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Once you've got that, you can do minus 7 times a vector Just take the vector, multiply it by Pi and flip it over.
明白这点之后,你就可以计算-7乘以矢量,只需用 π 去乘以那个矢量,然后将其方向调转
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sigma That is one pi orbital. There is one sigma, one pi and there is a second pi, and that is how we are getting the triple bond.
那是一个pi轨道，有一个，一个pi，还有第二个pi轨道，这就是我们如何得到三线态的。
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So let's have a clicker question here on how many total pi bonds do you expect to see in benzene?
让我们来做个课堂习题,你们觉得苯环里有一共多少个π键？
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Sorry, said that wrong, p1 radius 1 and angle 2, 2 radians is a little bit more than pi half.
而是半径和角度的表示，在这个例子中点，并不对应这个点,它实际上对应的是。
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That's -Pi times a vector.
就等于用 -π 乘以那个矢量
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So even though we see a nodal plane down the center, I just want to really point out that it's only when we have a nodal plane in the internuclear or the bond axis that we're calling that a pi orbital.
虽然在中间有个节面，我想要指出的是,只有节面在核间轴,或者键轴上时,我们才叫它π轨道。
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The reason that I wanted to point out this nodal plane here is because this is why it is called a pi orbital.
我指出这个节面的原因是因为,它就是为什么这个叫做π轨道的原因。
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These are the ones that are coming right out at you, so this is going to be on a second pi orbital.
它们朝向你们，所以这里有另一个π键。
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So it's very important to be keeping in mind that any time you see a double bond, you have a pi bond there, so you're not going to see any rotation around the bond axis.
所以你们要记住,任何时候你们看到一个双键，这里面有π键，你们不会看到关于键轴的任何转动。
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So if we have a single bond here, would you consider that a sigma bond or a pi bond?
如果这里有个单键，你觉得这是sigma键还是π键？
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And so both of these lobes together constitute a pi bond.
上下两片叶一起组成了一根π键。
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And we can simplify this expression as saying negative e squared over 4 pi, epsilon nought r squared. Epsilon nought is a constant, it's something you might see in physics as well.
也会遇到它,在这里，你可以就把它,理解为一个转换系数,我们需要做的。
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So that's exactly what our definition of a pi bond is, so we have one sigma bond, and one pi bond.
这是我们对π键的定义，我们有一个sigma键，和一个π键。
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But once you have a double bond here, we have our pi bond, as well as our sigma bond.
但一旦你有了双键，我们有π键，也有sigma键。
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So pi bonds have electron density both above and below the bond axis, but they actually have a nodal plane at this z, this bond axis here.
键在键轴之上,和之下都有电子密度，但它们在z方向有节面，这是键轴的地方。
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So would you expect this to be a pi bond or a sigma bond her PROFESSOR: OK, so I'm hearing some mixed answers.
你们觉得这是一个π键还是sigma键？,我听到有不同的答案。
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So in the first case of this first bond here that I've put in a square, what type of a bond is this, is the sigma or pi?
在这第一个键里,我用方框把它标出来了，这个键是什么类型的，sigma还是π？
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So it already should make sense why we have that p orbital there, in order to form a pi bond, we're going to need a p orbital.
这里有p轨道是很合理的,为什么我们在这里有P轨道，为了形成一个π键，我们需要一个p轨道。
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Do you predict that this will be a sigma or a pi orbital?
你们认为这是sigma轨道还是π轨道？
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n So the velocity is given by this product of the quantum number n Planck constant 2 pi mass of the electron time the radius of the orbit, which itself is a function of n.
速度是量子数,普朗克常数2π乘以轨道半径的值,它自身也是n的函数。
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So in order to rotate a double bond, you have to actually break the pi bond, so essentially what you're doing is breaking the double bond.
为了能够旋转双键，你必须打破一个π键，本质上我们要做的就是打破双键。
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Pi orbitals are a molecular orbital that have a nodal plane through the bond axis.
轨道是沿着键轴,有节面的分子轨道。
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So our second bond is going to be a pi bond.
第二个键是π键。
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So, as they're very quietly handing out your class notes, let's think about what this bond is here, this boxed bond, is it a pi bond or a sigma bond?
在他们发讲义的同时，我们来看看这个键，方框里的这个键，它是sigma键还是π键？
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Would this be a sigma or a pi?
这是sigma还是π？
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In contrast, if we talk about a double bond, what we're now talking about is having both a sigma bond and also one pi bond. And I apologize, I intended to set this up right before class, but that didn't happen today.
相反，如果我们讨论一个双键，我们现在讨论的是,一个sigma键和π键，抱歉，我应该在课前就把这个装好的，今天没装好。
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Is that a sigma or a pi bond?
这是sigma键还是π键？
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And again, this is between the p orbitals, these are not hybrid orbitals, so when we name this bond we're going to name it as a pi bond here, because it's between two p orbitals, and it's going to be between the carbon 2 p y orbital, and the other carbon 2 p y orbital.
同样，这是在p轨道之间的，它们不是杂化轨道，所以当我们命名这个键时,我们要命名它为π键，因为它在两个p轨道之间，而且是在碳2py轨道，和另一个碳2py轨道之间。
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All right, so what we see here is we have our sigma bond that's along the internuclear axis here, but we also have a pi bond, because each of these atoms now has electrons in it's in a p orbital, so we're going to overlap of electron density above and below the bond.
这里我们看到sigma键,是沿着核间轴的，但我们还有一个π键，因为每个原子的p轨道上,都有电子，所以电子密度在键的上面,和下面都有电子密度交叠。
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