Copernicium: A Relativistic Noble Liquid

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

Copernicium (Cn, Z = 112) is the latest addition to Group 12 (Zn, Cd, Hg) of the periodic table,a nd with an adecay half-life of 29 sf or the 285 Cn isotope,o ne of the most long-lived superheavy elements (SHEs). [1,2] Its lifetime is sufficient to perform atom-at-a-time experiments and explore periodic trends. [3][4][5] Concerning these trends,i ts lighter congener Hg is known to exhibit some very unusual behavior compared to both Zn and Cd, with reported low melting and boiling points (Figure 1), [6,7] rendering Hg the only metallic liquid at room temperature and as uperconductor with at ransition 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 af ar 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.
Moving down in the periodic table,r elativistic effects scale as Z 2 with the nuclear charge,l eading to as trong relativistic 7s contraction and 6d 5/2 expansion in Group 12 elements,and eventually to areversal of the energy ordering between these two levels for Cn. As aresult, and in contrast to all other members in this group,C nm ay be regarded as a d-block element, evident, for example,f rom the squareplanar structure of CnF 4 . [10] Moreover,the relativistic valence scontraction in combination with the weak chemical bonding of the 6d 5/2 orbitals leads to an increasing chemical inertness of the Group 12 elements, [16] which is reflected in the decrease of the cohesive energy E coh (see the green line in Figure 1). [4,7] This was first noted by Pitzer based on relativistic electronic-structure calculations,w ho in turn suggested that Cn will be chemically inert and more similar to the noble gases than its lighter congeners,and thus either avery volatile liquid bound by dispersion or gaseous at ambient conditions. [16] More recently,t his view has been challenged by atom-at-a-time experiments for Cn. [3,4] By directly comparing the adsorption of neutral Cn atoms on ag old surface to Rn (E coh = À0.23 eV) and Hg (E coh = À0.67 eV), the cohesive Melting and boiling points (in K) as well as cohesive energies (lattice energy of the most stable phase in eV/atom) of the Group 12 elements zinc (Zn), cadmium(Cd), mercury (Hg), and copernicium (Cn). [17,18] The yellow area indicates ambient conditions, for which we assume atemperature range of 288. 15 energy of Cn was estimated from its adsorption energy providing À0.39 AE 0.12 eV,w hich was later updated to À0.37 AE 0.11 eV. [19] As this is twice the value of the noble gas Rn, and the increase could not be explained by model calculations,itwas concluded that Cn must exhibit some kind of metallic interaction with the gold surface,a nd will presumably be solid at ambient conditions with an estimated evaporation temperature of 357 þ111 À108 K. [4] However,t he relatively strong interaction with the gold surface may as well be due to strong dispersion interactions.A lso considering the distinctly larger cohesive energy of the superheavy "noble gas" [20] oganesson (Og) of À0.45 eV, [21] Cn appears to lean towards the noble gases rather than towards its lighter metallic congeners.
Recently,t he solid phases of Cn have been explored by means of highly accurate method-of-incrementr elativistic coupled cluster (MOI-CC) calculations. [18] In excellent agreement with the experimental estimate,t hese calculations provided acohesive energy of À0.38 AE 0.03 eV,and moreover revealed that hcp is the most stable phase and quasidegenerate with fcc and bcc. While such ad egeneracy is characteristic of noble-gas solids,itisincontrast to the earlier Group 12 metals,which all exhibit aclear preference for hcp (Zn, Cd) or rhombohedral lattices (Hg) over fcc of about 30 meV compared to 1meV for Cn at the SO-DFT/PBEsol level.
Using these insights as ab asis,w eu ndertook the derivation and careful evaluation of an efficient density functional theory (DFT) based methodology to enable finitetemperature simulations of Cn. Forthis purpose,aprojectoraugmented wave potential (PAW )w ith al arge 20 electron (6s 2 6p 6 6d 10 7s 2 )v alence space was devised following the approach of Joubert and Kresse. [22,23] Surveying various density functionals,i tw as eventually established that the PBEsol functional [24] provides the best agreement with MOI-CC results for cohesive energies,t he impact of spin-orbit coupling,and the ordering as well as structural parameters of the solid phases (see Table 1and the Supporting Information for more functionals,a sw ell as Refs. [18] and [25] for more information on the PAW potential). Here,w ep resent the application of this methodology in the framework of freeenergy calculations to explore the physicochemical properties and determine the aggregate state of bulk Cn at ambient conditions.M oreover,t oe lucidate the role of relativistic effects,wea lso performed calculations in the non-relativistic limit.

Results and Discussion
Afirst hint towards the type of bonding in bulk Cn and the role of relativistic effects is evident from the cohesive energies and structural parameters calculated at the non-relativistic (NR), scalar-relativistic (SR), and spin-orbit (SO) relativistic levels provided in Table 1. Inspection reveals that in good agreement between DFT and MOI-CCSD(T), the influence of SO coupling is rather small. This is because the splitting of the lowest unoccupied 7p levels and highest occupied 6d levels only leads to aslight reduction of the band gap,but does not change their character.I nc ontrast, SR effects do cause the character of the highest occupied orbital to change from 7s in the non-relativistic limit to 6d. As the 7s orbital forms stronger chemical bonds than the 6d orbital, this strongly affects the reactivity. [16] Accordingly,c alculations in the NR limit reveal af ourfold increase in E coh compared to the relativistic calculations,and moreover asignificant impact on the structural parameters:While the optimizations at the SR and SO levels yield a c/a ratio very close to the ideal value of the hcp lattice of 1.633, which is again typical for weakly interacting systems,t he NR calculations converge to ad istorted hcp structure with aratio of 1.737 similar to the lighter Group 12 metals (Zn 1.804, Cd 1.886, Hg 1.710 (calc.)). [7,26] Moving on to the finite-temperature results,w ef irst determined the equilibrium volumes of the liquid and solid phases at 300 K, and subsequently calculated the Gibbs free energies.T oa ccount for the small yet relevant deviation between DFT and the high-level CCSD(T) reference (see Table 1and the discussion in the Supporting Information), all finite-temperature simulations were conducted not only with plain DFT/PBEsol, but also with as caled variant termed lDFT or lPBEsol that was matched to the CCSD(T) cohesive energy.M oreover,e xploiting al inear relation between the potential energy and the melting point, we also corrected the plain DFT results for this deviation, which will be referred to as l-shifting.Adetailed discussion of this relation, including an analytical proof,i sp rovided in the Supporting Information.
To obtain the volume,s everal NVT simulations were conducted at different volumes until the average pressure was reasonably close to zero (AE 0.2 kbar, for details see the Supporting Information). This approach provides as olid density of 1 300K s = 14.7 gcm À3 for 285 Cn (15.8 gcm À3 at 0K)a t the lDFT level, which decreases by 5.5 %u pon melting to [a] Estimated from the adsorption enthalpy on gold [4] using the updated relation from Ref. [19].See also Ref. [25].
[ b] SR-CCSD(T) calculations employ the same structure as SO.
[c] Because of the distorted c/a ratio, R nn is between in-plane atoms, whereas it is across two planes at the relativisticl evel.
al iquid density of 1 300K l = 14.0 gcm À3 .T hese results are in stark contrast to the most prominent previous estimate of 23.7 gcm À3 , [27] and show that Cn exhibts ar ather normal density for ah eavy element. Accordingly,C ni so nly slightly more dense than its lighter congener Hg (1 300K l = 13.55 gcm À3 , 1 227K s = 14.26 gcm À3 )b ecause the higher atomic mass is canceled by the larger interatomic distances.
Having determined the equilibrium volumes,w ec alculated Gibbs free energies,entropies S,and internal energies U of the solid and liquid phases at 300 Kusing thermodynamic integration as described in the Supporting Information. [28,29] To derive the melting point T m from the results obtained at 300 K(colored squares and circles in Figure 2), the solid and liquid Gibbs free energies were extrapolated linearly to their intersection as shown in Figure 2. This provides av alue of 263 AE 11 Kw ith plain DFT (dark colors), which increases to 282 AE 12 Ka fter l-shifting, and is thus consistent with the result of 284 AE 10 Kobtained with the scaled lDFT potential (light colors). These values are moreover consistent with further results for different cell sizes and simulation temperatures (273-294 K, see the Supporting Information), leading to our final estimate for T m of 283 AE 11 K( 10 8 8C).
To determine the boiling point T b ,t he free energy of the gas phase G g (orange line) was obtained analytically by using the ideal-gas law and including the first virial correction of only 0.25 meV/atom [Eqs.(S4)-(S6) in the Supporting Information]. [30] Theintersections with the liquid phase occur at 316 AE 2Kwith plain DFT (338 Ka fter l-shifting) and 331 AE 2K with lDFT.A lthough the statistical error of T b is much smaller due to the steeper intersection (see Figure 2), the deviation between the independent simulations is larger.F or an increased simulation temperature of 360 K, T b increases to 348 K( see the Supporting Information), which we take into account in our final estimate for T b of 340 AE 10 K ( 67 8 8C). Accordingly,C ni savolatile liquid with av apor pressure of p 293K % 0.3 bar, and at riple point at 283 Ka tapressure of approximately 0.25 bar.
Thec alculated thermodynamic quantities eventually allow us to shed some light on the nature of the interactions in bulk Cn. From the difference of the internal energies of the solid and liquid phases,w ec alculated ah eat of fusion of 26.5 meV/atom or 2.55 kJ mol À1 at the lDFT level. This is slightly above the value of 2.33 kJ mol À1 for Hg,a nd slightly below the 2.89 kJ mol À1 value for Rn. [31] Hence,d espite the much larger cohesive energy of Hg of À0.67 eV,i ts heat of fusion is distinctly smaller than that of Cn, while the opposite is the case for Rn (E coh = À0.23 eV). This seemingly counterintuitive ordering can be traced back to the nature of the interactions in the condensed phases.Incontrast to the longranged metallic bonding of Hg and its lighter congeners,t he dispersion interactions dominating in noble-gas-like elements exhibit am uch stronger 1/r 6 distance dependence.T his becomes evident from the plot of the relative lattice energy (E min lat ¼ À1Þ as afunction of the cell size (R min nn ¼ 1) displayed in Figure 3a.Evidently,there is adistinct difference between dispersion-bound elements Rn and apparently also Cn with narrow potentials on the one hand, and on the other hand the metallic (group 12) elements including non-relativistic Cn with wider potentials.C onsidering that the solid is more ordered and dense than the liquid phase,the different shapes of the interatomic potentials explain why the weakly interacting systems Rn and Cn exhibit alarger heat of fusion than Hg despite their smaller cohesive energies.
Eventually,t he differences in the nature of the interatomic interactions enable aclassification of these elements by plotting their melting points against their cohesive energies T m /E coh as shown in Figure 3b.Alinear fit for each of the groups (with forced intersection of the origin) reveals ac haracteristic slope for each of them that corresponds to the average T m /E coh and correlates qualitatively with the shapes of the potentials depicted in Figure 3a.O nt he left, there are the noble-gas-like elements with the narrowest potential and highest T m /E coh ,a nd on the right the heavy main-group metals with much wider potentials and in turn one of the lowest T m /E coh .Inbetween, there are the alkalineearth as well as most other metals (not shown) with ratios of 0.4 AE 0.1 KmeV À1 .F igure 3b shows the lighter Group 12 members Zn and Cd to be situated close to the alkalineearth metals,which is consistent with their chemical behavior. Compared to those,H ge xhibits as light shift towards the heavy main-group elements,which all attain a T m /E coh value of approximately 0.3 KmeV À1 .F or Cn, this trend does not continue but the opposite is the case.I te xhibits as trong increase of T m /E coh to 0.75 KmeV À1 ,p lacing it in direct proximity to the noble gases and far away from any metals. This is in line with the shape of the potential shown in Figure 3a,a nd strongly suggests that the interactions in bulk Cn resemble those in anoble-gas solid.
This similarity further extends to the electronic band gap. Accurate many-body perturbation theory in the form of the self-consistent quasi-particle GW method [20,33,34] affords aband gap of 6.4 AE 0.2 eV for Cn (hcp), clearly characterizing it as an insulator (see the Supporting Information for details on the calculations). In this respect, Cn is much more similar to the noble gas Rn (band gap 7.1 eV) than to its lighter congeners,and even more similar to Rn than oganesson (Og) as the actual Group 18 member of the seventh period (band gap 1.5 eV,s ee Figure 3c). [20] Together with the smaller cohesive energy of Cn (0.38 eV vs.0.45 eV) [21,25] ,this suggests that Cn is more noble-gas-like than Og.
Ther eason for the trend-breaking behavior of Cn becomes evident from the calculations conducted in the non-relativistic limit:I tl ies in the presence of very strong scalar-relativistic effects.C ompletely neglecting relativity causes the melting point to increase by about 300 K( !) to 591 AE 10 K, placing it much closer to both Zn and Cd in Figure 3b.This is in line with azero band gap obtained at the NR-DFT/PBEsol level for the energetically lowest hcp lattice, as well as with the shape of the potential depicted in Figure 3a,w hich resembles that of the lighter Group 12 metals.E xtrapolating the liquid free energy to the intersection point with the gas phase affords arough estimate for the boiling point of about 1000 K, similar to Zn with 1180 Kand Cd with 1040 K, corresponding to ahuge relativistic increase of 700 K. ForH g, calculations at the NR-DFT/PBEsol level reported in Ref. [7] afford as imilar increase of the melting point from 241 Kt o4 03 K. However,t he nature of Hg as reflected in T m /E coh is only weakly affected, and it remains in the typical range for (Group 12) metals.

Conclusion
In summary,w eh ave explored the physicochemical properties of bulk copernicium by means of free-energy and band-structure calculations.T his revealed that at ambient conditions,Cnisavolatile liquid with amelting point of 283 AE 11 Kand aboiling point of 340 AE 10 Kand only slightly more dense than Hg (1 300K l = 14.0 gcm À3 ). We can thus fully confirm Pitzerso riginal hypothesis that Cn is either gaseous or av olatile liquid bound by dispersion. [16] Although the calculated boiling point is just below and well within the error bars of the evaporation temperature of 357 þ111 À108 K suggested by Eichler, [4] we can most certainly exclude the inferred metallic character based on the calculated band gap of 6.4 eV.O nt he contrary,w ef ound ad ominance of dispersion interactions in bulk Cn very similar to Rn, which together with the band gap and the structural parameters of solid Cn strongly suggests aweakly interacting, noble-gas-like character.The similarity to the noble gases is reflected also in the reactivity of Cn towards fluorine,w hich has been predicted to be similar to that of Xe (data available for Rn is insufficient to draw any such conclusions). Like Xe,C n forms thermodynamically stable di-and tetrafluorides with calculated energies of formation (DU 0 with respect to F 2 and atomic Cn) of À2.5 eV for CnF 2 and À3.6 eV for CnF 4 at the SO-CCSD(T)/DZ level. [10] Taking into account the basis-set superposition error resulting from the small DZ basis,a nd moreover the absence of zero-point and thermo-chemical corrections in these calculations,the values for Cn are at least comparable to the respective standard enthalpies of formation (DH o f )ofXeF 2 (À1.0 eV) and XeF 4 (À2.5 eV). [35] Hence, while the noble-gas-like character of Cn certainly has to be confirmed in further investigations focusing on the chemical bonding of Cn with electropositive and electronegative elements,a nd specifically the comparison to Xe and Rn, our results strongly suggest that bulk Cn behaves more like anoble gas than Og as the actual Group 18 member,and may thus be seen as the clandestine noble gas of the seventh period. Finally,the non-group-conforming behavior of Cn was traced back to the presence of strong scalar-relativistic effects. Neglecting relativity leads to an almost fourfold increase of the cohesive energy,and in turn to an increase of the melting Figure 3. a) Normalized energy as afunction of cell size for Rn and the Group 12 metals including Cn as well as Cn in the non-relativisticlimit. All calculations at the SO-DFT/PBEsol level. The lines were obtained by fitting the calculated points in the relative size interval 0.85-1.5 with atenth-order polynomial. b) Plot of the melting points against the respective cohesive energies for the noble gases, alkaline-earth metals, heavy main-groupe lements (Tl, Pb, Bi, Po, At), and Group 12 elements including Cn, as well as non-relativistic Cn and Hg. The two additionalp oints for Cn correspond to the upper and lower limits based on the error bars of the reference E coh (see the SupportingI nformation). Data for non-relativisticH gfrom Ref. [7],f or At from Ref. [32],a ll other elements from Ref. [17].c )Experimentala nd calculated electronic band gaps of the Group 12 and Group 18 elements. Calculations for Hg, Cn, and Group 18 at the SO-GW level of theory as described in the SupportingInformation and Ref. [20] (Group 18). and boiling points by 300 Ka nd 700 K. Hence,t he liquid aggregate state as well as the weakly interacting nature of Cn are both due to relativistic effects or, in other words,C ni s arelativistic noble liquid.