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Science

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.

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Scientists Finally Reveal The Electronic Structure of Benzene -- in 126 Dimensions

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  • We can allow the rage to dissipate! I mean, yeah, I'm sorry we had to kill Dr zabronik, but dammit, the electronc structer is nothing we can afford to be wrong ahout.
  • 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

    • And a 126 element array can represent a vector in a 126-dimensional space. What's so weird about that? A university freshman understands that. The point is not the array in any case but rather studying the properties of this space.
      • Re: (Score:2, Interesting)

        by mykepredko ( 40154 )

        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

        • by sjames ( 1099 ) on Sunday March 08, 2020 @02:24PM (#59808834) Homepage Journal

          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.

        • The average person still has no chance of understanding what was done no matter how you describe it. But at least this way it's somewhat relevant to what was being done, unlike your "they were doing something with 126-element arrays". That's like describing the work of an architect with "he was moving his pencil across the drafting paper for half an hour and the house was done".
    • by HiThere ( 15173 )

      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

  • 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

    • 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.

  • The electrons -- they are gamboling.
  • Here dimension equals coordinate. Click-Bait.
    • by HiThere ( 15173 )

      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".

    • by nyet ( 19118 )

      You mean degree of freedom.

      See also state-space.

  • by DontBeAMoran ( 4843879 ) on Sunday March 08, 2020 @11:06AM (#59808426)

    Where it gets extremely tricky is when we consider the molecule's 42 electrons. [...] 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..."

    So this is why Earth was made? To compute the structure of benzene?! I was hoping for something with a deeper meaning...

  • "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.

    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.

    • If I'm reading correctly (and I am not a mathematician), solving for that vector reduction is part of what this research does along the way to a final solution. If they were completely independent, it would trivially reduce to 42 separate 3d problems, as noted. It isn't completely independent, and it isn't completely dependent -- note where they talk about breaking things down into tiles. But it is a 126-dimension problem to begin with... and it wasn't obvious how to slice the problem. Quoting the paper, em
  • 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.

Some people manage by the book, even though they don't know who wrote the book or even what book.

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