The method the NCSA researchers employ for modeling this high-density realm is called Path Integral Monte Carlo (PIMC), a quantum mechanical method that captures the thermodynamic properties of quantum systems. Since Ceperley began developing it in 1982 (along with Roy Pollock at Lawrence Livermore National Laboratory) it has gained a reputation as one of the most accurate methods in condensed matter physics, though it is restricted to systems of only a few atoms or molecules. Its strength is that it treats hydrogen as having two components of unequal mass (the heavier proton and lighter electron) and makes few approximations to reach results. Furthermore, because the exact orbit of an electron has no meaning, PIMC calculates a sample of the various paths an electron can take as it orbits the nucleus and attaches a probability to each path--the so-called Monte Carlo method. These paths are then summed to come up with an electron's average behavior. This path integral way of accounting for the behavior of electrons and other subatomic matter was proposed in the 1950s by Nobel Prize-winning physicist Richard Feynman. Ceperley expanded Feynman's ideas into this powerful numerical approach that was also used to predict that molecular hydrogen behaves as a superfluid under certain conditions.
When Ceperley and Militzer extended work initiated by Magro (now of Kuck and Associates) by simulating 32 atoms of hydrogen with PIMC they saw molecules beginning to exchange paths--a precursor to delocalizing--as the pressures approached 500 thousand atmospheres. A few bonds broke creating metallic molecular hydrogen liquid. The majority of the bonds, however, remained intact until they reached the transition point, when the energy in the system was such that they all broke in unison. Several related runs for different parameters produced a consistent picture.
The consistency is good news for Ceperley but insufficient to declare success. One reason for hesitating is that proponents of the popular density functional theory (DFT) see only a continual transition. Ceperley attributes this difference to DFT's considering "electrons as a fluid and not particles which is effective at extremes of temperature but not in the intermediate where bonds are breaking."
More vexing are results from Lawrence Livermore National Laboratory (LLNL) that both confirm and contradict Ceperley's findings. The LLNL data are especially important because they are the first direct experimental measurements of hydrogen ever collected at these temperature and pressure. The data agree with Ceperley's in showing an abrupt transition from a nonmetallic to metallic state; where they disagree is at much higher temperatures where hydrogen should be a plasma. The LLNL data show hydrogen as existing in some strange state that neither Ceperley's simulation nor the predictions of all other theoretical models say is possible.
To rule any potential sources of error in their methodology, Ceperley and Militzer are now systematically reevaluating their results. Militzer is preparing to run larger and longer simulations to test whether their data is fully converged--in the final state. "People say this transition can't exist," says Militzer. "We say it can. It is up to us to prove it."
Once they have done so--and other researchers have as well--they will be ready to make definitive statements about this personality of hydrogen. Getting to know high-density hydrogen has taken physicists more half a century. At last they are close.
