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Bonding to Hydrogen

The simplest molecule, made for connection

Roald Hoffmann

The First Element under Pressure

In the past few years, my colleague Neil Ashcroft and I have had a fruitful collaboration on the response of molecules and extended structures to extreme pressure. Three years ago we returned to a first love of Neil’s, hydrogen. In this we were joined by a talented French postdoc, Vanessa Labet.

Experimentally, one can learn much about matter under pressure (see “The Squeeze Is On,” American Scientist 97:108 [2009]) from studies in diamond anvil cells, where in a small reaction volume, between two tough diamonds and enveloped by (one hopes) an unreactive metal, a sample of matter is compressed. At what pressure solid, cold hydrogen (yes, hydrogen freezes, at 14 degrees kelvin) metallizes is the subject of hot, current dispute. But some things people agree on—solid hydrogen retains molecular diatomic units up to pressures such as those at the center of the Earth (3.5 million atmospheres). And from a spectroscopic measurement one can even deduce the internuclear distance in the confined diatomic. As the pressure rises, the H-H equilibrium separation contracts a little, then begins to stretch. The magnitude of the excursion is small, less than 2 percent of the 0.74 Å separation.

There are places in physics and chemistry where theory can afford a clearer picture of a phenomenon, and matter at extreme conditions is one such place. If one can trust the theory.… Vanessa Labet had a numerical laboratory at her disposal of the best structures calculated for compressed H2 by Chris Pickard and Richard Needs. We used that laboratory to get physical insight, to reason out why hydrogen did what it did. The figure above shows the small dance the calculated shortest, intramolecular H-H distance does with pressure—it goes down a little, up for a while, down again, up, down. The discontinuities, the jags in the curve are understandable—they are the consequence of abrupt changes from one preferred form to another, so-called phase transitions. The calculations matched experimental findings pretty well. But what was behind the small dance steps?

2012-09MargHoffmannFF.jpgClick to Enlarge ImageWe first thought about the effect of confinement, one hydrogen molecule simply squeezed by other hydrogen molecules in that tense space. Now a model for that was already there in earlier work of Dudley Herschbach and Richard LeSar. They looked at the energy levels of H2 confined in a rigid spheroidal box, as the dimensions of the box decreased. As one might expect, the internuclear separation responded by decreasing. Labet probed confinement by a slightly softer box, a hydrogen molecule imprisoned between two helium atoms, the most ungiving chemical walls we could think of. The earlier results were confirmed—such confinement only made the H2 distance contract. What else could it do?

But that’s not what our numerical laboratory and experiment showed; in a real and modeled crystal of H2, the hydrogen molecule shrank, expanded, expanded some more, shrank. By just a little. What could possibly make it grow longer? As it was squeezed? At this point I remembered Kubas’s wonderful organometallic complexes. In them the coordinated hydrogen molecules expanded, to 0.82–0.89 Å in length. And from the work Saillard and I did, we knew why! The metal fragment provided electrons to populate hydrogen σu*, depopulate σg, both weakening the H-H bond.

In compressed hydrogen, at pressures approaching those at the center of the Earth, there were no metals in sight. But under these extreme conditions, could other hydrogen molecules around a given H2 possibly play that role? We looked at the population of the molecular orbitals of a given molecule, and sure enough the effect was there. Model calculations confirmed that the little dance of H-H separations with pressure that experiment and theory observe in dense, cold H2 was the outcome of two competing effects: simple physical confinement, and the chemical effect of the molecular orbitals of confined and confining molecules interacting, mixing, transferring electrons, stretching that bond. I love it—the same bonding that occurs in discrete transition metal organometallic molecules is there in a highly compressed crystal of pure H2.

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