05 Chemistry in a Nutshell.srt

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这是第一期浓缩课程的第五讲
this is now the fifth lecture of the
condensed matter course in the first

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在四个讲座中，我们研究了固体中的振动，并研究了固体中的电子
four lectures we studied vibrations in
solids and we studied electrons in

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金属，我们在这些主题上学到了很多东西，但我们也开发了
metals and we learned quite a bit about
these topics but we also developed a

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相当长的我们无法理解的谜题清单，我写了一个清单
rather long list of puzzles things that
we couldn't understand I wrote a list of

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在上一堂课的结尾，他们中有一些是礼堂的正弦
them at the end of last lecture some of
them included the sine of the hall

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系数，我们无法弄清为什么有时会有一个正弦
coefficient we couldn't figure out why
it's sometimes there's one sine

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有时候，这是另一个迹象，我们也抓住了他们不合理的长期
sometimes is another sign we also had
grabbed their unreasonably long mean

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索默菲尔德理论中的自由之路，我们无法理解，如果你回去
free path in Sommerfeld theory and we
couldn't understand and if you go back

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在早期的迪拜理论中，还有一些我们没有想到的难题
to earlier in dubai theory there are
also some puzzles there we didn't

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了解为什么我们引入了一个临时截断我，我的意思是一些
understand why it was we introduced an
ad-hoc cutoff me against I mean some

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动机，但这当然是临时处方，所有这些
motivation for it but it was certainly
an ad hoc prescription and all of these

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问题来自同一地点，同一地点是我们没有采取
problems stem from the same place and
the same place is that we're not taking

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认真对待我们并未真正考虑的材料的微观结构
seriously the microscopic structure of
materials we're not really considering

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它们是由单个原子组成的，这些原子在
that they're made up of individual atoms
and the atoms are bonded together in

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非常特殊且通常是周期性的方式，因此该术语的其余部分大部分是
very particular and often periodic ways
so much of the remainder of the term is

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将致力于了解微观结构材料
going to be devoted to understanding how
the microscopic structure materials

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影响其宏观特性，但在这样做之前可能值得
affects its macroscopic properties but
before doing that is probably worth

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备份并了解为什么原子在原子内粘在一起
backing up and understanding why it is
that the atoms stick together in the

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制作材料的第一位，这使我们进入了以下领域
first place to make the materials so
this brings us to the the domain of

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化学以及我们不愿承认它给我们的朋友和我们的
chemistry and as much as we hate to
admit it to both our friends and our

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敌人的化学反应实际上很有趣，这很重要
enemies chemistry actually is
interesting it's a it's an important

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无论是科学上的问题，还是工业上的技术问题
subject both scientifically and it's
certainly industrially technologically

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而且实际上它也具有一些基本的深度，您可以
and it's actually has some fundamental
deepness to it as well and you could

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当然要花三到四年学习化学甚至更长的时间
certainly spend three or four years
studying chemistry or even longer and

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我们将只研究一两天，这可能就是我们所要做的全部
we're gonna study it for only a day or
two and that will probably be all we

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需要知道以便继续进行下去，如果您之前有化学反应
need to know in order to go on further
now if you had chemistry before some of

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如果您没有化学反应，这些东西可能会有点熟悉
these things might be a little bit
familiar if you haven't had chemistry

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在这之前不是什么大问题，因为我要去的大部分
before it's maybe not so much of a
problem because most of what I'm going

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介绍它是相当基本的，但是主要思想是重新考虑一些
to introduce it's fairly basic but the
main idea is to reconsider some of the

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从物理学的角度看化学，似乎有些事情
chemistry from a physics perspective
some of the things that may have seemed

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奇怪的是，当您第一次学习化学时，也许他们
strange when you've learned for
chemistry the first time well maybe they

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这次似乎更自然一些，这将使我们有所
seemed a little bit more natural this
time through and this will give us sort

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了解大部分内容的基础
of a foundation for understanding much
of what

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来晚了，所以一个好的开始是认识到
comes comes later so a good place to
start is to realize that you know

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化学都是基于薛定inger方程的
chemistry is all based on the
Schrodinger equation the Schrodinger

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您知道的等式可以解决所有问题，并告诉您电子为何粘附
equation you know solves everything it
tells you why the electrons stick to

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原子核，以及为什么原子核互相粘连等等
nuclei and why nuclei
stick to each other and so forth it's

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所有简短的内部方程式，但这实际上并不是思考的一种非常有用的方法
all the short inner equation but that's
not actually a very useful way to think

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因为解决薛定because方程不只一个
about things because solving the
Schrodinger equation for more than one

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或两个粒子变得难以置信，并且您永远无法开发出任何一种
or two particles becomes impossibly hard
and you can never develop any sort of

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直觉发生了什么，所以我们应该做的是我们应该思考
intuition of what's going on
so what we should do is we should think

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关于非常简单的卡通级问题，并尝试找出
about very very simple cartoon level
problems and try to figure out what the

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一般规则是化学反应，从一个好的地方开始是氢
general rules are of chemistry from that
a good place to start is with hydrogen

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氢或更一般地说是氢原子，表示它的原子核为
hydrogen or more generally a hydrogenic
atom meaning that it has a nucleus of

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 G中的一些电荷产生Z和一个电子的原子核， 
charge in G some generating nucleus
nucleus of charge Z and one electron and

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您会从原子物理学课程或量子力学中记住
you'll remember from your atomic physics
courses or your quantum mechanics

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当然，这个电子的本征态被许多
courses that the eigenstates of this one
electron are indexed by a number of

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量子数主量子数n等于一二三，所以
quantum numbers the principal quantum
number n equals one two three and so

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第四角动量量子数
forth the angular momentum quantum
number which it takes the number the

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值0 1 2到n减1，这些角动量量子数为
values 0 1 2 up to n minus 1 and these
angular momentum quantum numbers are

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有时称为s PDFG等，现在来自光谱符号
sometimes called s P D F G and so forth
coming from spectroscopic notation now

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有人知道一个巧克力棒的PD和F代表尖锐的是s 
for one chocolate bar does anyone know
that s P D and F stand for sharp is s

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那让你四分之一d是分散的，是的，你快到了
that gets you a quarter d is diffuse yes
you almost there

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另外两个校长有人说校长有人得到了谁是
two more principal someone said
principal someone who got it who was

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有人在那边说，你还好，所以他明白了
that someone said it over there it's you
okay so he gets it so sharp principal

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从光谱符号上扩散和精细，对不起，您的巧克力
diffuse and fine from spectroscopic
notations your chocolate sorry

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从你下面偷了哎呀，还有人再来一块巧克力吧
stolen out from under you
gee does anyone one more chocolate bar

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甚至告诉我G是什么意思，实际上什么都不是，是因为
even tell me what G is for it's not for
anything actually it's it's uh it's for

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长颈鹿，除了那好吧，他们只需要再写一封信
giraffe they just need another letter
after that okay um anyway in addition to

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角心态量子数M取负L到L的值，然后
the angular mental quantum numbers M
takes the values minus L to L and then

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最重要的是，自旋量子数可以为正负二分之一
the spin quantum number can be plus or
minus one-half the most important thing

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要跟踪的是，如果您具有电子本征态，也许应该
to keep track of is if you have s
electrons s eigenstates maybe how should

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我这样说，所以我认为本征态可以容纳两个有两个
I say this so in s shell I guess of of
eigenstates can hold two has two

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可能的本征态P壳，所以为什么-因为s意味着L等于零，所以
possible eigenstates P shell so why is
it - because s means L equals zero that

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表示M必须等于零，但自旋可以是正负1/2，所以两个
means M has to be equal zero but the
spin can be plus or minus 1/2 so two

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豌豆壳的可能性有六个，因为P表示l等于一个M 
possibilities with a pea shell there are
six because P means l equals one M can

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为负1 0 1为3，则自旋可以取两个值使6d 
be minus 1 0 1 that's 3 and then the
spin can take two values that make 6d

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给你十个，依此类推现在你拥有所有这些本征态
gives you 10 and so forth now you have
all these eigenstates in a particular

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原子，然后您认为自己在其中拥有许多电子
atom and then you suppose to yourself
that you have many electrons in that

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原子不仅仅是一个电子，原子我也应该大概
atom not just a single electron the atom
also I should probably should probably

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给你的能量以及这些本征态的能量是- 
give you the energies as well the
energies of these eigenstates are - the

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如果原子核的电荷更多，则在N平方乘以Z平方摆脱berg 
rid berg over N squared times Z squared
if the charge of the nucleus is more

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大于1加上小改正之类的东西，例如Hyper和Hyper的罚款就好
than 1 plus small Corrections things
like fine and Hyper's fine fine

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结构，但主要能量只是来自于原理量子数，所以
structure but the main energy just comes
from the principle quantum number ok so

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现在你的原子中有一束电子，你需要弄清楚
now you have a bunch of electrons in
your atom and you need to figure out

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这些本征态中的哪些充满电子，而哪些空着
which of these eigenstates you fill with
electrons and which ones you leave empty

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有几个规则可以解决这个问题，第一个规则称为
and there's several rules for figuring
this out the first rule is known as the

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阿尔贝勒原理奥夫鲍原理
alpha Belle principle Aufbau principle

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基本上只是被贝壳填充
which is basically just fill by shells

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因此，当您向原子中添加第一个电子时，您会在一个壳中开始并保持
so when you add the first electron to an
atom you start in one shell and you keep

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填满该壳，直到填满该壳为止
filling that shell until it's filled
when you finish filling that shell you

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开始填充下一个外壳，然后填充该外壳，直到
start filling the next shell and you
fill that one until it's

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现在您以什么顺序装满炮弹，然后由马德隆的装满炮弹
now in what order do you fill the shells
well you fill the shelves by madelung's

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像这样的肺炎法则，玛德隆氏法则
rule madelung's rule which has a nice
pneumonic like this you write out a

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表1s 2s 2p 3s 3p 3d 4s 4p 4d 4f 5s等
table 1s 2s 2p 3s 3p 3d 4s 4p 4d 4f 5s
and so forth

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 5P博士thot，然后您以对角线的方式填写，这是第一个，这是
5p dr. thot and then you fill in this
diagonal way this one is first this is

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第二，这是第三，这是第四，依此类推，这将是第五
second this is third this is fourth and
so forth and this would be fifth down

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这样的方式，所以填充壳的顺序就是给您结构的方式
that way okay so this order of filling
shells is what gives you the structure

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我们来看看我们的朋友，元素周期表
of the periodic table let's take a look
at our friend the periodic table oops I

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看不到哦
don't see the Oh

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停止停止停止停止停止停止停止停止停止好吧坚持
stop stop stop stop stop stop stop stop
stop okay hold on

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现在没有男孩了，我们有一个真正的问题停下来哦
no boy now we have a real problem stop
Oh

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好吧好吧，所以元素周期表让我们继续看我们是否可以得到这个
okay well okay so the periodic table
let's go on and see if we can get this

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稍后开始，所以每个人都在您的笔记中
started up a little bit later so
everyone kind of note you have in your

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沿着正确的方向前进，因此您首先要填充
head what it looks like right so you
start out by filling the the top row of

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当一个电子充满时，其中含有氢氦的元素周期表充满
the periodic table which has hydrogen
helium in it as one electron fills fills

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氢，下一个充满氦气，然后用锂开始下一行
hydrogen the next one fills helium then
you start the next row with with lithium

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和铍填充第二个弹壳，然后有六个
and beryllium that fills up the second
shell then you have the next six

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元素硼碳氮氧氟和氖让我再试一次
elements boron carbon nitrogen oxygen
fluorine and neon let me try this again

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看看那是否能使硼氮碳Neah氟氖起作用，然后
see if that's gonna work boron nitrogen
carbon Neah fluorine neon and then

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您正在填充2p外壳，依此类推，等等，然后完全填充它们
you're filling the 2p shell and so forth
and so on and you fill them at all on

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所有这些顺序，并为您提供元素周期表的结构，但您
all this order and that gives you the
structure of the periodic table but you

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可能会想知道自己稍等一下
might wonder to yourself well wait a
second

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为什么在3d外壳之前填充4s外壳，因为
why is it that we're filling the 4s
shell before the 3d shell because

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根据上面的公式，三个壳应该有较低的能量
according to that formula up there the
three shell should have lower energy

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而不是四个弹壳，那么是什么赋予了我们在开始之前充满4s的权利
than the four shell and so what gives us
the right to fill up 4s before before we

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填满3d，为此我们为什么要填满周期表哦，感谢上帝
fill up 3d and for that matter why are
we filling a periodic table oh thank god

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所以有周期表，我们按照这个顺序填写第一个
so there's the periodic table and we
fill in this order there's a the first

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给第二个壳加壳2 2's 2p 3s 3p，然后在前面加满4s 
shell the second shell two 2's 2p 3s 3p
and there's 4s filling up before the

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在3d之前，您可能会问得很好，为什么我们要填充2s 
before the 3d you might ask the question
well why is it we're filling up 2s

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在2p之前，因为根据该公式，他们有或多或少的
before 2p because according to that
formula up there they have more or less

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同样的能量，所以这个问题的答案基本上是因为
the same energy so the the answer to
this question is basically because V of

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 R在R上不等于1，它与库仑相互作用不成比例
R is not equal to 1 over R it's not
proportional to the Coulomb interaction

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很好，为什么不那么好，它不只是一个电子和一个原子核，而是一个
anymore well why not well it's not just
a single electron and a nucleus it's an

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电子与原子中所有其他电子相互作用以及
electron interacting with all of the
other electrons in the atom as well as

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原子核，这样电子越靠近原子核，它所看到的越多
the nucleus so as the electron gets
closer to the nucleus it sees more

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原子核和更少的其他电子，它到达的距离越远
nucleus and less of the other electrons
and it gets as far as it gets farther

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离开它会看到更多您可以想到的其他电子，因此拥有某种
away it sees more of the other electrons
you can think of so having some sort of

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有效电位是电子与电子之间的相互作用
effective potential which is the
interaction between the electron and

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其他电子的原子核和云都需要修改
both the nucleus and the cloud of the
other electrons so you need to modify

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这个电位的形状有些许，如果您尝试解决这个问题或径向
the shape of this potential somewhat and
if you try to solve this or the radial

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您解决的量子力学问题知道氢原子，但是您
quantum mechanics problem that you solve
you know for the hydrogen atom but you

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00:10:34,709 --> 00:10:39,029
改变这种潜力的形状，您会突然发现
change the shape of this potential
you'll all of a sudden discover that all

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这些弹壳现在具有不同的能量，它们会四处移动，这就是为什么这些
these shells have different energies now
they shift around and that's why these

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这些填充轨道的顺序不是您所期望的
the ordering of these filling of the
orbitals is not what you would expect

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从一个简单的氢原子实际上是我们在
from just a simple hydrogen atom
actually was we're on the subject of the

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与其他电子的相互作用，您可能会感到惊讶，我们可以
interaction with the other electrons you
might find it surprising that we can

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甚至描述了一般电子氢的本征态
even describe the eigenstates of the
hydrogen of a general electron the same

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我们可以像描述原子本征态的方式一样
way we can a general atom the same way
we can describe the eigenstates of a

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氢原子，因为您知道它不仅与原子核相互作用，而且
hydrogen atom because you know it's not
just interacting with the nucleus it's

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也与所有其他电子相互作用，但原因或多或少
interacting with all the other electrons
as well but the reason more or less you

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可以这样做是因为您可以治疗自己以外的所有其他电子
can do this is because you can treat all
of the other electrons besides yourself

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它只是球形的云，所以还是球形的
it's just some sort of spherical cloud
so it's still sort of a spherical

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问题，所以它遵循或多或少相同的规则，您仍然可以枚举
problem so it follows more or less the
same rules and you can still enumerate

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可能的本征态也一样，所以这是一般结构
the possible eigenstates in the same way
okay so this is a the general structure

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元素周期表的内容，现在我们可以继续探讨化学键
of the periodic table and we can now
move on to asking about chemical bonds

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在元素周期表中的原子之间，好了，玛德琳的法则充满了
between the atoms in the periodic table
okay there's filling up Madeleine's rule

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所以有很多不同类型的绑定，有一个图表看起来像
so there's a bunch of different types of
bonding there's a chart that looks like

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这本书中的告诉您五种不同类型的
this in the in the in the book which
tells you five different types of

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00:11:49,170 --> 00:11:53,670
键合离子共价金属分子氢及其一些
bonding ionic covalent metallic
molecular hydrogen and some of their

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属性及其原因是值得熟悉的
properties and what causes them it's
probably worth familiarizing yourself

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借助其网上图表，您今天知道我们将尝试涵盖我们的
with its chart over the net you know
today we're going to try to cover our

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离子ik和共价其他类型，我们稍后将在
ion ik and covalent the other types
we'll do a little bit later on in the in

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讲座系列，所以您知道基本的基本事实在您身上
the lecture series so the the you know
the basic basic facts are on this you

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应该知道这些，但是今天我们将从最简单的类型开始
should probably know these but we will
just start today with the simplest type

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00:12:15,240 --> 00:12:19,339
离子键的键合
of bonding which is ionic bonding

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00:12:21,500 --> 00:12:25,880
离子键的原理基本上是电子是
and the principle of an ionic bond is
basically that an electron is

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从一个原子从一个原子转移到另一个原子，然后
transferred from one atom from one atom
atom to another to another and then the

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离子吸引，然后离子吸引，所以这种反应是一种
ions attract then ions attract so the
kind of the kind of a sort of reaction

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我们可以拥有的是一个钠原子加一个氯原子，一个电子是
that we we can have is a sodium atom
plus a chlorine atom an electron is

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从钠转移到氯，所以我们得到钠加
transferred from the sodium to the
chlorine so we get sodium plus plus

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氯减去，然后我有两个带电物种，它们吸引每个
chlorine minus and then now I have two
charged species and they attract each

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其他形式的氯化钠听起来很容易，可能是最简单的方法
other in the form sodium chloride sounds
easy enough probably the easiest way to

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跟踪这种反应或评估这种分析
keep track of this kind of reaction or
to evaluate this kind of analyze this

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反应的类型是考虑与每个步骤相关的能量，因此
type of reaction is to think about the
energies associated with each step so

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00:13:26,420 --> 00:13:32,780
一种能量是电离能
one piece of the energy is the
ionization energy the ionization which

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00:13:32,780 --> 00:13:43,850
是将电子从钠原子上拉出来以产生钠离子的能量， 
is the energy to pull the electron off
the sodium atom to make a sodium ion and

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一个电子，所以您从钠原子中性开始，将电子拉开
an electron so you start with the sodium
atom neutral you pull the electron apart

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00:13:48,140 --> 00:13:52,100
从中取出无穷大，钠离子无限远
from it and put it out infinity and the
sodium ion infinitely far away at

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00:13:52,100 --> 00:13:56,330
无穷大，这将是能量上的差异，拉动
infinity and this will be the difference
in energies what's required to pull the

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离开原子的电子还有所谓的电子亲和力
electron off the atom there's also
what's known as the electron affinity

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00:14:03,610 --> 00:14:11,360
当您将电子放到
which is the energy that you get back
when you put the electron on the

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00:14:11,360 --> 00:14:17,060
氯原子生成氯离子，然后最后一块被称为
chlorine atom to make a chlorine ion and
then the last piece is known as the

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00:14:17,060 --> 00:14:21,700
内聚能或键能
cohesive energy or the bonding energy

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00:14:22,900 --> 00:14:31,280
当您将钠离子和
which is the energy you get out when you
put together the sodium ion and the

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00:14:31,280 --> 00:14:38,720
氯离子得到氯化钠还可以吗
chlorine ion
to get sodium chloride okay so the total

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00:14:38,720 --> 00:14:47,420
该反应的能量预算是离子，您返回的电离能
energy budget for this reaction is e ion
the ionization energy you get back the

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00:14:47,420 --> 00:14:52,689
亲和能与电子的亲和力，则返回内聚能， 
affinity energy the electron affinity
and you get back the cohesive energy and

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00:14:52,689 --> 00:14:59,990
如果总Delta e小于零，如果Delta e小于零，则您
if the total Delta e is less than zero
if Delta e is less than zero then you

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00:14:59,990 --> 00:15:05,540
得到一个反应，然后它就会反应
get a reaction then it reacts the
reaction goes towards now there's a

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关于这种说法的一些警告，第一个警告是，如果
couple of caveats about about this kind
of argument the first caveat is that if

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00:15:10,009 --> 00:15:14,449
你是化学家，你不可避免地在谈论吉布斯自由能，而不是
you're chemists you are inevitably
talking about Gibbs free energies rather

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00:15:14,449 --> 00:15:17,839
不仅仅是能量，而吉布斯自由能量的原因是因为你
than just energies and the reason it's
Gibbs free energies is because you're

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00:15:17,839 --> 00:15:21,680
在有限的温度（可能是室温）下进行实验
doing your experiment at finite
temperature probably room temperature

175
00:15:21,680 --> 00:15:26,269
和有限的压力，您的房间压力，我们会认为，就像我们在做
and finite pressure your room pressure
we're gonna think just as if we're doing

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一切都在零温度，零压力下进行，所以我们可以考虑一下
everything at zero temperature zero
pressure so we can just think about

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能量，但第二件事应该或多或少是同一件事
energies but it's more or less the same
thing the second thing one should be

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警告您是否正在读书是凝聚力或粘合一词
warned about if you're reading books is
that the word cohesive energy or bonding

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00:15:39,380 --> 00:15:42,529
每个人在不同的书中以不同的方式使用能量
energy is used in several different
senses in different books everyone

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00:15:42,529 --> 00:15:47,000
同意凝聚力或键合能量是放两件东西的能量。 
agrees that a cohesive energy or bonding
energy is the energy to put two things

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00:15:47,000 --> 00:15:50,899
在一起，但并非所有人都同意这两个东西应该是什么，所以他们会
together but not everyone agrees what
those two things should be so they'll

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00:15:50,899 --> 00:15:54,319
谈论氯化钠的内聚能，一些书会告诉你
talk about the cohesive energy for
sodium chloride and some books will tell

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00:15:54,319 --> 00:15:58,939
您，整个Delta e是凝聚力，有些书会告诉您
you that the whole Delta e is the
cohesive energy and some books will tell

184
00:15:58,939 --> 00:16:02,899
您，凝聚力只是将钠放在一起的能量
you that the cohesive energy is just the
energy for putting together the sodium

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00:16:02,899 --> 00:16:06,649
离子和氯离子，因此您会得到两个不同的结果
ion and the chlorine ion so you'll get
two different results depending on it

186
00:16:06,649 --> 00:16:09,139
是否要计算整个Delta e并称其为绑定
whether you're accounting the whole
Delta e and calling that the bonding

187
00:16:09,139 --> 00:16:12,709
能量，或者您只是在谈论将两个离子放在一起的能量
energy or if you're just talking about
the energy to put together the two ions

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00:16:12,709 --> 00:16:17,689
这是另一个警告，最后一个警告是您得到的结果
so that's another warning the last
warning is that the results that you get

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00:16:17,689 --> 00:16:22,550
结合能量的方法会截然不同，具体取决于您在说什么
for bonding energy will be extremely
different depending if you're talking

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00:16:22,550 --> 00:16:27,949
关于摄取一钠离子和一氯离子
about taking one ion of sodium and one
ion than chlorine and putting them

191
00:16:27,949 --> 00:16:31,189
一起制成氯化钠分子，或者如果您正在谈论
together to make a sodium chloride
molecule or if you're talking about

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00:16:31,189 --> 00:16:35,209
拿很多，把它们放在一起， 
taking lots of them and putting them
together to make a whole big chunk of

193
00:16:35,209 --> 00:16:39,230
氯化钠，其原因是因为您知道您的钠原子
sodium chloride and the reason for this
is because you know your sodium atom if

194
00:16:39,230 --> 00:16:42,680
它要么与一种氯结合，要么与许多不同的氯结合
it's either bonded to one chlorine or
it's bonded to a lot of different

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00:16:42,680 --> 00:16:45,740
氯将是完全不同的能量，具体取决于多少东西
chlorines it will be a totally different
energy depending on how many things

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00:16:45,740 --> 00:16:49,570
您与之紧密相连，这是另一件事
you're bonded to
so that's another thing to keep in mind

197
00:16:49,570 --> 00:16:55,910
要小心，所以在这组试图追踪的能量中
to be careful about okay so in this set
of energies that were try to keep track

198
00:16:55,910 --> 00:16:59,840
可能最容易理解的是
of probably the easiest thing to
understand is the bonding energy of the

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00:16:59,840 --> 00:17:08,800
内聚能，也称为马德隆能或库仑能
cohesive energy also known as the
madelung energy or the Coulomb energy

200
00:17:08,800 --> 00:17:16,430
因为这种库仑能量基本上就是库仑
because this Coulomb energy is basically
just it's basically just the Coulomb

201
00:17:16,430 --> 00:17:21,709
系统中相关离子之间的两个能量之间的关系
energy between the two between the
relevant ions in your in your system so

202
00:17:21,709 --> 00:17:33,140
在I和J之间的4个PI epsilon零距离上，我不等于j Qi QJ 
i not equal to j Qi QJ over 4 PI epsilon
nought distance between the I and J so

203
00:17:33,140 --> 00:17:41,300
 Qi是离子上的电荷，这就是离子J，所以如果我有一个
Qi is the charge on ion
this is charged ion J so if I have a

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00:17:41,300 --> 00:17:49,070
一堆-如果我-如果我有两个，我在JI上就照常服用库仑
bunch - if I - I on J I just take its
usual the usual Coulomb if I have two

205
00:17:49,070 --> 00:17:52,550
离子带正电荷的女人带负电荷的我只是总结
ions one with positive charge woman
negative charge I'm just summing up the

206
00:17:52,550 --> 00:17:57,260
这些离子之间通常的库仑能获得内聚能，这是
usual Coulomb energy between those ions
to get the cohesive energy now this is a

207
00:17:57,260 --> 00:18:02,900
表达键合能量或获得的能量的绝佳方法
perfectly good way to express the the
bonding energy or the energy you get by

208
00:18:02,900 --> 00:18:06,530
把这两种电荷带到一起，但是很明显
taking these two charge species and
bringing them together but it obviously

209
00:18:06,530 --> 00:18:10,730
实际上，对于大多数离子固体它也相当准确
and actually it's fairly accurate as
well for most ionic solids gives you a

210
00:18:10,730 --> 00:18:14,690
很好地估计了由此获得的内聚能的数量
very good estimate of the the amount of
cohesive energy you get by this

211
00:18:14,690 --> 00:18:19,250
定义，所以您只需要知道这些离子之间的距离
definition and so all you need to know
is how far apart those ions are and you

212
00:18:19,250 --> 00:18:23,390
知道你有多少键合能量当然会有一点问题
know how much bonding energy you got of
course there's a little bit of a problem

213
00:18:23,390 --> 00:18:27,440
这个表达式，如果带上
with this expression and that is it goes
to minus infinity if you bring the

214
00:18:27,440 --> 00:18:30,950
钠或离子，然后氯离子非常接近，这显然是
sodium or ion then the chlorine ion
extremely close and that's obviously

215
00:18:30,950 --> 00:18:39,260
没有任何意义，所以这里发生的实际情况是R IJ 
doesn't make any sense so what's really
happening here like this this is a R IJ

216
00:18:39,260 --> 00:18:44,840
在两个原子之间，这是能量，所以这是R上的1曲线
for between the two atoms and here's the
energy so this is the 1 over R curve

217
00:18:44,840 --> 00:18:50,450
您期望的库仑相互作用和获得的实际物理能量
that you expect for Coulomb interaction
and the actual physical energy you get

218
00:18:50,450 --> 00:18:54,500
看起来像是R上方的1看起来像是R上方的1，然后在某个时候它突然射出
looks like 1 over R looks like 1 over R
and then at some point it shoots off way

219
00:18:54,500 --> 00:19:00,740
直到无穷大，所以这是实际的，所以如果您知道2之间的距离
up to infinity so this is actual so if
you know the distance between the the 2

220
00:19:00,740 --> 00:19:05,450
亚当斯（Adams）就是您的兽医，只需将这种能量即库仑
Adams's you have a vet just by taking
this energy here which is the Coulomb

221
00:19:05,450 --> 00:19:10,490
预测它非常接近那里的实际结合能，因为
prediction it's extremely close to the
actual bonding energy there because you

222
00:19:10,490 --> 00:19:14,179
因为射击非常快，所以是什么原因导致
because the shoot-off is extremely rapid
so what's causing this shoot off to

223
00:19:14,179 --> 00:19:18,740
当你开始推动两个原子时，无穷远真的非常接近
infinity well when you start pushing two
atoms really close really close together

224
00:19:18,740 --> 00:19:22,070
你意识到他们不只是点收费了，他们将要开始
you realize they're not just point
charges anymore they're gonna start to

225
00:19:22,070 --> 00:19:25,429
重叠它们的轨道将开始重叠宝利排除原理是
overlap their orbitals are gonna start
to overlap Pauli exclusion principle is

226
00:19:25,429 --> 00:19:28,700
将要进入游戏，因为您也尝试放置两个
going to get into the game because
you're trying to put two too you know

227
00:19:28,700 --> 00:19:32,690
一处电子太多，能量就非常非常猛烈地射出
too many electrons in one place and the
energy just shoots right off very very

228
00:19:32,690 --> 00:19:37,790
速度非常快，但就目前而言，至少库仑估算值仍然是
very rapidly but right here by the
minimum the Coulomb estimate is still a

229
00:19:37,790 --> 00:19:41,990
很好地估计了内聚能，因此几乎所有东西
pretty good estimate of the cohesive
energy so that's pretty much everything

230
00:19:41,990 --> 00:19:46,670
我们现在需要了解内聚能，电离又如何
we need to know about the cohesive
energy now what about the ionization

231
00:19:46,670 --> 00:19:50,330
能量和电子亲和势能很好地电离能或电子
energy and electron affinity energies
well the ionization energy or electron

232
00:19:50,330 --> 00:19:53,630
亲和能与原子中的能级有关
affinity energy have to do with the
energy levels in the atoms and in order

233
00:19:53,630 --> 00:19:56,600
弄清楚我们真的​​需要解决那些的薛定inger方程
to figure that out we really need to
solve the Schrodinger equation of those

234
00:19:56,600 --> 00:20:00,020
原子，你知道一个电子和一些有效的电势与
atoms and you know an electron and some
effective potential which has to do with

235
00:20:00,020 --> 00:20:03,290
原子核以及所有其他电子，这是一个难题
the nucleus and also all of the other
electrons it's kind of a hard problem

236
00:20:03,290 --> 00:20:07,790
但即使我们不打算实际求解较短的方程
but even though we're not going to
actually solve the shorter equation

237
00:20:07,790 --> 00:20:12,350
有些趋势很容易跟踪，所以您知道
there's some trends which are pretty
easy to keep track of so this you know

238
00:20:12,350 --> 00:20:16,790
如果您已经完成了化学反应，您可能已经知道了，但是这个图
if you've done chemistry you probably
know this already but the this plot this

239
00:20:16,790 --> 00:20:20,210
元素周期表的图片向您展示了大的电子亲和力和
picture of the periodic table shows you
where the large electron affinities and

240
00:20:20,210 --> 00:20:24,500
大电离能还是小电离能
the large ionization energies or small
ionization energies are it's also down

241
00:20:24,500 --> 00:20:28,640
在这里，小电离能在这个角落被降低了，所以
here so the small ionization energies
are sort of down in this corner and so

242
00:20:28,640 --> 00:20:31,970
污点的大小是最小的电离能是多少
the size of the splotch is how big the
ionization energy the smallest one being

243
00:20:31,970 --> 00:20:37,160
你知道铯或在这里，大的电离能在上升
you know cesium or francium down here
and the large ionization energies way up

244
00:20:37,160 --> 00:20:40,940
在氦气中的稀有气体中，电子亲和力却相反
here in the noble gases in helium
electron affinities go the other way

245
00:20:40,940 --> 00:20:43,940
除了基本没有电子的稀有气体
with the exception of the noble gases
which have essentially no electron

246
00:20:43,940 --> 00:20:48,020
亲和力最高的电子亲和力在此角上方
affinity the highest electron affinities
are way over here in this corner up by

247
00:20:48,020 --> 00:20:53,420
氟，氯和溴在右侧，因此如果您想要
fluorine and chlorine and bromine over
on the right-hand side so if you want a

248
00:20:53,420 --> 00:20:57,830
好的离子固体，您需要什么，您知道离子反应是您需要
good ionic solid what you need you know
an ionic reaction is you need to be able

249
00:20:57,830 --> 00:21:01,880
轻松地将电子从一个物种中拉出，然后您想得到一个
to easily pull the electron off of one
species and then you want to get out a

250
00:21:01,880 --> 00:21:05,780
大量的能量用于其他方面，因此您需要小的电离
lot of energy for putting it on the
other so you want a small ionization

251
00:21:05,780 --> 00:21:11,900
能量和大的电子亲和力很好很好
energy and a large electron affinity so
good so good

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00:21:11,900 --> 00:21:16,940
离子性固体就像是您知道氯是氟化钠things 
ionic solids are things like you know
chlorine is sodium fluoride rubidium

253
00:21:16,940 --> 00:21:21,500
从这里经过的氯化物与从那里经过的物质捆绑在一起
chloride things from way over here bound
together with things from way over there

254
00:21:21,500 --> 00:21:28,789
现在化学家对此表示，电子壳是原子的
now chemists have an expression for this
that a shell of electrons an atomic

255
00:21:28,789 --> 00:21:34,460
壳要被填充，所以如果您有一个被填充的壳加上一个电子，例如
shell wants to be filled so if you have
a shell filled plus one electron like

256
00:21:34,460 --> 00:21:38,240
您将在第一列中在3秒内钠具有一个电子
you would have in this first column
sodium has a one electron in the 3s

257
00:21:38,240 --> 00:21:43,820
壳钾在4s壳中有一个电子，壳很容易被拉出
shell potassium has one electron in the
4s shell that shell is easily pulled off

258
00:21:43,820 --> 00:21:46,700
因为当外壳完全填满时，它是最快乐的
because the shell is most happy when
it's exactly filled

259
00:21:46,700 --> 00:21:51,169
类似地，氟是一种填充物，因此它具有高电子
similarly fluorine it's one short of
being filled so it has a high electron

260
00:21:51,169 --> 00:21:57,350
它想被填补的亲和力，所以我们能了解一点他们主要是
affinity it wants to be filled so can we
understand a little bit they're mostly

261
00:21:57,350 --> 00:21:59,990
右边的填充壳，它们具有很高的电子亲和力， 
filled shells on the on the right and
they have high electron affinity and

262
00:21:59,990 --> 00:22:05,539
高电离能，左侧则是小电离能
high ionization energy and on the Left
it's small ionization energy in small

263
00:22:05,539 --> 00:22:09,919
电子亲和力，所以我们可以通过某种物理方式理解为什么
electron affinities so can we understand
in some physical way why this is

264
00:22:09,919 --> 00:22:15,860
实际上，弄清楚为什么这至少可以使我们粗略了解并不是很困难
actually it's not too hard to figure out
why that is at least roughly we can make

265
00:22:15,860 --> 00:22:20,179
它的卡通图片，让我们尝试通过观察钠来弄清楚
a cartoon picture of it so let's try to
figure it out from looking at sodium so

266
00:22:20,179 --> 00:22:25,090
钠它有，如果你在这张桌子上看，它有11个元素周期表
sodium it has I'll let it's if you look
on this table a periodic table it has 11

267
00:22:25,090 --> 00:22:29,630
电子是它的第11个元素，所以看起来像是具有原子核的是什么
electrons its 11th element so what is
what does it look like it has a nucleus

268
00:22:29,630 --> 00:22:38,899
的电荷加上11加11的原子核，然后我们得到
of charged plus 11 plus 11 in the
nucleus and then then we have what we

269
00:22:38,899 --> 00:22:44,779
在1和2的壳中有10个电子，因此我们将绘制1s和
have 10 electrons in the 1 and 2's
shells so we'll draw a picture of 1s and

270
00:22:44,779 --> 00:22:52,130
 2s对不起和2p，在1s 2s 2p壳中，我们让10个电子与
2s sorry and 2p and in the 1s 2s 2p
shells we have a let 10 electrons with a

271
00:22:52,130 --> 00:22:57,230
负负10的电荷，那么我们的3s外壳中有1个电子
charge of minus minus 10 then we have
this 1 electron in the 3s shell out here

272
00:22:57,230 --> 00:23:02,779
所以这是3s外壳中的1个电子，如果您是1个电子
so this is 1 electron out here in the 3s
shell and to that 1 electron if you

273
00:23:02,779 --> 00:23:06,769
想象自己是一个电子，你实际上有多少核电荷
imagine yourself being that one electron
how much nuclear charge do you actually

274
00:23:06,769 --> 00:23:15,100
很好地看到总核电荷，您将看到这个电子看到Z等于1 
see well the total nuclear charge you
would see this electron sees Z equals 1

275
00:23:15,100 --> 00:23:20,450
为什么好，因为其中的这10个电子或多或少地被屏蔽了
why well because these 10 electrons
inside of it are more or less screening

276
00:23:20,450 --> 00:23:27,380
那是原子核中的正电荷，所以它看到的电荷只有加1，所以如果我们
that's positive charge in the nucleus so
it sees a charge of only plus 1 so if we

277
00:23:27,380 --> 00:23:30,950
想用我们的氢天鹰座来找出
wanted to
use our hydrogen aquila to figure out

278
00:23:30,950 --> 00:23:36,080
束缚能，我们可以说束缚能是burg乘以1 
the binding energy we would say that the
binding energy is a rid burg times one

279
00:23:36,080 --> 00:23:40,880
在C上平方，这是一个3 s除以三个平方N平方
squared over the C this is a three s
divided by three squared N squared

280
00:23:40,880 --> 00:23:47,870
现在楼下的这种结合能电离能有点
downstairs now this binding energy
ionization energy is a little bit of an

281
00:23:47,870 --> 00:23:52,430
低估了3s电子的实际结合结合能
underestimate of the actual binding
binding energy of the 3s electron and

282
00:23:52,430 --> 00:23:56,090
其原因是因为有时3s电子越来越靠近
the reason for this is because sometimes
that 3s electron gets closer to the

283
00:23:56,090 --> 00:24:00,380
并意识到实际上这不是+1的电荷，而是一个加号
nucleus and realizes that in fact it's
not a charge of +1 it's actually a plus

284
00:24:00,380 --> 00:24:04,280
电荷大于+1，因此约束范围比此估算值还要小
charge bigger than +1 so it's bound a
little bit tighter than this estimate

285
00:24:04,280 --> 00:24:08,510
会告诉我们好的，但是基本上您知道某种程度的近似
would would tell us okay but basically
you know at some level of approximation

286
00:24:08,510 --> 00:24:13,880
就像1个电子束缚在一个电荷上确实有意义
it's like 1 electron bound to just one
charge does that make sense yeah okay

287
00:24:13,880 --> 00:24:18,280
现在让我们看一下氟，而不是地板。 
now let's look at fluorine instead
floorings a little more complicated

288
00:24:18,280 --> 00:24:25,040
氟，这是第九个元素，几乎被填充以显示出什么
fluorine it's the ninth element right
over here almost filled to show so what

289
00:24:25,040 --> 00:24:28,880
是什么是氟很好吗，所以我们的核带有电荷
is the what is fluorine see well okay so
we have the nucleus with a charge of

290
00:24:28,880 --> 00:24:33,650
加9，然后我们将1s壳放在此处1s凝胶中，该凝胶可能会充电
plus nine and then we have the 1s shell
down here 1s gel which has might charge

291
00:24:33,650 --> 00:24:40,490
减去两个，然后在两个壳中，我们有七个电子在这里
of minus two and then in the two shell
we have seven electrons out here take it

292
00:24:40,490 --> 00:24:45,230
到一二三四五五六七七电子现在假设你是
to one two three four five six seven
seven electrons now suppose you're and

293
00:24:45,230 --> 00:24:50,540
它们或多或少处于相同的半径，因为它们都在两个壳中，因此
they're more or less at the same radius
because they're all in the two shell so

294
00:24:50,540 --> 00:24:56,840
假设您是电子，您看到的是Z的电荷等于
suppose you're this electron what do you
see you see a charge of Z equals well

295
00:24:56,840 --> 00:25:01,490
也许您会看到加上七个，因为这里的这些电子没有屏蔽
maybe you see plus seven because these
electrons here aren't screening the

296
00:25:01,490 --> 00:25:06,380
核，所以您只看到加9减两个现在加7有点
nucleus so you only see plus 9 minus two
now plus seven is a little bit of an

297
00:25:06,380 --> 00:25:11,870
高估您，您将获得摆脱困境的能量7 
over estimate you would you would then
get a binding energy of a rid burg seven

298
00:25:11,870 --> 00:25:16,730
平方，让我们看，这是两个电子，所以超过两个
squared over let's see so this is a two
electron out here so it's over two

299
00:25:16,730 --> 00:25:21,140
平方这个电子的主量子数平方这是一个巨大的
squared the principle quantum number
squared of this electron this is a huge

300
00:25:21,140 --> 00:25:25,400
高估了氟中的实际结合能，因为有时
over estimate of the actual binding
energy in fluorine because sometimes

301
00:25:25,400 --> 00:25:30,380
这些电子确实会进入该电子内部并更好地屏蔽核
these electrons do get inside of this
electron and screen the nucleus better

302
00:25:30,380 --> 00:25:34,730
比我们在这里估计的要多，但是您仍然看到有一个很好的理由
than we would estimate here but still
you see that there's a very good reason

303
00:25:34,730 --> 00:25:39,710
为什么它是一个几乎装满的炮弹，看到一个大核弹，一个几乎空
why it is an almost filled shell sees a
big nuclear charge and an almost empty

304
00:25:39,710 --> 00:25:45,090
炮弹看到一个小的核弹，所以这是为什么
shell sees a small nuclear charge
so this is behind the origin of why it

305
00:25:45,090 --> 00:25:49,320
是我们有这个卡通短语，一个几乎充满的贝壳想要成为
is that we have this this cartoon phrase
that an almost filled shell wants to be

306
00:25:49,320 --> 00:25:53,280
填充，几乎要清空的填充壳想要清空，这会使
filled and an almost empty fill shell
wants to be emptied does that make some

307
00:25:53,280 --> 00:25:58,770
感觉是的是的是的，好吧，所以这基本上是一个问题
sense yes yes yeah okay all right so
it's basically an issue of how well

308
00:25:58,770 --> 00:26:03,120
屏幕上的核是这样，这给了我们很好的画面
screen the nucleus is so this gives us a
pretty good picture of what's going on

309
00:26:03,120 --> 00:26:08,790
在离子键内，电子数量多少有差异
within ionic bonds there a differences
in how much the electrons are how much

310
00:26:08,790 --> 00:26:13,440
原子想要有一个多余的电子或想要放弃另一个电子， 
the atoms want to have an extra electron
or want to give up another electron and

311
00:26:13,440 --> 00:26:17,400
所以如果你有一个原子如果你有一个原子如钾和一个原子如
so if you have an atom if you have an
atom like potassium and an atom like

312
00:26:17,400 --> 00:26:20,790
氟钾很乐意放弃其电子氟
fluorine the potassium is happy to give
up its electron the fluorine wants to

313
00:26:20,790 --> 00:26:25,050
得到一样的额外电子，你得到两个离子，然后离子被吸引，所以它是一个
get that alike extra electron you get
two ions the ions then attract so it's a

314
00:26:25,050 --> 00:26:30,000
离子键的理想情况，但是您在两个键之间也有键
great picture of ionic bonding however
you also have bonding between two

315
00:26:30,000 --> 00:26:33,720
在两个原子之间需要电子的电子
electrons that want between two atoms
that want the electrons just as much as

316
00:26:33,720 --> 00:26:38,430
彼此之间，例如，两个氧原子之间会相互键合
it each other for example Oh to two
oxygen atoms will bond with each other

317
00:26:38,430 --> 00:26:42,120
当然，他们想要电子彼此一样多，所以这是
and of course they want the electrons
just as much as each other so this is

318
00:26:42,120 --> 00:26:47,720
给我们带给他们所谓的共价键共价键的图片
give brings us to the picture of what
they call covalent bonding covalent

319
00:26:47,720 --> 00:27:00,390
没关系，有一个化学家有这张共价键的图片
bonds which is okay there's a chemists
have this picture of covalent bonds

320
00:27:00,390 --> 00:27:05,760
他们喜欢说原子将共享电子，并且
which they like to say that the atoms
will share an electron and because

321
00:27:05,760 --> 00:27:10,650
他们正在共享将原子结合在一起的电子，现在我们可以理解
they're sharing electrons that binds the
atoms together now can we understand a

322
00:27:10,650 --> 00:27:15,090
从物理学上好一点点，这就是共享的意义
little bit better from physics what it
is that we mean by this that sharing

323
00:27:15,090 --> 00:27:19,800
电子将原子结合在一起，因此有一个很好的画面
electrons binds atoms together so
there's a nice picture of this which

324
00:27:19,800 --> 00:27:23,700
基本上只来自盒子物理中的粒子，可以放在这里
basically comes from just particle in a
box physics all right put it over here

325
00:27:23,700 --> 00:27:34,020
盒子中的一个粒子，我们将分析氢，然后氢进入
particle in a box in box and we're gonna
analyze hydrogen plus hydrogen goes to

326
00:27:34,020 --> 00:27:40,410
氢也只是基于我们对盒子中粒子的了解，我现在是什么
hydrogen too just based on what we know
about particle in a box now what am I

327
00:27:40,410 --> 00:27:43,320
谈论当我谈论氢原子是粒子盒时，让我们
talking about when I'm talking about a
hydrogen atom being a particle box let's

328
00:27:43,320 --> 00:27:47,760
在这里画一个小盒子，这个盒子应该代表了
draw a little box here that box is
supposed to represent the attraction to

329
00:27:47,760 --> 00:27:52,920
原子核，所以氢原子基本上是电子与
the nucleus so a hydrogen atom is
basically it's electron bound to the

330
00:27:52,920 --> 00:27:56,820
原子核好吧，这不是完全一样，除非我们是盒子，但还是有一定的约束力
nucleus so okay it's not exactly unis
we're box but it's still some binding

331
00:27:56,820 --> 00:28:01,350
通过原子核，所以我们将电子放到盒子里，给她一个盒子
through the nucleus so we'll put our
electron in our box and give her a box a

332
00:28:01,350 --> 00:28:07,230
 L和那个盒子中电子的氢的基态能量
size L and the ground state energy of
the hydrogen of the electron in that box

333
00:28:07,230 --> 00:28:14,100
 L的大小是h-bar平方，pi大于2m，l平方，现在我们有另一个
of size L is h-bar squared over 2m pi
over l squared now we have another

334
00:28:14,100 --> 00:28:20,520
氢原子在这里，所以我们给他一个盒子L，他的能量H 
hydrogen atom here so we'll give him a
box size L and he has the same energy H

335
00:28:20,520 --> 00:28:27,840
当我们有H 2时，在2m ah pi上平方的平方根pi在l平方上平方的平方现在在这里
bar squared over 2m ah pi over l squared
now over here when we have H 2 we get a

336
00:28:27,840 --> 00:28:35,070
更大的盒子，也许是2 L的氢分子，那是什么，所以我们
bigger box maybe a size 2 L for the
hydrogen molecule and what are the so we

337
00:28:35,070 --> 00:28:39,810
对这里较大的盒子和基态具有基波函数
have a ground state wave function for
the bigger box here and the ground state

338
00:28:39,810 --> 00:28:45,480
波函数是能量H bar平方2m PI平方2 l平方
wave function is an energy H bar squared
over 2m PI over 2 l squared which is

339
00:28:45,480 --> 00:28:48,480
当然，我们必须降低2个电子在这个基态波中
lower of course we have to put 2
electrons in this ground state wave

340
00:28:48,480 --> 00:28:54,500
现在可以运行，但是我们可以这样做，因为有2次旋转，我们发现
function now but we can do that because
there are 2 spins and we discover that

341
00:28:54,500 --> 00:28:59,880
等式的这一边低于这两个等式的总和，所以
this side of the equation is lower than
the sum of these two equations so what's

342
00:28:59,880 --> 00:29:03,780
这里发生的是我们允许电子波
going on here what's going on here is
that we're allowing the electron wave

343
00:29:03,780 --> 00:29:08,010
功能从局限在这里扩展到局限在
function to spread out from being
confined here and confined here to being

344
00:29:08,010 --> 00:29:11,520
在这里不那么受限制，通过让wave函数展开，我们降低了
less confined here and by letting the
wave function spread out we're lowering

345
00:29:11,520 --> 00:29:16,350
它的能量，这就是您知道海森堡不确定性而使Delta X 
its energy this is just you know
Heisenberg uncertainty you make Delta X

346
00:29:16,350 --> 00:29:20,250
 ΔP越大，ΔP越小，动力学就越低
bigger Delta P gets smaller with smaller
Delta P you can have a lower kinetic

347
00:29:20,250 --> 00:29:24,470
能量，所以通过散布波函数，可以降低动能
energy so by spreading out the wave
function you lower the kinetic energy

348
00:29:24,470 --> 00:29:29,820
现在我们可以考虑使用氦气做同样的事情，我们将看到
now we can consider the same thing with
helium and we'll see that actually

349
00:29:29,820 --> 00:29:33,990
氦气有些不同，所以氦气有一个盒子，你有一个
something is very different about helium
so helium you have a box you have your

350
00:29:33,990 --> 00:29:41,660
基态波函数，这里有两个电子
ground state wave function and you have
two electrons in it here again a box

351
00:29:41,660 --> 00:29:46,620
基态波函数在其中放了两个电子，然后问题是
ground state wave function put two
electrons in it and then the question is

352
00:29:46,620 --> 00:29:53,880
现在可以去氦气了吗2现在有一个更大的盒子，我们可以接地
does it go to helium two okay now here
we have a bigger box we get a ground

353
00:29:53,880 --> 00:29:57,450
状态波函数我们可以在其中放入两个电子然后我们必须开始
state wave function we can put two
electrons in it then we have to start

354
00:29:57,450 --> 00:30:02,130
也填充了激发波函数，因为我们填充了最低的
filling up an excited wave function as
well because we filled the lowest the

355
00:30:02,130 --> 00:30:06,690
基波函数我们也必须填补这个家伙，现在我们不
ground state wave function we have to
fill this guy as well and now we're not

356
00:30:06,690 --> 00:30:08,400
如果我什么都没得到
gaining so much matter if I'm not
getting any

357
00:30:08,400 --> 00:30:12,540
完全是因为我们不仅必须填充最低能量状态
at all because we had to as well as
filling the lowest energy state we have

358
00:30:12,540 --> 00:30:16,140
填充较高的能量状态以及较低的能量状态被称为
to fill a higher energy state as well
the lower energy state is known as the

359
00:30:16,140 --> 00:30:23,700
键合轨道键合轨道和高能态被称为
bonding orbital bonding orbital and the
higher energy state was known as the

360
00:30:23,700 --> 00:30:28,800
反粘结轨道，所以通常我们的粘结轨道
antibonding orbital
so generally bonding orbitals our ones

361
00:30:28,800 --> 00:30:33,630
其能量低于原始波函数和反键z'为
whose energy is lower than the original
wave functions and anti-bonding z' are

362
00:30:33,630 --> 00:30:38,850
高于或等于原始波函数，所以这就是为什么氦非常
higher or equal to the original wave
functions so this is why I helium very

363
00:30:38,850 --> 00:30:44,850
大概是为什么氦不结合而氢能结合的原因
roughly why it is that helium doesn't
bond but hydrogen does now this is

364
00:30:44,850 --> 00:30:51,170
显然非常卡通化，但是我们可以通过使用所谓的
obviously very cartoonish but we can do
a better job by using what's known as

365
00:30:51,170 --> 00:30:57,630
分子轨道理论分子轨道或原子轨道理论原子轨道
molecular orbital Theory molecular or
atomic orbital Theory Tomic orbital

366
00:30:57,630 --> 00:31:12,900
理论也称为紧密结合理论也称为线性结合
Theory also known as tight binding
Theory also known as linear lcao lcao

367
00:31:12,900 --> 00:31:18,740
等于
which equals linear combination of

368
00:31:19,610 --> 00:31:32,040
现在我想如果你最后走原子路线的话
atomic orbitals of atomic orbitals now I
think if you took the atomic course last

369
00:31:32,040 --> 00:31:36,300
学期，您甚至可能已经完成了此计算，我们将再次进行
term you may have even done this
calculation and we're gonna do it again

370
00:31:36,300 --> 00:31:39,450
但是我们会比上学期做得更简单，我之所以成为
but we're gonna do it simpler than you
did it last term and the reason I'm

371
00:31:39,450 --> 00:31:44,100
简化它是为了更容易看到潜在的物理原理，我们
simplifying it is so it's easier to see
the physics underlying okay and we're

372
00:31:44,100 --> 00:31:47,400
我们将在稍后的部分中使用其中一些技术
going to use sort of we're going to use
some of these techniques later on in the

373
00:31:47,400 --> 00:31:51,710
术语，使它们尽可能简单是一件好事，所以我们要做的第一件事是
term so it's good to make them as simple
as possible so the first thing we do is

374
00:31:51,710 --> 00:31:59,490
我们假设有两个分别位于r1和r2的原子核，哎呀，所以我
we imagine having two nuclei of
positions r1 and r2 and oops okay so I

375
00:31:59,490 --> 00:32:03,540
应该告诉您我们正在分析哪个问题，我们将这样做
should tell you which problem we're
analyzing right we're gonna do the so

376
00:32:03,540 --> 00:32:11,790
我们要看的问题是看h2 plus，所以这是两个质子
the problem we're gonna look at look at
look at h2 plus so this is two protons

377
00:32:11,790 --> 00:32:16,140
一个电子，两个质子和一个电子，我想你看着这个
and one electron two protons and one
electron I think you looked at this

378
00:32:16,140 --> 00:32:21,870
上学期前的问题好了，所以我们要去看看
problem before last term okay so we're
going to see

379
00:32:21,870 --> 00:32:27,390
允许该电子2d定位在两个原子核之间
allowing this electron 2d localize
between the two the two nuclei is going

380
00:32:27,390 --> 00:32:33,000
降低其能量，从而在两个原子核之间形成一个键
to lower its energy and therefore form a
bond between the two nuclei now the

381
00:32:33,000 --> 00:32:35,010
我们要做的第一件事就是使用天生的奥本海默
first thing we're gonna do is we're
going to use born-oppenheimer

382
00:32:35,010 --> 00:32:45,270
近似于天生的奥本海默J罗伯特·奥本海默是
approximation born-oppenheimer J robert
Oppenheimer was the father of the

383
00:32:45,270 --> 00:32:53,550
美国债券炸弹项目不是债券项目，麦克斯·伯恩（Max Born）我们已经讨论过了
American bond bomb project not bond
project and Max Born we've discussed him

384
00:32:53,550 --> 00:32:56,670
已经是量子力学和奥利维亚之父之一
already father one of the fathers of
quantum mechanics and Olivia

385
00:32:56,670 --> 00:32:59,760
牛顿·约翰的祖父只有一块巧克力棒，有人知道吗
newton-john's grandfather for one
chocolate bar does anyone know what

386
00:32:59,760 --> 00:33:04,710
奥利维亚·牛顿·约翰（Olivia Newton-John）的热门歌曲是我给你的提示
Olivia newton-john's biggest hit song
was I'll give you a hint it has

387
00:33:04,710 --> 00:33:08,610
与这个问题有关，我们正在研究是的，他说
something to do with this subject we're
studying yeah yeah who said that the

388
00:33:08,610 --> 00:33:12,480
同样的人好吧，你这个很好，身体很好，十周
same person okay you get this one all
right very good physical yeah ten weeks

389
00:33:12,480 --> 00:33:17,490
仍然是第一名，所以天生的奥本海默近似是
at number one okay anyway so the
born-oppenheimer approximation is

390
00:33:17,490 --> 00:33:23,550
基本上固定r1和r2固定原子核的位置并使电子移动
basically fix r1 and r2 fix the position
of the nuclei and let the electron move

391
00:33:23,550 --> 00:33:28,380
没关系，因为原子核非常重，它们会移动得非常快
and that's okay because the nuclei are
extremely heavy and they would move very

392
00:33:28,380 --> 00:33:32,790
缓慢地移动，因此电子可以非常快地到达其本征态
slowly so the electron can come to its
eigenstate very quickly and you know and

393
00:33:32,790 --> 00:33:35,970
那么您可以将所有放置在核子上并寻找
then you can sort of rece all that
wherever you put the nuclei and look for

394
00:33:35,970 --> 00:33:40,470
只要原子核具有尽可能低的能量，那么我们写一个
wherever the nuclei have their lowest
possible energy so then we write a

395
00:33:40,470 --> 00:33:48,090
哈密​​顿量哈密顿量为我们的电子P平方超过2m加上相互作用
Hamiltonian Hamiltonian for our electron
P squared over 2m plus the interaction

396
00:33:48,090 --> 00:33:51,690
与第一个原子核的库仑相互作用加库仑相互作用
the Coulomb interaction with the first
nucleus plus the Coulomb interaction

397
00:33:51,690 --> 00:34:01,440
第二个核，其中V在这里V是通常的负V平方超过4 PI 
with the second nucleus where V here V
is the usual minus V squared over 4 PI

398
00:34:01,440 --> 00:34:07,830
 epsilon n等于R减R等等，我将其缩写为
epsilon naught R minus R one so forth
I'm going to abbreviate this thing as

399
00:34:07,830 --> 00:34:12,750
这个项是K代表动能，这个项是V 1代表与动能相互作用
this term is K for kinetic energy this
term is V 1 for interaction with the

400
00:34:12,750 --> 00:34:18,449
第一个原子核现在是V 2，用于与第二个原子核相互作用
first nucleus this term is V 2 for
interaction with the second nucleus now

401
00:34:18,449 --> 00:34:21,989
这是一个很难的问题，因为两个原子核都存在，但这会
this is a hard problem because there's
both because of both nuclei but it would

402
00:34:21,989 --> 00:34:25,439
如果我们丢掉一个原子核，假装它不存在，那就简单得多

403
00:34:25,440 --> 00:34:33,359
好吧，让我们首先解决这个问题，然后我们可以让K加V 1为
okay so let's solve that that problem
first so we can then have K plus V 1 as

404
00:34:33,359 --> 00:34:37,389
我们的哈密顿量，我们称本征态一
our Hamiltonian
and we'll call the eigenstate one

405
00:34:37,389 --> 00:34:41,709
 epsilon不是一个，那么这个问题的答案到底是什么？ 

406
00:34:41,710 --> 00:34:48,380
你知道它在原子核上或原子核上的氢原子，所以一个是基态
hydrogen atom you know it's on on or on
nucleus one so one is the ground state

407
00:34:48,380 --> 00:34:52,100
如果您喜欢，原子核上的电子之一就是S壳中的电子
of the electron on nucleus one the
electron in the S shell if you like you

408
00:34:52,100 --> 00:35:01,940
可以对两个做相同的事情，所以这是如果我们只有两个原子核
can do the same thing for two so this is
if we only have nucleus two we would get

409
00:35:01,940 --> 00:35:06,890
第二核的本征态，所以我可以画这些，所以这是我们的一个
an eigenstate on nucleus two so I can
draw these if I want so here's our one

410
00:35:06,890 --> 00:35:11,990
这是我们的两个，那么电子将具有波函数
here's our two then there would be a
wave function here of the electron

411
00:35:11,990 --> 00:35:16,310
坐在那里，好像这个家伙不在那里，然后会有一波潮
sitting there as if this guy weren't
there and then there would be a wave

412
00:35:16,310 --> 00:35:20,960
那里有两个人坐在那里，好像这个家伙不在那里一样
function there two sitting there as if
this guy weren't there is that clear so

413
00:35:20,960 --> 00:35:25,310
这两个状态是我正在考虑的两个原子轨道上的电子
the two states the two atomic orbitals
I'm thinking about is the electron on

414
00:35:25,310 --> 00:35:31,070
绕一号核运动，好像两个核根本不存在，电子在
orbit on nucleus one as if nucleus two
are not there at all and the electron on

415
00:35:31,070 --> 00:35:38,470
核2好像核1根本不在那儿很好很好所以
nucleus two as if a nucleus one we're
not there at all good good yeah okay so

416
00:35:38,470 --> 00:35:42,950
您也可以将一和二视为本征态
you can also think about one and two as
being the eigenstates if the two

417
00:35:42,950 --> 00:35:48,520
两个原子核的轨道相距很远，在这种情况下， 
orbitals of the two nuclei taken very
very far apart in which case you have

418
00:35:48,520 --> 00:35:54,170
电子位于两种原子的轨道上的两种可能性
two possibilities the electron sits on
orbital one on nucleus one or the

419
00:35:54,170 --> 00:35:58,250
电子位于两个原子核上，我们期望发生的是
electron sits on nucleus two and what we
expect is going to happen is that when

420
00:35:58,250 --> 00:36:02,830
我们将它们结合在一起，将有一个较低的能量状态
we bring them together there's going to
be a lower energy state the bonding

421
00:36:02,830 --> 00:36:09,620
电子离域在两个原子核之间的状态
state where the electron delocalized is
between the two between the two nuclei

422
00:36:09,620 --> 00:36:18,170
并且还可能有一个反键态反键，能量更高
and there may also be an antibonding
state antibonding which is higher energy

423
00:36:18,170 --> 00:36:22,190
当我们将它们组合在一起时，化学家经常使用这种图表
when we bring them together this kind of
diagram is used a lot by chemists it's

424
00:36:22,190 --> 00:36:30,770
称为分子轨道图分子轨道图
known as a molecular orbital diagram
molecular orbital diagram which tries to

425
00:36:30,770 --> 00:36:34,070
开始移动物体时跟踪本征态发生了什么
keep track of what happens to the
eigenstates when you start moving things

426
00:36:34,070 --> 00:36:40,100
一起或分开好吧，我们如何才能很好地解决这个问题， 
together or apart alright so how are we
going to solve this problem well we're

427
00:36:40,100 --> 00:36:43,280
用试波函数来做它
going to do it with the trial
wavefunction a variational trial

428
00:36:43,280 --> 00:36:49,349
 wavefunction wavefunction，我相信您已经研究了变分
wavefunction wavefunction
and I believe you've studied variational

429
00:36:49,349 --> 00:36:54,420
之前的消息，因此我们将要使用的wave函数的形式为Phi 1 
message before so the wave function
we're going to use is of the form Phi 1

430
00:36:54,420 --> 00:37:00,540
 1乘Phi 2乘2，我们将尝试找到最佳系数
times 1 plus Phi 2 times 2 and we're
gonna try to find the best coefficients

431
00:37:00,540 --> 00:37:04,440
 Phi 1和Phi 2会尽可能降低能量，这是
Phi 1 and Phi 2 which will lower the
energy as much as possible okay this is

432
00:37:04,440 --> 00:37:08,460
您尝试获得最接近地面的变分原理
the variational principle you try to get
the best approximation to the ground

433
00:37:08,460 --> 00:37:13,410
可以通过任意改变系数来表示状态，现在可以
state as you can by varying the
coefficients arbitrarily okay now this

434
00:37:13,410 --> 00:37:18,329
实际上将方法的名称命名为方法的线性组合名称
actually gives the method its name the
name of the method linear combination of

435
00:37:18,329 --> 00:37:20,880
我们正在做的原子轨道就是原子轨道
atomic orbitals that's exactly what
we're doing these are the atomic

436
00:37:20,880 --> 00:37:24,750
轨道，我们正在对它们进行线性组合，好吧，这也众所周知
orbitals and we're making a linear
combination of them okay it's also known

437
00:37:24,750 --> 00:37:28,680
紧密结合，因为电子坐在轨道1上，我们认为
as tight binding because the electron
sitting on orbital 1 we think of it at

438
00:37:28,680 --> 00:37:32,670
我们认为核1与核1紧密结合
nucleus 1 we think it is tightly bound
to nucleus 1 and this one is tightly

439
00:37:32,670 --> 00:37:37,020
绑定到原子核2，然后我们对两者之一进行线性组合
bound to nucleus 2 and then we make some
linear combination of those two one of

440
00:37:37,020 --> 00:37:41,010
人们真正喜欢这种分析问题的方法的原因是
the reasons people really like this
method of analyzing problems is because

441
00:37:41,010 --> 00:37:47,010
您实际上可以通过以下方法使近似值越来越精确
you can you can actually make the
approximation more and more accurate by

442
00:37:47,010 --> 00:37:49,560
越来越多的东西添加到右侧
adding more and more things to the
right-hand side with more and more

443
00:37:49,560 --> 00:37:53,069
变化的参数，所以不仅仅是跟踪两种可能性
variational parameters so instead of
just keeping track of two possibilities

444
00:37:53,069 --> 00:37:57,089
电子在地核1的基态上处于轨道一
the electron is on orbital one on the
ground state of nucleus 1 in ground

445
00:37:57,089 --> 00:38:01,020
核2的状态您也可以开始添加系数等
state of nucleus 2 you can start also
adding coefficients and other possible

446
00:38:01,020 --> 00:38:05,670
表示电子可以在原子核1的轨道之一上处于激发态
states the electron can be in excited
States on on orbital one of nucleus 1

447
00:38:05,670 --> 00:38:09,900
在原子核2上激发态，并且你建立了越来越大的基础
excited States on nucleus 2 and you make
a bigger and bigger basis set and as you

448
00:38:09,900 --> 00:38:13,770
使右侧的更多可能性越来越多
make though the more possibilities on
the right-hand side more and more you

449
00:38:13,770 --> 00:38:19,680
越来越接近左侧确定中的确切波动函数，所以现在我们
get closer and closer to the exact wave
function on on the left ok so now we

450
00:38:19,680 --> 00:38:25,560
必须为此写出有效的较短方程
have to actually write down our
effective shorter equation for this

451
00:38:25,560 --> 00:38:29,819
试用wavefunction，这实际上是您要做的功课
trial wavefunction and that's something
you're actually going to do for homework

452
00:38:29,819 --> 00:38:35,700
我会写出答案，它看起来非常像一个较短的方程式
I'll write out the answer it's it looks
very much like a shorter equation it's

453
00:38:35,700 --> 00:38:41,819
没有太多理由就可以相信的东西
something to probably believe without
too much justification it looks entirely

454
00:38:41,819 --> 00:38:47,040
像一个更短的方程式，唯一的不同是这个HHIJ是2 
like a shorter equation the only
difference is that this H H I J is a 2

455
00:38:47,040 --> 00:38:53,940
乘2矩阵IHJI忘了告诉您一些我们假设我们说的内容
by 2 matrix I H J I forgot to tell you
something that we're assuming we put it

456
00:38:53,940 --> 00:39:03,940
在这里，所以这是一个糟糕的假设糟糕的假设糟糕的假设是
over here so this is a bad assumption
bad assumption the bad assumption is

457
00:39:03,940 --> 00:39:11,980
 IJ是delta IJ，换句话说1/2等于零
that I J is delta IJ in other words 1/2
equals zero okay that one into

458
00:39:11,980 --> 00:39:17,320
正交波函数现在是一个很好的近似
orthogonal wave functions now that's a
good approximation if the way if the

459
00:39:17,320 --> 00:39:20,680
原子核相距很远，但是如果您将原子核真正靠近在一起，那不是
nuclei are far apart but if you put the
nuclei really close together it's no

460
00:39:20,680 --> 00:39:24,940
再有一个好的假设，就是我们使这个糟糕的原因
longer a good assumption
the reason we're making this bad

461
00:39:24,940 --> 00:39:30,280
假设是因为它使我们的生活更加轻松，并且在许多情况下
assumption is because it makes our life
a lot easier and as in many cases making

462
00:39:30,280 --> 00:39:33,310
这个错误的假设不会丢掉关键的物理学，所以我们要
this bad assumption isn't going to throw
out the crucial physics so we're gonna

463
00:39:33,310 --> 00:39:36,670
保持这个错误的假设，如果您想在书中进行练习
keep this bad assumption for now there's
an exercise in the book if you want to

464
00:39:36,670 --> 00:39:40,360
通过它并更正确地进行操作，但是正确的关键物理
go through it and do it more properly
but you'll get the crucial physics right

465
00:39:40,360 --> 00:39:43,720
通过做出这个错误的假设，我们将继续前进
by making this bad assumption so we're
gonna go ahead and do it

466
00:39:43,720 --> 00:39:47,560
我相信上学期您这样做时并没有使用这个错误的假设
I believe when you did it last term you
did not use this bad assumption the

467
00:39:47,560 --> 00:39:50,800
代数变得更糟，因此将尝试使代数保持简单
algebra gets much worse so it's going to
try to keep the algebra as simple as

468
00:39:50,800 --> 00:39:55,660
假设这个错误的假设是
possible by making that bad assumption
given that bad assumption this is the

469
00:39:55,660 --> 00:40:00,730
需要解决的薛定inger方程，它看起来很像一个
Schrodinger equation that you have to
solve and it looks pretty much like a

470
00:40:00,730 --> 00:40:05,020
较短的方程式，您知道存在哈密顿波函数能量波
shorter equation you know there's a
Hamiltonian wavefunction energy wave

471
00:40:05,020 --> 00:40:08,500
功能的唯一区别是，它不是完整的哈密顿量
function the only difference is it's not
the full Hamiltonians just the way the

472
00:40:08,500 --> 00:40:13,570
哈密​​尔顿投影到我们的受限空间，其中仅包括波浪
hamiltonian projected to our restricted
space which includes only the wave

473
00:40:13,570 --> 00:40:18,430
函数1和波动函数2，所以它是一个投影的缩短方程，例如
function 1 and the wave function 2 so
it's a projected shortener equation like

474
00:40:18,430 --> 00:40:22,240
因此，要解决此问题，我们需要做的是2乘2 
so to solve this all we need to do is we
need to come up with this is a 2 by 2

475
00:40:22,240 --> 00:40:26,470
在我们的例子中，矩阵2乘2我们需要在这里写出矩阵元素
matrix 2 by 2 in our case we need to
write out the matrix elements here so

476
00:40:26,470 --> 00:40:36,340
让我们做一个H 1是1 K加上V 1我还有汉密尔顿吗
let's do that one H 1 is 1 K plus V 1 do
I still have the Hamilton yeah the

477
00:40:36,340 --> 00:40:38,380
哈密​​尔顿仍然在那儿，我希望它不会脱离常规
Hamiltonian is still up there I hope it
doesn't go off the board

478
00:40:38,380 --> 00:40:49,660
 1加1 V 2 1这个术语很容易，因为1 ket 1是k加V的本征态
1 plus 1 V 2 1 this term is easy because
1 the ket 1 is an eigenstate of k plus V

479
00:40:49,660 --> 00:40:54,700
 1这就是我们定义它的方式，因为特征值是epsilon，实际上不是这样
1 that's how we defined it and as
eigenvalue is epsilon not so in fact one

480
00:40:54,700 --> 00:40:58,960
在一个是1上，您会发现它是一个这样的东西，这给我们
on one is 1 you can find it to be so
this pretty piece here just gives us

481
00:40:58,960 --> 00:41:05,590
 epsilon不是这部分，我们不知道那是什么，我将其称为V 
epsilon not this part here we don't know
what that is I'm going to call it V

482
00:41:05,590 --> 00:41:12,640
越过V越过物理上，我们有一个电子坐在轨道上
cross and physically what is it V cross
we have an electron sitting on orbital

483
00:41:12,640 --> 00:41:17,890
一个在这里，所以这里是电子坐，这是轨道二， 
one over here and so here's the electron
sitting and here's orbital two and

484
00:41:17,890 --> 00:41:21,880
 v-cross是电子之间的相互作用
v-cross
is the interaction between the electron

485
00:41:21,880 --> 00:41:27,220
坐在一种状态，坐在一个核上，与两个核相互作用，这是
sitting on state one sitting on nucleus
one interacting with nucleus two that's

486
00:41:27,220 --> 00:41:33,190
我相信上个名词你可能曾称呼过V-直接互动
what V crosses I believe last term you
may have called it - direct interaction

487
00:41:33,190 --> 00:41:37,900
我可能已经说过，J从上学期开始听起来很耳熟吗？ 
I may have called it J does that sound
familiar from last term yeah okay the

488
00:41:37,900 --> 00:41:41,650
我之所以不直接称其为J是因为在凝聚态下
reason I'm not calling it direct and J
is because in condensed matter those

489
00:41:41,650 --> 00:41:45,010
单词用于某些不同的东西，我试图避免
words are used for something somewhat
different and I'm trying to avoid

490
00:41:45,010 --> 00:41:48,700
对此感到困惑，所以我将其称为V形交叉，其中有些
confusion about that so I'm gonna call
it V cross instead and there's some

491
00:41:48,700 --> 00:41:51,940
两把Naumann黏土椅子之间的关系，但不足以值得
relation between the two Naumann clay
chairs but not enough that it's worth

492
00:41:51,940 --> 00:41:58,180
保持它这样扔掉，我们从现在起将其称为V交叉-H-我们
keeping it so throw that out we're gonna
call it V cross from now on - H - we

493
00:41:58,180 --> 00:42:08,260
需要它也非常类似于K加B 2 2 + 1 2 V 1 2 
need that also it's very similar to K
plus B 2 2 + 1 2 V 1 2 and again this

494
00:42:08,260 --> 00:42:18,990
事情是ε零加V交叉，更有趣的是1 H 2这是
thing is epsilon naught plus V cross the
more interesting piece is 1 H 2 which is

495
00:42:18,990 --> 00:42:33,310
 1 K + V 2 2 + 1 V 1 2好的，所以这很容易，因为K + V 2 
1 K plus V 2 2 + 1 V 1 2 okay so this
thing is easy actually because K + V 2

496
00:42:33,310 --> 00:42:39,000
是epsilon naught 2，然后假设2 +1是正交的，所以得到0 
is epsilon naught 2 and then 2 + 1 have
been assumed orthogonal so that gives 0

497
00:42:39,000 --> 00:42:46,620
好吧，这大大简化了我们的生活，在这里我称之为跳车
okay so that's simplifies our life a lot
this one here I'm gonna call hopping

498
00:42:46,620 --> 00:42:54,420
跳，通常称为-TI相信您去年致电交易所
hopping and generally it's called - T I
believe last year you call the exchange

499
00:42:54,420 --> 00:43:03,250
我可能将其称为Kappa之类的东西，所以我不再使用
and I probably called it Kappa or
something so again I'm not going to use

500
00:43:03,250 --> 00:43:09,550
那南围墙，因为我们现在用交换来交换其他东西，为什么
that Nam enclosure because we use a
exchange for something else now why does

501
00:43:09,550 --> 00:43:14,670
如果您考虑与时间有关的薛定inger方程，就称其为跳跃
it call hopping if you think in terms of
the time-dependent schrodinger equation

502
00:43:14,670 --> 00:43:20,650
这种对角线会使您从2变到1，所以
it's this kind of term that sort of off
diagonal takes you from 2 to 1 so a

503
00:43:20,650 --> 00:43:24,040
跳变项可以给电子罐列表带来动力
hopping term can give dynamics to an
electron can list

504
00:43:24,040 --> 00:43:29,560
拿起一个从两个原子核开始并着陆在一个原子核上的电子
take an electron that starts on nucleus
two and lands it on nucleus one so it

505
00:43:29,560 --> 00:43:33,430
允许您从一个原子核跳到另一个原子核
allows you hop from one nucleus to the
other hence the name hopping reasonable

506
00:43:33,430 --> 00:43:36,750
名字好吧，鉴于此，我们快到了
name okay so given this we're almost
there

507
00:43:36,750 --> 00:43:45,370
我们有零乘两乘的哈密顿矩阵epsilon加V cross减
we have our two-by-two Hamiltonian
matrix epsilon naught plus V cross minus

508
00:43:45,370 --> 00:43:50,770
 t减去t如果它很复杂，它将在这里变成星星，然后epsilon 
t minus t if it's if it's complex it
would get a t star here then epsilon

509
00:43:50,770 --> 00:43:56,020
交叉是一个很好的厄米矩阵，我们可以对角化它
auspi the cross is a nice little
hermitian matrix we can diagonalize it

510
00:43:56,020 --> 00:44:04,260
我们得到零的特征值heigl epsilon加V叉正负
we get the eigenvalues heigl epsilon
naught plus V cross plus or minus

511
00:44:04,260 --> 00:44:10,060
 T的绝对值，现在我留下一小块，现在放
absolute value of T now I left off one
little piece which I'm now going to put

512
00:44:10,060 --> 00:44:19,690
回到我剩下的东西是inu清晰的核，你知道的能量
back in the thing I left off was the inu
clear nuclear that the energy you know

513
00:44:19,690 --> 00:44:22,510
两个原子核也相互作用，所以如果我改变
the two nuclei are interacting with each
other as well so if I change the

514
00:44:22,510 --> 00:44:26,440
两个原子核之间的距离会有库仑相互作用，但是
distance between the two nuclei they
would have some Coulomb interaction but

515
00:44:26,440 --> 00:44:29,950
事实证明，核原子大约等于负V 
it turns out that a nuclear nuclear is
very approximately equal to minus V

516
00:44:29,950 --> 00:44:34,200
十字架，从您所了解的知识中，这实际上应该很明显
cross and that actually should be
obvious from what you know about

517
00:44:34,200 --> 00:44:39,520
如果周围有球形电荷云，则产生静电
electrostatics if you have a spherical
charge cloud of charge around another

518
00:44:39,520 --> 00:44:44,290
球形云电荷云可以考虑整体电荷云
spherical cloud charge of cloud of
charge you can considering the whole

519
00:44:44,290 --> 00:44:48,490
电荷为原点，整个电荷为原点为零
charge as being at the origin and the
whole charge is that the origin is zero

520
00:44:48,490 --> 00:44:53,980
 e取消加号，减号1取消加号，所以最终这些
the e cancels the plus one the minus one
cancels plus one so this ends up these

521
00:44:53,980 --> 00:44:58,600
两块彼此抵消，所以我只想写e正负两点
two pieces cancel each other so I'm just
going to write e plus or minus the two

522
00:44:58,600 --> 00:45:04,420
可能的能量是Anat加上或减去绝对T，所以这就是X 
possible energies are Anat plus or minus
absolute T so this is something that X

523
00:45:04,420 --> 00:45:10,330
我们获得或获得或减少的能量数量似乎很自然
seems fairly natural that the amount of
gaining or lowering of the energy we get

524
00:45:10,330 --> 00:45:16,360
当我们走时，当我们允许电子在两个轨道之间跳跃时，由
when we go when we allow the electron to
hop between the two orbitals is given by

525
00:45:16,360 --> 00:45:19,750
我们通过散布电子波函数让他们跳多少
how much we allow them to hop so by
spreading out the electron wave function

526
00:45:19,750 --> 00:45:23,560
您降低它的能量，您越分散波函数，您越降低
you lower its energy the more you spread
out the wave function the more you lower

527
00:45:23,560 --> 00:45:31,990
能量，所以我们甚至可以在这里做，是的，我们甚至可以写下两个
the energy um so we can even maybe do it
here yeah we can even write down the two

528
00:45:31,990 --> 00:45:36,700
如果将矩阵定义为对角化，则其本征态
eigenstates of this if you diagonalize
that that matrix is defined its eigen

529
00:45:36,700 --> 00:45:40,570
向量，您会发现该边加1 
vectors
you would find that side plus 1 over

530
00:45:40,570 --> 00:45:49,810
根2 1加oops 1减2这是反键高能反键
root 2 1 plus oops 1 minus 2 this is the
antibonding the higher energy anti bond

531
00:45:49,810 --> 00:45:55,300
较高的能量波函数，然后较低的能量波函数1 over 
the higher energy wave function and then
the lower energy wave function 1 over

532
00:45:55,300 --> 00:46:04,240
根2 1加2，实际上wave函数的那些形式应该看起来很多
root 2 1 plus 2 and in fact those forms
of the wave function should look a lot

533
00:46:04,240 --> 00:46:08,350
就像我们在盒子中的粒子中所拥有的一样，在粒子中，但是在盒子中我们拥有
like what we had in the particle in the
box so in particle but in the box we had

534
00:46:08,350 --> 00:46:14,140
这里有一个键合轨道键，我们这里有一个反键轨道
a bonding orbital bond here and we have
an antibonding orbital here and e here

535
00:46:14,140 --> 00:46:20,410
中间有一个节点，现在我们有两个原子核键合轨道
with a node in the middle and now we
have two nuclei the bonding orbital

536
00:46:20,410 --> 00:46:29,550
看起来像是对称的键，而反键看起来像这样
looks like this it's symmetric a bond
bond and the anti bond looks like this

537
00:46:30,090 --> 00:46:38,320
加抗粘结，所以它与粒子中的粒子非常相似
plus plus antibonding so it's very
similar to what we have in the particle

538
00:46:38,320 --> 00:46:43,390
在两种情况下的方框中，节点的存在都会提高能量
in the box in both cases the existence
of the node raises the energy ok

539
00:46:43,390 --> 00:46:49,740
因此，您获得或失去的能量取决于跳跃的数量
so since the amount of energy you gain
or lose depends on the amount of hopping

540
00:46:49,740 --> 00:46:56,110
作为R 1减去R 2的函数，您可能会
as a function of R 1 minus R 2 the
distance between the nuclei you might

541
00:46:56,110 --> 00:47:00,940
当您将两个原子核放得更近时，期望跳跃会增加
expect that the hopping goes up as you
put the two nuclei closer together so

542
00:47:00,940 --> 00:47:06,010
您会期望防粘结看起来像这样，粘结看起来像
you would expect that the antibonding
looks like this the bonding looks like

543
00:47:06,010 --> 00:47:12,430
这或多或少是对的，但实际上更准确是
this and that's more or less right but
actually more accurate is something that

544
00:47:12,430 --> 00:47:21,880
 e R 1减R 2看起来像这样
looks like this e R 1 minus R 2
antibonding goes like this and bonding

545
00:47:21,880 --> 00:47:29,470
当两个原子核彼此靠得太近，以至于所有
goes like this again when the two nuclei
get too close together that all of a

546
00:47:29,470 --> 00:47:32,680
突然变得非常排斥，而变得排斥的原因是
sudden becomes extremely repulsive and
the reason it becomes repulsive is

547
00:47:32,680 --> 00:47:36,850
因为我们的许多近似都分解了这个近似分解
because a lot of our approximations
break down this approximation breaks

548
00:47:36,850 --> 00:47:40,810
下来，两个原子轨道正在使用的两个核不再
down that the two nuclear the two atomic
orbitals were using are no longer

549
00:47:40,810 --> 00:47:45,160
正交的，进一步说，我就两个电荷做出了陈述
orthogonal and further that statement I
made up there about the two charge

550
00:47:45,160 --> 00:47:50,350
一旦正电荷进入另一个云层，云消除就会分解
clouds canceling breaks down once the
positive charge gets inside the other

551
00:47:50,350 --> 00:47:53,380
一旦其他原子核获得，您就会知道电子
electrons
you know once the other nucleus gets

552
00:47:53,380 --> 00:47:57,130
在电子的电荷云中，那么您将无法再取消您
inside the charge cloud of the electron
then you can no longer cancel you

553
00:47:57,130 --> 00:47:59,890
记住这条规则，如果您在某些收费之内，则不算，如果
remember this rule that if you're inside
some charge you don't count it and if

554
00:47:59,890 --> 00:48:02,500
如果您在谈论球形的时候算了算，那么您就不在费用之列
you're outside the charge if you count
it when you're talking about a spherical

555
00:48:02,500 --> 00:48:05,859
电荷分配，将您体内的任何东西都靠近中心
charge distribution anything that's
inside you closer to the center you

556
00:48:05,859 --> 00:48:09,579
数，然后将所有内容置于中心，而您认为之外的所有内容
count and you put all the at the center
and anything is outside you think you

557
00:48:09,579 --> 00:48:15,010
扔掉，所以如果原子核进入电子的电荷云，那么它
throw away so if the nucleus gets inside
the charge cloud of the electron then it

558
00:48:15,010 --> 00:48:18,010
开始看到另一个核，并开始被另一个核排斥
starts to see the other nucleus and it
starts to be repelled by the other

559
00:48:18,010 --> 00:48:26,559
原子核，所以键的能量上升了，这里的另一件事
nucleus so the energy of the bond goes
goes way up one more thing here before

560
00:48:26,559 --> 00:48:32,559
如果我们有两个，我们在结束之前也可以考虑一个非常相似的物理学
we before we end you can also consider a
very similar physics if you have two

561
00:48:32,559 --> 00:48:37,240
不同的原子，所以我们有氢和氟，在这里我画了一个
different atoms so we have hydrogen and
fluorine and here I've drawn one up here

562
00:48:37,240 --> 00:48:41,289
还有一个在这里，因为如果你在氢上有一个电子，它们的能量
and one down here because their energies
if you just have an electron on hydrogen

563
00:48:41,289 --> 00:48:45,010
它的能量比氟上的电子高得多，哦，也许我应该
it's much higher energy than the
electron on fluorine oh maybe I should

564
00:48:45,010 --> 00:48:49,900
曾经说过氟中的钠和氟钠没关系，只是你知道
have said sodium and fluorine sodium in
the florium doesn't matter just you know

565
00:48:49,900 --> 00:48:53,650
在低电离能或想要少得多的电子的物体上
on something that has a low ionization
energy or wants the electron a lot less

566
00:48:53,650 --> 00:48:57,549
还有电子亲和力高或组织性高的东西
and something with a high electron
affinity or a high organization and she

567
00:48:57,549 --> 00:49:01,240
想要更多电子，您可以允许电子离域
wants the electron a lot more and you
can allow an electron to delocalized

568
00:49:01,240 --> 00:49:05,440
如果这样做的话，钠和氟之间会发生变化
between the sodium and the fluorine if
you do that the only thing that changes

569
00:49:05,440 --> 00:49:12,720
这是对角线上的这两个能量变成e钠和氟
here is that these two energies on the
diagonal become e sodium and a fluorine

570
00:49:12,720 --> 00:49:17,079
这样好，那两个可以彼此不同
like that okay and those two can be
different from each other

571
00:49:17,079 --> 00:49:22,589
如果将这个矩阵对角化，现在您将再次找到两个不同的能量
if you diagonalize this matrix now
you'll find two different energies again

572
00:49:22,589 --> 00:49:26,550
所以我们把它画成一个结合和反结合的轨道
so we'll draw that as a bonding and
antibonding orbital

573
00:49:26,550 --> 00:49:32,250
所以这里又有一个反键，使电子返回并
so there's antibonding down here again
allowing the electron to go back and

574
00:49:32,250 --> 00:49:38,579
第四改变了总能量，这里是反键，但是这些
forth changes the total energy and
here's antibonding up here but these

575
00:49:38,579 --> 00:49:44,690
系数将与反粘结轨道的系数不同
coefficients will not be the same that
for the antibonding orbital this this

576
00:49:44,690 --> 00:49:49,829
系数处于-alpha将更大beta将大于alpha 
coefficient being in - alpha will be
bigger beta would be bigger than alpha

577
00:49:49,829 --> 00:49:53,849
电子更有可能越过这里
there'll be a higher probability that
the electron will be over here for the

578
00:49:53,849 --> 00:50:00,770
反结合轨道，而对于像这样的结合轨道beta alpha， 
antibonding orbital whereas for the
bonding orbital beta alpha like this the

579
00:50:00,770 --> 00:50:04,950
波函数的最大权重将在此处
the most of the weight of the
wavefunction will be over here on

580
00:50:04,950 --> 00:50:09,839
氟，这是一个简单的二乘二矩阵对角化问题
fluorine it's sort of a simple two by
two matrix diagonalization problem

581
00:50:09,839 --> 00:50:14,460
这本书中也有一个练习，所以这个想法是，但是
there's an exercise in the book on this
as well so the idea is that but just by

582
00:50:14,460 --> 00:50:18,869
看看这个二乘二的矩阵，您可以看到如何从共价键形成
looking at this two-by-two matrix you
can see how you go from a covalent bond

583
00:50:18,869 --> 00:50:22,770
电子在两个原子核之间均等分布
where the electron is distributed
equally between the two the two nuclei

584
00:50:22,770 --> 00:50:27,660
离子键，我们实际上是较低能量的轨道，使电子几乎
to an ionic bond we're really the lower
energy orbital puts the electron almost

585
00:50:27,660 --> 00:50:33,660
完全在这里讨论低能物种，好吧，我想我停了下来
entirely over here on on the lower
energy species okay I guess I stopped

586
00:50:33,660 --> 00:50:39,860
在那里，我明天见[鼓掌] 
there and I see you tomorrow
[Applause]