Scientists Finally Reveal The Electronic Structure of Benzene -- in 126 Dimensions (sciencealert.com) 36
"Well, those crazy chemistry cats have done it," writes Science Alert:
Nearly 200 years after the molecule was discovered by Michael Faraday, researchers have finally revealed the complex electronic structure of benzene. This not only settles a debate that has been raging since the 1930s, this step has important implications for the future development of opto-electronic materials, many of which are built on benzenes.
The atomic structure of benzene is pretty well understood. It's a ring consisting of six carbon atoms, and six hydrogen atoms, one attached to each of the carbon atoms. Where it gets extremely tricky is when we consider the molecule's 42 electrons. "The mathematical function that describes benzene's electrons is 126-dimensional," chemist Timothy Schmidt of the ARC Centre of Excellence in Exciton Science and UNSW Sydney in Australia told ScienceAlert. "That means it is a function of 126 coordinates, three for each of the 42 electrons. The electrons are not independent, so we cannot break this down into 42 independent three-dimensional functions.The answer computed by a machine is not easy to interpret by a human, and we had to invent a way to get at the answer...."
"The electrons with what's known as up-spin double-bonded, where those with down-spin single-bonded, and vice versa," Schmidt said in statement. "That isn't how chemists think about benzene." The effect of this is that the electrons avoid each other when it is advantageous to do so, reducing the energy of the molecule, and making it more stable.
The atomic structure of benzene is pretty well understood. It's a ring consisting of six carbon atoms, and six hydrogen atoms, one attached to each of the carbon atoms. Where it gets extremely tricky is when we consider the molecule's 42 electrons. "The mathematical function that describes benzene's electrons is 126-dimensional," chemist Timothy Schmidt of the ARC Centre of Excellence in Exciton Science and UNSW Sydney in Australia told ScienceAlert. "That means it is a function of 126 coordinates, three for each of the 42 electrons. The electrons are not independent, so we cannot break this down into 42 independent three-dimensional functions.The answer computed by a machine is not easy to interpret by a human, and we had to invent a way to get at the answer...."
"The electrons with what's known as up-spin double-bonded, where those with down-spin single-bonded, and vice versa," Schmidt said in statement. "That isn't how chemists think about benzene." The effect of this is that the electrons avoid each other when it is advantageous to do so, reducing the energy of the molecule, and making it more stable.
Finally (Score:2)
Re: (Score:2)
Live long and prosper, in carbon dioxide saturated Shitstanistan
Kailash, when it rises.
Re:Ironic Science Alert (Score:4, Informative)
(1) https://www.researchgate.net/p... [researchgate.net]
Re: (Score:3)
Re: (Score:2)
If you have 42 elementary components of a system, each of which has a three-dimensional state, you indeed get a 126-dimensional phase space. What's so weird about that?
In a mathematical-sense, there is nothing weird about it because an extra dimension just means another variable.
But in a Hollywood-sense, an extra dimension means a parallel universe with evil doppelgängers and quantum wormholes.
Re:Ironic Science Alert (Score:4, Informative)
You have to marvel at the click-bait gall of Michelle Starr (author of the referenced article on the Science Alert web site), who somehow decided that because there are 42 electrons in Benezene and because the work was able to map each electron in three dimensions, that 42 x 3 = 126 and so there must have been 126 dimensions involved, right?
The published research (which Science Alert even linked) is called The electronic structure of benzene from a tiling of the correlated 126-dimensional wavefunction [nature.com]
It's best to be correct when making accusations about someones "galling" behavior.
Re: (Score:2)
Rule of thumb: on the internet, the word "hilarious" in a post is a fairly reliable marker of a complete idiot.
Isn't this a 126 element array (Score:2)
with each element of the array depicting one of the three waveform axis of the 42 electrons in the molecule? I realize that it sounds a lot more impressive to the layperson saying that you created mathematics supporting 126 "dimensions" than saying you've created a program that uses an array with 126 elements.
I know that many people consider array "elements" to be synonymous with array "dimensions" but this seems to be deliberately turning what should be a straight forward (in concept, I'm sure extremely d
Re: (Score:2)
Re: (Score:2, Interesting)
Nothing is weird about that and you're reiterating what I'm saying.
My point is that the article turns what is a difficult, but achievable with today's technology, accomplishment into something that appears to be so esoteric/magical that the average person has no chance of understanding what was done or thinking about how they could be part of the process of doing research like this.
I'm concerned that articles like this are more likely to turn off younger people into STEM rather than say "Look what you could
Re:Isn't this a 126 element array (Score:4, Informative)
Where did TFA do that? The language used is correct and not at all unusual for describing something like this.
Describing it as a 126 element array is a vast over-simplification since that might imply that it could be solved by iterating over it with a for loop.
Re: (Score:2)
Re: (Score:2)
It depends on your audience. The author probably considered his audience to be quantum researchers, chemists studying electron interactions, and mathematicians. For such people a dimension is something that has an independent measurement.
If you want to, you could reasonably castigate the journalist who rewrote his (probably abstract rather than paper) for the public, but not the guy who wrote the paper.
Unfortunately "an array of 126 elements" doesn't mean quite what 126 dimensions means, since arrays as s
Re: (Score:2)
No, you misunderstand. They're not doing maths in 126 dimensions. They're doing maths that takes into account 126 interrelated data points.
Those data points could be in one, two or a dozen dimensions, but they're sure as fuck not in 126.
Re: (Score:2)
They're not doing maths in 126 dimensions. They're doing maths that takes into account 126 interrelated data points.
That's literally an "up-to-126-dimensional" problem. Only through careful analysis of the space you can find out if there is a structure to the problem that effectively reduces the dimensionality (i.e., that you have fewer degrees of freedom).
Those data points could be in one, two or a dozen dimensions, but they're sure as fuck not in 126.
You don't learn multivariate calculus or linear algebra with teachers saying "oh, the thing we're solving here is really a univariate problem because you have 13 1-D variables".
That means... (Score:2)
Even the smallest throw-away utility programs I've made have been like 200+ dimensional at the assembly level.
While it's true that each gravity well in the molecule influences the path of every other - are they ignoring the rest of the universe?
That would make... let's see, about 3.28 x 10^80 dimensions of gravity and other accumulated force interactions to describe the movement exactly.
Then there's quantum interactions, that might involve some influence across time, so you've got to multiply that out for t
Re: (Score:2)
Even the smallest throw-away utility programs I've made have been like 200+ dimensional at the assembly level.
Every program you've ever written fits conceptually into a 2 dimensional matrix, 32 bits wide, and an arbitrary number of words long. That's how RAM works.
What's it all mean? (Score:2)
Spoiler alert. (Score:1)
Re: (Score:2)
No. Coordinate is ... well, I was going to say a superset of the meaning, but it isn't quite that, but it doesn't mean quite the same thing. Close, but not the same.
If I were to say what I believe this to be saying it would be something like "To specify the state of Benzene you must specify 126 values with certain constraints on them." They aren't really independent values, but they also have a range of flexibility as to what values are allowed that depends on the values of their "neighbors".
Re: (Score:2)
You mean degree of freedom.
See also state-space.
Sounds familiar... (Score:3)
So this is why Earth was made? To compute the structure of benzene?! I was hoping for something with a deeper meaning...
Re: (Score:2)
Says the pre-hydrocarbon...
Doesn't that imply there are fewer than 126 dimens (Score:3)
If the electrons' positions are not independent (presumably meaning they depend on each other), doesn't that imply that a 126 coordinate vector describing their state can be resolved down into fewer than 126 eigenvectors? e.g. The minute hand on a clock can move in two dimensions, but the x and y position of its tip are not independent. They're intricately linked with each other, so in fact the range of motion of the minute hand resolves down to just a single dimension, its eigenvector. Which in the example of a clock hand would be degrees past vertical.
Re: (Score:2)
42 Electrons - 42 is the answer to everything! (Score:2)
If you've read the Hitchhiker's Guide to the Galaxy Series, you would recognize that 42 is the answer to everything. I think these researchers with their 42 electron model have discovered the unknown question. Someone should notify the Nobel Prize Foundation because we have a clear winner here.