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. But finally in 2013 a computational proof of this was demonstrated for mercury. The proof was built up in three stages.
- Potential energy surfaces for the Hg2 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 1S0(6s2)→3P0(6s16p11/2) 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.
- 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.
- 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.
- 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 nor thallium, m.p. 577K, 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.
- A. Einstein, "Ist die Trägheit eines Körpers von seinem Energieinhalt abhängig?", Annalen der Physik, vol. 323, pp. 639-641, 1905. http://dx.doi.org/10.1002/andp.19053231314
- F. Calvo, E. Pahl, M. Wormit, and P. Schwerdtfeger, "Evidence for Low-Temperature Melting of Mercury owing to Relativity", Angewandte Chemie International Edition, vol. 52, pp. 7583-7585, 2013. http://dx.doi.org/10.1002/anie.201302742