Nice job. No doubt css is getting better and better with every new release and same goes for browsers.
Waiting for the day when all the browsers will become completely unified and one don't have to worry about cross-browser compatibility.
When I looked at chemical symbols before seeing this I had always assumed them to be a sort of vague outline of what was really happening. It's amazing to think that the way chemicals bond is the same in reality as drawn in textbooks.
In the two variants on the right, their edges seem to be curling upward making a bowl shape. Their edges are also brighter, which perhaps means they are closer to the probe than parts that are farther away. Additionally, the hexagons are also not all the same shape. I assume that's due to the curling.
I would be interested to know if my interpretation of the image is correct, or if the molecule is really flat and what I'm seeing is an artifact.
To answer your question (flat vs. artifact) directly: It's flat. Sorta. Bear with me a moment. If this is confusing, please let me know, and i'll try to clarify. Molecular symmetry isn't my strong point, unfortunately.
The trouble with all of this is the "picture" is not an actual picture-made-with-photons picture, but a visualization via computer. That isn't to say it's a poor reflection on reality, but that the limitations of the techniques should be accounted for. In this case, the electron density of the overall molecule is being measured. The brighter signals correspond to an increase in local electron density.
In such chemical structures as these, the aromaticity [1] is the main force at play. Without getting too technical, the brighter regions are those with increased electron density. (See figure 4 at the IBM Zurich page on pentacene [2])
The hexagons (and square and pentagons) in fact do not have idealized geometry, but not due to any curling. The unique environment of each carbon is more at play. Symmetry plays a large role; imagine a symmetric vs. unsymmetrical tug-of-war between the carbons with the electrons as the rope. The left hand side and lower right have a dihedral mirror plane, simplifying the density somewhat, where the upper right has a more muddled situation.
Getting back to the flatness, the target molecule is 'mounted' on a suitably uniform surface, such that only one side is being scanned/read by the probe. In a vacuum, the tug of war in the Z direction (into the plane) will cancel out between the +Z and -Z vectors, giving a 'flat' molecule. (Depending on your point of view, either because of this or due to this, each of these molecules has a mirror plane in the plane of the molecule, bisecting each atom.)
Setting all that aside, the entire process is really #$%*& cool, particularly to a chemist. (Yes, those crazy textbook pictures are often reflected in reality. If only the different atoms were color coded, though!)
True. Even having a decent grasp on the topic (or perhaps, because having a decent grasp), I find it difficult to try to peel apart bond energy, electron density, bond length, etc, from each other; They're all effectively functions of each other and the entire system.
It sounds like you might be more up on this stuff than I am. Since the probe measures force, I was picturing it sort of pushing on the bond and registering the resistance, i.e. the bond energy. But that was just an impression, and I'm certainly no authority on this.
You don't really need much math to see why this is happening. First, the bonds in a benzene ring aren't discrete like we draw them, alternating between single bonds and double bonds. It's also important to realize that although we typically represent benzene in 2D all molecules really have a 3D geometry.
Electron orbitals can overlap in different ways depending on the geometry of the atom and its electronics. See this for a picture: http://en.wikipedia.org/wiki/File:Benzene_Representations.sv...
So, the electrons in a benzene ring really form more of a cloud around the entire ring. You'd expect this to pull the atoms into a perfect circle with the carbon atoms all being equidistance from each other, all else being equal.
However, each carbon atom also has a hydrogen atom attached to it. So now you have a sort of a circle with 6 "strings" attached at points equidistant around the circle all pulling outward, perpendicular to the circle.
Imagine a perfectly circular piece of string with 6 strings attached equidistantly around the circle. You apply an equal force perpendicular to the surface of the circle.
Hopefully you can see how this would result in the original circular string being "deformed" into a hexagon.
It's a far leap from there to say why hexagons are "so common in nature." Are they? Relative to what? I don't know that any of this has anything to do with the shape of that storm you linked to.
> It's a far leap from there to say why hexagons are "so common in nature."
I was thinking of things (compared to other geometric shapes) like the storm, honey bee cells (honeycombs), basalt columns [1], turtle shells (although irregular), and a common snowflake shape.
There are three regular polygons you can use to tile a plane: triangles, squares, and hexagons. The regular hexagonal packing is the densest sphere packing in the plane, so any time you have objects constrained to a plane which for the sake of maximizing or minimizing some force want to be equidistant from each other you'll get something close to a hexagon.
I'll add that sometimes a shape like that might result from a more evolutionary process. In a 2D plane a circle is the structure which most equally distributes force, so it's the shape most able to hold up under pressure.
But a tile of circles isn't so fortunate. Of all the possible tilings, the hexagonal tiling holds up the best precisely because it's the densest sphere packing in the plane.
Other arrangements might appear, but over the course of time you're more likely to see hexagonal tilings since those are the ones that best survive external forces.
It has to do with the bond angles in water molecules. The bond angles are, in turn, determined by quantum mechanical wave functions. These quantum mechanical wave functions apply to all of chemistry, including benzene rings. So the shapes of snowflakes and the shapes of benzene rings are not totally independent events.
The short answer for why benzene rings are common is aromaticity, which makes it a very stable structure. Rings with fewer than 6 members are uncommon in chemistry, because the angles are not what the bonds naturally want to be and so they are increasingly unstable.
As for nature in general, you could probably come up with a convincing argument that boils down to: 6 is a nice round number. It has 2 and 3 as factors.
>Rings with fewer than 6 members are uncommon in chemistry
In chemistry, or in nature? five membered rings show up all over the place, both aromatic and otherwise. Granted, cyclobutyl (4 member, square) and cyclopropyl (3 membered, triangle) suffer from ring strain and are uncommon, but 5, 6, 7, (or higher) rings show up all over the place.
Examples off the top of my head are the cyclopentadienyl ion pervasive in inorganic chemistry (see ferrocene, et al) and amino acids tryptophan, tyrosine, histidine, and phynylalanine all feature cyclic aromatics 5 and 6 membered, as well as proline with a non-aromatic 5 member ring.
The takeaway point is that although ring-strain (having non ideal angles (120 or 109.5 degrees)) increases the internal energy of the molecule (destabilizing it), other factors, such as aromaticity, which decrease internal energy (stabilizing it) may balance or exceed the ring-strain, still giving a stabilized, if non-ideal geometry.
(But yeah, 3, 4 membered rings, ugh. Look up platonic alkanes for some really crazy strain angles.)
I don't know if there is a way for the person next to the person wearing a glass to tell whether the glass is on or off, but if there is no way then there has to be one which will take care of the security issues like recording a video, taking a picture etc while talking to a person and that person don't know about the same.
Many people involve themselves in weight training and cardio exercises because of which they miss out on ground exercises. I am sure this app will help them a lot.
