化學(xué)家們在126維中解決了一個世紀(jì)之久的數(shù)學(xué)謎題

化學(xué)家們在126維中解決了一個世紀(jì)之久的數(shù)學(xué)謎題

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.

苯分子在生物學(xué)中隨處可見，在化學(xué)中也很重要，甚至在外層空間也被發(fā)現(xiàn)。但其組成原子的電子是如何共享的，一個多世紀(jì)以來一直是個謎?，F(xiàn)在我們似乎有了一個解決方案，科學(xué)家們創(chuàng)造了一個126維的數(shù)學(xué)函數(shù)。

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.

這并不意味著苯的電子存在于126維空間中，這意味著如果我們?nèi)祟愊胍斫馑鼈冏鳛橐粋€整體是如何相互作用的，我們需要建立數(shù)學(xué)函數(shù)來考慮我們?nèi)S世界中每個電子的行為。苯有42個電子，所以42乘以三維空間等于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).

苯是一種非常重要的分子，盡管它的結(jié)構(gòu)比較簡單。六個碳原子組成一個六邊形的環(huán)，每個碳原子上都有一個氫原子。碳原子非常友好，它們最多可以與四個其他原子成鍵，但在苯中，碳原子只能與三個其他原子成鍵，所以碳原子之間的一個鍵是雙鍵(如上圖所示)。

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.

一直困擾著科學(xué)家的問題是雙鍵中的電子會發(fā)生什么變化。電子具有相同的電荷(負(fù)電荷);它們互相排斥，所以讓它們靠近并不容易。另一個起作用的性質(zhì)是每個電子的自旋，它可以有兩個值，“上”或“下”。到目前為止，分析這樣一個復(fù)雜的系統(tǒng)還不可能，所以汽油電子的精確行為還不為人所知，這意味著分子在技術(shù)應(yīng)用中的穩(wěn)定性還不能被完全理解。

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.

該研究小組在《自然通訊》雜志上發(fā)表報告稱，他們發(fā)現(xiàn)共享電子自旋的一致性或不一致性導(dǎo)致了三維構(gòu)型的產(chǎn)生，而三維構(gòu)型的能量更低。把它們看做亞原子的內(nèi)向者，它們會避開對方如果靠近另一個電子需要太多能量。

“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.”

“我們的發(fā)現(xiàn)非常令人驚訝，”新南威爾士大學(xué)的資深作者Timothy Schmidt教授在一份聲明中說。這不是化學(xué)家對苯的看法。從本質(zhì)上講，它減少了分子的能量，使其更加穩(wěn)定，因為它得到了互相排斥的電子。”

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.

這個解決方案是可行的，這要?dú)w功于一種復(fù)雜的算法，它為電子構(gòu)型的每一次變化創(chuàng)建“塊”，使它們能夠映射所有126維的波函數(shù)。這一解決方案將有助于完善我們對苯以及碳環(huán)的理論理解，這些碳環(huán)在石墨烯等應(yīng)用中非常重要。作者之一菲爾·基爾比(Phil Kilby)認(rèn)為，這種“符合約束條件”的軟件可以應(yīng)用于化學(xué)以外的領(lǐng)域。它可以用于一系列的系統(tǒng)，從員工名冊到腎臟交換項目。