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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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There's absolutely no reason I couldn't have switched it around and said that instead the pi orbitals form between these atoms instead of those first atoms I showed.
我完全没有理由,不能把它转过来,现在π键在这些原子间,而不是我开始展示的那些原子间。
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q1*q2/ That's simply q1, q2 over 4 pi epsilon zero R.
那只是简单的。
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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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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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Now let's think about this first pi bond, which will be above and below the bonding axis.
让我们先来看这个π键，它在键轴的上面和下面。
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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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px So we're talking about pi carbon 2 p x, 2px because it's the x axes combining to carbon 2 p x.
我们讨论的是π碳，因为它在x轴结合成碳。
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So let's fill it out in this way, 2p keeping in mind that we're going to fill sigma out the pi 2 p's before the sigma.
让我们这样填上去，记住我们先填π,轨道再填。
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Remember, we didn't hybridize the 2 p y orbital, so that's what we have left over to form these pi bonds.
记住，我们并没有杂化2py轨道，这是我们剩下的那个行成了π键。
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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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So, we can do that by using this equation, which is for s orbitals is going to be equal to dr 4 pi r squared times the wave function squared, d r.
用这个方程,对于s轨道，径向概率分布,4πr的平方,乘以波函数的平方,这很容易理解。
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When we look at this angular part, we see that it's always the square root of 1 over 4 pi, it doesn't matter what the angle is, it's not dependent on the angle.
当我们看这角向部分，可以看到它总是等于１除以４pai开根号，这和是什么角度没有关系，它和角度无关。
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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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That's 4 pi epsilon zero 3 r naught and so on and so on.
也就是，4πε0，3R圈,以此类推。
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And we wrote something that looks, the energy is equal to minus the Madelung constant times Avogadro's number, 0R0 q1 q2 over 4 pi epsilon zero R zero.
我们写下了，晶格能等于负的马德隆常数,乘以阿伏伽德罗常数，乘以q1q2除以4πε
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So that's why these are pi orbitals instead of sigma orbitals.
这就是为什么它们是π轨道而不是sigma轨道。
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There's not two bonds, that's one pi bond, and the reason is because it's 2 p orbitals coming together, and remember p orbitals have electron density above and below the axis, so when they come together, it kind of looks like one bonds, but essentially what we have here is one pi bond.
这不是两个键，这是一个π键，因为这是两个2p轨道组合而成的，记住p轨道在键轴之上,和键轴之下都有电子密度，当它们靠近时，这看着很像两个键，但本质上它是一个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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So that's two of our types of bonds in benzene, and we have one type left, that's going to actually be the double bond or the pi bond that So we can have one bond here between this carbon's p orbital and this carbon's p orbital.
这就是苯环里的两种键，我们还剩一种，那就是这些p轨道之间，形成的双键或者π键,我们可以在这个碳的p轨道,和这个碳的p轨道之间有个键。
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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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