Why does correlation increase when you dissociate an H2 molecule? The quick answer is that for the single determinant wavefunction at the equilibrium geometry the two electrons move independently: they could be located at the same nucleus (ionic configuration) or at different nuclei (covalent configuration) with equal probability. At infinite separation the two electrons are "statically" correlated: if the first electron is located at the first nucleus, the second electron has to be at the other nucleus and vice versa. More importantly, if you measured spin up for the electron at one of the nuclei, you would know with certainty that the electron at the other nucleus would be spin down. This leads us to the fancy answer: if you were somehow able to dissociate H2 in a fully coherent way, you would obtain two entangled hydrogen atoms, see also this paper by Garnet Chan.
Let's look at the math...
The closed shell wavefunction of H2
is given as the Slater determinant
At infinite separation the doubly excited determinant mixes into the wavefunction with equal weight to the closed shell
From the point of view of the atoms, there is another subtlety. A priori there is an equal probability that either one will have spin α or spin β. But if you do measure the spin on one of these atoms, you immediately know that the other one has the opposite spin, even if it is infinitely far away. This phenomenon is called entanglement.
These types of counterintuitive behaviour (entanglement and correlation at infinite separation) only come into play because of the special form of the wavefunction as given above. The more intuitive form
This leads us to the final point of the discussion. It makes sense to use the pure "coherent" wavefunction of the isolated H2 system as given above only if there were no interactions with the "bath". Otherwise we would have to describe the wavefunction of a larger part of the world (or use a density matrix formalism). In such a case this strange type of correlation and the entanglement would disappear. In summary: from a mathematical point of view it is clearly possible to find "static correlation" in the dissociated H2 system. But from an experimental point of view it is probably extremely difficult to create this situation. Should we discuss this at all then? Probably yes because we need a consistent theoretical framework. But we should remember that the situation is actually quite artificial.
A Defense of Journal Impact Factors - Vilified, journal impact factor may still be useful for scientists. But use it with caution.
3 days ago