The molecule benzene is seen everywhere in biology, is important in chemistry, and has even been detected in outer space. But the way the electrons of its constituent atoms are shared has been a mystery for over a century. Now we appear to have a solution, and it took scientists creating a mathematical function with 126 dimensions to get there.
苯分子在生物学中随处可见，在化学中也很重要，甚至在外层空间也被发现。但其组成原子的电子是如何共享的，一个多世纪以来一直是个谜。现在我们似乎有了一个解决方案，科学家们创造了一个126维的数学函数。
This doesn’t mean that the electrons of benzene exist in 126 dimensions, it means that if us humans want to understand how they interact as a whole we need to create mathematical functions that take each electron's behavior in our three-dimensional world into account. Benzene has 42 electrons, so 42 times three dimensions gives us 126.
这并不意味着苯的电子存在于126维空间中，这意味着如果我们人类想要理解它们作为一个整体是如何相互作用的，我们需要建立数学函数来考虑我们三维世界中每个电子的行为。苯有42个电子，所以42乘以三维空间等于126。
Alfredo Carpineti
Benzene is a very important molecule although it is moderately simple to picture. Six carbon atoms are positioned in a hexagonal ring, and attached to each of these carbons is a hydrogen atom. Carbon atoms are very friendly and they can bond with up to four other atoms, but in benzene carbon only has room to bond with three other atoms, so one of the bonds between carbon atoms is a double one (as shown in the image above).
苯是一种非常重要的分子，尽管它的结构比较简单。六个碳原子组成一个六边形的环，每个碳原子上都有一个氢原子。碳原子非常友好，它们最多可以与四个其他原子成键，但在苯中，碳原子只能与三个其他原子成键，所以碳原子之间的一个键是双键(如上图所示)。
The question that has been perplexing scientists is what happens to the electrons in this double bond. Electrons have the same charge (negative); they repel each other so it's not easy keeping them near each other. Another property that comes into play is the spin of each electron, which can have two values, “up” or “down”. Until now, analyzing a system this complex hasn't been possible, so the precise behavior of benzine electrons hasn't been known, which means the stability of the molecule in technology applications could not be wholly understood.
一直困扰着科学家的问题是双键中的电子会发生什么变化。电子具有相同的电荷(负电荷);它们互相排斥，所以让它们靠近并不容易。另一个起作用的性质是每个电子的自旋，它可以有两个值，“上”或“下”。到目前为止，分析这样一个复杂的系统还不可能，所以汽油电子的精确行为还不为人所知，这意味着分子在技术应用中的稳定性还不能被完全理解。
A. The electron positions of an arbitrary spin are shown as small yellow spheres. B. C–C bonding electrons are shown as blue lobes. C–H bonds are shown in grey. Liu et al. Nature Communications, 2020
Reporting in Nature Communications, the team found that the agreement or disagreement between the spin of the shared electrons gave rise to the three-dimensional configuration, which has lower energy. Think of them as subatomic introverts, they’ll avoid each other if it takes too much energy to be near another electron.
该研究小组在《自然通讯》杂志上发表报告称，他们发现共享电子自旋的一致性或不一致性导致了三维构型的产生，而三维构型的能量更低。把它们看做亚原子的内向者，它们会避开对方如果靠近另一个电子需要太多能量。
“What we found was very surprising,” senior author Professor Timothy Schmidt from the University of New South Wales, said in a statement. “That isn’t how chemists think about benzene. Essentially it reduces the energy of the molecule, making it more stable, by getting electrons, which repel each other, out of each other's way.”
“我们的发现非常令人惊讶，”新南威尔士大学的资深作者Timothy Schmidt教授在一份声明中说。这不是化学家对苯的看法。从本质上讲，它减少了分子的能量，使其更加稳定，因为它得到了互相排斥的电子。”
The solution was possible thanks to a sophisticated algorithm that created “tiles” for each change in electron configuration, allowing them to map the wavefunction of all 126 dimensions. The solution will help refine our theoretical understanding of not just benzene but also carbon rings, which are important in applications such as graphene, among others. The creator, co-author Phil Kilby, believes that this "matching with constraints" software can have applications beyond chemistry. It could be used for a range of systems, from staff rostering to kidney exchange programs.
这个解决方案是可行的，这要归功于一种复杂的算法，它为电子构型的每一次变化创建“块”，使它们能够映射所有126维的波函数。这一解决方案将有助于完善我们对苯以及碳环的理论理解，这些碳环在石墨烯等应用中非常重要。作者之一菲尔·基尔比(Phil Kilby)认为，这种“符合约束条件”的软件可以应用于化学以外的领域。它可以用于一系列的系统，从员工名册到肾脏交换项目。
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