# magnetic cryo-FTIR

## FTIR

[FTIR](https://en.wikipedia.org/wiki/Fourier-transform_infrared_spectroscopy) is a common way to determine what chemicals are present in a sample. For a molecule to absorb a photon, it must have some electric charges that can vibrate at about the same frequency as that photon. Many common bonds (such as C=O) have some charge separation and a vibrational frequency in the infrared spectrum that's fairly consistent.


## other modern techniques

If we're considering possible improvements to FTIR, we should think about other methods currently used to characterize molecules, and how they compare to FTIR.

[1H NMR](https://en.wikipedia.org/wiki/Proton_nuclear_magnetic_resonance) can determine what atoms are bonded to hydrogen or deuterium atoms, and what kind of hydrogen bonding is happening. If you want to know where a hydrogen atom came from in a reaction, using some deuterium is the only good way to tell. University chemistry departments often have small NMR machines now, but they're still much more expensive than FTIR.

[X-ray crystallography](https://en.wikipedia.org/wiki/X-ray_crystallography) has historically been the main way to determine crystal structures. The main problem is that a macroscopic crystal must be made, and that's often impractical for complex molecules.

[Cryo-EM](https://en.wikipedia.org/wiki/Cryogenic_electron_microscopy) is an alternative to X-ray crystallography that works on microscopic crystals, which are easier to make. This technique has determined many previously unknown protein structures. However, the machines for it are currently rare and very expensive, and (small) crystals still need to be made.


## cryo-FTIR

The frequency resolution for detecting what light was absorbed is theoretically limited only by [Doppler broadening](https://en.wikipedia.org/wiki/Doppler_broadening) from thermal vibrations. At low temperatures, it's possible to get very good resolution. So, cryogenic FTIR is used by some laboratories now.

The vibrational frequency of bonds is changed slightly by hydrogen bonding, nearby atoms in the molecule, and nearby charges. With good frequency resolution, it's possible to tell not just what bond types are present, but what's near them. But those small shifts in frequencies are only useful if you know what they mean.


## getting more data

Cryo-FTIR has good resolution, and understanding what its data means is a bigger problem than not having enough data. However, there are ways to get more data. 

IR spectra change somewhat with temperature, so FTIR can be done at multiple temperatures for more data.

Magnetic fields also affect IR spectra: they cause vibrating charges in molecules to take slightly curved paths, which affects their frequency and the strength of their interactions. This effect is anisotropic and averaged across every orientation of light-interacting molecules, but, molecules can only absorb a photon when their orientation matches the right vibrational mode to the photon polarization. So, IR spectra in a strong magnetic field should depend on the relative orientation of the field and the light source, as well as the field strength.


## magnetic cryo-FTIR

I think most of the useful data from magnetic effects on IR spectra could be collected by simply rotating the polarization of a light source that's perpendicular to field lines from a strong magnet, perhaps using a liquid crystal polarization rotator. For maximum field strength, the magnet should be shaped like a ring with a section cut out for the sample to go in.

Suppose an instrument is made which can determine, with good precision, the change in IR spectra that happens when light polarization is rotated relative to an applied magnetic field. What can be determined from that information?

For a given spectral line, the change in absorption with polarization should increase with increasing coplanarity of the associated atomic movements.

For a given spectral line, the shift in wavelength with polarization should be an indication of how the average frequency of the associated atomic movements varies with angle.

Differential magnetic cryo-FTIR could be a way to get information about the relative orientation of bonds in molecules that doesn't require forming crystals.


## previous work

"[Magnetic circular dichroism](https://en.wikipedia.org/wiki/Magnetic_circular_dichroism)" and "magnetic linear dichroism" are known effects, which have occasionally been used in experiments for decades, [mostly](https://scholar.google.com/scholar?hl=en&as_sdt=0%2C45&q=%22X-ray+Magnetic+Circular+Dichroism%22&btnG=) using [x-rays](https://scholar.google.com/scholar?hl=en&as_sdt=0%2C45&q=%22X-ray+Magnetic+Linear+Dichroism%22&btnG=).

If the above technique is useful, and the physical principles have been understood for decades, then why isn't it being used now? There are 2 basic reasons:
- infrared magnetic dichroism of most organic molecules is a weak effect
- results have been hard to interpret

When magnetic dichroism spectroscopy has been used with organic molecules, it's [mostly](https://www.nature.com/articles/241193a0) been used [on metalloproteins](https://www.sciencedirect.com/science/article/abs/pii/S001085450600172X), because spin effects (from a bound metal atom with an unpaired electron) make magnetic dichroism relatively strong and easier to interpret.

What I'm proposing here is to do magnetic dichroism spectroscopy of uncrystallized organic molecules using cryo-FTIR, and use molecular simulations to determine the meaning of small frequency shifts of spectral lines with light linear polarization relative to an applied magnetic field. (Cryo-FTIR should give sufficiently good frequency resolution for that.) However, those magnetic shifts of spectral lines of organic molecules involve magnetic fields affecting the energy transfer between different vibrational modes, which is complex and hard to predict.

As [this paper](https://doi.org/10.1039/B615870F) notes:
> Circular dichroism (CD) is an important technique in the structural characterisation of proteins, and especially for secondary structure determination. The CD of proteins can be calculated from first principles using the so-called matrix method, with an accuracy which is almost quantitative for helical proteins. Thus, for proteins of unknown structure, CD calculations and experimental data can be used in conjunction to aid structure analysis. Linear dichroism (LD) can be calculated using analogous methodology and has been used to establish the relative orientations of subunits in proteins and protein orientation in an environment such as a membrane. However, simple analysis of LD data is not possible, due to overlapping transitions.

What has changed to make that approach (potentially) more worthwhile?
- computers have gotten much faster
- molecular simulation algorithms have improved
- photodetectors have improved somewhat
- strong (neodymium) permanent magnets are available, potentially allowing for lower-cost instruments


## molecule simulation

Computers have gotten faster. Is it now possible to determine exactly what frequencies a molecule would absorb with simulation? Yes, but only for very small molecules of just a few atoms, even with supercomputers - and there are few enough of those that their properties can be found experimentally instead. For larger molecules, some simplifications are needed. [Here's a review](https://www.frontiersin.org/articles/10.3389/fchem.2019.00048/full) of some recent developments, and I'll describe some heuristics that can be used.

It's easy to add together the spectra of each bond's vibrations. The spectra of molecules is more complex than that because those vibrations can interact, which means transfer of energy between them. For a demonstration of this principle, we can look at [energy transfer between pendulums](https://www.youtube.com/watch?v=okdJp-YphhY). The energy transfer between a pair of pendulums depends on the relative phase. When frequency is slightly different, the relative phase stays similar for long enough for full energy transfer, then it changes and energy transfer happens in the opposite direction. You can see with those pendulums that energy transfer is greater when frequencies are similar. That's one way to simplify simulations: energy transfer between modes with large frequency differences can be ignored.

Another way to simplify simulations is by ignoring interactions that involve many vibration modes. In practice, the importance of interactions seems to decrease with their complexity, so most of the net impact comes from 2-mode and 3-mode interactions.

Another way to simplify simulations is to only consider sets of vibrational modes that are near each other. More-distant vibrations tend to have weaker interactions.

Even with these heuristics, accurate enough simulations to determine which large molecules are present from IR spectra are difficult. Different molecules can have spectral lines that are close to each other, so highly accurate predictions can be necessary. However, with magnetic linear dichroism spectroscopy, we don't need to predict the exact positions of spectral lines - we can just predict the *direction* in which spectral lines shift as polarization is changed, for several different lines. This could reduce the accuracy required from simulations.