Breaking van der Waals molecules with magnetic fields

[HelloCthulhu]

I was researching the relationship between magnetic dipoles and chemical bonding and I came across a very interesting paper. I'm hoping some of you can shed some light on how magnetic fields are making dissociation of a molecule possible and how to measure it.

http://arxiv.org/pdf/physics/0505044v1.pdf

 

[TeethWhitener]

I don't know what your background is, so I don't know what level to address this at. Basically, the paper suggests using Zeeman splitting for predissociation of van der Waals complexes.

When you put a magnetic molecule in an external magnetic field, the energy of the molecule depends on how its magnetic dipole is oriented with respect to the applied field. In classical terms, this is analogous to the fact that a magnetic compass needle wants to align itself with the Earth's magnetic field. In a spin-1/2 species, it's a little different because the magnetic moment can only be oriented in 1 of 2 directions ("up" or "down"--in other words, aligned or anti-aligned with the applied field). For the sake of simplicity, let's say that spin up is aligned with the applied field and spin down is anti-aligned. This means that a species which is spin up will have a lower energy than a species which is spin down. In the absence of an applied magnetic field, these two configurations would have the exact same energy (they would be "degenerate"). As you turn on an applied field, the degeneracy is broken and the energy levels split. This is called Zeeman splitting. The energy splitting of the levels increases as the field increases. What this paper suggests is that in a strong enough field, the splitting will be large enough such that a van der Waals species in an anti-aligned state will be "predissociated" with respect to the aligned state. What this means is that if a species in the anti-aligned state were to relax into the aligned state, this would release enough energy to overcome the (relatively weak) van der Waals forces holding the species together and dissociate the complex. Note that Zeeman splitting is usually pretty small, so in order for the process to be dissociative, the complex must be relatively weakly bound. That's why the paper looks at van der Waals complexes in particular.

As for detection, there are probably several ways to do this. I used to do some ultracold spectroscopy, so my mind immediately jumped to looking for intermolecular vibrational signatures. If they show up in the absence of an applied field and disappear in the presence of one above a threshold field strength, then that would provide pretty strong evidence for this effect. There's probably some clever way to do this using mass spectrometry, but my background there is a little shakier. The simplest thing would probably be to take an open shell ionic species and complex it with a weakly bound noble gas. Do a mass spec in a way that gives you a large parent peak and then monitor the intensity of the parent peak as the field is turned up. Just a couple of off-the-cuff ideas. It shouldn't be too hard to detect with the right equipment.

 

[HelloCthulhu]

Thank you so much for responding! I certainly have a lot more to learn about quantum chemistry. I know a little about Zeeman splitting and the effect of a magnetic field’s torque on a dipole. But how this translates into breaking a chemical bond is still a little fuzzy in my mind. I’ve seen a few examples of the Zeeman interaction equation, but I’m not sure how to use it to figure out how much magnetic field strength it would take to break a van der Waals bond.

 

[TeethWhitener]

I’ve seen a few examples of the Zeeman interaction equation, but I’m not sure how to use it to figure out how much magnetic field strength it would take to break a van der Waals bond.

Table 1 in the paper that you quoted in your first post gives calculated lifetimes of predissociated HeO complexes at various magnetic strengths (in the range of 0.1-3.0 Tesla).

 

[HelloCthulhu]

I don't know what your background is, so I don't know what level to address this at. Basically, the paper suggests using Zeeman splitting for predissociation of van der Waals complexes.
As you turn on an applied field, the degeneracy is broken and the energy levels split. This is called Zeeman splitting. The energy splitting of the levels increases as the field increases. .

I'm still not positive what this would look like mathematically. For example, I know how to write the Zeeman interaction for hydrogen in a mag field of 1 Tesla:

ΔE = m_lμ_BB = 5.79 x 10^-5 = 5.79 x 10^-5

m_l = orientation on z axis = 1

μ_B = Bohr magnenton = 5.788 x 10^-5

B = 1 Telsa

http://hyperphysics.phy-astr.gsu.edu/hbase/quantum/zeeman.html#c2

I'm still confused how to calculate what magnetic field strength will cause it's molecule to dissociate. Here's a quote from the paper:

"To form an idea of lifetimes for the Zeeman predissociation in complexes with open-shell atoms, we analyzed the predissociation of the He-O(3P) molecule in a magnetic field. The ground state of oxygen is3P2. It splits into five Zeeman levels with energies approximately equal to 3BBM/2, where B≈0.47 cm−1/Tesla. This suggests that the HeO molecules bound by 11.2 cm−1 or less may undergo the Zeeman predissociation at B= 4 Tesla."

Could you explain the math behind the dissociation at 4T? Your help is greatly appreciated! :)

 

[TeethWhitener]

Could you explain the math behind the dissociation at 4T?

I'll be honest; I'm not 100% sure what you're asking. Do you mean how do they get ##B = 4T##? The paper gives the expression
$$E_{Zeeman} \approx \frac{3B\mu_{B} M}{2}$$
and uses values of ##E_{binding}=11.2## and ##\mu_{B} = 0.47##. We have ##M_{max} = 2## (because ##J = L+S = 2##--you can see this from the term symbol, or from a straightforward analysis of the electron configuration--and ##M## is just the projection of ##J## onto the magnetic field axis). This means that ##M## is equal to one of ##{-2, -1, 0, 1, 2}##. The minimum magnetic field needed to break up a complex with a binding energy of 11.2 cm^-1 is therefore given by
$$E_{binding} = \Delta E \approx \frac{3B\mu_{B}}{2}(M_{max} - M_{min})$$
Solving for ##B## gives the value from the paper.

 

[HelloCthulhu]

Thank you so much for that clarification! The math makes much more sense now.