## Anslyn pp. 935 – 1000

The penultimate chapter of Anslyn is an excellent discussion of photochemistry, with lots of physics clearly explained but it leaves one question unanswered which has always puzzled me.  How long does it take for a photon of a given wavelength to be absorbed .  On p. 811 there is an excellent discussion of the way the quantum mechanical operator for kinetic energy (-hBar/2m * del^2) is related to kinetic energy.  The more the wavefunction changes in space, the higher the energy.  Note that the wavefunction applies to particles (like protons, neutrons, electrons) with mass.

Nonetheless, in a meatball sort of way, apply this to the (massless) photon.  Consider light from the classical point of view, as magnetic and electrical fields which fluctuate in time and space.  The fields of course exert force on charged particles, and one can imagine photons exerting forces on the electrons around a nucleus and  changing their momentum, hence doing work on them.  Since energy is conserved (even in quantum mechanics), it’s easy to see how the electrons get a higher energy as a result.  The faster the fields fluctuate, the more energy they impart to the electrons.

Now consider a photon going past an atom, and being absorbed by it.  It seems that a full cycle of field fluctuation must pass the atom.  So here’s a back of the envelope calculation, which seems to work out.  Figure an atomic diameter of 1 Angstrom (10^-10 meters).  The chapter is about photochemistry, which is absorption of light energetic enough to change electronic energy levels in an atom or a molecule.  All the colored things we see, are colored because their electronic energy levels are absorbing photons of visible light — the colors actually result from the photons NOT absorbed.  So choose light of 6000 Angstroms — which has a wavelength of 6 * 10^-7 meters.

In one second, light moves 3 * 10^8 meters, regardless of how many many wavelengths it contains. If the wavelength were 1 meter it would move past a point in 1/3 * 10^8 seconds But wavelength of the visible  light  I chose is 6 * 10 ^-7 meters, so the wavelength moves past in 6*10^-7/3 * 10^8 = 2 x 10^-15 seconds, which (I think) is how long it takes visible light to be absorbed.  Have I made a mistake?  Are there any cognoscenti out there to tell me different?

That was a classical way of looking at it.  Now for the bizarrity of quantum mechanics.  How does the wavelength of the photon get sucked up by something 1/6000th of itself, particularly when there are probably at least 10^9 atoms in a volume 6,000 on a side?  It gets worse with NMR, because the radioWave absorbed by a nucleus is 1 meter, and the nucleus is 10^-4 the size of an atom.  Essentially I’m asking about the collapse of the wavefunction of a photon (assuming they have one?).

p. 936 — “We show wavelength in the condoned (italics) unit of nanoMeter  . . . “  It may be condoned, but this chemist thinks in Angstroms, and my guess is that most chemists do, because atomic radii and diameters are small numbers in Angstroms, not fractions of a nanoMeter.

p. 939 — “Absorption of two photons or multiple photons . . . does not occur, execpt with special equipment . . . “  True enough, but the technique is now widely used in biologic research.   This is not new      [ Nature vol. 375 pp. 682 – 685 ’95 ] In contrast to conventional microscopy, two long wavelength photons are simultaneously absorbed in two photon fluoresence microscopy (multiphoton microscopy)   < [ Science vol. 300 p. 84 ’03 — actually within a few femtoSeconds — I thought simultaneity was asking too much > and combine their energies to excite a fluorophore not normally absorbing at this wavelength.  This permits the use of infrared light to excite the fluorophore. By using low energy (near infrared) light rather than higher energy visible light photons, light induced degradation of biological samples is minimized.

p. 939 — Manifold probably really refers to the potential energy surface associated with the different energy levels, rather than the numeric value of the energy level.

p. 940 — Look at transition dipoles very hard if you want to understand Forster resonance energy transfer (FRET), whch is widely used in biology to determine how proteins associate with each other.

p. 944 — How in the world did they get enough formaldehyde in the excited state to measure it — or is this calculation?

p. 947 — Nice exposition on GFP (Green Fluorescent Protein) which has revolutionized cellular biology.   But the organic chemist should ask themselves, why don’t chemical reactions between the hundreds of side chains on a protein happen all the time?  For more on this point see https://luysii.wordpress.com/2009/09/25/are-biochemists-looking-under-the-lamppost/

p. 951 — How do you tell phosphorescence from fluorescence — the lifetime for phosphorescence is much longer (.1 – 10 seconds), but is this enough.

p. 970 — The chemistry of photolyases, which repair thymine photodimers is interesting.  Here’s a bit more information.        [ Proc. Natl. Acad. Sci. vol. 99 pp. 1319 – 1322 ’02 ] Enzymes repairing cyclobutane dimerase are called photolyases.  The enzymes contain a redox active flavin adenine dinucleotide (FAD), and a light harvester (a methenyltetrahydrofolate < a pterin > in most species).    It has been proposed that the initial step in the DNA repair mechanism is a photoinduced single electron transfer from the FAD cofactor (which in the active enzyme is in its fully reduced form — FADH-) to the DNA lesion.  The extra electron goes into the antibonding orbital of one of the C C bonds of the dimer.  (The electron donated is on the adenine of FADH).  The entire process takes less than a nanoSecond.   Electron transfer to the dimer takes 250 picoSeconds.  The dimer then opens within 90 picoSeconds and the electron comes back to the FADH cofactor in 700 picoSeconds.  This all happens because the dimer has been flipped out of the DNA into a binding pocket of the photolyase (how long does this take?).

Interestingly, photolyases use less energetic light than the natural absorption of thymine dimers (2500 Angstroms).   Photoexcitation of the enzyme culminates in electron donation from the excited state flavin directly to the thymine dimer.

p. 973 –> The photochemical reactions are impressive synthetically, and represent a whole new ball game in making fused rings.   The synthesis of cubane is impressive, and I wouldn’t have though quadricyclane could have been made at all.

p. 980 — Caged compounds and their rapid release in incredibly important in biological research, particularly brain research.  Glutamic acid, is the main excitatory neurotransmitter in brain, and the ability to release it very locally in the brain and watch what happens subsequently is extremely useful in brain research.

p. 987 — Sinbce the bond dissociation energy of O2 is given (34 kiloCalories/Mole) and C=O bonds are stated to be quite strong, why not just say the BDE of C=O is 172 KCal/M?

p. 992 — Good to see Sam Danishevsky has somethng named for him.

• MJ  On December 29, 2011 at 9:56 pm

– As I understand it, the maturation of the GFP chromophore occurs after translation. Given that posttranslational modification research is hardly a closed book, I would not be surprised to find out that reactions between side chains do occur more often, but just haven’t been discovered. Presuming that the reactive side chains under investigation aren’t modified in some other way, of course!

– Fluorescence is typically presented, in my experience, as emission from an excited singlet state to a singlet state, while phosphorescence is from a excited triplet state to a singlet state (usually arrived at after an intersystem crossing of some sort). I understand that the more general definition is that there is no change in spin multiplicity in fluorescence, while there is such a change in phosphorescence.

– The length of time it takes to absorb a photon is naturally going to scale relative to the wavelength. The optical period for visible light is a few femtoseconds (just as you calculated). As a logical consequence of that, if you want to look at phenomenona that occur more quickly, one needs to start heading into the UV and beyond for light sources, since the wavelengths are shorter and will be absorbed more quickly. Which is exactly what is happening – attosecond physics & chemical physics are utilizing the advances in deep UV/X-ray light sources to do just that.

My potentially controversial thoughts –

It seems unlikely that there actually is absorption and emission of electromagnetic radiation in magnetic resonance. As I like to mention: one of the most exciting new technologies has been the development of NMR probes that dramatically reduce the extent of the sample’s exposure to the electric field component of the RF pulses, as that is what primarily contributes to sample heating. If you can (crudely speaking) toss out the E field but keep the B field, does it seem likely that the absorption of photons is that essential?

There is an unfortunate discontinuity regarding the foundations of magnetic resonance. People tend to use either a mostly classical view that is easily reconciled with the engineering practicalities (mostly on the MRI side of things) and there’s also a more quantum mechanical outlook (mostly on the chemistry/physics spectroscopy side of the field). I would recommend checking out Lars Hanson’s online tutorial first, and then if you’re still interested, I would recommend <a href="http://dx.doi.org/10.1002/(SICI)1099-0534(1997)9:53.0.CO;2-W“>David Hoult’s papers (which I can always pass along via email if you’re interested) and then a recent effort at a full-fledged QED development of magnetic resonance (again, I can pass along via email). I realize that this would certainly lead you astray from your stated goals for 2012, but this is probably why there is this issue. What we have currently works really well, and people are continuing to develop new and interesting experiments to garner more and more information in all realms of magnetic resonance. Taking the time to crank through a bunch of propagators and Feynman diagrams just to tidy up the theoretical underpinnings – unless it’s going to yield interesting new physics – seems like a riskier undertaking given the funding environment (and most people’s interests) than applying known methods to challenging problems in structural biology, materials science, and other pursuits where everyone wants results and wants them yesterday.

In general, though, this mix of classical/quantum mechanical approaches to understanding the interaction of electromagnetic radiation with matter (and, consequently, spectroscopy) is probably going to remain with us for the foreseeable future. Given that what one measures can usually be fairly well explained with a semiclassical mixture in many situations, it will be an uphill battle to change this state of affairs.

Best wishes for 2012!

• luysii  On December 30, 2011 at 9:31 am

MJ — thanks greatly for taking the time for your detailed response. Good to see that I wasn’t too far off with the meatball approach I tried. “If you can (crudely speaking) toss out the E field but keep the B field” sounds something like squeezed light, which I’ve read about in Nature, but don’t understand.

As for delving into physics in the coming year, I plan to, but in a slightly different direction, as the last post of the year on New Year’s resolutions will show. Thanks again for all your thoughtful comments this year and others.

Happy new year !