Copernicium is a Relativistic Noble Liquid
Jan-Michael Mewes,1, 2, ∗Odile R. Smits,1 , †Georg Kresse,3, ‡and Peter Schwerdtfeger1, §
1Centre for Theoretical Chemistry and Physics, The New Zealand Institute for Advanced Study,
Massey University Auckland, 0632 Auckland, New Zealand
2Mulliken Center for Theoretical Chemistry, University of Bonn, Beringstr. 4, 53115 Bonn, Germany
3University of Vienna, Faculty of Physics and Center for Computational
Materials Sciences, Sensengasse 8/12, 1090 Wien, Austria
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.
Keywords: Copernicium, Superheavy Elements, Aggre-
gate State, Free-Energy Calculations, Melting Point.
Copernicium (Cn, Z= 112) is the latest addition to
group 12 (Zn, Cd, Hg) of the periodic table, and with
an α-decay half-life of 29 s for the 285Cn isotope one of
the most long-lived super-heavy elements (SHEs).[1, 2]
Its lifetime is suﬃcient to perform atom-at-a-time ex-
periments and explore periodic trends.[3–5] 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 transi-
tion temperature of 4.15 K. These periodic anomalies
can be traced back to strong relativistic eﬀects within
this group,[8–14] and, albeit to a far lesser extent, the
lanthanide contraction originating from the poor nuclear
shielding by the ﬁlled 4f-shell. This renders it almost
impossible to predict the physical and chemical behavior
of Cn purely from periodic trends as originally proposed
Moving down in the periodic table, relativistic eﬀects
scale as Z2with the nuclear charge, leading to a strong
relativistic 7scontraction and 6d5/2expansion in group
12 elements, and eventually to a reversal of the energy
ordering between these two levels for Cn. As a re-
sult, and in contrast to all other members in this group,
Cn may be regarded as a d-block element, evident e.g.,
from quadratically planar structure of CnF4. More-
over, the relativistic valence s-contraction in combina-
tion with the weak chemical bonding of the 6d5/2orbitals
leads to an increasing chemical inertness of the group
12 elements, which is reﬂected in the decrease of the
cohesive energy Ecoh (cf. green line Fig. 1).[4, 7] This
FIG. 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 a temperature range
of 288.15−298.15 K (15-25◦C) based on the standard ambient
temperature and pressure (SAPT of IUPAC: 25◦C), normal
temperature and pressure (NTP of NIST, 15◦C) and interna-
tional standard atmosphere (ISA, 20◦C).
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 a very
volatile liquid or gaseous at ambient conditions. More
recently, this view has been challenged by atom-at-a-time
experiments for Cn.[3, 4] By directly comparing the ad-
sorption behavior of neutral Cn atoms on a gold surface
to Rn (Ecoh =−0.23 eV) and Hg (Ecoh =−0.67 eV),
the cohesive energy of Cn was estimated from its adsorp-
tion energy providing −0.39 ±0.12 eV, which was later
updated to −0.37 ±0.11 eV. Since this is twice the
value of the rare gas Rn, and the increase could not be
explained by model calculations, it was 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
−108 K. However, the relatively strong interaction
with the gold surface may as well be due to strong disper-
sion interactions. Also in face of the distinctly larger co-
hesive energy of the super-heavy “noble gas” oganes-
son (Og) of −0.45 eV, Cn appears to lean towards
the noble gases rather than towards its lighter metallic
Recently, the solid phases of Cn have been explored by
means of highly accurate method-of-increment relativis-
tic coupled-cluster (MOI-CC) calculations. In excel-
lent agreement with the experimental estimate, these cal-
culations provided a cohesive 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 a
degeneracy is characteristic of noble-gas solids, it is in
contrast to the earlier group 12 metals, which all exhibit
a clear preference for hcp (Zn, Cd) or rhombohedral lat-
tices (Hg) over fcc of about 30 meV compared to 1 meV
for Cn (all DFT/PBEsol).
Using these insights as a basis, we undertook a care-
ful evaluation of an eﬃcient density-functional theory
(DFT) based methodology to enable ﬁnite-temperature
simulations of Cn. For this purpose, a projector-
augmented wave potential (PAW) with a large 20 elec-
tron (6s26p66d107s2) valence space was devised following
the approach of Joubert and Kresse.[22, 23] Surveying
various density functionals, it was eventually established
that the PBEsol functional provides excellent agree-
ment with MOI-CC results for cohesive energies, the im-
pact of spin-orbit coupling, and the ordering as well as
structural parameters of the solid phases (cf. Tab. I and
SI for more functionals, as well as refs.  and ref. 
for more information on the employed PAW potentials).
Here, we present the application of this methodology in
the framework of free-energy calculations to explore the
physico-chemical properties and determine the aggregate
state of bulk Cn at ambient conditions. Moreover, to
elucidate the role of relativistic eﬀects, we also perform
calculations in the non-relativistic limit.
TABLE I. Experimental and calculated cohesive energies
(Ecoh, in eV) and nearest-neighbor distances (Rnn , in ˚
the most stable hcp phase of Cn at the reference method-
of-increments CCSD(T) level compared to spin-orbit, scalar-
relativistic and non-relativistic DFT/PBEsol. More function-
als are shown in the SI.
Level Ecoh ∆ref Rnn
MOI-CCSD(T) −0.376 ±0.030 3.465
PBEsol (c/a = 1.635) −0.349 +0.027 3.478
λPBEsol −0.373 +0.003 3.478
PBEsol (c/a = 1.620) −0.298 +0.021 3.503
λPBEsol −0.317 +0.002 3.503
PBEsol (c/a = 1.737) −1.333 3.503
aestimated from the adsorption enthalpy on gold  using the
updated relation from . See also ; bSR-CCSD(T)
calculations employ the same structure as SO; cdue to the
distorted c/a ratio Rnn is between in-plane atoms, whereas it is
across two planes at the relativistic level
RESULTS AND DISCUSSION
A ﬁrst hint towards the bonding in bulk Cn and the
role of relativistic eﬀects is evident from the cohesive en-
ergies and structural parameters calculated at the non-
relativistic (NR), scalar relativistic (SR) and spin-orbit
(SO) relativistic levels provided in Tab. I. 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
7plevels and highest occupied 6dlevels only leads to a
slight reduction of the band gap, but does not change
their character. In contrast, scalar-relativistic eﬀects do
cause the character of the highest occupied orbital to
change from 7sin the non-relativistic limit to 6d. Since
the 7sorbital forms stronger chemical bonds than the 6d
orbital, this strongly aﬀects the reactivity. Accord-
ingly, calculations in the non-relativistic limit reveal a
fourfold increase of Ecoh compared to the fully relativis-
tic calculation, and moreover a signiﬁcant impact on the
structural parameters: While the optimizations at the
SR and SO level 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, the non-relativistic calcu-
lations converge to a distorted hcp structure with a ratio
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, we ﬁrst de-
termine the equilibrium volumes of the liquid and solid
FIG. 2. Gibbs free energies of the solid (green), liquid (blue)
and gas phases (orange) of Cn based on the free-energy
calculations at 300 K with DFT/PBEsol (dark colors) and
λDFT/PBEsol (light colors). Shown here are results for 64
atom solid and 61 atom liquid conﬁgurations. The melting
and boiling points corresponding to the intersections are also
shown with the λ-shifted values given in paranthesis (DFT
only). *The ﬁnal estimate of Tbincludes results from further
simulations which are not shown in this plot (see discussion).
phases at 300 K, and subsequently calculate the Gibbs
free energies. To account for the small yet relevant de-
viation between DFT and the high-level CCSD(T) ref-
erence (cf. Tab. I and discussion in the SI), all ﬁnite
temperature simulations are conducted not only with
plain DFT/PBEsol, but also with a scaled variant termed
λDFT or λPBEsol that is matched to the CCSD(T) co-
hesive energy. Moreover, exploiting a linear relation be-
tween the potential energy and the melting point, we also
correct the plain DFT results for this deviation, which
will be referred to as λ-shifting. A detailed discussion of
this relation, including an anlytical proof, is provided in
To obtain the volume, several NVT simulations are
conducted at diﬀerent volumes until the average pres-
sure is reasonably close to zero (±0.2 kbar, for de-
tails see SI). This approach provides a solid density of
s= 14.7 g/cm3for 285Cn (15.8 g/cm3at 0 K) at the
λDFT level, which decreases by 5.5% upon melting to a
liquid density of ρ300K
l= 14.0 g/cm3. These results show
that — in stark contrast to the most prominent previous
estimate of 23.7 g/cm3 — Cn has a rather normal
density for a heavy element, and is only slightly more
dense than its lighter congener Hg (ρ300K
l= 13.55 g/cm3,
s= 14.26 g/cm3) because the higher atomic mass is
cancelled by the larger inter-atomic distances.
Having determined the equilibrium volumes, we calcu-
late Gibbs free energies, entropies Sand internal energies
Uof the solid and liquid phases at 300 K using thermo-
dynamic integration as described in the SI.[28, 29] To
derive the melting point Tmfrom the results obtained at
300 K (colored squares and circles in Fig. 2), the solid
and liquid Gibbs free energies are extrapolated linearly
to their intersection as is shown in Fig. 2. This pro-
vides a Tm(black diamonds) of 263 ±11 K with plain
DFT, which increases to 282±12 K after λ-shifting. The
scaled λDFT potential provides a nearly identical Tmof
284 ±10 K, which is moreover consistent with further re-
sults for diﬀerent cell sizes and simulation temperatures
(273−294 K, see SI). We combine these to a ﬁnal estimate
for Tmof 283 ±11 K (10◦C).
To determine the boiling point Tb, the free energy of
the gas phase Gg(orange line) is obtained analytically
using the ideal-gas law including the ﬁrst virial correc-
tion of only 0.25 meV/atom (eqs. 4-6 in the SI). The
intersections with the liquid (open circles) occur at a Tb
of 316 ±2 K (plain DFT, 338 K after λ-shifting) and
331 ±2 K with λDFT. Although the statistical error of
Tbis much smaller due to the steeper intersection (cf.
Fig. 2), the deviation between the simulations is larger.
For an increased simulation temperature of 360 K, Tb
increases to 348 K (see SI). This is taken into account
in our ﬁnal estimate for Tbof 340 ±10 K (67◦C). Ac-
cordingly, Cn is a volatile liquid with a vapor pressure of
p293K≈0.3 bar, and a triple point at 283 K at a pressure
of ≈0.25 bar.
The calculated thermodynamical quantities eventually
allow us to shed some light on the nature of the inter-
actions in bulk Cn. From the diﬀerence of the inter-
nal energies of the solid and liquid phases, we calcu-
late a heat of fusion of 26.5 meV/atom or 2.55 kJ/mol
at the λDFT level, which is slightly above the value of
2.33 kJ/mol for Hg, and slightly below the 2.89 kJ/mol
for Rn. Hence, despite the much larger cohesive en-
ergy 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 interac-
tions in the condensed phases. In contrast to the long-
ranged metallic bonding of Hg and its lighter congeners,
the dispersion interactions dominating in noble-gas-like
elements exhibit a much stronger 1/r6distance depen-
dence. This becomes evident from the plot of the rela-
tive lattice energy (Emin
lat =−1) as a function of the cell
nn = 1) displayed in Fig. 3a. Evidently, there is
a distinct diﬀerence between dispersion-bound elements
Rn and apparently also Cn with narrow potentials on
the one hand, and on the other the metallic (group 12)
elements including non-relativistic Cn with wider poten-
tials. Considering that the solid is more ordered and
dense than the liquid phase, the diﬀerent shape of the
inter-atomic potentials explain why the weakly interact-
ing systems Rn and Cn exhibit a larger heat of fusion
than Hg despite their smaller cohesive energies.
FIG. 3. a) Normalized energy as a function of cell size for Rn and the group 12 metals including Cn as well as Cn in the
non-relativistic limit. All calculations at the SO-DFT/PBEsol level. The lines are obtained by ﬁtting the calculated points in
the relative size interval 0.85 −1.5 with a tenth-order polynomial. b) Plot of the melting points against the respective cohesive
energies for the noble gases, alkaline-earth metals, heavy main-group elements (Tl, Pb, Bi, Po, At) and group 12 elements
including Cn, as well as non-relativistic Cn and Hg. The two additional points for Cn correspond to the upper and lower
limits based on the error bars of the reference Ecoh (see SI). Data for non-relativistic Hg from ref. , for At from ref. ,
all other elements from ref. . c) Experimental and 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 SI and ref. 20 (group 18).
The diﬀerences in the nature of the inter-atomic inter-
actions enable a classiﬁcation of these elements by plot-
ting their melting points against their cohesive energies
Tm/Ecoh as shown in Fig. 3b. A linear ﬁt for each of
the groups (with forced intersection of the origin) reveals
a characteristic slope for each of them that corresponds
to the average Tm/Ecoh and correlates qualitatively with
the shapes of the potentials depicted in Fig. 3a. On the
left, there are the noble-gas-like elements with the nar-
rowest potential and highest Tm/Ecoh, and on the right
the heavy main-group metals with much wider poten-
tials and in turn one of the lowest Tm/Ecoh. In between,
there are the alkaline-earth as well as most other met-
als (not shown) with ratios of 0.4±0.1 K/meV. Fig. 3b
shows the lighter group 12 members Zn and Cd to be
situated close to the alkaline-earth metals, which is con-
sistent with their chemical behavior. Compared to those,
Hg exhibits a slight shift towards the heavy main group
elements, which all attain a Tm/Ecoh of approximately
0.3 K/meV. For Cn, this trend does not continue but
the opposite is the case. It exhibits a strong increase of
Tm/Ecoh to 0.75 K/meV, 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 Fig. 3a,
and may be seen as another hint that bulk Cn behaves
similar to a noble gas.
The similarity further extents 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 a band gap of 6.4±0.2 eV for Cn, clearly
characterizing it as an insulator. 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, cf. Fig. 3c).
It thus appears that Cn is more noble-gas like than Og,
which is further supported by its smaller cohesive energy
(0.38 eV vs. 0.45 eV).[21, 25]
The reason for the trend-breaking behavior of Cn be-
comes evident from the calculations conducted in the
non-relativistic limit and lies in the presence of very
strong scalar-relativistic eﬀects. Completely neglecting
relativity causes the Tmto increase by about 300 K (!)
to 591 ±10 K, placing it much closer to both Zn and Cd
in Fig. 3b. This is in line with a zero-band-gap obtained
at the DFT/PBEsol level for the energetically lowest hcp
lattice, as well as with the shape of the potential de-
picted in Fig. 3a. Extrapolating to the intersection point
with the ideal gas aﬀords an estimate for the Tbof about
1000 K, similar to Zn with 1180 K and Cd with 1040 K,
corresponding to a huge relativistic increase of 700 K for
the Tb. For Hg, calculations at the DFT/PBEsol level
in the non-relativistic limit reported in ref.  aﬀord a
similar increase of Tmfrom 241 K to 403 K. However,
its nature as reﬂected in Tm/Ecoh is only weakly aﬀected
and Hg remains in the typical range for group 12 metals.
In summary, we have explored the physico-chemical
properties of bulk copernicium by means of free-energy
and band-structure calculations. This revealed that at
ambient conditions, Cn is a volatile liquid with a melting
point at 283±11 K and a boiling point at 340 ±10 K and
only slightly more dense than Hg (ρ300K
l= 14.0 g/cm3).
We can thus fully conﬁrm Pitzer’s original hypothesis
that Cn is either gaseous or a volatile liquid bound by
dispersion. Although the calculated boiling point is
just below and well within the error bars of the evapo-
ration temperature of 357+111
−108 K suggested by Eichler,
we can most certainly exclude the inferred metallic char-
acter based on the calculated band gap of 6.4 eV. On
the contrary, we found a dominance of dispersive inter-
actions in bulk Cn very similar to Rn, which together
with the band gap and the structural parameters of solid
Cn strongly suggests a weakly 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 tetraﬂu-
orides with calculated energies of formation (∆U0with
respect to F2and atomic Cn) of −2.5 eV for CnF2and
−3.6 eV for CnF4at the SO-CCSD(T)/DZ level. Tak-
ing into account the small basis set used in the calcula-
tions (basis-set superposition error), and moreover the
absence of zero-point and thermo-chemical corrections,
the values for Cn are comparable to the respective stan-
dard enthalpies of formation (∆H◦
f) of XeF2(−1.0 eV)
and XeF4(−2.5 eV). Hence, while the noble-gas-like
character of Cn certianly 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 noble-gas-
like 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 rel-
ativistic eﬀects. Neglecting relativity leads to an almost
four-fold increase of the cohesive energy, and in turn to
an increase of the melting and boiling points by 300 K
and 700 K. Hence, the liquid aggregate state as well as
the weakly interacting nature of Cn are both due to rel-
ativistic eﬀects, or on other words: Cn is a relativistic
Acknowledgements We acknowledge ﬁnancial sup-
port by the Alexander-von-Humboldt Foundation (Bonn)
and the Marsden Fund (17-MAU-021) of the Royal
Society of New Zealand (Wellington). We moreover
acknowledge the use of New Zealand eScience Infras-
tructure (NeSI) high performance computing facilities
(nesi000474). JMM wants to thank M. Piibeleht ans S.
A. Mewes for helpful comments on the manuscript.
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