atoms. The coarse horizontal pseudo-periodicity in seven rows of 2, 8, 8, 18, 18, 32, 32 members is triggered by the low energy of and large gap above the 1s and n sp valence shells (2 ≤ n ≤ 6 !). The pseudo-periodicity, in particular the wavy variation of the elemental properties in the four longer rows, is due to the different behaviors of the s and p vs. d and f pairs of atomic valence shells along the ordered array of elements. The so-called secondary or vertical periodicity is related to pseudo-periodic changes of the atomic core shells. The Periodic Law of the naturally given System of Elements describes the trends of the many chemical properties displayed inside the Chemical Periodic Tables. While the general physical laws of quantum mechanics form a simple network, their application to the unlimited field of chemical materials under ambient ‘human’ conditions results in a complex and somewhat accidental structure inside the Table that fits to some more or less symmetric outer shape. Periodic Tables designed after some creative concept for the overall appearance are of interest in non-chemical fields of wisdom and art.
... In addition to its chemical reactivity, the possibility was discussed that, under ambient conditions, Cn can be a gas or a very volatile liquid (metal) [73]. Recent calculations [74][75][76] predict that a very volatile Cn would still retain a metallic character which would allow bond formation with metallic surfaces like Au [76]. On inert surfaces, however, no adsorption is expected [75]. ...
Article
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.
... Since then, much debate followed among experimentalists and theoreticians on whether Cn first and Fl later behave more like metals, as do lighter homologues of their respective group, or noble gases. [12][13][14][15][16][17] Uuo (Z = 118, featuring destabilized 7p 3/2 electrons due to spinorbit splitting), on the other side, is expected to be rather reactive compared to lighter noble gases. 18 Experiments are ongoing and the issue remains open, with consequences which may possibly impact even on the naming of the new elements. ...
Article
Full-text available
The chemistry of superheavy elements (Z ≥ 104) is actively investigated in atom-at-a-time experiments of volatility through adsorption on gold surfaces. In this context, common guidelines for interpretation based on group trends in the periodic table should be used cautiously, because relativistic effects play a central role and may cause predictions to fall short. In this paper, we present an all-electron four-component Dirac-Kohn-Sham comparative study of the interaction of gold with Cn (Z = 112), Fl (Z = 114), and Uuo (Z = 118) versus their lighter homologues of the 6th period, Hg, Pb, and Rn plus the noble gas Xe. Calculations were carried out for Au–E (E = Hg, Cn, Pb, Fl, Xe, Rn, Uuo), Au 7– and Au 20–E (E = Hg, Cn, Pb, Fl, Rn) complexes, where Au 7 (planar) and Au 20 (pyramidal) are experimentally determined clusters having structures of increasing complexity. Results are analysed both in terms of the energetics of the complexes and of the electron charge rearrangement accompanying their formation. In line with the available experimental data, Cn and more markedly Fl are found to be less reactive than their lighter homologues. On the contrary, Uuo is found to be more reactive than Rn and Xe. Cn forms the weakest bond with the gold atom, compared to Fl and Uuo. The reactivity of Fl decreases with increasing gold-fragment size more rapidly than that of Cn and, as a consequence, the order of the reactivity of these two elements is inverted upon reaching the Au 20-cluster adduct. Density difference maps between adducts and fragments reveal similarities in the behaviour of Cn and Xe, and in that of Uuo and the more reactive species Hg and Pb. These findings are given a quantitative ground via charge-displacement analysis.
... 5 In recent years, electronic structure calculations have been done for elements heavier than the actinides. [6][7][8] Even if these elements have never been synthesized in macroscopic samples big enough for experimental probing of crystal structure, it is only natural to ask if the accepted theories still hold for the heavier transition metals. One particularly important question is the role of relativistic terms. ...
Article
The phase stability of the 6d transition metals (elements 103–111) is investigated using first-principles electronic-structure calculations. Comparison with the lighter transition metals reveals that the structural sequence trend is broken at the end of the 6d series. To account for this anomalous behavior, the effect of relativity on the lattice stability is scrutinized, taking different approximations into consideration. It is found that the mass-velocity and Darwin terms give important contributions to the electronic structure, leading to changes in the interstitial charge density and, thus, in the structural energy difference.
... Furthermore, they investigated the relativistic effects and found to be about 5, 8, 19% of the binding energies for Zn 2 , Cd 2 , and Hg 2 , respectively. Finally the last member of the group Cn 2 , copernicium, has an academic interest [14][15][16] due the chemical character of the bonding in comparison to Hg 2 (and the lighter dimers of the group), and the influence of the relativistic effects on the atomic orbitals providing a change of the boding character in the dimer to more covalent or Van der Waals type. ...
Article
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I present a time-dependent density functional study of the 20 low-lying excited states as well the ground states of the zinc dimer Zn2, analyze its spectrum obtained from all electrons calculations performed using time-depended density functional with a relativistic 4-component and relativistic spin-free Hamiltonian as implemented in Dirac-Package, and show a comparison of the results obtained from different well-known and newly developed density functional approximations, a comparison with the literature and experimental values as far as available. The results are very encouraging, especially for the lowest excited states of this dimer. However, the results show that long-range corrected functionals such as CAMB3LYP gives the correct asymptotic behavior for the higher states, and for which the best result is obtained. A comparable result is obtained from PBE0 functional. Spin-free Hamiltonian is shown to be very efficient for relativistic systems such as Zn2. http://www.hindawi.com/journals/jamp/2012/361947/
... Figure 13(a) demonstrates this for the ratio q nlj ¼ hri R nlj =hri NR nlj of the relativistic (R) to nonrelativistic (NR) hri nlj expectation values for the element Cn (Z ¼ 112; ½Rn5f 14 6d 10 7s 2 configuration). The rather large 7s valence shell contraction (stabilization) shown in the figure makes Cn chemically more inert compared to the lighter congener Hg (Pitzer, 1975;Gaston et al., 2007;Eichler et al., 2008; , where relativistic effects are known to be large; they are responsible for Hg being the only elemental liquid metal at room temperature (Calvo et al., 2013;. Relativistic effects are also responsible for changing the ground-state configuration of Rg (Z ¼ 111) from 6d 10 7s 1 ( 2 S 1=2 ) to 6d 9 7s 2 ( 2 D 5=2 ) and halving its atomic size, making Rg as small as copper in the same periodic group (Eliav et al., 1994). ...
Article
During the last decade, six new superheavy elements were added into the seventh period of the periodic table, with the approval of their names and symbols. This milestone was followed by proclaiming 2019 the International Year of the Periodic Table of Chemical Elements by the United Nations General Assembly. According to theory, due to their large atomic numbers, the new arrivals are expected to be qualitatively and quantitatively different from lighter species. The questions pertaining to superheavy atoms and nuclei are in the forefront of research in nuclear and atomic physics and chemistry. This Colloquium offers a broad perspective on the field and outlines future challenges.
... 18 The accurate modelling of the electronic structure of SHE containing compounds requires a rigorous inclusion of relativistic effects as well as an accurate description of static and dynamic electron correlation effects for open shells with well above 100 electrons, roughly as many as in a medium-sized organic molecule. [23][24][25][26][27][28][29][30][31] Since this is computationally demanding, the modelling of the condensed phases of SHEs or, e.g. the adsorption experiments on gold surfaces typically used for the chemical characterisation of SHEs 18 requires a very efficient methodology and, in turn, a careful introduction of several approximations. [32][33][34] One very successful approximation for the description of heavy elements is the use of pseudopotentials (PPs). ...
Article
We present and evaluate a computationally efficient approach for exploring the chemical nature and bulk properties of the super-heavy main-group elements (SHEs) Cn-Og. https://pubs.rsc.org/en/content/articlelanding/2019/cp/c9cp02455g#!divAbstract
... Taking this into account for the heavier rare gas solids our best estimates for the cohesive energies are 230 and 500 meV for Rn and Og, respectively. The cohesive energy for Og is unusually large for a rare gas element and comparable to the estimated cohesive energies of Cn (390( +120 −100 ) meV) [38][39][40] and Fl (500 meV from theory [41] and 220( +230 −20 ) meV from experiment [42,43]). Eichler and Eichler predicted thermochemical data for the superheavy elements empirically [44]. ...
Article
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In the last two decades cold and hot fusion experiments lead to the production of new elements for the Periodic Table up to nuclear charge 118. Recent developments in relativistic quantum theory have made it possible to obtain accurate electronic properties for the trans-actinide elements with the aim to predict their potential chemical and physical behaviour. Here we report on first results of solid-state calculations for Og (element 118) to support future atom-at-a-time gas-phase adsorption experiments on surfaces such as gold or quartz.
Article
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Relativistic and electron correlation effects are investigated for the closed-shell superheavy-element monohydrides RgH, 112H+, 113H, 114H+, 117H, 118H+, 119H, and 120H+. Periodic trends are discussed by comparing the calculated properties to the ones for the lighter elements. The size of the relativistic effects varies considerably between the different molecules with the s-block elements being dominated by scalar relativistic effects and the p-block elements dominated by spin-orbit effects. In most cases, relativistic effects are more important than electron correlation effects and both are nonadditive as one expects. 120H+ behaves in a counterintuitive way as it shows a relativistic bond-length expansion together with a large relativistic decrease in the dissociation energy. The reason behind this anomalous behavior is due to the relativistically diminished valence-7d participation in the 120-H bond.
Article
In previous works on Zn2 and Cd2 dimers we found that the long-range corrected CAMB3LYP gives better results than other density functional approximations for the excited states, especially in the asymptotic region. In this paper, we use it to present a time-dependent density functional (TDDFT) study for the ground-state as well as the excited states corresponding to the (6s(2) + 6s6p), (6s(2) + 6s7s), and (6s(2) + 6s7p) atomic asymptotes for the mercury dimer Hg2. We analyze its spectrum obtained from all-electron calculations performed with the relativistic Dirac-Coulomb and relativistic spinfree Hamiltonian as implemented in DIRAC-PACKAGE. A comparison with the literature is given as far as available. Our result is excellent for the most of the lower excited states and very encouraging for the higher excited states, it shows generally good agreements with experimental results and outperforms other theoretical results. This enables us to give a detailed analysis of the spectrum of the Hg2 including a comparative analysis with the lighter dimers of the group 12, Cd2, and Zn2, especially for the relativistic effects, the spin-orbit interaction, and the performance of CAMB3LYP and is enlightened for similar systems. The result shows, as expected, that spinfree Hamiltonian is less efficient than Dirac-Coulomb Hamiltonian for systems containing heavy elements such as Hg2.
Article
The structural and electronic properties of rutherfordium, the latest group IV B element, have been evaluated by first principles density functional theory in scalar relativistic formalism with and without spin–orbit coupling and compared with its 5d homologue Hf. It is found that Rf will crystallize in the hexagonal close packed structure as in Hf. However, under pressure, it will have different sequence of phase transitions than Hf: hcp→bcchcp→bcc instead of hcp→ω→bcchcp→ω→bcc. An explanation is offered for this difference in terms of the competition between the band structure and the Ewald energy contributions.
Article
In this letter we address the problem of phase stability in the relatively new element 112, namely Copernicium (Cn). The ground state properties as well as the thermodynamic quantities were computed from a first-principles approach based on the local density approximation with spin orbit (SO) consideration. We found that relativistic effects play a vital role in the phase stability and electronic properties of Cn. The obtained results reveal some unusual energetic competition between the crystallographic forms that Cn may adopt, i.e., sc, bcc, fcc and hcp. Nevertheless, relativistic SO coupling increases the energetic stability of the bcc phase over the other structures; moreover dynamical calculations via phonon dispersion provide strong support for our findings. Band structure results indicate that Copernicium is at least a semiconductor in all possible phases. The valence bands of Cn have strong 6d6d character, with a significant mixing between the fully occupied 7s7s and 6d6d bands.
Article
The unsaturated hexathia-18-crown-6 (UHT18C6) molecule was investigated for the extraction of Hg(II) in HCl and HNO3 media. This extractant can be directly compared to the recently studied saturated hexathia-18-crown-6 (HT18C6). The default conformation of the S lone pairs in UHT18C6 is endodentate, where the pocket of the charge density, according to the crystal structures, is oriented toward the center of the ring, which should allow better extraction for Hg(II) compared to the exodentate HT18C6. Batch study experiments showed that Hg(II) had better extraction at low acid molarity (ca. 99% in HCl and ca. 95% in HNO3), while almost no extraction was observed above 0.4 M HCl and 4 M HNO3 (<5%). Speciation studies were conducted with the goal of delineating a plausible extraction mechanism. Density functional theory calculations including relativistic effects were carried out on both Hg(II)-encapsulated HT18C6 and UHT18C6 complexes to shed light on the binding strength and the nature of bonding. Our calculations offer insights into the extraction mechanism. In addition to Hg(II), calculations were performed on the hypothetical divalent Cn(II) ion, and showed that HT18C6 and UHT18C6 could extract Cn(II). Finally, the extraction kinetics were explored to assess whether this crown can extract the short-lived Cn(II) species in a future online experiment.
Article
Spectroscopic properties of group-1 M2 and MAu (M=K, Rb, Cs, Fr, and element 119) were calculated using the 4c-DFT method. The results show that the relativistic contraction and stabilization of the ns(M) AO result in the inversion of trends both in atomic and molecular properties in group 1 beyond Cs. Electronegativity χ of the elements proves to decrease from Cs, the most electropositive element of all elements, to element 119, with its χ value approaching that of Na. Due to the largest relativistic effects on the 8s(119) AO in group 1, bonding in (119)2 appears to be stronger than that of K2, while bonding in 119Au should be the weakest out of all group-1 MAu. Using calculated dissociation energies of M2, sublimation enthalpies, ΔHsub, of Fr of 77kJ/mol and element 119 of 94kJ/mol were estimated using a linear correlation between these quantities in the chemical group. Using the M–Au binding energies, the adsorption enthalpies, −ΔHads, of 106kJ/mol on gold, 76kJ/mol on platinum, and 63kJ/mol on silver were estimated for element 119 via a correlation with known ΔHads in the chemical group. These moderate ΔHads values are indicative of a possibility of chromatography adsorption studies of element 119 on the noble metal surfaces.
Article
Relativistic electronic structure calculations of superheavy elements (Z=>104) are analyzed. Preference is given to those related to experimental research. The role of relativistic effects is discussed.
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Relativistic pseudopotential approach to the electronic structure simulation of superheavy elements (SHE) compounds is presented. Advanced formulations of this approach leaving both valence and outer-core electronic shells for explicit treatment give rise to simple and efficient computational techniques ensuring highly accurate description of most chemical properties of SHE. At present, the errors due to the use of approximate methods for solving the correlation problem for a subsystem of valence electrons are much larger than those stemming from the pseudopotential approximation itself. Recent applications to the studies of the chemistry of elements 112 (eka-Hg) and 114 (eka-Pb) are reviewed; properties of these elements and their lighter homologues, Hg and Pb, are compared.
Article
A study was conducted to report advancements in the production and chemistry of the heaviest elements. The study dealt with the latest advancements in the synthesis, chemical characterization, and theoretical studies of the heaviest elements. The heaviest stable known nucleus had been reached with 208Pb and all isotopes of heavier elements, including some elements such as Bi, Th, and U were found in nature as remnants of the last nucleosynthesis process. These isotopes of heavier elements were radioactive and decay preferentially by successive α-particle and β-particle emissions back to the last stable element Pb. Accurate calculations of properties of the heavier transactinide elements and their compounds were possible due to the latest developments in relativistic quantum theory, computational algorithms, and techniques.
Article
We have calculated some of the physical properties of the recently discovered 6d elements by density functional theory. Comparison with those of the 5d metals shows that there is a close analogy for the crystal structures, for parabolic variation of equilibrium atomic volumes and bulk moduli, and an almost linearly increasing behavior of the pressure derivative of the bulk modulus across the 6d series. The Friedel model that is used to explain these trends for homologous series also holds for 6d metals. These elements also seem to be placed correctly in the Periodic Table.
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Chemistry has arrived on the shore of the Island of Stability with the first chemical investigation of the superheavy elements Cn, 113, and 114. The results of three experimental series leading to first measured thermodynamic data and qualitatively evaluated chemical properties for these elements are described. An interesting volatile compound class has been observed in the on-line experiments for the elements Bi and Po. Hence, an exciting chemical study of their heavier transactinide homologues, elements 115 and 116 is suggested.
Article
An analysis of theoretical studies on the electronic structures and chemical properties of superheavy elements has structures and chemical properties of superheavy elements has been performed. It is noted that the specific features of been performed. It is noted that the specific features of calculations of molecular systems including superheavy ele-calculations of molecular systems including superheavy ele-ment atoms are determined by the exceptional role of relativ-ment atoms are determined by the exceptional role of relativ-istic effects that should be taken into account at all stages of istic effects that should be taken into account at all stages of electronic structure modelling. The main approximations for electronic structure modelling. The main approximations for relativistic Hamiltonians and general approaches to the sol-relativistic Hamiltonians and general approaches to the sol-ution of the many-electron problem for both superheavy ution of the many-electron problem for both superheavy element atoms and their compounds have been considered element atoms and their compounds have been considered and compared. The results of modelling the chemical proper-and compared. The results of modelling the chemical proper-ties of superheavy elements by ties of superheavy elements by ab initio ab initio methods and density methods and density functional theory have been analysed. The bibliography functional theory have been analysed. The bibliography includes 143 references includes 143 references. .
Article
Jedes Atom zählt: Neue Daten zum adsorptionschromatographischen Verhalten einzelner Atome des Elements 112 bestätigen dessen metallischen Charakter in der Wechselwirkung mit einer Goldoberfläche ähnlich zu seinen Homologen Zn, Cd und Hg. Den experimentellen Resultaten zufolge hat Element 112 eine deutlich höhere Flüchtigkeit als die leichteren Homologen der Gruppe 12 des Periodensystems.
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In this chapter dedicated to the 70th anniversary of Professor Mikhail Grigorievich Itkis the achievements and prospective in the field of the chemistry of superheavy elements are covered with emphasis on the results obtained by the collaboration of the Paul Scherrer Institute, Villigen, Switzerland with the Flerov Laboratory for Nuclear Reactions, Dubna, Russia. The status of chemical research with elements Cn and Fl is presented. From the obtained first results interesting scientific questions are deduced and discussed together with some crucial technical developments required to experimentally address these questions in the future.
Article
Accurate all-electron standard and hybrid density function (DFT) calculations was used to model the equilibrium lattice constants, bulk modulus, and band structure of 6d super heavy elements.•Atomic volumes, bulk moduli, cohesive energies are in a one-to-one correspondence with the 5d transition metal homologues,•Scalar relativistic DFT is sufficient to describe the structural and electronic properties of their metallic ground state of Lr–Rg, and•Cn (also known as eka-mercury) is an insulator whose electronic spectrum description requires spin–orbit coupling.
Article
Spectacular developments in relativistic quantum theory and computational algorithms in the last two decades allowed for accurate predictions of properties of the heaviest elements and their experimental behaviour. The most recent works in this area of investigations are overviewed. Preference is given to those related to experimental research. The role of relativistic effects is elucidated.
Article
Metallic catcher foils have been investigated on their thermal release capabilities for future superheavy element studies. These catcher materials shall serve as connection between production and chemical investigation of superheavy elements (SHE) at vacuum conditions. The diffusion constants and activation energies of diffusion have been extrapolated for various catcher materials using an atomic volume based model. Release rates can now be estimated for predefined experimental conditions using the determined diffusion values. The potential release behavior of the volatile SHE Cn (E112), E113, Fl (E114), E115, and Lv (E116) from polycrystalline, metallic foils of Ni, Y, Zr, Nb, Mo, Hf, Ta, and W is predicted. Example calculations showed that Zr is the best suited material in terms of on-line release efficiency and long-term operation stability. If higher temperatures up to 2773 K are applicable, tungsten is suggested to be the material of choice for such experiments.
Article
Chemical studies at the upper end of the periodic table have reached atomic number 114. Recent experiments aiming at investigating chemical properties of elements Cn, 113, and 114 are summarized. Though partly preliminary, all these elements behave as expected: due to the filled 6d(10) shell, they do not behave like transition metals anymore, as observed for the lighter transactinides. They exhibit a volatile behavior as expected for 7s and 7p elements. On the other hand, due to the extremely low signal to noise ratio in detectors used to identify separated products highest precaution on identifying single atoms is mandatory. As an example, published early attempts to synthesize Cn and to perform chemical studies with this element that could not be confirmed in later studies are summarized.
Article
Spectacular developments in the relativistic quantum theory and computational algorithms in the last few decades allowed for accurate calculations of properties of the superheavy elements (SHE) and their compounds. Often conducted in a close link to the experimental research, these investigations helped predict and interpret an outcome of sophisticated and expensive experiments with single atoms. Most of the works, particularly those related to the experimental studies, are overviewed in this publication. The role of relativistic effects being of paramount importance for the heaviest elements is elucidated.
Article
As the heaviest group 12 element known currently, copernicium (Cn) often presents the oxidation states of I+, II+, and rarely IV+ as in its homologue mercury. In this work we systematically studied the stability of some oxides, fluorides, and oxyfluorides of Cn by two-component relativistic calculations and found that the CnF6 molecule with an oxidation state of VI+ has an extraordinary stability. CnF6 may decompose into CnF4 by conquering an energy barrier of about 34 kcal mol-1 without markedly releasing heat. Our results indicate that CnF6 may exist under some special conditions.
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This chapter summarizes gas chemical studies of transactinides using two approaches, gas thermochromatography and isothermal gas chromatography. Both techniques enabled successful chemical studies of the transactinides, rutherfordium (Z = 104, Rf) , dubnium (Z = 105, Db), seaborgium (Z = 106, Sg), bohrium (Z = 107, Bh), hassium (Z = 108; Hs), copernicium (Z = 112, Cn), and the recently named flerovium (Z = 114, Fl). Typically, these chemical investigations were performed one-atom-at-a-time with a total of less than 20 atoms. For their synthesis, hot heavy-ion fusion reactions with actinide targets were used. The elements Rf through Hs show the typical behavior of d-elements, representing the expected trend within their respective group of the Periodic Table. The chemical species investigated were volatile halides, oxyhalides, oxide hydroxides, and oxides. The elements copernicium and flerovium were studied in their elemental state.
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Theoretical chemical research in the area of the heaviest elements is extremely important. It deals with predictions of properties of exotic species and their behavior in sophisticated and expensive experiments with single atoms and permits the interpretation of experimental results. Spectacular developments in the relativistic quantum theory and computational algorithms have allowed for accurate calculations of electronic structures of the heaviest elements and their compounds. Due to the experimental restrictions in this area, the theoretical studies are often the only source of useful chemical information. The works on relativistic calculations and predictions of chemical properties of elements with Z ≥ 104 are overviewed. Preference is given to those related to the experimental research. The increasingly important role of relativistic effects in this part of the Periodic Table is demonstrated.
Article
Compared with its lighter congener HgF4, copernicium tetrafluoride, CnF4, is predicted to be significantly more stable with respect to decomposition to the elements. Tetravalent flerovium on the other hand is unlikely to be experimentally accessible, except possibly as FlF4. Because of the large 7p1/2-3/2 energy splitting, many divalent flerovium compounds are also expected to be thermodynamically unstable. The two dihalides FlF2 and FlCl2, however, are predicted to be thermodynamically stable; flerovium thus is not quite as noble as xenon, which is not known to form a chloride.
Article
Production and investigation of properties of superheavy elements (SHEs) belong to the most fundamental areas of physical science. They seek to probe the uppermost reaches of the periodic table of the elements where the nuclei are extremely unstable and relativistic effects on the electron shells are increasingly strong. Theoretical chemical research in this area is very important. Due to experimental restrictions, it is often the only source of useful chemical information. It enables one to predict the behavior of the heaviest elements in the sophisticated and demanding experiments with single atoms and to interpret their results. Spectacular developments in the relativistic quantum theory and computational algorithms in the last few decades allowed for accurate calculations of electronic structures and properties of SHE and their compounds. Results of those investigations, particularly those related to the experimental research, are overviewed in this chapter. The role of relativistic effects is elucidated.
Chapter
Production and investigation of properties of superheavy elements (SHEs) belong to the most fundamental areas of physical science. They seek to probe the uppermost reaches of the periodic table of the elements where the nuclei are extremely unstable and relativistic effects on the electron shells are increasingly strong. Theoretical chemical research in this area is very important. Due to experimental restrictions, it is often the only source of useful chemical information. It enables one to predict the behavior of the heaviest elements in the sophisticated and demanding experiments with single atoms and to interpret their results. Spectacular developments in the relativistic quantum theory and computational algorithms in the last few decades allowed for accurate calculations of electronic structures and properties of SHE and their compounds. Results of those investigations, particularly those related to the experimental research, are overviewed in this chapter. The role of relativistic effects is elucidated.
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We report the structures and properties of the cyanide complexes of three superheavy elements (darmstadtium, roentgenium, and copernicium) studied using two- and four-component relativistic methodologies. The electronic and structural properties of these complexes are compared to the corresponding complexes of platinum, gold, and mercury. The results indicate that these superheavy elements form strong bonds with cyanide. Moreover, the calculated absorption spectra of these superheavy-element cyanides show similar trends to those of the corresponding heavy-atom cyanides. The calculated vibrational frequencies of the heavy-metal cyanides are in good agreement with available experimental results lending support to the quality of our calculated vibrational frequencies for the superheavy-atom cyanides.
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The cohesive energy of bulk Copernicium is accurately determined using the incremental method within a relativistic coupled-cluster approach. For the lowest energy structure of hexagonal close-packed (hcp) symmetry, we obtain a cohesive energy of -36.3 kJ/mol (inclusion of uncertainties lead to a lower bound of -39.6 kJ/mol), in excellent agreement with the experimentally estimated sublimation enthalpy of -38⁺¹²-10 kJ/mol [R. Eichler \textit{et al., Angew. Chem. Int. Ed.}, 2008, \textbf{47}, 3262]. At the coupled-cluster singles, doubles and perturbative triples level of theory, we find that the hcp structure is energetically quasi-degenerate with both the face-centred and body-centred cubic structures. These results provide a basis for testing various density-functionals, of which the PBEsol functional yields a cohesive energy of -34.1~kJ/mol in good agreement with our coupled-cluster value.
Article
The phase stability of the various crystalline structures of the super-heavy element Copernicium was determined based on the first-principles calculations with different levels of the relativistic effects. We utilized the Darwin term, mass-velocity, and spin-orbit interaction with the single electron framework of the density functional theory while treating the exchange and correlation effects using local density approximations. It is found that the spin-orbit coupling is the key component to stabilize the body-centered cubic (bcc) structure over the hexagonal closed packed (hcp) structure, which is in accord with Sol. Stat. Comm. 152 (2012) 530, but in contrast to Atta-Fynn and Ray (2015) [11], Gaston et al. (2007) [10], Papaconstantopoulos (2015) [9]. It seems that the main role here is the correct description of the semi-core relativistic 6p1/2 orbitals. The all other investigated structures, i.e. face-centered cubic (fcc), simple cubic (sc) as well as rhombohedral (rh) structures are higher in energy. The criteria of mechanical stability were investigated based on the calculated elastic constants, identifying the phase instability of fcc and rh structures, but surprisingly confirm the stability of the energetically higher sc structure. In addition, the pressure-induced structural transition between two stable sc and bcc phases has been detected. The ground-state bcc structure exhibits the highest elastic anisotropy from single elements of the Periodic table. At last, we support the experimental findings that Copernicium is a metal.
Article
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 6 th 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.
Article
In this paper I present a time-dependent density functional study for the ground-state as well the 20-lowest laying excited states of the cadmium dimer \cd, I analyze this spectrum obtained from all electrons calculations performed with time-depended density functional for the relativistic Dirac-Coulomb- and relativistic spin-free-Hamiltonian as implemented in \Dirac$\!$. The results are obtained from different density functional approximations, and a comparison with literature is given as far as available. The result is very encouraging, especially for the lowest excited states of this dimer, and is expected to be enlightened for similar systems. However, the results show that only long-range corrected functionals such CAMB3LYP, gives the correct asymptotic behavior for the higher states. A comparable result but less satisfactory is obtained from B3LYP and PBE0 functionals. Spin-free-Hamiltonian is shown to be very efficient for systems containing heavy elements such as \cd in framework of (time-dependent) density functional without introducing large errors.
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A correlation is established between thermodynamic data for hypothetical macroscopic amounts of elements and experimentally accessible data on gold surfaces. The correlation between the experimentally determined standard adsorption enthalpies of elements on gold surfaces and their standard sublimation enthalpies is shown to be valid over a broad data range for various elements from light noble gases (Kr) up to heavy metals (Pb, Bi). This type of correlation is indispensable to derive thermodynamic data for macroscopic amounts of elements from results of adsorption chromatographic experiments with single atom amounts. It is also necessary to predict the behavior of single atoms from given or estimated thermochemical data. The conditions under which this correlation is valid are elaborated. Finally, predicted data for the elements 112 and 114 are used to link them to the corresponding sublimation or adsorption data. The obtained prediction intervals are of exceptional importance for the design of sophisticated experimental setups for the chemical investigation of transactinide elements on a single atom scale.
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We have studied the dependence of the production cross sections of the isotopes 282,283112 and 286,287114 on the excitation energy of the compound nuclei 286112 and 290114. The maximum cross section values of the xn-evaporation channels for the reaction 238U(48Ca,xn)286−x112 were measured to be σ3n=2.5−1.1+1.8 pb and σ4n=0.6−0.5+1.6 pb; for the reaction 242Pu(48Ca,xn)290−x114: σ2n∼0.5 pb, σ3n=3.6−1.7+3.4 pb, and σ4n=4.5−1.9+3.6 pb. In the reaction 233U(48Ca,2–4n)277–279112 at E*=34.9±2.2 MeV we measured an upper cross section limit of σxn⩽0.6 pb. The observed shift of the excitation energy associated with the maximum sum evaporation residue cross section σER(E*) to values significantly higher than that associated with the calculated Coulomb barrier can be caused by the orientation of the deformed target nucleus in the entrance channel of the reaction. An increase of σER in the reactions of actinide targets with 48Ca is consistent with the expected increase of the survivability of the excited compound nucleus upon closer approach to the closed neutron shell N=184. In the present work we detected 33 decay chains arising in the decay of the known nuclei 282112, 283112, 286114, 287114, and 288114. In the decay of 287114(α)→283112(α)→279110(SF), in two cases out of 22, we observed decay chains of four and five sequential α transitions that end in spontaneous fission of 271Sg (Tα∕SF=2.4−1.0+4.3 min) and 267Rf (TSF∼2.3 h), longer decay chains than reported previously. We observed the new nuclide 292116 (Tα=18−6+16 ms,Eα=10.66±0.07 MeV) in the irradiation of the 248Cm target at a higher energy than in previous experiments. The observed nuclear decay properties of the nuclides with Z=104–118 are compared with theoretical nuclear mass calculations and the systematic trends of spontaneous fission properties. As a whole, they give a consistent pattern of decay of the 18 even-Z neutron-rich nuclides with Z=104–118 and N=163–177. The experiments were performed with the heavy-ion beam delivered by the U400 cyclotron of the FLNR (JINR, Dubna) employing the Dubna gas-filled recoil separator.
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We have studied the excitation functions of the reactions 244Pu(48Ca,xn). Maximum cross sections for the evaporation of 3–5 neutrons in the complete-fusion reaction 244Pu+48Ca were measured to be σ3n=2 pb, σ4n=5 pb, and σ5n=1 pb. The decay properties of 3n-evaporation product 289114, in the decay chains observed at low 48Ca energy coincide well with those previously observed in the 244Pu+48Ca and 248Cm+48Ca reactions and assigned to 288114. Two isotopes of element 114 and their descendant nuclei were identified for the first time at higher bombarding energies: 288114 (Eα=9.95 MeV, T1∕2=0.6 s) and 287114 (Eα=10.04 MeV, T1∕2=1 s). We also report on the observation of new isotopes of element 116, 290,291116, produced in the 245Cm+48Ca reaction with cross sections of about 1 pb. A discussion of self-consistent interpretations of all observed decay chains originating at Z=118, 116, and 114 is presented.
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The results of experiments designed to synthesize element 115 isotopes in the 243Am+48Ca reaction are presented. With a beam dose of 4.3×1018 248-MeV 48Ca projectiles, we observed three similar decay chains consisting of five consecutive α decays, all detected in time intervals of about 20 s and terminated at a later time by a spontaneous fission with a high-energy release (total kinetic energy ∼220 MeV). At a higher bombarding energy of 253 MeV, with an equal 48Ca beam dose, we registered a different decay chain of four consecutive α decays detected in a time interval of about 0.5 s, also terminated by spontaneous fission. The α decay energies and half-lives for nine new α-decaying nuclei are given. The decay properties of these synthesized nuclei are consistent with consecutive α decays originating from the parent isotopes of the new element 115, 288115 and 287115, produced in the 3n- and 4n-evaporation channels with cross sections of about 3 pb and 1 pb, respectively. The radioactive properties of the new odd-Z nuclei (105–115) are compared with the predictions of the macroscopic-microscopic theory. The experiments were carried out at the U400 cyclotron with the recoil separator DGFRS at FLNR, JINR.
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The many-body expansion V-int=Sigma V-i < j((2))(r(ij))+Sigma V-i < j < k((3))(r(ij),r(ik),r(jk))+center dot, in terms of interaction potentials between rare-gas atoms converges fast at distances r>r(HS), with r(HS) being the hard-sphere radius at the start of the repulsive wall of the interaction potential. Hence, for the solid state where the minimum distance is always above r(HS), a reasonable accuracy is already obtained for the lattice parameters and cohesive energies of the rare-gas elements using precise two-body terms. All tested two-body potentials show a preference of the hcp over the fcc structure. We demonstrate that this is always the case for the Lennard-Jones potential. We extend the Lennard-Jones potential to obtain analytical expressions for the lattice parameters, cohesive energy, and bulk modulus using the solid-state parameters of Lennard-Jones and Ingham [Proc. R. Soc. London, Ser. A 107, 636 (1925)], which we evaluate up to computer precision for the cubic lattices and hcp. The inclusion of three-body terms does not change the preference of hcp over fcc, and zero-point vibrational effects are responsible for the transition from hcp to fcc as shown recently by Rosciszewski [Phys. Rev. B 62, 5482 (2000)]. More precisely, we show that it is the coupling between the harmonic modes which leads to the preference of fcc over hcp, as the simple Einstein approximation of moving an atom in the static field of all other atoms fails to describe this difference accurately. Anharmonicity corrections to the crystal stability are found to be small for argon and krypton. We show that at pressures higher than 15 GPa three-body effects become very important for argon and good agreement is reached with experimental high-pressure density measurements up to 30 GPa, where higher than three-body effects become important. At high pressures we find that fcc is preferred over the hcp structure. Zero-point vibrational effects for the solid can be successfully estimated from an extrapolation of the cluster zero-point vibrational energies with increasing cluster size N. For He, the harmonic zero-point vibrational energy is predicted to be always above the potential energy contribution for all cluster sizes up to the solid state at structures obtained from the two-body force. Here anharmonicity effects are very large which is typical for a quantum solid.
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Adsorption / Transactinides / Element 112 / Thermochromatography Summary. Two experiments aiming at the chemical inves-tigation of element 112 produced in the heavy ion induced nuclear fusion reaction of 48 Ca with 238 U were performed at the Gesellschaft für Schwerionenforschung (GSI), Darm-stadt, Germany. Both experiments were designed to determine the adsorption enthalpy of element 112 on a gold surface using a thermochromatography setup. The temperature range covered in the thermochromatography experiments allowed the adsorption of Hg at about 35 • C and of Rn at about −180 • C. Reports from the Flerov Laboratory for Nuclear Re-actions (FLNR), Dubna, Russia claim production of a 5-min spontaneous fission (SF) activity assigned to 283 112 for the 238 U(48 Ca,3n) 283 112 reaction. Hence, Experiment I was de-signed to detect spontaneously fissioning (SF) isotopes of element 112 with half-lives (t 1/2) longer than about 20 s. 11 high-energy events were detected. 7 events exhibit a deposi-tion pattern resembling a chromatographic peak in the vicinity of Rn deposition. However, the energy of the events observed in Experiment I was lower than expected for a SF-decay of 283 112. Therefore, these events could not be unambigu-ously attributed to the decay of 283 112. In contradiction with earlier publications newer reports from FLNR Dubna claim that 283 112 decays by α-particle emission (E α = 9.5 MeV) with t 1/2 = 4 s followed by a SF-decay of 279 Ds (t 1/2 = 0.2 s). Therefore, Experiment II was designed to be sensitive to both claimed decay properties of 283 112. However, during this experiment neither short α-SF correlations nor SF co-incidences were detected. The conclusion is that 283 112 was not unambiguously detected, neither in Experiment I nor in Experiment II.
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From first-principles total-energy calculations on Hg over a wide volume range, we predict: (i) a pressure-induced bct (β-Hg) to hcp phase transition near 100 GPa (1 Mbar); (ii) a stable, low-temperature hcp structure from 100 GPa to at least 1 TPa (10 Mbar), with a high but increasing c/a ratio approaching a limiting value of 1.83; and (iii) three additional distorted, metastable phases (including α-Hg), all possibly energetically accessible at high temperature.
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The nuclear shell model predicts that the next doubly magic shell closure beyond 208Pb is at a proton number between Z=114 and 126 and at a neutron number N=184. The outstanding aim of experimental investigations is the exploration of this region of spherical superheavy elements (SHE’s). This article describes the experimental methods that led to the identification of elements 107 to 112 at GSI, Darmstadt. Excitation functions were measured for the one-neutron evaporation channel of cold-fusion reactions using lead and bismuth targets. The maximum cross section was measured at beam energies well below a fusion barrier estimated in one dimension. These studies indicate that the transfer of nucleons is an important process for the initiation of fusion. The recent efforts at JINR, Dubna, to investigate the hot-fusion reaction for the production of SHE’s using actinide targets are also presented. First results were obtained on the synthesis of neutron-rich isotopes of elements 112 and 114. However, the most surprising result was achieved in 1999 at LBNL, Berkeley. In a study of the reaction 86Kr+208Pb→294118*, three decay chains were measured and assigned to the superheavy nucleus 293118. The decay data reveal that, for the heaviest elements, the dominant decay mode is alpha emission, not fission. The results are discussed in the framework of theoretical models. This article also presents plans for the further development of the experimental setup and the application of new techniques. At a higher sensitivity, the exploration of the region of spherical SHE’s now seems to be feasible, more than 30 years after its prediction.
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An open access copy of this article is available and complies with the copyright holder/publisher conditions. One- and two-component (spin–orbit coupled) relativistic and nonrelativistic energy adjusted pseudopotentials and basis sets for the elements 111 and 112 are presented. Calculations on the positively charged monohydride of the recently discovered superheavy element 112 are reported. Electron correlation is treated at the multireference configuration interaction and coupled cluster level and fine structure effects are derived from a single-reference configuration interaction treatment. Relativistic effects decrease the (112) H+ bond distance by 0.41 Å. This bond contraction is similar to the one calculated recently for (111) H [Chem. Phys. Lett. 250, 461 (1996)]. As a result the bond distance of (112)H1 (1.52 Å) is predicted to be smaller compared to those of the hydrides of the lighter congeners HgH1 (1.59 Å), CdH1 (1.60 Å) and similar to that of ZnH1 (1.52 Å). We predict that (112)H1 is the most stable hydride in the Group 12 series due to relativistic effects. As in the case of (111)H the relativistic increase of the stretching force constant is quite large, from 1.5 to 4.3 mdyn/Å at the coupled cluster level. The trend in the dipole polarizabilities of the Group 12 elements is discussed. Relativistic and electron correlation effects are nonadditive and due to the relativistic ns contraction (n57 for 112), correlation effects out of the (n21)d core are more important at the relativistic than the nonrelativistic level. We also show evidence that element 112 behaves like a typical transition element, and as a consequence the high oxidation state 14 in element 112 might be accessible.
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The periodic table provides a classification of the chemical properties of the elements. But for the heaviest elements, the transactinides, this role of the periodic table reaches its limits because increasingly strong relativistic effects on the valence electron shells can induce deviations from known trends in chemical properties. In the case of the first two transactinides, elements 104 and 105, relativistic effects do indeed influence their chemical properties, whereas elements 106 and 107 both behave as expected from their position within the periodic table. Here we report the chemical separation and characterization of only seven detected atoms of element 108 (hassium, Hs), which were generated as isotopes (269)Hs (refs 8, 9) and (270)Hs (ref. 10) in the fusion reaction between (26)Mg and (248)Cm. The hassium atoms are immediately oxidized to a highly volatile oxide, presumably HsO(4), for which we determine an enthalpy of adsorption on our detector surface that is comparable to the adsorption enthalpy determined under identical conditions for the osmium oxide OsO(4). These results provide evidence that the chemical properties of hassium and its lighter homologue osmium are similar, thus confirming that hassium exhibits properties as expected from its position in group 8 of the periodic table.
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The number of chemical elements has increased considerably in the last few decades. Most excitingly, these heaviest, man-made elements at the far-end of the Periodic Table are located in the area of the long-awaited superheavy elements. While physical techniques currently play a leading role in these discoveries, the chemistry of superheavy elements is now beginning to be developed. Advanced and very sensitive techniques allow the chemical properties of these elusive elements to be probed. Often, less than ten short-lived atoms, chemically separated one-atom-at-a-time, provide crucial information on basic chemical properties. These results place the architecture of the far-end of the Periodic Table on the test bench and probe the increasingly strong relativistic effects that influence the chemical properties there. This review is focused mainly on the experimental work on superheavy element chemistry. It contains a short contribution on relativistic theory, and some important historical and nuclear aspects.
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We report the first results of relativistic correlation calculation of the spectroscopic properties for the ground state of E112H and its cation in which spin-orbit interaction is taken into account non-perturbatively. Studying the properties of E112 (eka-Hg) is required for chemical identification of its long-lived isotope, (283)112. It is shown that appropriate accounting for spin-orbit effects leads to dramatic impact on the properties of E112H whereas they are not so important for E112H(+). The calculated equilibrium distance, R(e) (calc)=1.662 Angstrom, in E112H is notably smaller than R(e) (expt)=(1.738+/-0.003) Angstrom and R(e) (calc)=1.738 Angstrom in HgH, whereas the dissociation energy, D(e) (calc)=0.42 eV, in E112H is close to D(e) (expt)=0.46 eV and D(e) (calc)=0.41 eV in HgH. These data are quite different from R(e) (NH)=1.829 Angstrom and D(e) (NH)=0.06 eV obtained for E112H within the scalar-relativistic Douglas-Kroll approximation. Our results indicate that E112 should not be expected to behave like a noble gas in contrast to the results by other authors.
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The results of calculations outlining aspects of the chemistry of element 112, element 114, and element 118 are compared to those for their 6th row analogues Hg, Pb, and Rn, respectively. Element 112 and element 114 are found to be relatively inert as compared to Hg and Pb, while element 118 is much more active than radon. Spin-orbit coupling plays a dominant role in this behavior.
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This chapter provides insight into the application of relativistic electronic structure theory to solids, focusing on the determination of the electronic ground state. Density functional theory (DFT) establishes the general frame for this task. At first, the fundamentals of relativistic DFT are sketched. This includes introductory considerations on the ground state energy, a brief review of four-current DFT, and the outline of approximations needed to arrive at digestible Kohn-Sham-Dirac equations. The second part is devoted to the numerical solution of these equations. One particular method, the relativistic version of the full-potential localorbital minimum-basis (FPLO) scheme is explained in detail. Though this method is by far not the only possible one, it is distinguished by the combination of three advantages: accuracy, efficiency, and straightforward interpretation of its outcomes in chemical terms. In the final section, the importance of relativistic effects in solid state physics is illustrated with the help of some examples, both from literature and from application of the described relativistic FPLO method. This collection includes specific effects on electronic structure and structural properties, on magnetic ground state properties (orbital moments, magnetocrystalline anisotropy) and on excitations (magneto-optics).
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This chapter summarizes gas chemical studies of transactinides using two approaches, gas thermochromatography and isothermal gas chromatography. Both techniques enabled successful chemical studies of the transactinides, rutherfordium (Z = 104, Rf), dubnium (Z = 105, Db), seaborgium (Z = 106, Sg), bohrium (Z = 107, Bh), hassium (Z = 108; Hs), copernicium (Z = 112, Cn), and the recently named flerovium (Z = 114, Fl). Typically, these chemical investigations were performed one-atom-at-a-time with a total of less than 20 atoms. For their synthesis, hot heavy-ion fusion reactions with actinide targets were used. The elements Rf through Hs show the typical behavior of d-elements, representing the expected trend within their respective group of the Periodic Table. The chemical species investigated were volatile halides, oxyhalides, oxide hydroxides, and oxides. The elements copernicium and flerovium were studied in their elemental state. © 2014 Springer-Verlag Berlin Heidelberg. All rights are reserved.
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In preparation for the experimental investigation of chemical properties of element 112 model studies were conducted based on the assumed similarity of element 112 to either the noble gas Rn or the transition metal Hg, its supposed lighter homologue in group 12. The adsorption behavior of elemental Hg on the transition metals Ag, Au, Ni, Pd, and Pt were investigated experimentally by off-line gas thermochromatography. The deduced adsorption data of Hg were compared with new values calculated using the Eichler–Miedema model. The observed sequence of increasing Hg-metal-interactions for Ag < Ni < Au < Pd < Pt confirms the predicted trend. The only exception was Pd, on which Hg was calculated to adsorb at a higher temperature than on Pt. Difficulties to obtain reproducible clean surfaces of Ag, Ni, Pd, and Pt led to the choice of Au as the best metal surface suitable to adsorb Hg. For fast on-line gas thermochromatography studies on metallic surfaces a new set-up was developed based on the
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The decay properties of 290116 and 291116, and the dependence of their production cross sections on the excitation energies of the compound nucleus, 293116, have been measured in the 245Cm (48Ca, xn)293-x116 reaction. These isotopes of element 116 are the decay daughters of element 118 isotopes, which are produced via the 249Cf+48Ca reaction. We performed the element 118 experiment at two projectile energies, corresponding to 297118 compound nucleus excitation energies of E*=29.2±2.5 and 34.4±2.3 MeV. During an irradiation with a total beam dose of 4.1×1019 48Ca projectiles, three similar decay chains consisting of two or three consecutive α decays and terminated by a spontaneous fission (SF) with high total kinetic energy of about 230 MeV were observed. The three decay chains originated from the even-even isotope 294118 (Eα=11.65±0.06 MeV, Tα=0.89-0.31+1.07 ms) produced in the 3n-evaporation channel of the 249Cf+48Ca reaction with a maximum cross section of 0.5-0.3+1.6 pb.
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We present a full-potential band-structure scheme based on the linear combination of overlapping nonorthogonal orbitals. The crystal potential and density are represented as a lattice sum of local overlapping nonspherical contributions. The decomposition of the exchange and correlation potential into local parts is done using a technique of partitioning of unity resulting in local shape functions, which add exactly to unity in the whole crystal and which are very easily treated numerically. The method is all-electron, which means that core relaxation is properly taken into account. Nevertheless, the eigenvalue problem is reduced to the dimension of a minimum valence orbital basis only. Calculations on sp and transition metals give results comparable to other full-potential methods. The calculations on the diamond lattice demonstrate the applicability of our approach to open structures. The consequent local description of all real-space functions allows the treatment of substitutional disordered materials.
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Initial results of the application of relativistic Hartree–Fock (DHF) orbitals to the covalent ponding of elements 112, 114, and 118 lead to the conclusion that these elements are volatile and relatively inept. (AIP)
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We assess various approximate forms for the correlation energy per particle of the spin-polarized homogeneous electron gas that have frequently been used in applications of the local spin density approximation to the exchange-correlation energy functional. By accurately recalculating the RPA correlation energy as a function of electron density and spin polarization we demonstrate the inadequacies of the usual approximation for interpolating between the para- and ferro-magnetic states and present an accurate new interpolation formula. A Padé approximant technique is used to accurately interpolate the recent Monte Carlo results (para and ferro) of Ceperley and Alder into the important range of densities for atoms, molecules, and metals. These results can be combined with the RPA spin-dependence so as to produce a correlation energy for a spin-polarized homogeneous electron gas with an estimated maximum error of 1 mRy and thus should reliably determine the magnitude of non-local corrections to the local spin density approximation in real systems.
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Mercury condenses at 233K into the rhombohedral structure with an angle of 70.53°. Theoretical predictions of this structure are difficult. While a Hartree-Fock treatment yields no binding at all, density-functional theory (DFT) approaches with gradient-corrected functionals predict a structure with a significantly too large lattice constant and an orthorhombic angle of about 60°, which corresponds to an fcc structure. Surprisingly, the use of the simple local density approximation (LDA) functional yields the correct structure and lattice constants in very good agreement with experiment; relativistic effects are shown to be essential for reaching this agreement. In addition to DFT results, we present a wave-function-based correlation treatment of mercury and discuss in detail the effects of electron correlation on the lattice parameters of mercury including d -shell correlation and the influence of three-body terms in the many-body decomposition of the interatomic correlation energy. The lattice parameters obtained with this scheme at the coupled cluster level of theory agree within 1.5% with the experimental values. We further present the bulk modulus calculated within the wave-function approach, and compare to LDA and experimental values.
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In den letzten Jahrzehnten sind immer mehr neue chemische Elemente entdeckt worden. Dass die schwersten, künstlich erzeugten Elemente am Ende des Periodensystems im Gebiet der lang erwarteten superschweren Elemente liegen, macht dies besonders spannend. Derzeit kommen bei diesen Entdeckungen noch hauptsächlich rein physikalische Techniken zum Einsatz, chemische Methoden haben allerdings stark aufgeholt. Fortgeschrittene, hochempfindliche Techniken ermöglichen es, die chemischen Eigenschaften dieser schwer fassbaren Elemente zu untersuchen. Oft sind es insgesamt weniger als zehn kurzlebige Atome – jedes einzelne individuell chemisch abgetrennt (“one atom at a time”) –, die entscheidende Informationen über grundlegende chemische Eigenschaften liefern. Diese Ergebnisse ermöglichen es, den Aufbau des Periodensystems der Elemente an seinem Ende zu bestimmen und den Einfluss der zunehmend starken relativistischen Effekte auf die chemischen Eigenschaften zu untersuchen. Dieser Aufsatz beschreibt schwerpunktmäßig die experimentellen Arbeiten zur Chemie superschwerer Elemente. Er enthält einen kurzen Abriss der relativistischen Theorie und behandelt einige wichtige historische und nukleare Aspekte.
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Fully relativistic (four-component) density-functional calculations were performed for the element 112 dimers (112)X (X = Pd, Cu, Ag and Au) and those of its lighter homolog, Hg. A relatively small decrease of about 15–20 kJ/mol in bonding was found from the HgX to (112)X compounds. Respectively, the bond lengths were increased by 0.06 Å on the average. The Mulliken population analysis has shown this effect to be a result of a decreasing contribution of the relativistically stabilized 7s-AO of element 112 to bonding. The following trend in the binding energies was predicted for (112)X as a function of X: Pd >Cu>Au>Ag, exactly as the trend obtained experimentally for adsorption of Hg on the corresponding metal surfaces.
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The non-collinear and collinear descriptions within relativistic density functional theory is described. We present results of both non-collinear and collinear calculations for atoms, diatomic molecules, and some larger molecules. We find that the accuracy of our density functional calculations for the smaller systems is comparable to good quantum chemical calculations, and thus this method provides a sound basis for larger systems where no such comparison is possible.
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The relativistic coupled-cluster method is used to calculate ionization potentials and excitation energies of Hg and element 112, as well as their mono- and dications. Large basis sets are used, with {ital l} up to 5, the Dirac-Fock or Dirac-Fock-Breit orbitals found, and the external 34 electrons of each atom are correlated by the coupled-cluster method with single and double excitations. Very good agreement with experiment is obtained for the Hg transition energies, with the exception of the high ({gt}12 eV) excitation energies of the dication. As in the case of element 111 [Eliav {ital et} {ital al}., Phys. Rev. Lett. {bold 73}, 3203 (1994)], relativistic stabilization of the 7{ital s} orbital leads to the ground state of 112{sup +} being 6{ital d}{sup 9}7{ital s}{sup 2}, rather than the {ital d}{sup 10}{ital s} ground states of the lighter group 12 elements. The 112{sup 2+} ion shows very strong mixing of the {ital d}{sup 8}{ital s}{sup 2}, {ital d}{sup 9}{ital s}, and {ital d}{sup 10} configurations. The lowest state of the dication is 6{ital d}{sup 8}7{ital s}{sup 2} {ital J}=4, with a very close (0.05 eV) {ital J}=2 state with strong {ital d}{sup 8}{ital s}{sup 2} and {ital d}{sup 9}{ital s} mixing. No bound states were found for the anions of the two atoms.
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The ground-state correlation energy per particle in a uniform electron gas with spin densities n↑ and n↓ may be expressed as εc(zeta,rs)=I(zeta,rs)εc(0,rs), where rs=[3/4pi(n↑+n↓)]1/3 is the density parameter and zeta=(n↑-n↓)/(n↑+n↓) is the relative spin polarization. We find an analytic expression for the spin-scaling factor (SSF) I(zeta,rs) in the high-density limit rs-->0. It decreases from the value 1 at zeta=0, approaching the value 1/2 with slope -∞ as zeta approaches 1. A simple approximation to this SSF which displays the correct qualitative behavior is g3(zeta), where g(zeta)=[(1+zeta)2/3+(1-zeta)2/3]/2. We find that g(zeta) is the SSF for the coefficient of the ||∇n||2/n4/3 term of the spin-density gradient expansion of the exchange energy, and a good approximation to the SSF for that of correlation: scrCx(zeta)/scrCx(0)=g(zeta) and scrCc(zeta, rs-->0)/scrCc(0, rs-->0)~=g(zeta). We also find that the ||∇zeta||2 contribution to the correlation energy is always negligible.
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For a uniform electron gas of density n=n↑+n↓=3/4pir3s=pik6s/192 and spin polarization zeta=(n↑-n↓)/n, we study the Fourier transform rho¯c(k,rs,zeta) of the correlation hole, as well as the correlation energy εc(rs,zeta)=F∞0dk rho¯c/pi. In the high-density (rs-->0) limit, we find a simple scaling relation ksrho¯c/pig2-->f(z,zeta), where z=k/gks, g=[(1+zeta)2/3+(1-zeta)2/3]/2, and f(z,1)=f(z,0). The function f(z,zeta) is only weakly zeta dependent, and its small-z expansion -3z/pi2+4 &surd;3 z2/pi2+... is also the exact small-wave-vector (k-->0) expansion for any rs or zeta. Motivated by these considerations, and by a discussion of the large-wave-vector and low-density limits, we present two Padé representations for rho¯c at any k, rs, or zeta, one within and one beyond the random-phase approximation (RPA). We also show that rho¯ RPAc obeys a generalization of Misawa's spin-scaling relation for εRPAc, and that the low-density (rs-->∞) limit of εRPAc is ~r-3/4s.
Article
We propose a simple analytic representation of the correlation energy εc for a uniform electron gas, as a function of density parameter rs and relative spin polarization zeta. Within the random-phase approximation (RPA), this representation allows for the r-3/4s behavior as rs-->∞. Close agreement with numerical RPA values for εc(rs,0), εc(rs,1), and the spin stiffness alphac(rs)=∂2εc(rs, zeta=0)/deltazeta2, and recovery of the correct rslnrs term for rs-->0, indicate the appropriateness of the chosen analytic form. Beyond RPA, different parameters for the same analytic form are found by fitting to the Green's-function Monte Carlo data of Ceperley and Alder [Phys. Rev. Lett. 45, 566 (1980)], taking into account data uncertainties that have been ignored in earlier fits by Vosko, Wilk, and Nusair (VWN) [Can. J. Phys. 58, 1200 (1980)] or by Perdew and Zunger (PZ) [Phys. Rev. B 23, 5048 (1981)]. While we confirm the practical accuracy of the VWN and PZ representations, we eliminate some minor problems with these forms. We study the zeta-dependent coefficients in the high- and low-density expansions, and the rs-dependent spin susceptibility. We also present a conjecture for the exact low-density limit. The correlation potential musigmac(rs,zeta) is evaluated for use in self-consistent density-functional calculations.
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A system of additive covalent radii is proposed for σ2 π4 triple bonds involving elements from Be to E 112 (eka-mercury). Borderline cases with weak multiple bonding are included. Only the elements in Group 1, the elements Zn–Hg in Group 12 and Ne in Group 18 are then totally excluded. Gaps are left at late actinides and some lanthanides. The standard deviation for the 324 included data points is 3.2 pm. Alkuaineille Be–(E 112) on määrätty σ2 π4-kolmoissidoksille luonteenomaiset kovalenttiset säteet, rajatapaukset mukaan lukien. Vain ryhmän 1 alkuaineet, ryhmän 12 alkuaineet Zn–Hg, ryhmän 18 Ne sekä osa lantanoideista ja myöhemmät aktinoidit on tällöin kokonaan jätetty tarkastelun ulkopuolelle. Aineisto käsittää 324 pistettä ja tulosten standardipoikkeama on 3.2 pm.Abstract in German:Ein System additiver kovalenter Radien für σ2 π4Dreifachbindungen fast aller Elemente von Be bis E 112 (Eka-Quecksilber) wird vorgestellt. Grenzfälle mit schwachen Mehrfachbindungen wurden mit einbezogen. Die Elemente in Gruppe 1, Zn–Hg in Gruppe 12, Ne, die meisten Lantanide und einige Actinide wurden wegen mangelnder Daten nicht berücksichtigt. Die Standardabweichung für die 324 verwendeten Datenpunkte beträgt 3.2 pm.
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