See first link about a synchrotron projection TV, because we need something like that light-source here, and see the second link about carbon bicarbonate, because it provides the background chemistry that this Idea is about (and sulfur is mentioned in an annotation, too!).
OK, the main problem with
making carbon bicarbonate is that the carbon atom is a quite-small atom (significantly smaller than oxygen). I suspect this is the main reason why there is no such thing as "poly-CO2" (see link) except under extreme pressure. Therefore, even if we could catalyze the formation of carbon bicarbonate, with its central carbon surrounded by and single-bonded with 4 oxygen atoms, it probably could not be expected to persist.
Sulfur, however, is nicely different. While not as plentiful as carbon, it could be plentiful ENOUGH (see link). Certainly it is routinely extracted from carbon-containing fossil fuels (to mostly prevent acid rain). It is a much larger atom than carbon (significantly larger than oxygen, also), and likely can accommodate 6 single-bonded oxygen atoms (its "chemical valence" is occasionally +6, as in "sulfur trioxide"). Sulfur BiCarbonate would have the formula S(HCO3)6.
In more detail, consider how one BiCarbonate group would extend from one of those six oxygen atoms. That oxygen's second bond would connect to the carbon atom in the BiCarbonate. That carbon atom is double-bonded to a second oxygen, and single-bonded to the third oxygen. That last oxygen's second bond is connected to the hydrogen atom. I'm fairly confident there is enough space surrounding a sulfur atom for 6 BiCarbonate groups.
The next problem concerns the "electronegativity" of Sulfur. See link. In general, to make a BiCarbonate molecule, you need Carbonic Acid to react with something. Carbonic Acid has two hydrogen atoms; the second one is connected to that first oxygen atom described above (when there is no Sulfur attached to that oxygen). So, this means we need to replace the chemical bond between that hydrogen and that oxygen with a new chemical bond between that oxygen and the Sulfur atom.
So, compare the electronegativities of Hydrogen and Sulfur. The desired reaction could occur spontaneously if Sulfur had a LOWER number than Hydrogen, but it doesn't; Sulfur actually has a higher electronegativity than Hydrogen. Therefore it is necessary to catalyze this reaction, if we want it to happen.
Note that the electronegativity numbers indicate the same would be true if we wanted to make Carbon BiCarbonate. At the time of writing that Idea I wasn't aware of any catalyst that could do it, but now I think I've identified one. I'm focusing on sulfur here because, as mentioned above, it may be superior to carbon for the purpose of sequestering carbon dioxide.
I'm planning on employing a special PHYSICAL catalyst, not any sort of chemical catalyst. This catalyst is the synchrotron light source, which can very efficiently generate quite bright light of just about any pure frequency we want. I'm quite certain it can generate the light-frequencies needed to do the thing I'm about to describe, even if I don't know the exact frequencies needed.
The subdivision of Physics known as "Spectroscopy" deals with reactions between atoms and photons, which cause those atoms to become either "excited" or "ionized". An excited atom is one in which an electron is boosted from its normal "orbit" to a higher orbit. An ionized atom is one in which the electron is boosted to a kind of "escape velocity" --it leaves the vicinity of the atom altogether.
Now consider an ordinary sulfur atom in its "ground state", with all its electrons orbiting as close-in as they can get. The Electronegativity value of Sulfur is based on THAT atom. If we boosted an electron to a higher orbit (by giving it an appropriate photon to absorb), it would be less-tightly-bound to the sulfur atom, and could participate more easily in a chemical reaction. In effect, the electronegativity of that sulfur atom would be temporarily reduced (it is temporary because after some time passes the electron falls back down to its original lower orbit, releasing the previously-absorbed photon).
The overall CO2-sequestering apparatus can now be described. We start with the gas and pressure-dissolve it in water, which will cause lots of Carbonic Acid to spontaneously form. I will ASSUME that the special light-frequencies we want to generate can be transmitted reasonably efficiently through water. It won't have to go very far if our water container is shaped something like the child's science toy known as an "ant farm", only VERY long.
We will grind sulfur to a fine powder and mix it with the water at one end of the long container, as a fairly dense "suspension". The water needs to be agitated lightly to keep it in suspension, but that's OK because we also want to pump the water SLOWLY through the long container. When first started, our clear acidified water container will contain a yellow cloud, of suspended sulfur particles, at one end. We imagine that long container as having 6 segments. We may need 6 different frequencies of light, one for each segment --the synchrotron can be 6-sided, of course-- and light should be shone through both sides of the water container (use mirrors or even two synchrotrons).
From Spectroscopy we know that if an atom encounters a photon of just the right frequency, it will be strongly absorbed. This means we should be able to efficiently boost the first electron of each of many sulfur atoms to a high-enough orbit that the Carbonic Acid molecules in the water can now react with those sulfur atoms. Also note we want that reaction to proceed "cooly"; only a very tiny amount energy should be released when it happens. SOME MUST be released, else the reaction will hardly take place at all, but we don't want to be wasteful! A long-enough water container can offer plenty of room for a slow reaction rate.
As the reactions happen, Hydrogen atoms will be released (one from each Carbonic Acid molecule) and will bubble upwards, where they can be captured and sold as fuel. Note that as Carbonic Acid in the water is used up, becoming combined with sulfur atoms, more can continue to be formed if we keep applying CO2 gas pressure to the water container (and agitating the water).
According to the Electronegativity numbers, the amount of energy needed to cause the hydrogen to be released is related to the numerical difference between Hydrogen and Sulfur, but the amount of energy we can GAIN from combining that Hydrogen with more Oxygen (from the air) is related to the numerical difference between Hydrogen and Oxygen (about 3 and 1/2 times as much energy!).
We should probably combine them in a fuel cell that generates electricity (one of the most efficient ways known, to do that), and use it to run the synchrotron, and the water agitator/pumps, and the CO2 pressurization stuff. Overall, but mostly depending on the efficiencies at which we produce the necessary light-frequencies, this could be anything from a low-cost to an actually-profitable way to sequester CO2!
When a molecule of S(HCO3)1 forms, this will have different physical properties from sulfur, and this is the reason why a different-energy photon is likely required, to boost the next sulfur-atom electron to a sufficiently high orbit for another Carbonic Acid reaction to occur. That's why I described the water container as having sections; the 2nd section is where we want to concentrate light of that frequency, to operate on all the molecules that were formed in the first section. In this section, of course, we want S(HCO3)1 to become S(HCO3)2.
We repeat the preceding for the next 4 sections, after which, hopefully, allmost all the sulfur that started at one end of the water container has been chemically combined with Carbonic Acid, yielding S(HCO3)6. Then we extract it from the water and sequester it (it will most certainly be a solid!), perhaps in abandoned open-pit mines.