What decides the colour of light?

[DaveC426913]

But it's got nothing to do with energy levels. It's a structural change in a protein (a macromolecule) in a process called photoisomerisation.

Yes. What is it exactly that you think provides the energy to make the change? A wavelength is not energy; it is simply a magnitude of distance.

 

[sophiecentaur]

since previous studies likely haven't distinguished wavelength and frequency.

But they have. That first wiki hit talks about photon energy. I am not aware of anywhere that the wavelength is used directly to give photon energy. Can you? We have already accepted that the wavelength of light is conventionally used in spectroscopy but that's just history.
Your suggestion that wavelength could be relevant, due to the dimensions of the molecules, does sort of have legs, however. The coupling of energy into a structure can be affected by the physical dimension (in a classical system). However, this is a QM situation so I am not sure that it would really be a valid idea. But. of course, the wavelength inside the material would be affected by the bulk properties. But I still stick with E = hν as the clincher for frequency.

 

[madness]

Yes. What is it exactly that you think provides the energy to make the change? A wavelength is not energy; it is simply a magnitude of distance.

I guess if you presume that it takes exactly one photon to induce the structural change, this argument would make sense, but I'm not sure that this is the case. You can get the same amount of energy from light at different frequencies/wavelengths depending on the intensity (i.e., number of photons). I also don't understand by your argument why cells would be tuned to a particular frequency, rather than just a minimum frequency based on an energy threshold. You would expect sigmoidal rather than gaussian sensitivity curves if your explanation is correct.

 

[collinsmark]

I guess if you presume that it takes exactly one photon to induce the structural change, this argument would make sense, but I'm not sure that this is the case. You can get the same amount of energy from light at different frequencies/wavelengths depending on the intensity (i.e., number of photons). I also don't understand by your argument why cells would be tuned to a particular frequency, rather than just a minimum frequency based on an energy threshold. You would expect sigmoidal rather than gaussian sensitivity curves if your explanation is correct.

Yes, it only takes a single photon of the right energy to induce an excited electron state*, if it is absorbed by the photoreceptor.

*[Edit: from one particular state to another particular state. The energy must be enough to cause the state change, but not so much to excite the electron to an even higher state (and certainly not so much as to blow it clean off the photoreceptor molecule).]

Photoreception is a quantum process at its heart. That means only certain energy levels are allowed (and for what it's worth that's even why it's called "quantum mechanics" in the first place, since energy levels are quantized). Going back to the original post, that means frequency governs the interaction through the E = h \nu relationship (from Einstein's photoelectric effect paper circa 1905).

A single photon (even with the correct energy) is not probably enough to register perception in a typical human, but it is enough to excite an electron in the photosensitive cell. Add enough of these photons of the right energy and the human can perceive the light.

You are correct that twice the number of photons at half the frequency (i.e., half the energy per photon) altogether contain the same overall energy, but humans won't see it (because no electrons in the photoreceptors get excited appropriately).** That's the crux of quantum mechanics right there; it's the rabbit's hole if you will (a rabbit hole that goes very deep).

**[Another edit: similarly, half the number of photons at twice the frequency (twice the energy per photon) also altogether contain the same overall energy, but humans won't see that either. However in this latter case bad things can happen such as cellular damage (as a matter of fact, the photons might not even make their way to the retina, due to being scattered by the lens and aqueous humor, etc. as molecules in those tissues are subject to being damaged/destroyed in the process if the energy per photon is great enough). Make sure your sunglasses have UV protection and don't forget to wear your sunscreen!]

 

[Buzz Bloom]

Hi everyone:

I think a concept related to color perception has mostly been ignored so far in this thread. See

https://en.wikipedia.org/wiki/Cone_cell .​

Each of the cones of the eye measures the the intensity of the light's spectrum with respect to the sensitivity spectrum of the cone's pigment. In the normal eye there are three kinds of cones, each with a different pigment. The relative intensities of three cones with different pigments maps onto a perceived color.

There is also a very unusual color perception phenomenon discovered by Edwin Land. See

http://www.greatreality.com/Color2Color.htm .​

I remember seeing a demonstration. I saw a picture projected on a screen for a brief time as having a normal range of colors. As I recall, the image was an American flag. The projection was made using two black and white transparencies, each projected with a slightly different yellow light. The time of projection was kept short because a longer projection would have spoiled the effect.

Regards,
Buzz

 

[FactChecker]

I always say that human colour perception is a really poor spectrometer. It is sooo easy to fool. And it doesn't matter at all.

I have actually been banned from one of these discussions for saying that. There is a "perception is all that counts" mind set here.

 

[evan-e-cent]

A doctor's perspective. I think we should be able to answer this by referring to the chemical process in the eye. The retina produces a chemical called retinal which can exist as two isomers. The cis isomer of the double bond has a higher energy state than the trans isomer due to steric interference between the adjacent parts of the molecule. The cells in the retina expend energy to convert the trans isomer into the cis isomer which is only semi-stable.

When the cis isomer gets hit by a photon the added energy causes it to flip back into the trans form. The molecule is housed inside a large protein called rhodopsin and with the change to trans configuration the protein also changes its shape. This sets off a chain reaction which causes a nerve signal to be sent to the brain. There are three types of cone cells detecting three colors of light red, green and blue. Each responds with a bell shaped curve and the eye is most sensitive to green as our surroundings are dominated by green foliage (unless we live in a town).

So the question becomes "Is it the wave length or the frequency of light that determines whether it causes the structure of retinal to change". I think the answer is: it is the energy of the photon that is important and that will not vary as the photon travels through different media so I think it is frequency that is the deciding factor not wavelength.

PS Have you ever wondered why water is perfectly clear?

 

[madness]

Yes, it only takes a single photon of the right energy to induce an excited electron state*, if it is absorbed by the photoreceptor.

*[Edit: from one particular state to another particular state. The energy must be enough to cause the state change, but not so much to excite the electron to an even higher state (and certainly not so much as to blow it clean off the photoreceptor molecule).]

Photoreception is a quantum process at its heart. That means only certain energy levels are allowed (and for what it's worth that's even why it's called "quantum mechanics" in the first place, since energy levels are quantized). Going back to the original post, that means frequency governs the interaction through the E = h \nu relationship (from Einstein's photoelectric effect paper circa 1905).

A single photon (even with the correct energy) is not probably enough to register perception in a typical human, but it is enough to excite an electron in the photosensitive cell. Add enough of these photons of the right energy and the human can perceive the light.

You are correct that twice the number of photons at half the frequency (i.e., half the energy per photon) altogether contain the same overall energy, but humans won't see it (because no electrons in the photoreceptors get excited appropriately).** That's the crux of quantum mechanics right there; it's the rabbit's hole if you will (a rabbit hole that goes very deep).

**[Another edit: similarly, half the number of photons at twice the frequency (twice the energy per photon) also altogether contain the same overall energy, but humans won't see that either. However in this latter case bad things can happen such as cellular damage (as a matter of fact, the photons might not even make their way to the retina, due to being scattered by the lens and aqueous humor, etc. as molecules in those tissues are subject to being damaged/destroyed in the process if the energy per photon is great enough). Make sure your sunglasses have UV protection and don't forget to wear your sunscreen!]

Maybe this is just because my knowledge of chemistry is too rusty, but I'm not making the link between the excitation of an electron when it absorbs a photon that you are disucssing, and the conformal change in the structure of a macromolecule that underlies phototransduction in the retina. It seems a perfectly reasonable hypothesis to me that this conformal change would only occur when a wavelength of the right length scale to excite the molecular structure in the correct way would be present. Moreover, this would explain the Gaussian sensitivity curves to wavelength/frequency observed in the retina, whereas your mechanism would predict a monotonically increasing response curve with increasing frequency, in contrast to what is actually observed.

 

[collinsmark]

Maybe this is just because my knowledge of chemistry is too rusty, but I'm not making the link between the excitation of an electron when it absorbs a photon that you are disucssing, and the conformal change in the structure of a macromolecule that underlies phototransduction in the retina.

It's still based on quantum principles. That means only photons of a relatively narrow range of energy values (seen more below) will be absorbed that would cause the proper excitation of the electron, which is the trigger that ultimately leads to the brain perceiving the stimulus (after a very complicated process; @evan-e-cent gave a more detailed description in post #67). Any more energy or less energy in the photon, and the excitation does not happen.

It seems a perfectly reasonable hypothesis to me that this conformal change would only occur when a wavelength of the right length scale to excite the molecular structure in the correct way would be present. Moreover, this would explain the Gaussian sensitivity curves to wavelength/frequency observed in the retina,

It's the photon energy that is critical here. (And the photon energy is directly proportional to its frequency, so if you had to pick between frequency and wavelength here, frequency would be the one to choose, given its proportionality to energy).

whereas your mechanism would predict a monotonically increasing response curve with increasing frequency, in contrast to what is actually observed.

That's not correct. It is certainly not what I meant convey anyway.

“Red” photoreceptor cones are not particularly sensitive to blue light even though blue light has a higher photon energy. And that is completely consistent with the underlying quantum nature at its core. Just because a photon's energy is significantly greater than the allowed change of electron energy states it does not mean that the electron will necessarily absorb some or all of that energy. Instead, quantum theory predicts that that the electron state will likely not be impacted by the photon at all.

(Light frequencies anywhere from near-infrared all the way through ultraviolet will be absorbed by the eye in one way or another. It’s just that a particular color cone type is only sensitive to photon energies within a limited range. And that is not inconsistent with quantum theory.)

Let me illustrate a more simple example.

Consider a light source with a uniform spectrum of light (with no gaps in the spectrum, and let’s assume the spectrum spans at least the visible band, if not the infrared and ultraviolet too). Shine that light through a cold gas (any gas will work, but hydrogen or neon might make good choices), then observe the resulting spectrum. You'll notice that now there are very narrow gaps (called spectral lines) in the resulting spectrum (after passing through the gas)! Photon energies higher than a given spectral line passed right through the gas as did photons of lower energies. Only certain energies are absorbed.*

*(In this simple gas case, the spectral lines are not infinitesimally thin, but do contain a very small bandwidth, which can be explained by the Doppler effect of the moving gas molecules. It's way more complex for [non-gaseous] huge molecules working together as a tissue.)

The molecular structures of human photoreceptors are far, far more complex than a simple gas (not to mention not being in a gaseous state). There’s more complex mechanisms for absorption and thusly the absorption bandwidths are larger than the simple gas example. Yet extraordinarily more complex as they may be, they still follow the same quantum rules.

 

[collinsmark]

Regarding the wider bandwidths of the human color cone photoreceptors compared to the very narrow bandwidths of the simple gas example, let me present another analogy. (This is just an analogy; the human eye is far more complex than a photo-diode, but I think it's still a useful analogy).

I'm sure you are familiar with light emitting diodes (LEDs). One can design a circuit to use an LED in reverse, so to speak, so it detects light rather than emitting it. And the sensitivity does have a bell-curve shape to it larger than the corresponding simple gas example that I used in the last post. as a matter of fact, the LED sensitivity bandwidth is not too terribly different than the photoreceptors in the human eye.

I use this analogy because the sensitivity bandwidths of LEDs (used as photo-diodes) can be predicted with great precision using quantum mechanics.

The larger bandwidth comes from the fact that atoms in the diode form a well defined structure. And when that happens the allowed electron energies form "bands" rather than single values*. Each energy band has a "thickness" (in terms of energy) so to speak. The bands are discrete from one another, but unlike the simple gas example, they are not single values of energy.* So for a photon to be absorbed, it must have the energy which is no less than the smallest energy difference between the bands and no greater than the largest difference. The result produces a bell-like curve shape for sensitivity.

I highly speculate that the human eye has even other mechanisms of widening the sensitivity bandwidth. This comparison to photo-diodes and LEDs is just an analogy, but I think it's a pertinent one.

*(the learned reader will recognize that when I say "single value" of allowed energy for a particular state of an electron in an atom, I am ignoring such things such as fine and hyperfine splitting, as well as Doppler shifting. I don't want to get into that stuff here since it's not really relevant.)

[Edit: This link explains what I was getting at involving the energy band theory:
http://hyperphysics.phy-astr.gsu.edu/hbase/solids/band.html
In order for the material to absorb a photon, the photon energy must be greater than the bandgap but less than the combined widths of the bandgap plus valance state bandwidth plus conduction state bandwidth. The nonzero bandwidths of the conduction band and the valance bands, combined with statistical properties of electrons within those bands, lead to a bell-like shaped curve of absorption sensitivity as a function of photon energy.
Of course the photoreceptor proteins in the eye area far more complex to analyze than what is discussed in this link regarding simple solids. But the same sort of ideas apply, at least in principle (and at least in part).]

 

[jack476]

It's very rare to encounter light that is only a single frequency, light from most sources in the real world is actually a mixture of light at a number of different frequencies. What happens when light passes through a filter is that some of those frequencies are absorbed and some are not.

To give an example, think about the greenhouse effect. You know that it's due to certain gases having a really good ability to absorb radiation that's been reflected from the Earth, the energy of that radiation is absorbed by the gas (technically, at the molecular scale the radiation is actually being scattered, but the net result is that the gas as a whole absorbs energy) causing the atmosphere to warm. A common misconception is that climate change will "balance out" because the understanding is that it's reflecting radiation, therefore reflecting the solar radiation that would warm the Earth in the first place, but the reason that's not true is down to that frequency-dependent absorption: Carbon dioxide is a filter for light in some ranges of the IR spectrum, not a reflector.

Frequency can be directly changed in some cases, for instance in Doppler shifting, but that's very different from what's happening in a color filter.

 

[evan-e-cent]

When the cis isomer gets hit by a photon the added energy causes it to flip back into the trans form.

I don't think this mechanism of light detection corresponds with the excited state of electrons. It is more like a chemical reaction which requires a certain thermal activation energy to get over the energy hump and then drop into a lower energy state. This mechanism would not depend so precisely on the quantum of energy in the photon and may respond to a broad range of light energies.

In fact it may respond to light of a wide range of frequencies. The fact that some species of insect use a colored oil droplet in front of the light sensor suggests that different types of color filters are used in the various cones and rods that detect different colors. The literature talks about different color pigments in the different types of cones and I think these act as color filters. The rods probably use the same chemical mechanism without filters, making them more sensitive to light but unable to distinguish colors (they are also more compact and there are more sensors packed into a small space giving greater sensitivity.)

For those unfamiliar with cis / trans isomers may find these diagrams from Wikipedia useful. In the model you can see how the two large CH3 groups can interact with each other causing a higher energy state than the trans configuration of the same molecule where the CH3 groups are on opposite sides of the double bond. If the CH3 groups were replaced with long chains as in retinal, the interactions are more severe.

The graph below shows the concept of activation energy Ea. Although the cis isomer is in a higher energy state than the trans, it requires additional energy to distort the double bond and transition from one state to the other. During the transition a temporary high energy transitional state exists where it is neither cis nor trans. So the cis isomer can exist for long periods of time before that extra energy becomes available. In the eye the extra energy is provided by a photon. Photons providing excessive energy would also cause the transition so it may not be particularly color sensitive unless filters are used.

The fact that cis-retinal can get used up faster than its rate of production causes the after-image if you stare at a bright image for a long time and then look into the dark.

https://en.wikipedia.org/wiki/Cis–trans_isomerism

CIS ISOMER (higher energy state)

TRANS ISOMER (Lower energy state)

https://en.wikipedia.org/wiki/Activation_energy

 

[evan-e-cent]

Further reading of Wikipedia on opsin proteins revealed:

https://en.wikipedia.org/wiki/Photopsin

In humans there are 3 different iodopsins (rhodopsin analogs) that contain the protein-pigment complexes photopsin I, II, and III.
The 3 types of iodopsins are called erythrolabe(photopsin I + retinal), chlorolabe(photopsin II + retinal), and cyanolabe(photopsin III + retinal).[3]
These photopsins have absorption maxima for red ["erythr"-red] (photopsin I), green ["chlor"-green] (photopsin II), and bluish-violet light ["cyan"-bluish violet] (photopsin III).

This indicates that the "color filter properties" are built into the proteins that contain the retinal light sensing molecule. The Greek roots refer to the colors; erythro means red, cholera means green and cyano refers to blue or cyan.

 

[sophiecentaur]

I have actually been banned from one of these discussions for saying that. There is a "perception is all that counts" mind set here.

Which "here" were you referring to, at the time? The 'here' of this thread or the 'here' of the PF site in general?

 

[FactChecker]

Which "here" were you referring to, at the time? The 'here' of this thread or the 'here' of the PF site in general?

About a year ago on another similar thread (definition of color) on PF.

 

[sophiecentaur]

About a year ago on another similar thread (definition of color) on PF.

I skimmed through that thread and it is almost a re-run of this one. The same misconceptions and mis-used words are there and the continued Colour = Wavelength nonsense, plus a large number of 'personal theories' that PF mods would normally stamp on. I think any thread that drifts into how we see colour should probably be shunted, PDQ, into a Forum that's more appropriate to Psychology.

 

[madness]

It's still based on quantum principles. That means only photons of a relatively narrow range of energy values (seen more below) will be absorbed that would cause the proper excitation of the electron, which is the trigger that ultimately leads to the brain perceiving the stimulus (after a very complicated process; @evan-e-cent gave a more detailed description in post #67). Any more energy or less energy in the photon, and the excitation does not happen.
It's the photon energy that is critical here. (And the photon energy is directly proportional to its frequency, so if you had to pick between frequency and wavelength here, frequency would be the one to choose, given its proportionality to energy).
That's not correct. It is certainly not what I meant convey anyway.

“Red” photoreceptor cones are not particularly sensitive to blue light even though blue light has a higher photon energy. And that is completely consistent with the underlying quantum nature at its core. Just because a photon's energy is significantly greater than the allowed change of electron energy states it does not mean that the electron will necessarily absorb some or all of that energy. Instead, quantum theory predicts that that the electron state will likely not be impacted by the photon at all.

(Light frequencies anywhere from near-infrared all the way through ultraviolet will be absorbed by the eye in one way or another. It’s just that a particular color cone type is only sensitive to photon energies within a limited range. And that is not inconsistent with quantum theory.)

Let me illustrate a more simple example.

Consider a light source with a uniform spectrum of light (with no gaps in the spectrum, and let’s assume the spectrum spans at least the visible band, if not the infrared and ultraviolet too). Shine that light through a cold gas (any gas will work, but hydrogen or neon might make good choices), then observe the resulting spectrum. You'll notice that now there are very narrow gaps (called spectral lines) in the resulting spectrum (after passing through the gas)! Photon energies higher than a given spectral line passed right through the gas as did photons of lower energies. Only certain energies are absorbed.*

*(In this simple gas case, the spectral lines are not infinitesimally thin, but do contain a very small bandwidth, which can be explained by the Doppler effect of the moving gas molecules. It's way more complex for [non-gaseous] huge molecules working together as a tissue.)

The molecular structures of human photoreceptors are far, far more complex than a simple gas (not to mention not being in a gaseous state). There’s more complex mechanisms for absorption and thusly the absorption bandwidths are larger than the simple gas example. Yet extraordinarily more complex as they may be, they still follow the same quantum rules.

This whole post is still clinging to the idea that phototransduction is caused by an excitation of an electron into another energy level, which has been repeatedly demonstrated not to be the case in this thread. As I and evan-e-cent have said, it is a conformal change in the structure of a macromolecule (and by the way, the majority of macromolecular physics is treated with classical rather than quantum principles). The process is related to chemical bonding and activation energies, not excitation of electrons into discrete bands.

 

[sophiecentaur]

caused by an excitation of an electron into another energy level,

Yes; very annoying. But you have to remember that the Hydrogen Atom model is a hard one to shift. In many eyes, QM starts and stops with it - although how that could ever square with infra red and microwave transitions, I cannot imagine. The first QM lesson shows a ladder of energy levels and photons shifting 'an electron' between them - but there is quite a bit more to learn , isn't there? That includes the energy states of molecules and the bulk properties of matter. Pity to spoil a good story with some facts, though.

 

[madness]

Yes; very annoying. But you have to remember that the Hydrogen Atom model is a hard one to shift. In many eyes, QM starts and stops with it - although how that could ever square with infra red and microwave transitions, I cannot imagine. The first QM lesson shows a ladder of energy levels and photons shifting 'an electron' between them - but there is quite a bit more to learn , isn't there? That includes the energy states of molecules and the bulk properties of matter. Pity to spoil a good story with some facts, though.

I don't think this thread has come anywhere close to explaining how a macromolecule can undergo a conformal change in the presence of light in a narrow range of frequencies/wavelengths. The activation energy picture would suggest a frequency threshold above which the change in structure will occur. The hydrogen atom picture could explain it, but we're looking at chemical bonds rather than a ladder of electron energy levels here.

 

[sophiecentaur]

, but we're looking at chemical bonds rather than a ladder of electron energy levels here.

Of course we should be but, from what is written in this thread, I doubt that everyone in thinking along those lines. The term 'electron energy level' is not an apt description of what happens in a molecule yet it still turns up in 'explanations' of complex processes due to the energy states of systems with a large number of charges.
And we are nowhere near a description of that.
But I take the key word Colour (in the title) as involving much more than the interaction of a photon with a molecule. However the retinal cells are stimulated, there is the important process of the way the three resulting signals are treated by the nervous system and how the sensation of colour is arrived at, along with the way it's categorised in the brain. That 'top down' study will avoid the risk of oversimplification of the word Colour.

 

[madness]

But I take the key word Colour (in the title) as involving much more than the interaction of a photon with a molecule. However the retinal cells are stimulated, there is the important process of the way the three resulting signals are treated by the nervous system and how the sensation of colour is arrived at, along with the way it's categorised in the brain. That 'top down' study will avoid the risk of oversimplification of the word Colour.

I fully understand this, but what you have to consider is that the brain can only work with the signals it transduces at sensory receptors. Of course, the perception of colour is a complex and poorly understood process, but it all starts with the conversion of light into electrical signals at the retina (unless you are dreaming or hallucinating!).

 

[Ygggdrasil]

I don't think this thread has come anywhere close to explaining how a macromolecule can undergo a conformal change in the presence of light in a narrow range of frequencies/wavelengths. The activation energy picture would suggest a frequency threshold above which the change in structure will occur. The hydrogen atom picture could explain it, but we're looking at chemical bonds rather than a ladder of electron energy levels here.

The activation energy picture is not really an accurate way of looking at photochemical reactions such as the photoisomerization of retinal. In this case, you can think of the first step as a chemical reaction between retinal (R) and a photon of a specific wavelength that changes R from its ground state to its excited state (R*).

Remember that the bond order, a measure of the strength of a chemical bond, can be calculated by taking the number of electrons in bonding orbitals and subtracting the number of electrons in anti-bonding orbitals (then dividing by two). Therefore, by promoting an electron from a bonding orbital to a non-bonding or anti-bonding orbital, you are decreasing the bond order of chemical bonds in retinal. This can, for example, make one of the C-C bonds in retinal resemble more of a single bond (around which rotation can occur) rather than a double-bond (around which rotation is forbidden at typical temperatures). This free rotation about one of the bonds means that when the molecule relaxes back into its ground state, it has some probability of relaxing into the trans- configuration and some probability of relaxing into the cis-configuration.

As to why absorption spectra of molecules are much wider than typical atomic spectra, this is due to the fact that molecules have vibrational and rotational states in addition to different electronic states: see https://www.physicsforums.com/threa...t-of-absorption-emission-spectroscopy.433712/. Band theory is not really applicable to this case.

 

[collinsmark]

I didn't mean to use the band theory application of the LED semiconductors as anything more than an analogy. Sometimes studying more simple systems can lead to insights of more complex ones. It was just an analogy. (I thought I made that clear. Did I? I thought so anyway.)

In the case of the simple gas absorption spectra the photon energy absorbed ultimately gets converted to other types of energy. In the case of a monotonic gas like neon, this is translational energy (heat on the macroscopic scale). [Edit: not to mention other photons in the infrared and microwave regions as the result of the atom interacting with other atoms in the gas -- again, ultimately heat though.] In the case of more complicated hydrogen molecules it also involves changes in rotational energy in addition to translational -- and the initial absorption mechanism is also more complex since two hydrogen atoms are initially bonded. We don't need to rely on quantum mechanics (QM) to macroscopically describe the thermal activity of the gases, but QM is necessary to describe the mechanism of that initial photon absorption.

In the case of the even more complicated protein molecule that photon energy ultimately becomes not just changes in translational and rotational energies, but also conformational and vibrational changes (and there may be more vibrational modes than you can shake a stick at). We don't necessarily need QM to model the resulting conformational, vibrational, rotational and translational characteristics. We can use the tools of chemistry and classical physics for most of those.

But even with a complex protein, that initial photon absorption does require quantum theory (particularly given the relatively low temperatures and relatively high photon energies in question [we are talking about photons in the visible range here and molecules near room temperture]). Could we use QM to predict the photon energy absorption spectrum of a complex protein practically? Probably not with today's computers or those to come in the near-foreseeable future. But it could be done at least in principle.

And that's the crux of my point. Classical physics cannot adequately model the mechanism of that initial photon absorption even in principle.

And all of this is relevant to this thread. The OP asked about whether the color of light relates to wavelength or frequency. The correct answer is frequency because it relates to the photon's energy. And energy is the correct answer because that's what governs the underlying quantum mechanics of that initial photon absorption (not wavelengths and not length scales of the photoreceptor or what-not).

(And btw, I'm sorry if that is annoying. )

 

[sophiecentaur]

absorption spectra of molecules are much wider than typical atomic spectra,

Isn't that a consequence of the Pauli Exclusion Principle that operates in dense materials? Solid state (of which I know a certain amount) exhibits band structures and not lines, as a result of the PEP, too.

 

[sophiecentaur]

(And btw, I'm sorry if that is annoying. )

Not at all. We all need putting straight about things we don't know about.

 

[collinsmark]

Isn't that a consequence of the Pauli Exclusion Principle that operates in dense materials? Solid state (of which I know a certain amount) exhibits band structures and not lines, as a result of the PEP, too.

As I recall it is not necessary to invoke the Pauil Exclusion Principle (PEP) to explain the energy band model of solids. Sure, in any physical real-world solid one can't get away from the PEP, but I'm just saying that I don't think it's necessary to explain the energy bands vs. single values.

If you take just a single electron and place it in a 3-dimensional, vast array of energy wells (and even simple, Dirac delta wells will suffice) -- perhaps an infinite array of potential wells -- and use standard, non-relativistic quantum mechanics to determine the allowed energies of the electron, bands will naturally result. So the band theory of solids is a very basic outcome of QM and doesn't even require the exclusion principle, as I recall.

And fascinating thing is that this problem (as I recall) is it is not too tough to calculate and show. It relies the assumption that the three dimensional array of potential wells can be approximated as infinitely large. This is one of the few cases where having an infinite number of particles actually simplifies the problem rather than making it infinitely complex. I've always found that fascinating.

The buggers are those systems with an in-between number of particles. Using today's computational resources we can use QM to make very precise predictions for a handful of particles (~10 or less maybe?) or for an infinite number of particles, assuming they have an organized structure. It's those in-between number of particles that are the buggers.

Proteins fall into the latter category. It's not that quantum mechanics isn't up for the challenge, but rather it's just that our computers and computational resources are not. But it eases my mind that QM can be used to fully analyze a protein at least in principle anyway.

 

[madness]

Therefore, by promoting an electron from a bonding orbital to a non-bonding or anti-bonding orbital, you are decreasing the bond order of chemical bonds in retinal. This can, for example, make one of the C-C bonds in retinal resemble more of a single bond (around which rotation can occur) rather than a double-bond (around which rotation is forbidden at typical temperatures).

Focussing just on this step, can we understand why only photons in a particular frequency band would do the job? Can we understand how selectivity for different frequency bands in different cells emerges? I would guess that it's actually more complex, and that the selectivity of different cells to different frequency bands requires more of a systems perspective.

By the way, I've found these last few posts to be very informative!

 

[Ygggdrasil]

Focussing just on this step, can we understand why only photons in a particular frequency band would do the job?

Essentially this has to do with the energy difference between the ground state of the molecule (the HOMO — highest occupied molecular orbital) and its excited state (the LUMO — lowest unoccupied molecular orbital). Only photons with energies matching the energy difference between the orbitals (the HOMO-LUMO gap) will be able to promote the electron to its excited state. Interaction with photons of the wrong frequency will promote the electron to "virtual states" but if these virtual states do not match the electronic states of the molecule, they will be extremely short lived, and decay back to the ground state almost immediately with re-emission of the absorbed photon. Only when the electron gets promoted to a stable electronic excited state will the excited state have a long enough lifetime for chemical processes to occur (e.g. the bond rotation required to convert the cis-form to the trans-form).

Can we understand how selectivity for different frequency bands in different cells emerges? I would guess that it's actually more complex, and that the selectivity of different cells to different frequency bands requires more of a systems perspective.

All opsins contain the same chromophore (11-cis retinal), yet different opsins have different sensitivities to different frequencies of light. This can occur because the retinal chromophore lies buried deep within a pocket in the opsin protein. The chromophore makes extensive non-covalent interactions with parts of the protein, and these interactions can affect the distribution of electrons throughout the retinal molecule, therefore, changing the energies of the molecular orbitals and the HOMO-LUMO gap. You can essentially think of this as the protein applying an external electric field to the molecule which can change the potential energy function of the electrons in 11-cis retinal. Thus, the frequency selectivity of cone cells depends entirely on the type of opsin protein they make.

This strategy has also been used on fluorescent proteins. Many fluorescent proteins have identical or very similar chromophores, but by introducing specific mutations around the chromophore-binding site, scientists have been able to fine tune the colors of the fluorescent proteins in order to generate a rainbow of colors:

 

[madness]

Essentially this has to do with the energy difference between the ground state of the molecule (the HOMO — highest occupied molecular orbital) and its excited state (the LUMO — lowest unoccupied molecular orbital). Only photons with energies matching the energy difference between the orbitals (the HOMO-LUMO gap) will be able to promote the electron to its excited state. Interaction with photons of the wrong frequency will promote the electron to "virtual states" but if these virtual states do not match the electronic states of the molecule, they will be extremely short lived, and decay back to the ground state almost immediately with re-emission of the absorbed photon. Only when the electron gets promoted to a stable electronic excited state will the excited state have a long enough lifetime for chemical processes to occur (e.g. the bond rotation required to convert the cis-form to the trans-form).

Very cool. So, if two photons at exactly half the energy were to arrive simultaneously, they might achieve the same result, but the intermediate state is so short lived that any delay in their arrival times would stop this from happening. Is this correct or incorrect?

I suppose this is also where the classical picture breaks down entirely, since classically you would expect that a photon at a higher energy than required would just induce some additional rotational or translational energy, or perhaps just excite the electron to an even higher state.

All opsins contain the same chromophore (11-cis retinal), yet different opsins have different sensitivities to different frequencies of light. This can occur because the retinal chromophore lies buried deep within a pocket in the opsin protein. The chromophore makes extensive non-covalent interactions with parts of the protein, and these interactions can affect the distribution of electrons throughout the retinal molecule, therefore, changing the energies of the molecular orbitals and the HOMO-LUMO gap. You can essentially think of this as the protein applying an external electric field to the molecule which can change the potential energy function of the electrons in 11-cis retinal. Thus, the frequency selectivity of cone cells depends entirely on the type of opsin protein they make.

I see, it's interesting that there is a purely molecular basis for all of this.

This strategy has also been used on fluorescent proteins. Many fluorescent proteins have identical or very similar chromophores, but by introducing specific mutations around the chromophore-binding site, scientists have been able to fine tune the colors of the fluorescent proteins in order to generate a rainbow of colors:

I've come across opsins mostly in the context of optogenetics, where the most commonly used opsins are channelrhodopsin and halorhodopsin. They have really revolutionised neuroscience research.

 

[Ygggdrasil]

Very cool. So, if two photons at exactly half the energy were to arrive simultaneously, they might achieve the same result, but the intermediate state is so short lived that any delay in their arrival times would stop this from happening. Is this correct or incorrect?

Yes, this is correct. This is what occurs in two photon absorption and other nonlinear optical phenomena.

I suppose this is also where the classical picture breaks down entirely, since classically you would expect that a photon at a higher energy than required would just induce some additional rotational or translational energy, or perhaps just excite the electron to an even higher state.

Light cannot really induce many changes in translational energy due to conservation of momentum. Light can excite rotational or vibrational excited states, but these are also quantized. The basic idea is that if the energy of the ground state + the energy of the photon gives an energy that is an eigenvalue of your particular molecule's hamiltonian, you will get a stable, stationary state. Otherwise, the resulting state will be a very unstable virtual state that will quickly revert back to the ground state.