Every now and again when I’m studying I discover something which I think is just cool. And relativistic quantum chemistry — is just cool! Quantum mechanics and general relativity aren’t the best of friends. This much is pretty well known, and a great many people (physicists and otherwise) have waxed lyrical about it. Finding a way of combining the effects of the two into a single theory is the goal of any theorist working towards the so-called “theory of everything.” General relativity has difficulty fitting into the world of particles. Special relativity, on the other hand, bears no such hindrance.
In fact, special relativity underpins a huge amount of modern physics. It shouldn’t come as any surprise, then, that relativity rears its head in physical chemistry too. A lot of chemists may not need to care about relativistic effects, particularly organic chemists. It only really becomes an issue with the heavyweights near the bottom of the periodic table.
Dating back to Bertha Swirles’ 1935 paper, “The relativistic self-consistent field,” the idea is quite intuitive. Special relativity asserts that the faster an object travels, the greater its effective mass. The key to all of this is in the ever-curious fine structure constant, α;
α is a ubiquitous little thing. It seems to crop up all over physics, but in this case it denotes something quite simple — the speed of an electron orbiting a hydrogen nucleus. Hydrogen is the simplest atom. One proton and one electron. In a hydrogen nucleus, an electron will travel at roughly 137th the speed of light.
Increase the size of the atomic nucleus though, and you increase its charge. The increase in charge causes the electrons to accelerate to increasingly higher speeds. Nuclear charge is usually denoted by a Z, and it’s blissfully easy to plug this into the equation. Just multiply by Z to find the speed of the innermost electron in the shell. Like so;
For instance, that atomic nucleus up at the top of this post is uranium. Everyone’s favourite actinide. Uranium has 92 protons and thus, a charge of 92 on its nucleus. As a result, its innermost electrons will be travelling at around 67% of the speed of light. This increases their mass by around 34%, causing those electrons to orbit sligtly closer to the atomic nucleus. In turn, this has a knock-on effect, causing the entire atom to shrink slightly!
Interestingly enough, a whole range of effects are opened up by this relativistic malarkey. It contributes to many of the heavier elements having smaller atomic radii than they should. It explains why lead doesn’t have the same crystal structure as diamond. It explains why gold is actually gold! The electronic energy levels in gold are shifted by the relativistic effect, causing it to absorb the right optical frequencies to make it appear golden.
Most dramatically, it explains why mercury is liquid at room temperature. Relativistic effects cause the contraction of mercury’s 6s2 orbital, severely weakening its ability to form bonds. Subsequently, mercury remains liquid down to nearly -39°C. When it boils at around 357°C, it’s atoms drift away independently as a monatomic gas. Gaseous mercury is thus sometimes referred to as a “pseudo-noble gas.”
Ahhh. I love finding things out.
…wait, what do you mean quantum chemistry isn’t cool?