Imperial College London

Henry Rzepa

Computational quantum chemistry has made fantastic strides in the last
30 years. Often deep insight into all sorts of questions regarding
reactions and structures of molecules has become possible. But sometimes
the simplest of questions can prove incredibly difficult to answer. One
such is how accurately can the boiling point of water be predicted from
first principles? Or its melting point? Another classic case is why
mercury is a liquid at room temperatures? The answer to that question
(along with another, why is gold the colour it is?) is often anecdotally
attributed to Einstein. More accurately, to his special theory of
relativity.\[cite\]10.1002/andp.19053231314\[/cite\] But finally in 2013
a computational proof of this was demonstrated for
mercury.\[cite\]10.1002/anie.201302742\[/cite\] The proof was built up
in three stages.

1.  Potential energy surfaces for the Hg~2~ dimer showed that inclusion
    of a relativistic Hamiltonian contracts the Hg-Hg distance by 0.2Å.
    This can be traced back to the value of the
    ^1^S~0~(6s^2^)→^3^P~0~(6s^1^6p^1^~1/2~) electronic excitation in the
    atom being 4.67eV, compared to a non-relativistic value of 3.40eV.
    This in turn is the result of the strong relativistic 6s shell
    contraction and hence stabilisation. But it has previously been
    shown that bulk mercury cannot be described by such a simple
    two-body interaction.
2.  Next many-body clusters of various sizes were built. This is a
    complex task, since for each size, various types of packing might be
    possible. The largest was  a "two-layer Mackay icosahedron", with 55
    Hg atoms. These clusters however did not show any monotonic
    convergence to a clear melting point.
3.  Finally, using Monte Carlo (MC) simulations within a quantum
    diatomics-in-molecules (DIM) model and with periodic boundary
    conditions to simulate the bulk metal, it was possible to show that
    without a relativistic Hamiltonian, the predicted melting point was
    predicted as 355K (82°C) but when the relativistic effects were
    switched on, this decreased to 250K (-23°C). This lowering of 105K
    is dominated by scalar relativistic effects through many-body
    contributions.
4.  The experimental melting point is 234K. The density is well
    predicted as well (the non-relativistic model predicts mercury to be
    denser than it actually is).

What I did not get from this article is why mercury is such a very
special case (*i.e.* why neither gold, m.p.
[1337K]{style="color: #000000;"} nor thallium, m.p.
[577K,]{style="color: #000000;"} are liquids at room temperature). No
doubt someone will explain. In the past, gold and mercury were said to
be the only two visual manifestations of Einstein's special theory in
every-day objects. I say the past, because mercury is now rarely seen in
any every-day objects (digital thermometers have taken over, and the
mercury barometer has long since gone). If anyone knows of other
examples, do let us know.

------------------------------------------------------------------------

**Note added in 2019:** Similar calculations have now been performed on
Copernicium\[cite\]10.1002/anie.201906966\[/cite\] predicting it too is
a liquid (MP 283 ± 11K) and has noble gas character (group 18) due to
both relativistic and dispersion effects. Without those, it would simply
be a common group 12 element.

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Computational quantum chemistry has made fantastic strides in the last 30 years. Often deep insight into all sorts of questions regarding reactions and structures of molecules has become possible. But sometimes the simplest of questions can prove incredibly difficult to answer. One such is how accurately can the boiling point of water be predicted from first principles? Or its melting point?

Messaggi di Rogue Scholar

Why is mercury a liquid at room temperatures?