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.

Full text

German Edition:DOI:10.1002/ange.201906966
Superheavy Elements International Edition:DOI:10.1002/anie.201906966
Copernicium:ARelativistic Noble Liquid
Jan-Michael Mewes,* Odile R. Smits,Georg Kresse,and Peter Schwerdtfeger
Abstract: The chemical nature and aggregate state of super-
heavy copernicium (Cn) have been subject of speculation for
many years.While strong relativistic effects render Cn chemi-
cally inert, which led Pitzer to suggest anoble-gas-like
behavior in 1975, Eichler and co-workers in 2008 reported
substantial interactions with agold surface in atom-at-a-time
experiments,suggesting ametallic character and asolid
aggregate state.Herein, we explore the physicochemical
properties of Cn by means of first-principles free-energy
calculations,whichconfirm PitzerQsoriginal hypothesis:With
predicted melting and boiling points of 283 :11 Kand 340 :
10 K, Cn is indeed avolatile liquid and exhibits adensity very
similar to that of mercury.However,instark contrast to
mercury and the lighter Group 12 metals,wefind bulk Cn to be
bound by dispersion and to exhibit alarge band gap of 6.4 eV,
which is consistent with anoble-gas-like character.This non-
group-conforming behavior is eventually traced backtostrong
scalar-relativistic effects,and in the non-relativistic limit, Cn
appears as acommon Group 12 metal.
Copernicium (Cn, Z=112) is the latest addition to
Group 12 (Zn, Cd, Hg) of the periodic table,and with an a-
decay half-life of 29 sfor the 285Cn isotope,one 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.[3–5] Concerning these trends,its lighter con-
gener 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 asuperconductor with
atransition temperature of 4.15 K.[8] These periodic anoma-
lies can be traced back to strong relativistic effects within this
group,[8–14] and, albeit to afar 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,relativistic effects
scale as Z2with the nuclear charge,leading to astrong
relativistic 7s contraction and 6d5/2 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,Cnmay be regarded as a
d-block element, evident, for example,from the square-
planar structure of CnF4.[10] Moreover,the relativistic valence
scontraction in combination with the weak chemical bonding
of the 6d5/2 orbitals leads to an increasing chemical inertness
of the Group 12 elements,[16] which is reflected in the decrease
of the cohesive energy Ecoh (see the green line in Figure 1).[4, 7]
This was first noted by Pitzer based on relativistic
electronic-structure calculations,who 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 condi-
tions.[16] More recently,this view has been challenged by
atom-at-a-time experiments for Cn.[3,4] By directly comparing
the adsorption of neutral Cn atoms on agold surface to Rn
(Ecoh =@0.23 eV) and Hg (Ecoh =@0.67 eV), the cohesive
Figure 1. 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 288.15–298.15 K(15–25 88C) based on
the standard ambient temperature and pressure (SAPT of IUPAC:
2588C), normal temperature and pressure (NTP of NIST,1588C), and
internationalstandard atmosphere (ISA, 20 88C).
[*] Dr.J
.-M. Mewes, Dr.O
.R
.S
mits, Prof. Dr.P
.S
chwerdtfeger
Centre for Theoretical Chemistry and Physics
The New Zealand Institute for Advanced Study
Massey University Auckland
0632 Auckland (New Zealand)
Dr.J.-M. Mewes
Mulliken Center for Theoretical Chemistry
UniversityofBonn
Beringstr. 4, 53115 Bonn (Germany)
E-mail:janmewes@janmewes.de
Prof. Dr.G.Kresse
UniversityofVienna
Faculty of Physics and Center for Computational Materials Sciences
Sensengasse 8/12, 1090 Wien (Austria)
Supportinginformation and the ORCID identification number(s) for
the author(s) of this article can be found under:
https://doi.org/10.1002/anie.201906966.
T2019 The Authors. Published by Wiley-VCH Verlag GmbH &Co.
KGaA. This is an open access article under the terms of the Creative
Commons AttributionLicense, which permits use, distribution and
reproduction in any medium, provided the original work is properly
cited.
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energy of Cn was estimated from its adsorption energy
providing @0.39 :0.12 eV,which was later updated to
@0.37 :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,and will
presumably be solid at ambient conditions with an estimated
evaporation temperature of 357þ111
@108 K.[4] However,the rela-
tively strong interaction with the gold surface may as well be
due to strong dispersion interactions.Also considering the
distinctly larger cohesive energy of the superheavy “noble
gas”[20] oganesson (Og) of @0.45 eV,[21] Cn appears to lean
towards the noble gases rather than towards its lighter
metallic congeners.
Recently,the solid phases of Cn have been explored by
means of highly accurate method-of-incrementrelativistic
coupled cluster (MOI-CC) calculations.[18] In excellent agree-
ment with the experimental estimate,these calculations
provided acohesive energy of @0.38 :0.03 eV,and moreover
revealed that hcp is the most stable phase and quasi-
degenerate with fcc and bcc. While such adegeneracy 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 abasis,weundertook the
derivation and careful evaluation of an efficient density
functional theory (DFT) based methodology to enable finite-
temperature simulations of Cn. Forthis purpose,aprojector-
augmented wave potential (PAW)with alarge 20 electron
(6s26p66d107s2)valence space was devised following the
approach of Joubert and Kresse.[22,23] Surveying various
density functionals,itwas eventually established that the
PBEsol functional[24] provides the best agreement with MOI-
CC results for cohesive energies,the 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,aswell as Refs.[18] and [25] for more
information on the PAW potential). Here,wepresent the
application of this methodology in the framework of free-
energy calculations to explore the physicochemical properties
and determine the aggregate state of bulk Cn at ambient
conditions.Moreover,toelucidate the role of relativistic
effects,wealso 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.Incontrast, 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,calculations in the NR
limit reveal afourfold increase in Ecoh 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/aratio very close to the ideal value of
the hcp lattice of 1.633, which is again typical for weakly
interacting systems,the NR calculations converge to adis-
torted 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,wefirst
determined the equilibrium volumes of the liquid and solid
phases at 300 K, and subsequently calculated the Gibbs free
energies.Toaccount 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 ascaled variant termed
lDFTor lPBEsol that was matched to the CCSD(T) cohesive
energy.Moreover,exploiting alinear 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,isprovided in the Supporting Informa-
tion.
To obtain the volume,several NVT simulations were
conducted at different volumes until the average pressure was
reasonably close to zero (:0.2 kbar, for details see the
Supporting Information). This approach provides asolid
density of 1300K
s=14.7 gcm@3for 285Cn (15.8 gcm@3at 0K)at
the lDFT level, which decreases by 5.5 %upon melting to
Table 1: Experimentaland calculated cohesive energies (Ecoh,ineV) and
nearest-neighbor distances (Rnn,inb)for the most stable hcp phase of
Cn at the reference method-of-incrementsCCSD(T) level compared to
spin–orbit, scalar-relativistic, and non-relativisticDFT/PBEsol.More
functionals are shown in the Supporting Information.
Level Ecoh Dref Rnn
Experimental[a] @0.37:0.11
spin–orbit relativistic
MOI-CCSD(T) @0.376:0.030 3.465
PBEsol (c/a=1.635) @0.349 +0.027 3.478
lPBEsol @0.373 +0.003 3.478
scalar-relativistic
MOI-CCSD(T)[b] @0.319 3.465
PBEsol (c/a=1.620) @0.298 +0.021 3.503
lPBEsol @0.317 +0.002 3.503
non-relativistic[c]
PBEsol (c/a=1.737) @1.333 3.503
[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/aratio,
Rnn is between in-plane atoms, whereas it is across two planes at the
relativisticlevel.
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aliquid density of 1300K
l=14.0 gcm@3.These results are in
stark contrast to the most prominent previous estimate of
23.7 gcm@3,[27] and show that Cn exhibts arather normal
density for aheavy element. Accordingly,Cnisonly slightly
more dense than its lighter congener Hg (1300K
l=13.55 gcm@3,
1227K
s=14.26 gcm@3)because the higher atomic mass is
canceled by the larger interatomic distances.
Having determined the equilibrium volumes,wecalcu-
lated 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 Tmfrom 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 avalue of
263 :11 Kwith plain DFT (dark colors), which increases to
282 :12 Kafter l-shifting, and is thus consistent with the
result of 284 :10 Kobtained with the scaled lDFT potential
(light colors). These values are moreover consistent with
further results for different cell sizes and simulation temper-
atures (273–294 K, see the Supporting Information), leading
to our final estimate for Tmof 283 :11 K(1088C).
To determine the boiling point Tb,the free energy of the
gas phase Gg(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 In-
formation].[30] Theintersections with the liquid phase occur at
316 :2Kwith plain DFT (338 Kafter l-shifting) and 331 :
2Kwith lDFT.Although the statistical error of Tbis much
smaller due to the steeper intersection (see Figure 2), the
deviation between the independent simulations is larger.For
an increased simulation temperature of 360 K, Tbincreases to
348 K(see the Supporting Information), which we take into
account in our final estimate for Tbof 340 :10 K(67 88C).
Accordingly,Cnisavolatile liquid with avapor pressure of
p293K &0.3 bar, and atriple point at 283 Katapressure of
approximately 0.25 bar.
Thecalculated 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,wecalculated aheat of fusion of
26.5 meV/atom or 2.55 kJmol@1at the lDFT level. This is
slightly above the value of 2.33 kJ mol@1for Hg,and slightly
below the 2.89 kJmol@1value for Rn.[31] Hence,despite the
much larger cohesive energy of Hg of @0.67 eV,its heat of
fusion is distinctly smaller than that of Cn, while the opposite
is the case for Rn (Ecoh =@0.23 eV). This seemingly counter-
intuitive ordering can be traced back to the nature of the
interactions in the condensed phases.Incontrast to the long-
ranged metallic bonding of Hg and its lighter congeners,the
dispersion interactions dominating in noble-gas-like elements
exhibit amuch stronger 1/r6distance dependence.This
becomes evident from the plot of the relative lattice energy
(Emin
lat ¼@1Þas afunction of the cell size (Rmin
nn ¼1) 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.Considering that the solid is more
ordered and dense than the liquid phase,the different shapes
of the interatomic potentials explain why the weakly inter-
acting systems Rn and Cn exhibit alarger heat of fusion than
Hg despite their smaller cohesive energies.
Eventually,the differences in the nature of the intera-
tomic interactions enable aclassification of these elements by
plotting their melting points against their cohesive energies
Tm/Ecoh as shown in Figure 3b.Alinear fit for each of the
groups (with forced intersection of the origin) reveals
acharacteristic slope for each of them that corresponds to
the average Tm/Ecoh and correlates qualitatively with the
shapes of the potentials depicted in Figure 3a.Onthe left,
there are the noble-gas-like elements with the narrowest
potential and highest Tm/Ecoh,and on the right the heavy
main-group metals with much wider potentials and in turn
one of the lowest Tm/Ecoh.Inbetween, there are the alkaline-
earth as well as most other metals (not shown) with ratios of
0.4 :0.1 KmeV@1.Figure 3b shows the lighter Group 12
members Zn and Cd to be situated close to the alkaline-
earth metals,which is consistent with their chemical behavior.
Compared to those,Hgexhibits aslight shift towards the
heavy main-group elements,which all attain a Tm/Ecoh value of
approximately 0.3 KmeV@1.For Cn, this trend does not
continue but the opposite is the case.Itexhibits astrong
increase of Tm/Ecoh to 0.75 KmeV@1,placing 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,and 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
Figure 2. Gibbs free energies of the solid (green), liquid (blue), and
gas phases (orange) of Cn based on the free-energycalculations at
300 Kwith DFT/PBEsol (dark colors) and lDFT/PBEsol (light colors).
Shown here are results for 64-atom solid and 61-atomliquid config-
urations. The melting and boiling points corresponding to the inter-
sections are also shown with the l-shifted values given in parentheses
(DFT only). *The final estimate of Tbincludes results from further
simulationsthat are not shown in this plot (see the discussion).
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aband gap of 6.4 :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,see 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.
Thereason for the trend-breaking behavior of Cn
becomes evident from the calculations conducted in the
non-relativistic limit:Itlies in the presence of very strong
scalar-relativistic effects.Completely neglecting relativity
causes the melting point to increase by about 300 K(!) to
591 :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,which resembles that of the lighter Group 12
metals.Extrapolating the liquid free energy to the intersec-
tion 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. ForHg, calculations at the NR-DFT/PBEsol level
reported in Ref.[7] afford asimilar increase of the melting
point from 241 Kto403 K. However,the nature of Hg as
reflected in Tm/Ecoh is only weakly affected, and it remains in
the typical range for (Group 12) metals.
Conclusion
In summary,wehave explored the physicochemical
properties of bulk copernicium by means of free-energy and
band-structure calculations.This revealed that at ambient
conditions,Cnisavolatile liquid with amelting point of 283 :
11 Kand aboiling point of 340 :10 Kand only slightly more
dense than Hg (1300K
l=14.0 gcm@3). We can thus fully confirm
PitzerQsoriginal hypothesis that Cn is either gaseous or
avolatile liquid bound by dispersion.[16] Although the
calculated boiling point is just below and well within the
error bars of the evaporation temperature of 357þ111
@108 K
suggested by Eichler,[4] we can most certainly exclude the
inferred metallic character based on the calculated band gap
of 6.4 eV.Onthe contrary,wefound adominance 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,which has been
predicted to be similar to that of Xe (data available for Rn
is insufficient to draw any such conclusions). Like Xe,Cn
forms thermodynamically stable di- and tetrafluorides with
calculated energies of formation (DU0with respect to F2and
atomic Cn) of @2.5 eV for CnF2and @3.6 eV for CnF4at the
SO–CCSD(T)/DZ level.[10] Taking into account the basis-set
superposition error resulting from the small DZ basis,and
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 forma-
tion (DHo
f)ofXeF2(@1.0 eV) and XeF4(@2.5 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,and 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-groupelements (Tl, Pb, Bi, Po, At), and Group 12 elements including Cn, as well as non-relativistic Cn and Hg. The two additionalpoints
for Cn correspond to the upper and lower limits based on the error bars of the reference Ecoh (see the SupportingInformation). Data for non-
relativisticHgfrom Ref.[7],for At from Ref. [32],all other elements from Ref. [17].c)Experimentaland 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).
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and boiling points by 300 Kand 700 K. Hence,the liquid
aggregate state as well as the weakly interacting nature of Cn
are both due to relativistic effects or, in other words,Cnis
arelativistic noble liquid.
Acknowledgements
We acknowledge financial support by the Alexander von
Humboldt Foundation (Bonn) and the Marsden Fund (17-
MAU-021) of the Royal Society of New Zealand (Well-
ington). We moreover acknowledge the use of New Zealand
eScience Infrastructure (NeSI) high performance computing
facilities (nesi000474). J.-M.M. thanks M. Piibeleht and S. A.
Mewes for helpful comments on the manuscript.
Conflict of interest
Theauthors declare no conflict of interest.
Keywords: aggregate states ·copernicium ·
free-energy calculations ·melting point ·superheavy elements
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Manuscript received:June 5, 2019
Revised manuscript received: October 1, 2019
Acceptedmanuscript online: October 9, 2019
Version of record online: October 25, 2019
A
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