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JEFFREY C. GROSSMAN: All right.

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So we are here.

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00:00:28,570 --> 00:00:30,580
I'm highlighting
two, because I really

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want to keep talking
about solar thermal fuels,

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mostly because it really
captures a key problem

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that only quantum
mechanics can solve.

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OK?

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00:00:41,980 --> 00:00:43,930
So I really want to
hit that home hard.

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Also, because it's the
topic of your next homework,

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00:00:48,560 --> 00:00:50,830
and also because I'm biased.

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00:00:50,830 --> 00:00:52,553
I'm more excited
about this than this.

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00:00:52,553 --> 00:00:54,970
But I want to tell you a little
bit about hydrogen storage

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00:00:54,970 --> 00:00:58,450
too, and why I think
that's a perfect problem

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00:00:58,450 --> 00:01:01,000
for atomic-scale
computational modeling.

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00:01:01,000 --> 00:01:01,960
OK?

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00:01:01,960 --> 00:01:07,030
So we're going to do a lot
more of solar thermal fuels,

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00:01:07,030 --> 00:01:09,370
picking up where we did
before, and then a little bit

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00:01:09,370 --> 00:01:10,540
of hydrogen storage.

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00:01:10,540 --> 00:01:13,930
Now, before we do that,
I want to keep blending

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00:01:13,930 --> 00:01:18,280
in some reinforcement
of key basic concepts

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00:01:18,280 --> 00:01:21,760
that we have touched on,
and we need to make sure

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00:01:21,760 --> 00:01:22,890
we feel good about them.

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00:01:22,890 --> 00:01:25,240
So we're going to
feel good today

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00:01:25,240 --> 00:01:28,240
about energy levels, first
bullet of the outline,

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00:01:28,240 --> 00:01:30,243
feeling good.

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00:01:30,243 --> 00:01:31,660
It's a good way
to start, I think.

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00:01:34,560 --> 00:01:36,900
I didn't need to put
that there, because you

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00:01:36,900 --> 00:01:38,430
would have felt good anyway.

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00:01:38,430 --> 00:01:39,180
Right?

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00:01:39,180 --> 00:01:40,740
But there it is in writing.

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00:01:40,740 --> 00:01:43,248
We're going to feel good
about energy levels,

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00:01:43,248 --> 00:01:45,540
and then we're going to keep
talking about solar fuels.

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00:01:45,540 --> 00:01:49,440
And we'll do a few
calculations, more calculations

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00:01:49,440 --> 00:01:51,150
on the nanoHUB together.

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00:01:51,150 --> 00:01:51,780
Right?

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00:01:51,780 --> 00:01:54,510
Again, no better
way to pass time.

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00:01:54,510 --> 00:01:55,140
OK?

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00:01:55,140 --> 00:01:57,720
And then we'll talk
about hydrogen storage.

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00:01:57,720 --> 00:02:00,960
That's our plan.

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00:02:00,960 --> 00:02:05,880
Now, like I said, I want
to keep reinforcing--

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00:02:05,880 --> 00:02:09,180
I did this, and it
put me off balance.

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00:02:09,180 --> 00:02:10,470
It's excitement.

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00:02:10,470 --> 00:02:14,430
That's a little bit
more than my usual even.

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00:02:14,430 --> 00:02:16,080
It's also, I think,
just old age.

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00:02:16,080 --> 00:02:18,420
I think sometimes, you
get a little off balance.

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00:02:18,420 --> 00:02:25,410
Anyway, now, point is
that I think probably I

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like watch the NBA so
much, because I still

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00:02:27,510 --> 00:02:31,620
don't want to give up the
idea that I could someday

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00:02:31,620 --> 00:02:33,990
be in the NBA myself.

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00:02:33,990 --> 00:02:35,490
So I'm not letting
go of that dream,

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00:02:35,490 --> 00:02:41,070
but anyway, I want to go back to
one of my original excitements

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00:02:41,070 --> 00:02:45,430
here about materials
design which

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00:02:45,430 --> 00:02:47,020
is one of the
things I really want

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to make sure we
capture in this class,

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00:02:49,300 --> 00:02:51,530
designing materials
and computers.

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Right?

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00:02:52,030 --> 00:02:53,930
So I want to take
carbon, and I just

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have two or three slides here.

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So I want to touch
on what I think

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00:02:56,920 --> 00:03:01,750
is a really exciting
example of materials design,

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and you all know this.

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Right?

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You know carbon can do this
and this, and many of you

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know that carbon can do--

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well, where are my fullerenes?

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Well, there's some nanotubes.

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There's fullerenes inside
of nanotubes, p-pods.

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00:03:13,720 --> 00:03:14,650
Right?

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00:03:14,650 --> 00:03:17,320
Now, there's all kinds
of forms of carbon

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that there didn't used to
be, or there used to be,

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but we didn't see them, and
we couldn't control them.

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OK?

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00:03:24,010 --> 00:03:26,330
And I want to give
you a really, I think,

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00:03:26,330 --> 00:03:31,510
interesting analysis of one
thing you can do with carbon.

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OK?

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00:03:32,260 --> 00:03:36,100
And then another thing you can
do with it, when you design it,

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00:03:36,100 --> 00:03:38,480
when you can do
materials design.

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So this is what we do with
carbon now that we find in oil.

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Right?

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00:03:43,090 --> 00:03:47,440
We burn it, and there's 1.73
megawatt hours of energy

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00:03:47,440 --> 00:03:49,150
when you burn a barrel of oil.

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00:03:49,150 --> 00:03:50,138
Right?

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00:03:50,138 --> 00:03:51,430
I didn't show you this example.

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00:03:51,430 --> 00:03:52,150
Did I?

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00:03:52,150 --> 00:03:52,780
OK.

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00:03:52,780 --> 00:03:54,920
Because I think it's
a really neat one.

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00:03:54,920 --> 00:03:56,920
So that's how much energy
is in a barrel of oil,

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00:03:56,920 --> 00:03:58,300
and it's a lot of energy.

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00:03:58,300 --> 00:03:59,840
That's a really nice--

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00:03:59,840 --> 00:04:01,490
oil is amazing.

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00:04:01,490 --> 00:04:06,040
It's like this incredible
energy-dense, safe,

99
00:04:06,040 --> 00:04:13,040
transportable, storage system.

100
00:04:13,040 --> 00:04:13,910
Right?

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00:04:13,910 --> 00:04:14,910
It's solar powered.

102
00:04:14,910 --> 00:04:15,410
Right?

103
00:04:15,410 --> 00:04:18,079
You all know that
it's made by the sun,

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00:04:18,079 --> 00:04:20,420
but it's not renewable,
which is a problem,

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00:04:20,420 --> 00:04:24,300
but it's a really
beautiful fuel.

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00:04:24,300 --> 00:04:27,437
Now, oil has a lot
of carbon in it

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00:04:27,437 --> 00:04:29,770
which is what's burning there
and giving you that energy

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00:04:29,770 --> 00:04:31,265
release.

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00:04:31,265 --> 00:04:33,640
But there are other things
you can do with that material,

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00:04:33,640 --> 00:04:36,310
and one thing you can do is
you can make these other forms

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00:04:36,310 --> 00:04:37,660
of carbon from the oil.

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00:04:37,660 --> 00:04:40,420
In fact, that's how we
make a lot of our plastics.

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00:04:40,420 --> 00:04:41,110
OK?

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00:04:41,110 --> 00:04:43,750
We make a lot of
plastics using oil.

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00:04:43,750 --> 00:04:50,290
If I take 1%, just 1% of the
carbon in these 159 liters

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00:04:50,290 --> 00:04:55,390
of oil, just 1% of it, and
I make that into plastic,

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00:04:55,390 --> 00:04:59,170
then because I know how to
design carbon to be something

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00:04:59,170 --> 00:05:04,000
else, like fullerenes, I can
make polymers and fullerenes

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00:05:04,000 --> 00:05:07,300
out of that same element
carbon and put them together--

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00:05:07,300 --> 00:05:09,430
gesundheit, whoever that was--

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00:05:09,430 --> 00:05:12,610
and make solar cells,
new kinds of solar cells,

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00:05:12,610 --> 00:05:16,600
in fact, solar cells made
out of mostly carbon.

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00:05:16,600 --> 00:05:20,350
If I take 1% of that
carbon that was in here,

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00:05:20,350 --> 00:05:23,620
and I turn it into this,
which we now know how to do,

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00:05:23,620 --> 00:05:28,540
then I can make really
bad solar cells.

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00:05:28,540 --> 00:05:34,200
5% efficient, not so
good, die in one year,

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00:05:34,200 --> 00:05:35,220
not so good. right?

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00:05:35,220 --> 00:05:36,390
The efficiency goes down.

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00:05:36,390 --> 00:05:38,580
Most solar cells, you
get a 20-year warranty.

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00:05:38,580 --> 00:05:42,180
This one, one-year warranty,
then efficiency is gone.

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00:05:42,180 --> 00:05:44,940
Even in that case,
this solar cell

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00:05:44,940 --> 00:05:48,150
over that one year of
really crappy efficiency

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00:05:48,150 --> 00:05:53,070
will give me 10,000
times as much energy than

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00:05:53,070 --> 00:05:56,060
by burning the carbon, 10,000.

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00:05:56,060 --> 00:05:58,340
Now, these are hand-waving
arguments that are

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00:05:58,340 --> 00:05:59,870
back-of-the-envelope
calculations,

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00:05:59,870 --> 00:06:03,050
but when you've got five orders
of magnitude to play with,

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00:06:03,050 --> 00:06:04,370
things are good.

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00:06:04,370 --> 00:06:04,970
Right?

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00:06:04,970 --> 00:06:08,550
And this is an example
in the energy space.

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00:06:08,550 --> 00:06:12,350
This is why I get so excited
about designing materials,

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00:06:12,350 --> 00:06:17,360
and this in particular, this
is only 100 nanometers thick.

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00:06:17,360 --> 00:06:18,070
Right?

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00:06:18,070 --> 00:06:19,653
The solar cell's
thicker, because it's

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00:06:19,653 --> 00:06:22,330
packaged but the active layer,
the part of the material that's

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00:06:22,330 --> 00:06:25,150
making the sun turn into
electrons and holes,

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00:06:25,150 --> 00:06:27,590
something we're going to talk
about in our next example,

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00:06:27,590 --> 00:06:30,820
in a few weeks.

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00:06:30,820 --> 00:06:32,890
That part is 100
nanometers thick.

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00:06:32,890 --> 00:06:35,050
That's atomic scale.

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00:06:35,050 --> 00:06:36,430
That's the atomic scale.

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00:06:36,430 --> 00:06:38,560
You can't pack that many
polymers and fullerenes

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00:06:38,560 --> 00:06:40,300
into 100 nanometers.

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00:06:40,300 --> 00:06:44,230
Things at the atomic scale and
the quantum mechanical aspects

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00:06:44,230 --> 00:06:47,410
of that material are
critical, and designing

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00:06:47,410 --> 00:06:49,420
that material is
something you can

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00:06:49,420 --> 00:06:51,430
do using atomistic modeling.

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So this is what I mean.

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00:06:52,690 --> 00:06:58,820
You want to give elements
completely new possibilities,

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00:06:58,820 --> 00:07:01,510
and you can see the
power of doing that.

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00:07:01,510 --> 00:07:06,580
It changes the way we know
how to use those elements,

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and I think that's just
a very powerful concept.

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OK.

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00:07:11,770 --> 00:07:13,220
Any questions
about that example.

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00:07:13,220 --> 00:07:17,320
So that's my little my material
design example of the day,

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if you will.

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00:07:18,340 --> 00:07:22,190
We should make like a
calendar, each day a new--

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00:07:22,190 --> 00:07:23,680
OK.

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00:07:23,680 --> 00:07:27,940
Now, I want to pause and feel
our oneness with energy levels

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00:07:27,940 --> 00:07:29,300
and basis sets.

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So this is, again, going back
to some important key elements

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00:07:33,970 --> 00:07:35,455
of the computations,
and then we're

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00:07:35,455 --> 00:07:37,705
going to come back to the
calculations and the example

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00:07:37,705 --> 00:07:39,130
of the solar thermal fuels.

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00:07:39,130 --> 00:07:40,570
OK?

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00:07:40,570 --> 00:07:45,580
Now these are things that
we have talked about,

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00:07:45,580 --> 00:07:47,220
but they're so
important that I want

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00:07:47,220 --> 00:07:49,720
to talk about them again and
make sure there's no questions.

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00:07:49,720 --> 00:07:52,690
Make sure that we are
all on the same page

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00:07:52,690 --> 00:07:54,190
and know what these things mean.

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00:07:54,190 --> 00:07:54,760
OK?

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00:07:54,760 --> 00:07:58,630
So I want to give you,
this is my attempt

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00:07:58,630 --> 00:08:04,430
at summarizing our beautiful
path to the energy level.

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00:08:04,430 --> 00:08:04,930
OK?

185
00:08:04,930 --> 00:08:06,620
So let's make sure
we're with it.

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00:08:06,620 --> 00:08:07,270
All right?

187
00:08:07,270 --> 00:08:11,590
So it all started back
in the day in lecture one

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00:08:11,590 --> 00:08:13,420
with the Schrodinger equation.

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00:08:13,420 --> 00:08:15,070
Does everybody recognized that?

190
00:08:15,070 --> 00:08:17,710
Now, that is the
equation we're solving.

191
00:08:17,710 --> 00:08:20,320
When you click
Simulate to calculate

192
00:08:20,320 --> 00:08:24,010
the energy versus separation
in say, I don't know,

193
00:08:24,010 --> 00:08:28,000
n-2, then the equation that's
being solved in a computer

194
00:08:28,000 --> 00:08:30,370
is this one, the
Schrodinger equation.

195
00:08:30,370 --> 00:08:32,840
Now, what are you getting
out of that equation?

196
00:08:32,840 --> 00:08:35,734
Well, what you're
getting are what?

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00:08:35,734 --> 00:08:38,247
These, what are these?

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00:08:38,247 --> 00:08:39,289
AUDIENCE: Wave functions.

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00:08:39,289 --> 00:08:40,289
JEFFREY C. GROSSMAN: OK.

200
00:08:40,289 --> 00:08:43,490
Thank you, and why
do I want those?

201
00:08:43,490 --> 00:08:46,440
What do they tell me?

202
00:08:46,440 --> 00:08:47,940
AUDIENCE: Probability.

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00:08:47,940 --> 00:08:48,330
JEFFREY C. GROSSMAN: OK.

204
00:08:48,330 --> 00:08:48,630
Yeah.

205
00:08:48,630 --> 00:08:50,922
The tell me the probability,
and they tell me more than

206
00:08:50,922 --> 00:08:53,230
that which is what we need
to make sure we understand.

207
00:08:53,230 --> 00:08:57,045
So you see, solving
that equation gives me

208
00:08:57,045 --> 00:09:03,390
wave function, and the wave
functions, well, they're waves.

209
00:09:03,390 --> 00:09:03,890
Right?

210
00:09:03,890 --> 00:09:07,340
They have some shape to them.

211
00:09:07,340 --> 00:09:09,190
They may change in time.

212
00:09:09,190 --> 00:09:12,100
Do we care about that?

213
00:09:12,100 --> 00:09:15,390
Not in this class, not in
this class, in this class,

214
00:09:15,390 --> 00:09:16,900
its all time independent.

215
00:09:16,900 --> 00:09:20,560
So we're doing like a snapshot,
but they may change in time.

216
00:09:20,560 --> 00:09:24,090
But they certainly vary
in space, and that is psi.

217
00:09:24,090 --> 00:09:25,020
Right?

218
00:09:25,020 --> 00:09:30,250
Now, what we talked about
is how these wave functions

219
00:09:30,250 --> 00:09:35,390
themselves, we don't know how
to draw physical meaning from.

220
00:09:35,390 --> 00:09:37,250
That doesn't mean that
they're meaningless,

221
00:09:37,250 --> 00:09:39,380
and this is a really
important point

222
00:09:39,380 --> 00:09:42,590
that we have to feel good about.

223
00:09:42,590 --> 00:09:43,090
OK?

224
00:09:43,090 --> 00:09:45,070
So I'm going to
come back to that,

225
00:09:45,070 --> 00:09:47,770
but we know that when you square
them, we know what they mean,

226
00:09:47,770 --> 00:09:48,550
and that's this.

227
00:09:48,550 --> 00:09:49,440
Right?

228
00:09:49,440 --> 00:09:51,844
So what are These do you
guys remember what these are?

229
00:09:51,844 --> 00:09:53,740
AUDIENCE: Orbitals.

230
00:09:53,740 --> 00:09:56,330
JEFFREY C. GROSSMAN:
Orbitals, such a bad name,

231
00:09:56,330 --> 00:09:59,120
but anyway, because
why is it a bad name?

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00:09:59,120 --> 00:10:00,870
AUDIENCE: Because they
don't really orbit.

233
00:10:00,870 --> 00:10:03,630
JEFFREY C. GROSSMAN:
Yeah, totally, but anyway,

234
00:10:03,630 --> 00:10:04,950
these are orbitals.

235
00:10:04,950 --> 00:10:07,350
So these are those wave
functions squared for what?

236
00:10:10,730 --> 00:10:14,836
Who knows what-- but
what system is this?

237
00:10:14,836 --> 00:10:18,700
These are the atomic
orbitals of a hydrogen

238
00:10:18,700 --> 00:10:21,240
atom, one electron, one proton.

239
00:10:21,240 --> 00:10:23,670
OK?

240
00:10:23,670 --> 00:10:25,441
You can solve that analytically.

241
00:10:28,810 --> 00:10:34,560
Now, so we said, OK,
well, this gives us

242
00:10:34,560 --> 00:10:38,380
like an electron sitting in
one of these little wiggles.

243
00:10:38,380 --> 00:10:38,880
OK?

244
00:10:38,880 --> 00:10:41,670
We said that they
go up in energy.

245
00:10:41,670 --> 00:10:43,440
They have different energies.

246
00:10:43,440 --> 00:10:45,390
That's really important.

247
00:10:45,390 --> 00:10:48,910
Each wave function you solve
for has a different energy.

248
00:10:48,910 --> 00:10:49,410
Right?

249
00:10:49,410 --> 00:10:52,290
So you get these functions, and
they have different energies,

250
00:10:52,290 --> 00:10:54,960
and there it is for
hydrogen. There's

251
00:10:54,960 --> 00:10:58,290
the energy for hydrogen. It just
depends on 1 over the principle

252
00:10:58,290 --> 00:10:59,700
quantum number squared.

253
00:10:59,700 --> 00:11:00,720
Right?

254
00:11:00,720 --> 00:11:02,670
Remember, we talked
about how it's quantized?

255
00:11:05,490 --> 00:11:07,470
But these little wiggles,
when you square them,

256
00:11:07,470 --> 00:11:11,850
they give you the picture of
where that electron is going

257
00:11:11,850 --> 00:11:14,610
to be, where it's likely to be.

258
00:11:14,610 --> 00:11:16,845
And we looked at how the
shapes got more complicated,

259
00:11:16,845 --> 00:11:18,345
and what are these
type of orbitals?

260
00:11:18,345 --> 00:11:19,382
AUDIENCE: P

261
00:11:19,382 --> 00:11:20,340
JEFFREY C. GROSSMAN: p?

262
00:11:20,340 --> 00:11:24,810
And then it goes to other
things, d and then f.

263
00:11:29,200 --> 00:11:31,210
And then we said,
OK, that's nice.

264
00:11:31,210 --> 00:11:33,890
That's great, but also there's
this thing called spin.

265
00:11:33,890 --> 00:11:34,870
OK?

266
00:11:34,870 --> 00:11:37,360
And somebody remind
me what spin is.

267
00:11:40,186 --> 00:11:42,070
AUDIENCE: Property
of the material.

268
00:11:42,070 --> 00:11:46,060
JEFFREY C. GROSSMAN: Property
of what thing in particular?

269
00:11:46,060 --> 00:11:46,673
Yeah?

270
00:11:46,673 --> 00:11:48,590
AUDIENCE: It's some
intrinsic angular momentum

271
00:11:48,590 --> 00:11:49,840
that a particle has.

272
00:11:49,840 --> 00:11:50,290
JEFFREY C. GROSSMAN: OK.

273
00:11:50,290 --> 00:11:51,470
AUDIENCE: Regardless
of its motion.

274
00:11:51,470 --> 00:11:53,178
JEFFREY C. GROSSMAN:
And if that particle

275
00:11:53,178 --> 00:11:56,110
happens to be an electron,
what are your options?

276
00:11:56,110 --> 00:11:59,778
AUDIENCE: In the first one?

277
00:11:59,778 --> 00:12:00,820
JEFFREY C. GROSSMAN: Yes.

278
00:12:00,820 --> 00:12:01,900
AUDIENCE: Plus or minus.

279
00:12:01,900 --> 00:12:03,358
JEFFREY C. GROSSMAN:
Plus or minus.

280
00:12:03,358 --> 00:12:04,990
It can only be--

281
00:12:04,990 --> 00:12:09,910
or as we like to say
up or down or as we

282
00:12:09,910 --> 00:12:13,670
like to draw this or that.

283
00:12:13,670 --> 00:12:17,270
Lots of ways of doing this,
but I think you get the point.

284
00:12:17,270 --> 00:12:19,540
And then we talked
about poly which

285
00:12:19,540 --> 00:12:26,130
gave us rules for how
electrons can be together

286
00:12:26,130 --> 00:12:29,180
in one of these orbitals.

287
00:12:29,180 --> 00:12:30,210
OK?

288
00:12:30,210 --> 00:12:32,730
So you have wave
functions that wiggle.

289
00:12:35,283 --> 00:12:37,200
We don't know how to
interpret what they mean,

290
00:12:37,200 --> 00:12:40,320
but we know that their square
gives you the probability

291
00:12:40,320 --> 00:12:43,560
distribution of that electron.

292
00:12:43,560 --> 00:12:45,990
And we know that
these electrons also

293
00:12:45,990 --> 00:12:49,710
have another important quantity
associated with them, a spin,

294
00:12:49,710 --> 00:12:53,710
and the spin can only be one
of two values, up or down.

295
00:12:53,710 --> 00:12:55,660
OK?

296
00:12:55,660 --> 00:12:59,960
That is the information we
need to go to energy levels.

297
00:12:59,960 --> 00:13:00,460
OK?

298
00:13:04,500 --> 00:13:07,560
To this point, this is a
review, but it's about to be--

299
00:13:07,560 --> 00:13:09,083
well, maybe
something some of you

300
00:13:09,083 --> 00:13:11,000
know, but it's about to
be a little different.

301
00:13:11,000 --> 00:13:11,550
OK?

302
00:13:11,550 --> 00:13:14,140
So I want to make sure
we all understand this.

303
00:13:14,140 --> 00:13:17,650
Once I know that you can
have two kinds of spin,

304
00:13:17,650 --> 00:13:20,920
and once I know that you get
energies out of this equation,

305
00:13:20,920 --> 00:13:23,860
then the answer to
the energy levels,

306
00:13:23,860 --> 00:13:27,370
to what energy
levels are, is there

307
00:13:27,370 --> 00:13:29,382
are these things that you fill.

308
00:13:29,382 --> 00:13:31,630
There are these things that
you fill with electrons.

309
00:13:31,630 --> 00:13:33,450
How do you fill them?

310
00:13:33,450 --> 00:13:37,500
I keep blocking the screen,
but it's fun to go in there.

311
00:13:37,500 --> 00:13:39,660
It makes me feel
important maybe.

312
00:13:39,660 --> 00:13:40,500
I don't know.

313
00:13:40,500 --> 00:13:42,240
Never mind.

314
00:13:42,240 --> 00:13:45,070
How do you fill them?

315
00:13:45,070 --> 00:13:47,640
I'll use this.

316
00:13:47,640 --> 00:13:49,770
Oh, yeah.

317
00:13:49,770 --> 00:13:51,210
What do you do here?

318
00:13:51,210 --> 00:13:53,160
What's going on?

319
00:13:53,160 --> 00:13:56,250
I want to fill these orbitals.

320
00:13:56,250 --> 00:13:57,000
Do I fill this one

321
00:13:57,000 --> 00:13:58,542
AUDIENCE: You start
at the lowest end

322
00:13:58,542 --> 00:13:59,840
and work to the highest.

323
00:13:59,840 --> 00:14:03,380
JEFFREY C. GROSSMAN:
Yeah, and when do I stop?

324
00:14:03,380 --> 00:14:05,540
AUDIENCE: When you
run out of electrons.

325
00:14:05,540 --> 00:14:08,450
JEFFREY C. GROSSMAN: When
you run out of electrons.

326
00:14:08,450 --> 00:14:10,420
How many electrons did I have?

327
00:14:10,420 --> 00:14:12,920
AUDIENCE: 29.

328
00:14:12,920 --> 00:14:16,970
JEFFREY C. GROSSMAN: It depends
on the atom or molecule which

329
00:14:16,970 --> 00:14:18,690
is where we are now or solid.

330
00:14:22,880 --> 00:14:28,410
Now, that is really
in a way-- the reason

331
00:14:28,410 --> 00:14:32,430
I'm focusing on it is this
is the key quantum mechanical

332
00:14:32,430 --> 00:14:37,750
nature thingy,
property of materials,

333
00:14:37,750 --> 00:14:40,000
I want you to come away with
being able to understand

334
00:14:40,000 --> 00:14:41,720
and calculate in this class.

335
00:14:41,720 --> 00:14:42,220
OK?

336
00:14:42,220 --> 00:14:44,290
It's these energy levels.

337
00:14:44,290 --> 00:14:46,750
This is the most important
thing I want you to come away

338
00:14:46,750 --> 00:14:47,290
with from this class.

339
00:14:47,290 --> 00:14:47,890
Why?

340
00:14:47,890 --> 00:14:49,600
Well, we can calculate
other things,

341
00:14:49,600 --> 00:14:51,520
and I've talked about that.

342
00:14:51,520 --> 00:14:53,733
We can calculate energies.

343
00:14:53,733 --> 00:14:55,150
We can calculate
binding energies.

344
00:14:55,150 --> 00:14:57,970
We can calculate
all kinds of things,

345
00:14:57,970 --> 00:15:02,020
but these energy levels are
purely quantum mechanical.

346
00:15:02,020 --> 00:15:02,710
Right?

347
00:15:02,710 --> 00:15:06,160
There where those electrons
want to be in energy,

348
00:15:06,160 --> 00:15:08,990
and they matter so much to
the properties of materials.

349
00:15:08,990 --> 00:15:13,630
So I want to focus on
these and connect them

350
00:15:13,630 --> 00:15:15,610
to real exciting problems.

351
00:15:15,610 --> 00:15:16,330
OK?

352
00:15:16,330 --> 00:15:17,830
And make sure that
you understand

353
00:15:17,830 --> 00:15:22,030
where they come from and
also how to calculate them

354
00:15:22,030 --> 00:15:23,830
and what they can mean.

355
00:15:23,830 --> 00:15:25,160
So that's where we are.

356
00:15:25,160 --> 00:15:27,360
So that's why I keep
drawing things like this.

357
00:15:27,360 --> 00:15:29,350
You see me just drawing this.

358
00:15:29,350 --> 00:15:30,035
Right?

359
00:15:30,035 --> 00:15:30,910
Now, what did I draw?

360
00:15:30,910 --> 00:15:31,570
I don't know.

361
00:15:31,570 --> 00:15:33,700
I drew a bunch of levels.

362
00:15:33,700 --> 00:15:35,380
Right?

363
00:15:35,380 --> 00:15:43,230
If I'm a little more
careful, and I do this,

364
00:15:43,230 --> 00:15:44,550
now what am I drawing?

365
00:15:47,500 --> 00:15:48,130
What is that?

366
00:15:53,018 --> 00:15:54,060
AUDIENCE: Energy diagram.

367
00:15:54,060 --> 00:15:56,190
JEFFREY C. GROSSMAN:
Energy diagram.

368
00:15:56,190 --> 00:15:56,970
OK, good.

369
00:16:00,730 --> 00:16:03,310
What is it though?

370
00:16:03,310 --> 00:16:06,125
Do we know?

371
00:16:06,125 --> 00:16:08,000
AUDIENCE: Like there's
no electrons in there.

372
00:16:08,000 --> 00:16:09,540
JEFFREY C. GROSSMAN:
OK, and it's

373
00:16:09,540 --> 00:16:12,895
the solution to which problem?

374
00:16:12,895 --> 00:16:14,520
Actually, this is
infinite square well.

375
00:16:14,520 --> 00:16:16,970
So that's not the
hydrogen atom, but those

376
00:16:16,970 --> 00:16:19,580
are the energy levels
you get for the solution

377
00:16:19,580 --> 00:16:21,670
of the hydrogen atom.

378
00:16:21,670 --> 00:16:22,270
OK?

379
00:16:22,270 --> 00:16:25,120
Now, if I ask you what this
is though without putting

380
00:16:25,120 --> 00:16:31,210
any electrons down, we don't
know, but what if I do this?

381
00:16:31,210 --> 00:16:34,070
Now, what is it?

382
00:16:34,070 --> 00:16:37,046
Hydrogen, what about now?

383
00:16:37,046 --> 00:16:38,820
AUDIENCE: Lithium.

384
00:16:38,820 --> 00:16:42,930
JEFFREY C. GROSSMAN:
Lithium, what is this?

385
00:16:42,930 --> 00:16:43,980
Oh, I love this one.

386
00:16:43,980 --> 00:16:45,090
AUDIENCE: Carbon.

387
00:16:45,090 --> 00:16:48,000
JEFFREY C. GROSSMAN:
Carbon, carbon,

388
00:16:48,000 --> 00:16:52,030
it's a beautiful material.

389
00:16:52,030 --> 00:16:53,280
I love carbon.

390
00:16:53,280 --> 00:16:55,647
OK?

391
00:16:55,647 --> 00:16:57,480
I almost feel like you
need a little moment.

392
00:16:57,480 --> 00:16:59,446
When you draw the
energy levels of carbon,

393
00:16:59,446 --> 00:17:03,160
you need a little
moment of respect.

394
00:17:03,160 --> 00:17:06,089
Now, but you see,
this is what we did.

395
00:17:06,089 --> 00:17:08,880
We solved for these wiggles.

396
00:17:08,880 --> 00:17:13,170
We got energies, and
we put them in order

397
00:17:13,170 --> 00:17:14,589
from lowest to highest.

398
00:17:14,589 --> 00:17:16,547
And then we said how many
electrons do we have?

399
00:17:16,547 --> 00:17:18,030
Six, OK, fill them,
and then there

400
00:17:18,030 --> 00:17:20,322
are rules that we talked
about about how you fill them.

401
00:17:20,322 --> 00:17:21,990
Now, why am I
going through this?

402
00:17:21,990 --> 00:17:28,500
Well, because that is only
good for what kind of material?

403
00:17:28,500 --> 00:17:32,040
That is only a correct picture
for what kind of material?

404
00:17:40,560 --> 00:17:44,700
Atoms, that's an atomic picture.

405
00:17:44,700 --> 00:17:47,730
We solve for the atom, and
this is true-- and remember,

406
00:17:47,730 --> 00:17:49,880
I said that we can solve
for the hydrogen atom

407
00:17:49,880 --> 00:17:53,340
and see the whole
periodic table.

408
00:17:53,340 --> 00:17:54,030
Right?

409
00:17:54,030 --> 00:17:58,723
Powerful stuff, but
this is only an atom.

410
00:17:58,723 --> 00:18:01,140
These are how you would fill
the energy levels of an atom,

411
00:18:01,140 --> 00:18:02,390
and we've talked about this.

412
00:18:02,390 --> 00:18:06,270
But see now, we're going
onto other things, where

413
00:18:06,270 --> 00:18:09,010
you bring atoms together,
and you form molecules.

414
00:18:09,010 --> 00:18:10,320
This is not a chemistry class.

415
00:18:10,320 --> 00:18:14,160
So I'm not going to spend
a lot of time telling you

416
00:18:14,160 --> 00:18:19,470
about sigma orbitals, pi
orbitals, bonding orbitals,

417
00:18:19,470 --> 00:18:20,580
antibonding orbitals.

418
00:18:20,580 --> 00:18:24,160
That's not what
we're about, but I

419
00:18:24,160 --> 00:18:28,660
do need you to understand that,
when you bring atoms together,

420
00:18:28,660 --> 00:18:32,550
the orbitals from those
atoms come together

421
00:18:32,550 --> 00:18:34,590
and form new orbitals.

422
00:18:34,590 --> 00:18:36,810
They form molecular orbitals.

423
00:18:36,810 --> 00:18:37,920
OK?

424
00:18:37,920 --> 00:18:42,350
Now, in this case, you're
seeing the H2 molecule,

425
00:18:42,350 --> 00:18:43,680
and this is from this website.

426
00:18:43,680 --> 00:18:45,347
There's lots of great
websites that talk

427
00:18:45,347 --> 00:18:47,130
about molecular orbital theory.

428
00:18:47,130 --> 00:18:49,580
OK?

429
00:18:49,580 --> 00:18:52,760
And in this case, you
brought two s electrons

430
00:18:52,760 --> 00:18:56,390
together, see, from a hydrogen
atom over here and a hydrogen

431
00:18:56,390 --> 00:18:59,300
atom over there, and they
drew those energy levels.

432
00:18:59,300 --> 00:19:00,850
And then they brought
them together,

433
00:19:00,850 --> 00:19:03,410
and it turns out, when
you bring to 1s levels

434
00:19:03,410 --> 00:19:08,690
together to form a molecule,
you get two new levels.

435
00:19:08,690 --> 00:19:09,190
Right?

436
00:19:09,190 --> 00:19:13,990
And the chemists love names, and
so they gave this one a sigma

437
00:19:13,990 --> 00:19:16,420
1s, and that's a sigma star 1s.

438
00:19:16,420 --> 00:19:18,040
Those are just two
new levels that

439
00:19:18,040 --> 00:19:21,370
are formed, when you bring
these atomic levels together.

440
00:19:21,370 --> 00:19:30,800
Now, all the same rules-- and
one of them, ah, two points--

441
00:19:30,800 --> 00:19:34,400
one of them is a
bonding orbital.

442
00:19:34,400 --> 00:19:38,120
See, this actually looks like
I brought two circles together,

443
00:19:38,120 --> 00:19:39,380
and they overlapped.

444
00:19:39,380 --> 00:19:40,940
That's a bonding orbital.

445
00:19:40,940 --> 00:19:43,370
OK?

446
00:19:43,370 --> 00:19:48,880
Another one of them, though,
is an antibonding orbital.

447
00:19:48,880 --> 00:19:50,220
All right?

448
00:19:50,220 --> 00:19:53,050
And an antibonding orbital
is higher in energy.

449
00:19:53,050 --> 00:19:54,480
So it's going to come up higher.

450
00:19:54,480 --> 00:19:57,510
Its energy is going to be
higher than the bonding orbital,

451
00:19:57,510 --> 00:20:00,000
when you bring two
orbitals together.

452
00:20:00,000 --> 00:20:02,205
And often, an
antibonding orbital

453
00:20:02,205 --> 00:20:04,260
will actually have
a node, which means

454
00:20:04,260 --> 00:20:07,020
there's zero chance
of any electron being

455
00:20:07,020 --> 00:20:09,390
in between, exactly in between.

456
00:20:09,390 --> 00:20:13,050
That doesn't sound
very binding-y.

457
00:20:13,050 --> 00:20:14,210
Right?

458
00:20:14,210 --> 00:20:16,290
Doesn't have a lot of
appeal for bonding,

459
00:20:16,290 --> 00:20:23,400
if there's like a
plane of no existing.

460
00:20:23,400 --> 00:20:25,590
Now, why would that be possible?

461
00:20:25,590 --> 00:20:27,870
Doesn't it seem
from this picture--

462
00:20:27,870 --> 00:20:32,320
I took to 1s orbitals, and
I brought them together.

463
00:20:32,320 --> 00:20:32,820
Right?

464
00:20:32,820 --> 00:20:34,440
How can I get a
node between them?

465
00:20:37,709 --> 00:20:40,168
AUDIENCE: Is it [INAUDIBLE]

466
00:20:40,168 --> 00:20:41,460
JEFFREY C. GROSSMAN: Not quite.

467
00:20:41,460 --> 00:20:42,684
What is it?

468
00:20:42,684 --> 00:20:43,967
AUDIENCE: Coulomb repulsion.

469
00:20:43,967 --> 00:20:45,050
JEFFREY C. GROSSMAN: Yeah.

470
00:20:45,050 --> 00:20:47,500
It is actually.

471
00:20:47,500 --> 00:20:49,250
It does have to do
with Coulomb repulsion,

472
00:20:49,250 --> 00:20:53,400
but there's something
more basic here at play.

473
00:20:53,400 --> 00:20:55,920
How is it that I can
bring two spheres,

474
00:20:55,920 --> 00:20:57,900
probability spheres
like this together

475
00:20:57,900 --> 00:21:03,170
and have two orbitals
that form, one of which

476
00:21:03,170 --> 00:21:04,920
has a node in between,
and one of which is

477
00:21:04,920 --> 00:21:08,190
like really nicely happy bound.

478
00:21:08,190 --> 00:21:11,010
AUDIENCE: [INAUDIBLE]

479
00:21:11,010 --> 00:21:13,350
JEFFREY C. GROSSMAN:
Not quite, any other?

480
00:21:13,350 --> 00:21:14,268
Yeah?

481
00:21:14,268 --> 00:21:16,560
AUDIENCE: It looks like the
infinite square well there.

482
00:21:16,560 --> 00:21:18,852
You've got the ground state
that doesn't have any nodes

483
00:21:18,852 --> 00:21:21,690
and then the first excited
state does, the same deal.

484
00:21:21,690 --> 00:21:22,898
JEFFREY C. GROSSMAN: Exactly.

485
00:21:22,898 --> 00:21:25,330
Well, so that's exactly right.

486
00:21:25,330 --> 00:21:28,680
We're not bringing together
probability distributions.

487
00:21:28,680 --> 00:21:29,310
OK?

488
00:21:29,310 --> 00:21:31,143
That is not the right
way to think about it.

489
00:21:31,143 --> 00:21:33,010
I won't stand in front anymore.

490
00:21:33,010 --> 00:21:36,180
We're not bringing together
probability distributions.

491
00:21:36,180 --> 00:21:39,510
We're bringing together
wave functions,

492
00:21:39,510 --> 00:21:41,910
and then when those
come together,

493
00:21:41,910 --> 00:21:46,200
they form a probability
distribution or two,

494
00:21:46,200 --> 00:21:48,480
in the case I just showed you.

495
00:21:48,480 --> 00:21:51,180
And we all know that,
when waves come together,

496
00:21:51,180 --> 00:21:54,210
they can do what and what?

497
00:21:54,210 --> 00:21:56,190
AUDIENCE: Construct
and deconstruct.

498
00:21:56,190 --> 00:21:57,810
JEFFREY C. GROSSMAN: Exactly.

499
00:21:57,810 --> 00:22:03,515
They can construct, and they
can deconstruct one another.

500
00:22:03,515 --> 00:22:04,890
Sounds like they're
going to have

501
00:22:04,890 --> 00:22:09,030
like a philosophical discussion.

502
00:22:09,030 --> 00:22:10,650
So that's what's happening.

503
00:22:10,650 --> 00:22:14,160
We're bringing the
wave function together,

504
00:22:14,160 --> 00:22:16,500
when we bring atoms together
and molecules together.

505
00:22:16,500 --> 00:22:18,750
We're bringing
their size together.

506
00:22:18,750 --> 00:22:22,170
Oh, size, you can't get away
from size being so important,

507
00:22:22,170 --> 00:22:24,630
and we're solving for
the collective psi.

508
00:22:24,630 --> 00:22:28,740
And when you bring waves
together, they have phase,

509
00:22:28,740 --> 00:22:31,240
and they can form constructive
and destructive interference,

510
00:22:31,240 --> 00:22:33,660
as we talked about in
lectures one and two,

511
00:22:33,660 --> 00:22:35,320
and that's what's
happening here.

512
00:22:35,320 --> 00:22:38,950
And then you square those,
and you get new orbitals

513
00:22:38,950 --> 00:22:40,380
which have those properties.

514
00:22:40,380 --> 00:22:40,880
OK?

515
00:22:40,880 --> 00:22:44,820
So this is the simplest
example which is H2 molecule,

516
00:22:44,820 --> 00:22:47,400
and then we fill those orbitals.

517
00:22:47,400 --> 00:22:50,730
And when we fill these
orbitals, when we draw them

518
00:22:50,730 --> 00:22:54,390
for a molecule, very often,
I'll lose this notation,

519
00:22:54,390 --> 00:22:55,380
because there isn't--

520
00:22:55,380 --> 00:22:58,770
and I'm not going to go
through this notation,

521
00:22:58,770 --> 00:23:02,640
mostly because I can't
remember past sigma and pi.

522
00:23:02,640 --> 00:23:04,170
But there's a whole
lot of notation

523
00:23:04,170 --> 00:23:05,700
out there for
molecular orbitals,

524
00:23:05,700 --> 00:23:07,980
and it depends on the
symmetry and the group

525
00:23:07,980 --> 00:23:11,395
symmetry of the molecule
you're working with,

526
00:23:11,395 --> 00:23:13,020
and there are rules
and all that stuff.

527
00:23:13,020 --> 00:23:14,728
But all we're going
to need in this class

528
00:23:14,728 --> 00:23:17,880
is to know that, when
you have a molecule,

529
00:23:17,880 --> 00:23:22,810
and you calculate
this wave function

530
00:23:22,810 --> 00:23:24,630
which gives you the wiggles.

531
00:23:24,630 --> 00:23:27,030
And then you square it,
you get the distributions,

532
00:23:27,030 --> 00:23:28,758
and that helps set
the energy levels.

533
00:23:28,758 --> 00:23:31,050
It tells you where those
energy levels are going to be,

534
00:23:31,050 --> 00:23:32,508
that will just draw
them like this.

535
00:23:32,508 --> 00:23:35,250
Right?

536
00:23:35,250 --> 00:23:37,740
Now, this is how
I'll draw molecules,

537
00:23:37,740 --> 00:23:40,150
the energy levels of molecules,
and again this is it.

538
00:23:40,150 --> 00:23:42,600
This is one of the most
important properties

539
00:23:42,600 --> 00:23:45,850
I want to focus on,
because this is everything.

540
00:23:45,850 --> 00:23:49,860
This is where those electrons
are in energy space,

541
00:23:49,860 --> 00:23:51,420
and I can plot them.

542
00:23:51,420 --> 00:23:54,510
I can look at their energy,
and there's all kinds

543
00:23:54,510 --> 00:23:56,400
of important information here.

544
00:23:56,400 --> 00:23:57,810
OK?

545
00:23:57,810 --> 00:24:00,900
And so what this
means is usually I'll

546
00:24:00,900 --> 00:24:01,860
leave a space here.

547
00:24:01,860 --> 00:24:04,104
Does anybody know
what this is called?

548
00:24:04,104 --> 00:24:06,270
AUDIENCE: Gap.

549
00:24:06,270 --> 00:24:07,980
JEFFREY C. GROSSMAN: Right.

550
00:24:07,980 --> 00:24:12,610
This is the gap,
because that's how many

551
00:24:12,610 --> 00:24:15,310
electrons I had in my molecule.

552
00:24:15,310 --> 00:24:17,420
Not my atom, but in my molecule.

553
00:24:17,420 --> 00:24:18,430
So I do the same thing.

554
00:24:18,430 --> 00:24:23,050
I calculate energy levels,
I fill them up, and I stop.

555
00:24:23,050 --> 00:24:27,070
I apply some rules,
like you wouldn't

556
00:24:27,070 --> 00:24:34,120
have one level with two
electrons up, Pauli exclusion.

557
00:24:34,120 --> 00:24:34,620
Right?

558
00:24:38,090 --> 00:24:40,160
And then I stop,
and then there's

559
00:24:40,160 --> 00:24:41,720
another level beyond that.

560
00:24:41,720 --> 00:24:43,233
Oh, that's important.

561
00:24:43,233 --> 00:24:44,900
So we're going to
talk about that today.

562
00:24:44,900 --> 00:24:47,990
There's another level beyond
that that's not filled,

563
00:24:47,990 --> 00:24:50,600
but the distance in
energy between these

564
00:24:50,600 --> 00:24:53,060
is called the gap, and
it's really important.

565
00:24:53,060 --> 00:24:55,760
And the energy gap is
what determines all kinds

566
00:24:55,760 --> 00:24:58,440
of properties about a material.

567
00:24:58,440 --> 00:25:00,840
It determines how
it absorbs light.

568
00:25:00,840 --> 00:25:02,760
It determines how
it conducts charge.

569
00:25:06,330 --> 00:25:11,160
It can determine things about
its magnetic properties,

570
00:25:11,160 --> 00:25:13,290
certainly transport properties.

571
00:25:13,290 --> 00:25:15,378
And what's going to
happen, and that's

572
00:25:15,378 --> 00:25:16,920
why I really want
to make sure we all

573
00:25:16,920 --> 00:25:18,570
understand this for a molecule.

574
00:25:18,570 --> 00:25:20,730
What's going to happen
is, when we go to solids--

575
00:25:20,730 --> 00:25:22,438
on Thursday, we're
going to start talking

576
00:25:22,438 --> 00:25:23,910
about moving to solids--

577
00:25:23,910 --> 00:25:25,140
this is going to happen.

578
00:25:25,140 --> 00:25:27,360
These are no longer
simple lines.

579
00:25:27,360 --> 00:25:34,783
These go like this,
and that's really cool.

580
00:25:34,783 --> 00:25:36,450
That happens because
you're putting them

581
00:25:36,450 --> 00:25:38,010
in a periodic arrangement.

582
00:25:38,010 --> 00:25:40,430
That's called a band structure.

583
00:25:40,430 --> 00:25:41,970
It doesn't happen for molecules.

584
00:25:41,970 --> 00:25:44,320
They're just little flat
lines, like they are in atoms.

585
00:25:44,320 --> 00:25:45,900
OK?

586
00:25:45,900 --> 00:25:48,390
So are we all good with this?

587
00:25:48,390 --> 00:25:49,770
Are there questions?

588
00:25:49,770 --> 00:25:54,990
Energy levels,
energy levels, need

589
00:25:54,990 --> 00:25:57,670
to know about energy levels.

590
00:25:57,670 --> 00:25:58,760
No questions?

591
00:25:58,760 --> 00:26:00,520
Yeah?

592
00:26:00,520 --> 00:26:03,250
AUDIENCE: So when you
put up every central gas

593
00:26:03,250 --> 00:26:06,640
and you calculated
all the total energy,

594
00:26:06,640 --> 00:26:08,117
if you like have big molecules--

595
00:26:08,117 --> 00:26:09,200
JEFFREY C. GROSSMAN: Yeah.

596
00:26:09,200 --> 00:26:12,878
AUDIENCE: --you got huge gap and
it's harder to identify that.

597
00:26:12,878 --> 00:26:14,170
JEFFREY C. GROSSMAN: Which one?

598
00:26:14,170 --> 00:26:16,660
What's harder to identify?

599
00:26:16,660 --> 00:26:17,425
AUDIENCE: Ammonia.

600
00:26:17,425 --> 00:26:21,330
Because if you have one
more unit, for example--

601
00:26:21,330 --> 00:26:22,580
JEFFREY C. GROSSMAN: One more.

602
00:26:22,580 --> 00:26:25,160
AUDIENCE: --some group.

603
00:26:25,160 --> 00:26:26,180
JEFFREY C. GROSSMAN: OK.

604
00:26:26,180 --> 00:26:28,550
So you put an electron here?

605
00:26:28,550 --> 00:26:29,810
Or what do you mean?

606
00:26:29,810 --> 00:26:31,977
AUDIENCE: So when you
calculated the wave function--

607
00:26:31,977 --> 00:26:33,060
JEFFREY C. GROSSMAN: Yeah.

608
00:26:33,060 --> 00:26:35,580
AUDIENCE: --how did you know
the electron wave function

609
00:26:35,580 --> 00:26:37,700
for this type of ammonia?

610
00:26:37,700 --> 00:26:39,170
JEFFREY C. GROSSMAN:
Well, that's--

611
00:26:39,170 --> 00:26:39,670
Yeah.

612
00:26:39,670 --> 00:26:49,460
So that's where really
lecture three covers that.

613
00:26:49,460 --> 00:26:53,030
Where basically, you need
to use an approximation

614
00:26:53,030 --> 00:26:55,585
to the Schrodinger equation,
and that approximation

615
00:26:55,585 --> 00:26:56,960
that we're using
in this class is

616
00:26:56,960 --> 00:26:58,640
called density function theory.

617
00:26:58,640 --> 00:27:03,290
But then you simply what
goes into that equation

618
00:27:03,290 --> 00:27:05,870
is the approximations
you choose,

619
00:27:05,870 --> 00:27:10,340
and the positions of the atoms
and the number of electrons.

620
00:27:10,340 --> 00:27:12,940
And once you have
that, you basically

621
00:27:12,940 --> 00:27:13,940
are solving for the psi.

622
00:27:13,940 --> 00:27:16,980
You're solving for these.

623
00:27:16,980 --> 00:27:17,480
Right?

624
00:27:17,480 --> 00:27:20,440
And you get them and
their energies out,

625
00:27:20,440 --> 00:27:23,710
and it's in the outputs
of the nanoHUB runs.

626
00:27:23,710 --> 00:27:24,790
OK?

627
00:27:24,790 --> 00:27:28,870
Now, one last thing before
we go back to solar fuels

628
00:27:28,870 --> 00:27:31,660
that I want to make sure
we feel our oneness with

629
00:27:31,660 --> 00:27:33,220
are these basis functions.

630
00:27:33,220 --> 00:27:39,130
So this is a slide from another
lecture, an older lecture,

631
00:27:39,130 --> 00:27:41,800
but I just want to
be sure we understand

632
00:27:41,800 --> 00:27:42,770
what we're doing here.

633
00:27:42,770 --> 00:27:43,690
OK?

634
00:27:43,690 --> 00:27:53,480
So we said we needed to
make size for our materials.

635
00:27:53,480 --> 00:27:55,850
We need the code to give us psi.

636
00:27:55,850 --> 00:27:59,000
Now, for a hydrogen atom,
these are analytic functions.

637
00:27:59,000 --> 00:27:59,540
Right?

638
00:27:59,540 --> 00:28:04,130
They're like sines, cosines,
but for more complex material,

639
00:28:04,130 --> 00:28:08,180
a complex atom, they
can look like this.

640
00:28:08,180 --> 00:28:10,220
They can be really complicated.

641
00:28:10,220 --> 00:28:13,080
OK?

642
00:28:13,080 --> 00:28:15,900
So but a computer
can't just draw lines.

643
00:28:15,900 --> 00:28:16,890
Right?

644
00:28:16,890 --> 00:28:18,000
A computer can't do that.

645
00:28:18,000 --> 00:28:21,390
It needs to have some
mathematical representation

646
00:28:21,390 --> 00:28:25,890
for that function, and
that's what a basis set is.

647
00:28:25,890 --> 00:28:27,990
But as I stressed
last week, this

648
00:28:27,990 --> 00:28:36,000
is a new sort of not
a problem, but it's

649
00:28:36,000 --> 00:28:39,930
a parameter that is not present
in classical simulations.

650
00:28:39,930 --> 00:28:42,390
But it's one you have to
be very carefully aware of,

651
00:28:42,390 --> 00:28:45,460
and you have to know
when you've converted it.

652
00:28:45,460 --> 00:28:46,440
OK?

653
00:28:46,440 --> 00:28:49,800
And the question
came up last week

654
00:28:49,800 --> 00:28:52,865
of when is a basis
set converged?

655
00:28:52,865 --> 00:28:53,365
OK?

656
00:28:57,058 --> 00:28:57,850
And what do I mean?

657
00:28:57,850 --> 00:29:01,360
Well, I can make a
basis out of anything--

658
00:29:01,360 --> 00:29:06,130
Gaussians, exponents,
plane waves.

659
00:29:06,130 --> 00:29:09,950
I can make a basis
out of wavelets

660
00:29:09,950 --> 00:29:13,040
which are really interesting
hat-like functions.

661
00:29:13,040 --> 00:29:16,910
But I can take any function,
and if I add enough of them

662
00:29:16,910 --> 00:29:22,550
in the right places, and they
have the right width and size,

663
00:29:22,550 --> 00:29:25,190
I can recreate a curve.

664
00:29:25,190 --> 00:29:27,780
That's what we're
doing, but I want

665
00:29:27,780 --> 00:29:29,760
to have as few as possible.

666
00:29:29,760 --> 00:29:30,270
OK?

667
00:29:30,270 --> 00:29:34,290
So this is a basis set
study that somebody did

668
00:29:34,290 --> 00:29:38,610
and randomly put on the
web, which I randomly

669
00:29:38,610 --> 00:29:42,920
found and didn't credit,
which I should have.

670
00:29:42,920 --> 00:29:48,060
Anyway, this is the
number of basis functions

671
00:29:48,060 --> 00:29:51,360
going this way, number
of basis functions,

672
00:29:51,360 --> 00:29:53,380
and that's the energy.

673
00:29:53,380 --> 00:29:56,430
And you can see that the
energy is going to change,

674
00:29:56,430 --> 00:29:58,920
as you increase the
number of basis functions,

675
00:29:58,920 --> 00:30:02,020
and there's this thing
called the basis set limit.

676
00:30:02,020 --> 00:30:04,530
Sometimes it's called the
complete basis set limit,

677
00:30:04,530 --> 00:30:08,650
and that complete basis set
limit is basically just saying,

678
00:30:08,650 --> 00:30:10,470
hey, I've represented
my wave function

679
00:30:10,470 --> 00:30:13,170
now numerically correctly.

680
00:30:13,170 --> 00:30:17,070
So infinite number of basis
functions should give you that.

681
00:30:17,070 --> 00:30:18,705
We don't have
enough computer time

682
00:30:18,705 --> 00:30:20,580
to have that many basis
functions, because it

683
00:30:20,580 --> 00:30:22,230
gets really long and slow.

684
00:30:22,230 --> 00:30:24,260
So we don't do that.

685
00:30:24,260 --> 00:30:29,070
Usually, we do calculations out
here, and maybe we extrapolate.

686
00:30:29,070 --> 00:30:30,020
OK?

687
00:30:30,020 --> 00:30:33,300
Or we just do a few
cases, and we say,

688
00:30:33,300 --> 00:30:35,930
well, my results are converged.

689
00:30:35,930 --> 00:30:38,470
But when is a basis
set converged?

690
00:30:38,470 --> 00:30:42,600
It's a really important
point of quantum mechanical--

691
00:30:42,600 --> 00:30:44,640
hey, that would be like
a good quiz question.

692
00:30:44,640 --> 00:30:45,650
Right?

693
00:30:45,650 --> 00:30:47,580
Like it's a really
important part of quantum

694
00:30:47,580 --> 00:30:50,430
mechanical simulations are
always a quiz question.

695
00:30:50,430 --> 00:30:51,450
It's not a bad one.

696
00:30:54,120 --> 00:30:59,330
Is it converged here,
or is it converged here?

697
00:30:59,330 --> 00:31:01,695
You know what answer
I'm looking for.

698
00:31:01,695 --> 00:31:03,070
AUDIENCE: Depends
on the problem.

699
00:31:03,070 --> 00:31:05,410
JEFFREY C. GROSSMAN: It depends.

700
00:31:05,410 --> 00:31:07,930
I love that answer
for this class.

701
00:31:07,930 --> 00:31:12,780
It depends, because
here, I'm plotting

702
00:31:12,780 --> 00:31:16,890
the total energy of
the whole system,

703
00:31:16,890 --> 00:31:18,820
but is that what I want?

704
00:31:18,820 --> 00:31:21,060
Is that what I'm calculating?

705
00:31:21,060 --> 00:31:25,080
I don't know, maybe, but what if
I'm actually calculating this?

706
00:31:25,080 --> 00:31:27,840
What if I'm calculating the gap
between the highest occupied

707
00:31:27,840 --> 00:31:29,550
and lowest occupied level?

708
00:31:29,550 --> 00:31:33,060
Well then, I should plot
that versus the basis set,

709
00:31:33,060 --> 00:31:41,400
and that, this line, the total
energy may converge like this.

710
00:31:41,400 --> 00:31:45,540
Whereas, if I do the gap, it
kind of goes-- maybe it's here,

711
00:31:45,540 --> 00:31:47,250
and then I get
another value here,

712
00:31:47,250 --> 00:31:50,670
and then everything is fully
converged all the way in.

713
00:31:50,670 --> 00:31:53,185
So the gap value
converged there.

714
00:31:53,185 --> 00:31:53,810
You don't know.

715
00:31:53,810 --> 00:31:57,380
Different properties will
converge differently,

716
00:31:57,380 --> 00:31:58,880
and you start to
get a feel for it,

717
00:31:58,880 --> 00:32:00,840
as you do more calculations.

718
00:32:00,840 --> 00:32:03,500
I'm not expecting you to get
to that point in this class,

719
00:32:03,500 --> 00:32:04,950
but I want you to
understand this.

720
00:32:04,950 --> 00:32:06,300
It's really important.

721
00:32:06,300 --> 00:32:07,510
OK?

722
00:32:07,510 --> 00:32:10,210
So basis sets must be converged.

723
00:32:10,210 --> 00:32:11,470
That's one point.

724
00:32:11,470 --> 00:32:13,630
This can lead to big tables.

725
00:32:13,630 --> 00:32:15,850
Chemists love big tables.

726
00:32:15,850 --> 00:32:19,190
So it's actually a perfect fit.

727
00:32:19,190 --> 00:32:20,860
So you see papers like this.

728
00:32:20,860 --> 00:32:28,550
Oh, you can go to bse.pnl.gov,
and let's see, maybe I can just

729
00:32:28,550 --> 00:32:29,970
go there really quickly.

730
00:32:29,970 --> 00:32:32,230
And you can see,
oh, look at that.

731
00:32:32,230 --> 00:32:33,800
There's the nanoHUB.

732
00:32:33,800 --> 00:32:34,550
We're coming.

733
00:32:34,550 --> 00:32:38,000
We're coming, and look at this.

734
00:32:38,000 --> 00:32:39,230
Oh, this is beautiful.

735
00:32:39,230 --> 00:32:44,080
See, many basis sets have
been made over the years.

736
00:32:44,080 --> 00:32:44,580
Right?

737
00:32:48,340 --> 00:32:49,600
And so here, they are.

738
00:32:49,600 --> 00:32:52,300
Look at all these basis sets
for different-- and you see,

739
00:32:52,300 --> 00:32:53,530
I can scroll down here.

740
00:32:53,530 --> 00:32:54,580
Look at these basis sets.

741
00:32:54,580 --> 00:32:58,360
You have a few of these to
choose from in the nanoHUB,

742
00:32:58,360 --> 00:33:00,730
but look at how many there are.

743
00:33:00,730 --> 00:33:02,320
These are all
published basis sets,

744
00:33:02,320 --> 00:33:04,030
and you can go to
a place like this.

745
00:33:04,030 --> 00:33:09,880
And you can click on one, like
3-21G*, and you can click on--

746
00:33:09,880 --> 00:33:11,290
well, I don't think that--

747
00:33:11,290 --> 00:33:14,310
and you can say what
code am I going to use?

748
00:33:14,310 --> 00:33:15,130
Right?

749
00:33:15,130 --> 00:33:19,100
And then, you can say get the
basis sets, and there they are.

750
00:33:19,100 --> 00:33:22,150
And there are the papers,
where basically, they're

751
00:33:22,150 --> 00:33:26,530
trying to say what is the
fewest number of Gaussians

752
00:33:26,530 --> 00:33:31,230
that we can use to
represent these atoms?

753
00:33:31,230 --> 00:33:35,720
So basis sets are fit to
atomic orbital wave functions.

754
00:33:35,720 --> 00:33:37,910
OK?

755
00:33:37,910 --> 00:33:39,620
And this is just a
certain form, where

756
00:33:39,620 --> 00:33:42,470
you have the exponent
of the Gaussian

757
00:33:42,470 --> 00:33:45,110
and a coefficient
of the Gaussian.

758
00:33:45,110 --> 00:33:47,570
And I'm not going
to go into details,

759
00:33:47,570 --> 00:33:48,810
because we don't need them.

760
00:33:48,810 --> 00:33:49,310
OK?

761
00:33:52,370 --> 00:33:55,420
There's a lot of
work on basis sets.

762
00:33:55,420 --> 00:33:59,330
There's also a
lot of papers that

763
00:33:59,330 --> 00:34:03,800
were published in the 1970s
and also '80s using basis sets,

764
00:34:03,800 --> 00:34:08,120
like this, that show
really good answers using

765
00:34:08,120 --> 00:34:10,969
like Hartree-Fock theory or
density functional theory

766
00:34:10,969 --> 00:34:14,780
even but for the
completely wrong reason.

767
00:34:14,780 --> 00:34:17,960
Because they used a level of
theory that wasn't accurate

768
00:34:17,960 --> 00:34:20,480
and a basis set that
wasn't converged,

769
00:34:20,480 --> 00:34:23,030
because the computers couldn't
go to larger basis sets,

770
00:34:23,030 --> 00:34:25,280
and so the errors canceled.

771
00:34:25,280 --> 00:34:28,909
So there are many papers
with really nice agreement

772
00:34:28,909 --> 00:34:34,139
with experiment from theory
that are complete nonsense,

773
00:34:34,139 --> 00:34:39,080
because they're using very
inaccurate theory and really

774
00:34:39,080 --> 00:34:40,280
bad basis sets.

775
00:34:40,280 --> 00:34:45,050
And so the errors cancel, and
you get beautiful results.

776
00:34:45,050 --> 00:34:50,659
It's something that
we need to be aware of

777
00:34:50,659 --> 00:34:53,600
and understand in this
class, but we're not

778
00:34:53,600 --> 00:34:57,287
going to go into great detail in
all these different basis sets.

779
00:34:57,287 --> 00:34:59,120
But you can go there,
and there's just a lot

780
00:34:59,120 --> 00:34:59,995
of information there.

781
00:34:59,995 --> 00:35:03,170
And you can play around, and you
can make big tables like this.

782
00:35:03,170 --> 00:35:04,940
I don't recommend
that you do this.

783
00:35:04,940 --> 00:35:07,490
But this was a study, this
is like the kind of thing--

784
00:35:07,490 --> 00:35:13,620
I think that some people
really like big tables.

785
00:35:13,620 --> 00:35:16,460
This one goes on and
on and on, by the way.

786
00:35:16,460 --> 00:35:17,360
It never stops.

787
00:35:17,360 --> 00:35:20,790
It almost never stops.

788
00:35:20,790 --> 00:35:24,682
And you see, different
levels theory here.

789
00:35:24,682 --> 00:35:26,140
These ones we
haven't talked about.

790
00:35:26,140 --> 00:35:30,640
That's LDA, Hartree-Fock and
then different basis sets.

791
00:35:30,640 --> 00:35:31,270
You see?

792
00:35:31,270 --> 00:35:33,700
And some property,
the binding energy

793
00:35:33,700 --> 00:35:36,070
and some other properties
that they care about.

794
00:35:36,070 --> 00:35:37,990
OK?

795
00:35:37,990 --> 00:35:39,570
Yeah.

796
00:35:39,570 --> 00:35:41,370
Not expecting you
to do that, but I

797
00:35:41,370 --> 00:35:43,990
want you to be aware
of how big of a concern

798
00:35:43,990 --> 00:35:47,130
this is in quantum
mechanical calculations.

799
00:35:47,130 --> 00:35:50,850
Any questions about basis sets?

800
00:35:50,850 --> 00:35:52,410
Basis sets.

801
00:35:52,410 --> 00:36:00,270
The last theory
point, last question

802
00:36:00,270 --> 00:36:05,330
I want to ask, so we
asked, with basis sets,

803
00:36:05,330 --> 00:36:06,830
how do we know when
we're converged?

804
00:36:06,830 --> 00:36:09,650
Well, it depends.

805
00:36:09,650 --> 00:36:12,320
When you add more basis
functions or do a larger basis

806
00:36:12,320 --> 00:36:15,750
and things don't
change, your converged.

807
00:36:15,750 --> 00:36:17,250
But there's another
bigger question,

808
00:36:17,250 --> 00:36:20,640
which is how do we know when
the calculation is right,

809
00:36:20,640 --> 00:36:22,470
that we talked about here.

810
00:36:22,470 --> 00:36:24,840
Now, this is very
important, and it

811
00:36:24,840 --> 00:36:27,520
goes to the point I just made.

812
00:36:27,520 --> 00:36:29,650
Just because you
agree with experiment,

813
00:36:29,650 --> 00:36:31,990
if you're not doing your
calculations carefully,

814
00:36:31,990 --> 00:36:34,190
it can be still dangerous.

815
00:36:34,190 --> 00:36:34,810
OK?

816
00:36:34,810 --> 00:36:37,090
But let's suppose that you
have done your calculations

817
00:36:37,090 --> 00:36:40,540
carefully, and you have
converged your basis set.

818
00:36:40,540 --> 00:36:45,220
And you have checked everything
else about your code,

819
00:36:45,220 --> 00:36:47,020
and you're asking
the question of which

820
00:36:47,020 --> 00:36:48,850
of these structures of carbon--

821
00:36:48,850 --> 00:36:51,330
remember, I really like carbon.

822
00:36:51,330 --> 00:36:54,280
Which of these three
structures-- a ring,

823
00:36:54,280 --> 00:36:56,800
a kind of bowl, or a cage--

824
00:36:56,800 --> 00:37:01,520
gives you-- is most
stable for 20 atoms?

825
00:37:01,520 --> 00:37:03,560
That's a pretty simple question.

826
00:37:03,560 --> 00:37:04,850
Right?

827
00:37:04,850 --> 00:37:08,900
This is the question I asked
as a second-year grad student,

828
00:37:08,900 --> 00:37:11,570
a few years ago now.

829
00:37:11,570 --> 00:37:12,210
Who laughed?

830
00:37:12,210 --> 00:37:12,710
Sam?

831
00:37:16,220 --> 00:37:18,290
And it was really
cool, because see,

832
00:37:18,290 --> 00:37:19,880
you could try one
level of theory

833
00:37:19,880 --> 00:37:22,280
and work really hard to
converge it completely.

834
00:37:22,280 --> 00:37:24,680
And you'd get, for
example with LDA--

835
00:37:24,680 --> 00:37:26,540
something you can
do on the nanoHUB--

836
00:37:26,540 --> 00:37:30,870
you would get that the cage,
this guy, is the lowest energy.

837
00:37:30,870 --> 00:37:33,320
This means the most stable.

838
00:37:33,320 --> 00:37:36,440
And then you would do another
level of theory, Hartree-Fock

839
00:37:36,440 --> 00:37:38,780
or this other thing
that you also have,

840
00:37:38,780 --> 00:37:40,580
this is called the GGA.

841
00:37:40,580 --> 00:37:43,100
It's another flavor of
density function theory,

842
00:37:43,100 --> 00:37:44,990
and you would get
exactly the opposite.

843
00:37:44,990 --> 00:37:47,510
You would get that the
ring is the most stable,

844
00:37:47,510 --> 00:37:49,040
and the cage is
the least stable.

845
00:37:49,040 --> 00:37:54,710
So what's going on?

846
00:37:54,710 --> 00:37:56,420
What's going on?

847
00:37:56,420 --> 00:37:59,840
Two different DFT
functionals gave me

848
00:37:59,840 --> 00:38:03,324
completely different answers,
and I've converged everything.

849
00:38:06,868 --> 00:38:08,160
AUDIENCE: Two more functionals.

850
00:38:08,160 --> 00:38:10,980
JEFFREY C. GROSSMAN:
Two more functionals.

851
00:38:10,980 --> 00:38:13,560
Now, that's actually
a really good idea,

852
00:38:13,560 --> 00:38:16,020
and it's actually
what people do.

853
00:38:16,020 --> 00:38:17,880
OK?

854
00:38:17,880 --> 00:38:21,010
In fact, you see, if you go to--

855
00:38:21,010 --> 00:38:23,890
I think I left
this web page open.

856
00:38:23,890 --> 00:38:26,290
Here's one of the
codes that does

857
00:38:26,290 --> 00:38:28,690
density functional theory
and other quantum chemistry

858
00:38:28,690 --> 00:38:29,300
calculations.

859
00:38:29,300 --> 00:38:30,175
It's called Gaussian.

860
00:38:32,800 --> 00:38:36,802
And if you look in
their 2009 version,

861
00:38:36,802 --> 00:38:38,260
this is a code you
have to pay for.

862
00:38:38,260 --> 00:38:41,560
There's lots of codes
that are free, by the way.

863
00:38:41,560 --> 00:38:45,430
NWChem, if anybody wants to
play with a code, download it,

864
00:38:45,430 --> 00:38:47,140
that does quantum
chemistry, that's

865
00:38:47,140 --> 00:38:52,150
a pretty darn good one that's
free which you can download,

866
00:38:52,150 --> 00:38:53,080
and there are others.

867
00:38:53,080 --> 00:38:56,320
I'm happy to provide a list.

868
00:38:56,320 --> 00:39:00,790
But look at the
number of functionals

869
00:39:00,790 --> 00:39:02,240
you have to choose from.

870
00:39:02,240 --> 00:39:02,830
OK?

871
00:39:02,830 --> 00:39:04,663
Here's a little bit
about density functional

872
00:39:04,663 --> 00:39:08,230
theory and the methods, and
then here are the functionals.

873
00:39:08,230 --> 00:39:09,880
exchange functionals.

874
00:39:09,880 --> 00:39:15,970
You see S, XA, B, PW, G96, PBE.

875
00:39:15,970 --> 00:39:18,220
That's one of the
ones on the nanoHUB.

876
00:39:18,220 --> 00:39:19,060
Right?

877
00:39:19,060 --> 00:39:24,632
And correlation functionals,
VWN, LYP, B95, and so

878
00:39:24,632 --> 00:39:26,590
what you wind up getting--
and then it goes on,

879
00:39:26,590 --> 00:39:30,580
standalone functionals,
hybrid functionals.

880
00:39:30,580 --> 00:39:31,120
OK?

881
00:39:31,120 --> 00:39:31,840
Here's some more.

882
00:39:34,610 --> 00:39:38,890
User defined functionals, you
can actually make up your own.

883
00:39:38,890 --> 00:39:39,550
Right?

884
00:39:39,550 --> 00:39:43,360
So here's a short list
of some of the keywords

885
00:39:43,360 --> 00:39:46,960
you can enter and get
different functionals out.

886
00:39:46,960 --> 00:39:49,620
So now, what do I do?

887
00:39:49,620 --> 00:39:50,930
AUDIENCE: All of them.

888
00:39:50,930 --> 00:39:52,610
JEFFREY C. GROSSMAN:
All of them.

889
00:39:52,610 --> 00:40:00,070
Well, sadly, I think
some researchers do that.

890
00:40:03,120 --> 00:40:06,160
So here's the broader point.

891
00:40:06,160 --> 00:40:07,290
OK?

892
00:40:07,290 --> 00:40:10,980
Density functional theory is
an approximation in the way

893
00:40:10,980 --> 00:40:13,910
that we use it in our codes.

894
00:40:13,910 --> 00:40:17,760
The actual theory
itself could be exact,

895
00:40:17,760 --> 00:40:20,910
but the way that it
has to be implemented

896
00:40:20,910 --> 00:40:23,730
requires this
approximate functional,

897
00:40:23,730 --> 00:40:26,160
as you learned in lecture three.

898
00:40:26,160 --> 00:40:27,960
OK?

899
00:40:27,960 --> 00:40:30,600
What functional do I use?

900
00:40:30,600 --> 00:40:34,170
Well, some of these
have been well tested

901
00:40:34,170 --> 00:40:36,060
for broad classes
of materials and are

902
00:40:36,060 --> 00:40:39,210
known to do well for certain
properties, certain materials,

903
00:40:39,210 --> 00:40:41,910
and known to do not
as well for others,

904
00:40:41,910 --> 00:40:45,120
but it's mostly empirical in
terms of our understanding.

905
00:40:45,120 --> 00:40:47,640
It's because it's been
tried for many systems.

906
00:40:47,640 --> 00:40:48,270
OK?

907
00:40:48,270 --> 00:40:52,320
And so in a way,
we're a little bit

908
00:40:52,320 --> 00:40:55,420
back to the classical world.

909
00:40:55,420 --> 00:40:58,810
In the sense that
density functional theory

910
00:40:58,810 --> 00:41:01,700
is a beautiful theory,
but to make it practical,

911
00:41:01,700 --> 00:41:04,060
you have to make
approximations that make it

912
00:41:04,060 --> 00:41:07,570
so that you have almost
an empirical nature to it,

913
00:41:07,570 --> 00:41:10,600
or a semi-empirical
nature which is what you

914
00:41:10,600 --> 00:41:12,220
have in classical force fields.

915
00:41:12,220 --> 00:41:13,020
Right?

916
00:41:13,020 --> 00:41:15,460
In classical force
fields, the potential

917
00:41:15,460 --> 00:41:22,000
is as good as the
complexity of the potential

918
00:41:22,000 --> 00:41:24,650
and what you fit it to.

919
00:41:24,650 --> 00:41:26,780
Right?

920
00:41:26,780 --> 00:41:30,350
Density function theory is,
I think, much more powerful,

921
00:41:30,350 --> 00:41:32,340
in the sense that
you can really solve

922
00:41:32,340 --> 00:41:34,190
for the electronic
structure, but we

923
00:41:34,190 --> 00:41:38,170
have the same kind of problem
in density functional theory.

924
00:41:38,170 --> 00:41:40,860
So the functionals that I've
given you on the nanoHUB

925
00:41:40,860 --> 00:41:44,730
are some of the
most popular ones,

926
00:41:44,730 --> 00:41:47,610
but you always
need to be aware--

927
00:41:47,610 --> 00:41:52,910
[NON-ENGLISH]---- of the fact that
we're making an approximation.

928
00:41:52,910 --> 00:41:57,280
And yes, one way to check
is to try two functionals,

929
00:41:57,280 --> 00:42:01,480
and if they don't disagree
too much, you may be OK.

930
00:42:01,480 --> 00:42:05,580
That's not the most
gratifying way to do it.

931
00:42:05,580 --> 00:42:07,967
Another way would be to
compare with experiment,

932
00:42:07,967 --> 00:42:09,800
and that's actually the
most gratifying way.

933
00:42:09,800 --> 00:42:11,480
Once you converge
everything else,

934
00:42:11,480 --> 00:42:14,870
if you're functional
agrees with experiment

935
00:42:14,870 --> 00:42:16,580
for the kind of
problem you're trying

936
00:42:16,580 --> 00:42:20,120
to solve, then that's a pretty
good indication that it's

937
00:42:20,120 --> 00:42:23,750
an accurate solution to
the Schrodinger equation,

938
00:42:23,750 --> 00:42:26,270
but you are making
a approximations.

939
00:42:26,270 --> 00:42:28,150
OK?

940
00:42:28,150 --> 00:42:32,890
And that is something
that we won't--

941
00:42:32,890 --> 00:42:35,500
as you can see, I don't
give you much options

942
00:42:35,500 --> 00:42:38,530
on the nanoHUB, because I
don't really want to go there,

943
00:42:38,530 --> 00:42:40,280
but I do want you
to be aware of this.

944
00:42:40,280 --> 00:42:42,430
We are not solving
quantum mechanics exactly.

945
00:42:42,430 --> 00:42:46,390
We cannot, and with
density functional theory,

946
00:42:46,390 --> 00:42:48,930
there are some systems.

947
00:42:48,930 --> 00:42:53,320
So in my graduate days,
I worked on a method

948
00:42:53,320 --> 00:42:55,690
that goes beyond density
functional theory inaccuracy.

949
00:42:55,690 --> 00:42:59,810
So it's a very accurate method,
very slow but very accurate.

950
00:42:59,810 --> 00:43:01,720
And so I was
purposefully looking

951
00:43:01,720 --> 00:43:07,720
for systems where DFT fails, and
I was very happy with this one,

952
00:43:07,720 --> 00:43:09,520
where you basically
don't know the answer.

953
00:43:09,520 --> 00:43:10,978
You can try
functionals, and you'll

954
00:43:10,978 --> 00:43:14,060
get all kinds of
different results.

955
00:43:14,060 --> 00:43:16,060
So the only thing you
can do in that case

956
00:43:16,060 --> 00:43:18,350
is go to a higher
accuracy method.

957
00:43:18,350 --> 00:43:18,850
OK?

958
00:43:21,370 --> 00:43:23,980
What I found out is
that this method here

959
00:43:23,980 --> 00:43:27,340
is the most accurate one, that
actually none of the functions

960
00:43:27,340 --> 00:43:29,810
were right, and the bowl
was the most stable.

961
00:43:29,810 --> 00:43:32,830
So it's pretty cool.

962
00:43:32,830 --> 00:43:34,330
It was exciting.

963
00:43:34,330 --> 00:43:37,070
What can I say?

964
00:43:37,070 --> 00:43:39,320
I was a physicist at
the time, so you know.

965
00:43:42,370 --> 00:43:44,040
I won't say anything more.

966
00:43:44,040 --> 00:43:44,540
OK.

967
00:43:44,540 --> 00:43:48,520
Now, let's go back to our
first application example.

968
00:43:53,180 --> 00:43:56,120
Does everybody remember
this from last week?

969
00:43:56,120 --> 00:43:56,810
OK.

970
00:43:56,810 --> 00:44:01,190
So let me make sure we know why.

971
00:44:01,190 --> 00:44:03,505
OK.

972
00:44:03,505 --> 00:44:04,880
I want to make
sure we understand

973
00:44:04,880 --> 00:44:09,920
why this is such an important
problem for quantum mechanics.

974
00:44:09,920 --> 00:44:10,550
OK?

975
00:44:10,550 --> 00:44:16,740
So sun shines on a molecule,
the molecule changes shape,

976
00:44:16,740 --> 00:44:21,190
and that changed shape
is a higher energy.

977
00:44:21,190 --> 00:44:25,080
So if you draw the
reaction, if you

978
00:44:25,080 --> 00:44:31,960
draw the reaction
coordinate for this system,

979
00:44:31,960 --> 00:44:33,370
It looks like this.

980
00:44:33,370 --> 00:44:33,870
OK?

981
00:44:33,870 --> 00:44:37,060
So that would be the trans
state and the cis state,

982
00:44:37,060 --> 00:44:40,350
and this is the higher
energy that that forms,

983
00:44:40,350 --> 00:44:43,020
and it stores that much
energy in the molecule.

984
00:44:43,020 --> 00:44:45,960
OK?

985
00:44:45,960 --> 00:44:48,300
Now, what we found
is that there's

986
00:44:48,300 --> 00:44:50,100
all these molecules
that do this,

987
00:44:50,100 --> 00:44:51,760
but they're not very
good solar fuels.

988
00:44:51,760 --> 00:44:52,260
OK?

989
00:44:52,260 --> 00:44:54,930
So there's lots of
them that do this trans

990
00:44:54,930 --> 00:44:57,990
to cis photoisomerization.

991
00:44:57,990 --> 00:45:01,680
So the sun makes it go, or light
makes it go, from one state

992
00:45:01,680 --> 00:45:02,550
to another.

993
00:45:02,550 --> 00:45:05,020
None of them are good
solar fuels on their own,

994
00:45:05,020 --> 00:45:11,713
but we found this way of making
them in general into good ones.

995
00:45:11,713 --> 00:45:13,380
And this is a slide
I skipped last week,

996
00:45:13,380 --> 00:45:17,670
so I want to just very
quickly explain this again.

997
00:45:17,670 --> 00:45:21,600
Because it's really
important to understand why

998
00:45:21,600 --> 00:45:23,080
we're so excited about this.

999
00:45:23,080 --> 00:45:25,740
If you put these molecules
that switch back and forth

1000
00:45:25,740 --> 00:45:30,150
onto a template, and the
template can be anything,

1001
00:45:30,150 --> 00:45:31,470
but here it's a nanotube.

1002
00:45:31,470 --> 00:45:34,080
But if you put them onto it,
and you covalently bind them--

1003
00:45:34,080 --> 00:45:36,210
that means you attach
them really strongly,

1004
00:45:36,210 --> 00:45:37,770
so they're not
going to come off.

1005
00:45:37,770 --> 00:45:40,950
Then, what you've done is
you've packed them in a way

1006
00:45:40,950 --> 00:45:43,200
that they're not
able to get out of.

1007
00:45:43,200 --> 00:45:46,800
So you've packed them
together, and they're not

1008
00:45:46,800 --> 00:45:49,830
allowed to get out, because
they're covalently bound.

1009
00:45:49,830 --> 00:45:53,970
Some self-assembly
work is weakly bound.

1010
00:45:53,970 --> 00:45:55,200
Some is not.

1011
00:45:55,200 --> 00:45:56,920
Here, it's really
strongly bound.

1012
00:45:56,920 --> 00:45:59,310
So they're really forced
into this packing.

1013
00:45:59,310 --> 00:46:00,610
Now, what does that mean?

1014
00:46:00,610 --> 00:46:02,140
Well, look up here for a minute.

1015
00:46:02,140 --> 00:46:05,580
It's a little busy,
but look at that cyan

1016
00:46:05,580 --> 00:46:08,540
curve, the light blue.

1017
00:46:08,540 --> 00:46:11,750
This is the spacing that they're
packing on on this template.

1018
00:46:11,750 --> 00:46:14,610
This is it, 4.2 angstroms.

1019
00:46:14,610 --> 00:46:15,620
OK?

1020
00:46:15,620 --> 00:46:20,120
And that's also exactly the
minimum of that molecule,

1021
00:46:20,120 --> 00:46:22,790
when it's in the T state, here.

1022
00:46:22,790 --> 00:46:26,950
When it's in the T state,
it's happy at that spacing.

1023
00:46:26,950 --> 00:46:29,020
It's happiest.

1024
00:46:29,020 --> 00:46:29,560
Right?

1025
00:46:29,560 --> 00:46:31,330
But when it's in
the cis state, you

1026
00:46:31,330 --> 00:46:34,510
see the cis state has
a different spacing

1027
00:46:34,510 --> 00:46:35,470
that it wants to be at.

1028
00:46:35,470 --> 00:46:36,700
That's the red curve.

1029
00:46:36,700 --> 00:46:37,350
Right?

1030
00:46:37,350 --> 00:46:38,725
These are the
kinds of curves you

1031
00:46:38,725 --> 00:46:43,060
should be getting in your
homework for problem two.

1032
00:46:43,060 --> 00:46:44,810
That's the curve
for the cis state,

1033
00:46:44,810 --> 00:46:47,650
and you can see that it's a
happy place is much further

1034
00:46:47,650 --> 00:46:49,990
out, but it can't
be much further out.

1035
00:46:49,990 --> 00:46:52,850
It does not have that
flexibility anymore.

1036
00:46:52,850 --> 00:46:55,240
So you've constrained
it to always

1037
00:46:55,240 --> 00:47:00,570
be in the trans, happy place,
in terms of its spacing.

1038
00:47:00,570 --> 00:47:03,690
Now, what that means is that,
you can see right away, what

1039
00:47:03,690 --> 00:47:06,920
that means is that, when
it's in the cis state,

1040
00:47:06,920 --> 00:47:09,120
the energy of the cis state
is going to be higher.

1041
00:47:09,120 --> 00:47:12,740
So already, what you've done is
you've made this state go up,

1042
00:47:12,740 --> 00:47:15,750
because you've sterically
inhibited it just

1043
00:47:15,750 --> 00:47:20,070
by forcing it to be this
close and never further apart.

1044
00:47:20,070 --> 00:47:25,720
In the gas phase or in solution,
when it goes back and forth

1045
00:47:25,720 --> 00:47:26,740
between trans and cis.

1046
00:47:26,740 --> 00:47:28,660
It's always going to
find its happy place.

1047
00:47:28,660 --> 00:47:32,230
They're not going to worry
about this, but here they can't.

1048
00:47:32,230 --> 00:47:36,640
But as I mentioned last week,
much more importantly even,

1049
00:47:36,640 --> 00:47:41,200
when you're in this highly
confined geometry, this highly

1050
00:47:41,200 --> 00:47:44,350
constrained rigid packing,
what you can do now

1051
00:47:44,350 --> 00:47:47,480
is you can play
chemistry between them.

1052
00:47:47,480 --> 00:47:50,530
So I can actually
create functional groups

1053
00:47:50,530 --> 00:47:54,190
on these molecules that
bond them to each other

1054
00:47:54,190 --> 00:47:57,190
and to themselves
in different ways,

1055
00:47:57,190 --> 00:48:00,160
depending on whether they're
in the cis or the trans state.

1056
00:48:00,160 --> 00:48:00,910
OK?

1057
00:48:00,910 --> 00:48:03,430
And what that does
is that allows me

1058
00:48:03,430 --> 00:48:09,170
to lower this and lower this.

1059
00:48:09,170 --> 00:48:10,290
That's the key.

1060
00:48:10,290 --> 00:48:11,210
OK?

1061
00:48:11,210 --> 00:48:13,880
So now, because the
key is, remember,

1062
00:48:13,880 --> 00:48:26,300
goal is to increase
this and this barrier.

1063
00:48:26,300 --> 00:48:32,067
Going back, we want to be
able to tune it separately.

1064
00:48:36,180 --> 00:48:40,250
And you can see that, if you
just look at this reaction

1065
00:48:40,250 --> 00:48:42,390
coordinate, if I
increase delta H,

1066
00:48:42,390 --> 00:48:44,900
it looks like I'm going
to probably decrease

1067
00:48:44,900 --> 00:48:47,450
the activation barrier
which is not a good thing.

1068
00:48:47,450 --> 00:48:50,600
Because that's related to the
stability of the fuel, when

1069
00:48:50,600 --> 00:48:52,830
it's charged, the lifetime.

1070
00:48:52,830 --> 00:48:54,620
These molecules
on their own last

1071
00:48:54,620 --> 00:48:56,930
in the charged state
for a few minutes.

1072
00:48:56,930 --> 00:48:57,992
That's not very useful.

1073
00:48:57,992 --> 00:49:00,200
So what we'd like to do is
to be able to change both,

1074
00:49:00,200 --> 00:49:02,360
and this trick
allows us to do that.

1075
00:49:02,360 --> 00:49:04,970
We push this up from
steric inhibition,

1076
00:49:04,970 --> 00:49:07,260
but we pull it back
down from reactions.

1077
00:49:07,260 --> 00:49:11,470
We pull this, from interactions,
we pull this down even more,

1078
00:49:11,470 --> 00:49:13,570
because we can customize
the interactions that

1079
00:49:13,570 --> 00:49:16,640
happen between these molecules
and within the molecule.

1080
00:49:16,640 --> 00:49:17,770
So that's the key.

1081
00:49:17,770 --> 00:49:21,150
That's the magic sauce.

1082
00:49:21,150 --> 00:49:21,650
Right?

1083
00:49:24,700 --> 00:49:27,800
Now, all that is fine,
except that, as I--

1084
00:49:27,800 --> 00:49:28,300
OK.

1085
00:49:28,300 --> 00:49:30,070
So we have this new
class of materials

1086
00:49:30,070 --> 00:49:31,150
we're very excited about.

1087
00:49:31,150 --> 00:49:32,650
We're making them in the lab.

1088
00:49:32,650 --> 00:49:34,690
We're designing
them on a computer.

1089
00:49:34,690 --> 00:49:37,870
They're going to save the
world, or maybe they'll

1090
00:49:37,870 --> 00:49:42,670
just de-ice windows, but
anyway, that's very exciting.

1091
00:49:42,670 --> 00:49:52,250
Now, all of that can be done
using classical force fields.

1092
00:49:52,250 --> 00:49:54,620
You can calculate
delta H. You could

1093
00:49:54,620 --> 00:49:59,983
try to get a good model of
potentials for these molecules.

1094
00:49:59,983 --> 00:50:01,650
You could maybe try
different potentials

1095
00:50:01,650 --> 00:50:04,170
and see when it agrees with
experiment and all that

1096
00:50:04,170 --> 00:50:08,100
and try to explore this phase
space using classical force

1097
00:50:08,100 --> 00:50:09,060
fields.

1098
00:50:09,060 --> 00:50:10,050
That is accessible.

1099
00:50:10,050 --> 00:50:15,030
You may not-- gesundheit--
you may not be accurate.

1100
00:50:15,030 --> 00:50:16,860
You may have some
worries about validating

1101
00:50:16,860 --> 00:50:18,000
the potentials and
all that, but you

1102
00:50:18,000 --> 00:50:19,860
can do this with
classical force fields.

1103
00:50:19,860 --> 00:50:22,920
You can get energies as a
function of these twists

1104
00:50:22,920 --> 00:50:26,070
in the bonds and try to
engineer it this way,

1105
00:50:26,070 --> 00:50:29,370
but you cannot talk about
the optical properties.

1106
00:50:29,370 --> 00:50:32,530
You cannot do that using
classical potentials.

1107
00:50:32,530 --> 00:50:36,300
You need the electrons, and this
goes back to our energy levels.

1108
00:50:36,300 --> 00:50:36,940
OK?

1109
00:50:36,940 --> 00:50:43,640
So now, it will come
in to play here.

1110
00:50:43,640 --> 00:50:47,290
We're going to go
back to energy levels.

1111
00:50:47,290 --> 00:50:49,570
You see, I can make
a really dense energy

1112
00:50:49,570 --> 00:50:53,790
fuel, a really highly
energy dense fuel,

1113
00:50:53,790 --> 00:50:56,640
but if it doesn't absorb
the sunlight efficiently,

1114
00:50:56,640 --> 00:50:59,010
then I can never charge it.

1115
00:50:59,010 --> 00:51:00,420
Right?

1116
00:51:00,420 --> 00:51:02,220
So that's a critical
part of this.

1117
00:51:02,220 --> 00:51:06,330
If it doesn't absorb sunlight
well, it's useless to me.

1118
00:51:06,330 --> 00:51:07,380
OK?

1119
00:51:07,380 --> 00:51:11,460
Now, so this is the thing
that we've been talking about,

1120
00:51:11,460 --> 00:51:16,140
but that part can be looked at
with potentials, if you wanted.

1121
00:51:16,140 --> 00:51:18,750
This part here, where you
absorb the light, cannot.

1122
00:51:18,750 --> 00:51:21,090
So here's the light that
comes down to Earth.

1123
00:51:21,090 --> 00:51:21,600
Right?

1124
00:51:21,600 --> 00:51:22,475
We talked about this.

1125
00:51:22,475 --> 00:51:25,290
That's the solar flux.

1126
00:51:25,290 --> 00:51:30,685
And the key point here is that--

1127
00:51:30,685 --> 00:51:32,620
I keep that?

1128
00:51:32,620 --> 00:51:34,285
We don't need that anymore.

1129
00:51:34,285 --> 00:51:39,520
The key point here is that those
molecules have energy levels,

1130
00:51:39,520 --> 00:51:43,510
like this and like this,
and they have a gap.

1131
00:51:46,930 --> 00:51:47,530
Right?

1132
00:51:47,530 --> 00:51:55,390
These are what we call occupied,
and these are unoccupied.

1133
00:51:55,390 --> 00:51:58,180
Unoccupied levels,
occupied levels,

1134
00:51:58,180 --> 00:52:01,090
I just don't want
to draw the arrows,

1135
00:52:01,090 --> 00:52:03,070
and that's the energy gap.

1136
00:52:03,070 --> 00:52:06,310
Now, why does the energy
gap matter with respect

1137
00:52:06,310 --> 00:52:07,090
to this picture?

1138
00:52:12,590 --> 00:52:14,510
Yeah?

1139
00:52:14,510 --> 00:52:15,540
At the same time--

1140
00:52:15,540 --> 00:52:17,930
one, two, no.

1141
00:52:17,930 --> 00:52:19,070
Go ahead.

1142
00:52:19,070 --> 00:52:20,570
AUDIENCE: Because
all the absorption

1143
00:52:20,570 --> 00:52:23,435
are at certain frequencies--
or certain light

1144
00:52:23,435 --> 00:52:26,765
coming in at frequencies
with great enough energy that

1145
00:52:26,765 --> 00:52:28,408
surpass the energy gap.

1146
00:52:28,408 --> 00:52:29,450
JEFFREY C. GROSSMAN: Why?

1147
00:52:29,450 --> 00:52:30,242
That's really good.

1148
00:52:30,242 --> 00:52:31,547
That's exactly right.

1149
00:52:31,547 --> 00:52:32,630
AUDIENCE: So it's too low.

1150
00:52:32,630 --> 00:52:34,463
It's not enough
energy to shut it off

1151
00:52:34,463 --> 00:52:35,630
from occupied to unoccupied.

1152
00:52:35,630 --> 00:52:36,520
JEFFREY C. GROSSMAN: Yeah.

1153
00:52:36,520 --> 00:52:37,460
AUDIENCE: I mean,
too low of energy.

1154
00:52:37,460 --> 00:52:39,502
JEFFREY C. GROSSMAN: Too
low of an energy, right?

1155
00:52:39,502 --> 00:52:41,120
So this is energy going--

1156
00:52:41,120 --> 00:52:43,350
this is wavelength
going that way.

1157
00:52:43,350 --> 00:52:45,060
So energy goes this way.

1158
00:52:45,060 --> 00:52:46,600
OK?

1159
00:52:46,600 --> 00:52:49,020
Right?

1160
00:52:49,020 --> 00:52:58,980
So there is going to be some
minimum energy below which

1161
00:52:58,980 --> 00:53:00,540
you can no longer absorb light.

1162
00:53:00,540 --> 00:53:03,000
The molecule is transparent.

1163
00:53:03,000 --> 00:53:05,310
That is the energy gap.

1164
00:53:05,310 --> 00:53:07,770
That's this energy gap here.

1165
00:53:07,770 --> 00:53:10,200
Any energy that that
molecule receives

1166
00:53:10,200 --> 00:53:12,550
that's from those photons--

1167
00:53:12,550 --> 00:53:14,130
and this is the energy.

1168
00:53:14,130 --> 00:53:17,010
Wavelength, as we know
same, as the energy.

1169
00:53:17,010 --> 00:53:21,180
Any photons it receives
from the sun that's less

1170
00:53:21,180 --> 00:53:23,220
than this just go right past.

1171
00:53:23,220 --> 00:53:24,300
They cannot get absorbed.

1172
00:53:26,890 --> 00:53:29,200
If I don't absorb a
photon, I don't do this.

1173
00:53:29,200 --> 00:53:30,710
I don't switch.

1174
00:53:30,710 --> 00:53:31,210
OK?

1175
00:53:31,210 --> 00:53:33,820
So this is important.

1176
00:53:33,820 --> 00:53:37,060
Now, the question
is what do I want?

1177
00:53:37,060 --> 00:53:41,740
Well, do I want the material to
have a very high gap or a very

1178
00:53:41,740 --> 00:53:43,350
low gap?

1179
00:53:43,350 --> 00:53:46,160
Out here would be a
very low energy gap,

1180
00:53:46,160 --> 00:53:48,500
and over here, it would
be a very high energy gap.

1181
00:53:48,500 --> 00:53:51,480
What do you guys
think I want here?

1182
00:53:51,480 --> 00:53:54,930
How would I get-- and I'm
going to collect energy only

1183
00:53:54,930 --> 00:53:56,040
above the gap.

1184
00:53:56,040 --> 00:53:58,470
So if my energy
gap is here, it's

1185
00:53:58,470 --> 00:54:01,110
only going to be this part
of the sun I can collect.

1186
00:54:01,110 --> 00:54:04,960
So where do you think
I want my gap to be?

1187
00:54:04,960 --> 00:54:07,060
Over here?

1188
00:54:07,060 --> 00:54:09,650
That's definitely
what you would think.

1189
00:54:09,650 --> 00:54:12,880
Why not just make this
material have almost no gap?

1190
00:54:12,880 --> 00:54:13,420
Right?

1191
00:54:13,420 --> 00:54:21,230
If it had almost no gap, then
if this were the gap, then

1192
00:54:21,230 --> 00:54:27,790
any little bit of sunlight
would excite electrons up,

1193
00:54:27,790 --> 00:54:30,010
and you'd absorbed the photon.

1194
00:54:30,010 --> 00:54:33,073
Why is that not a
good solar fuel?

1195
00:54:33,073 --> 00:54:34,198
AUDIENCE: They fall easily.

1196
00:54:34,198 --> 00:54:35,698
JEFFREY C. GROSSMAN:
Say that again.

1197
00:54:35,698 --> 00:54:37,240
AUDIENCE: They fall
back down easily.

1198
00:54:37,240 --> 00:54:39,865
JEFFREY C. GROSSMAN: Well, they
certainly could fall back down,

1199
00:54:39,865 --> 00:54:42,110
and actually usually, they'd
be absorbed say up here,

1200
00:54:42,110 --> 00:54:44,780
and they'd usually trickle
down to here anyway

1201
00:54:44,780 --> 00:54:46,370
to the LUMO state.

1202
00:54:46,370 --> 00:54:49,190
That's called thermalization.

1203
00:54:49,190 --> 00:54:51,860
They could also fall back
down to the homo state

1204
00:54:51,860 --> 00:54:52,940
and re-emit a photon.

1205
00:54:52,940 --> 00:54:56,120
That's absolutely right,
but there's another reason.

1206
00:54:58,958 --> 00:55:00,380
AUDIENCE: Lower energy density.

1207
00:55:00,380 --> 00:55:00,620
JEFFREY C. GROSSMAN: Yeah.

1208
00:55:00,620 --> 00:55:01,120
Why?

1209
00:55:04,890 --> 00:55:07,770
AUDIENCE: There's a band
gap in the partial delta H.

1210
00:55:07,770 --> 00:55:09,040
JEFFREY C. GROSSMAN: Yeah.

1211
00:55:09,040 --> 00:55:09,540
That's it.

1212
00:55:09,540 --> 00:55:14,600
So what are we doing
in storage materials?

1213
00:55:14,600 --> 00:55:17,640
What are we doing with
electrons in batteries,

1214
00:55:17,640 --> 00:55:20,460
in solar thermal fuels?

1215
00:55:20,460 --> 00:55:22,405
What are we doing
with those electrons?

1216
00:55:22,405 --> 00:55:24,452
AUDIENCE: Storing them.

1217
00:55:24,452 --> 00:55:26,160
JEFFREY C. GROSSMAN:
We are storing them.

1218
00:55:26,160 --> 00:55:32,245
Yes, but what are we
doing to make them--

1219
00:55:32,245 --> 00:55:33,870
what are we doing
when we convert them?

1220
00:55:33,870 --> 00:55:35,682
Maybe I should say it that way.

1221
00:55:35,682 --> 00:55:37,140
Same thing happens
in a solar cell.

1222
00:55:37,140 --> 00:55:38,640
I'm doing something
to these electrons.

1223
00:55:38,640 --> 00:55:39,990
AUDIENCE: Putting
them on a shelf.

1224
00:55:39,990 --> 00:55:41,073
JEFFREY C. GROSSMAN: Yeah.

1225
00:55:41,073 --> 00:55:42,720
You know I love that analogy.

1226
00:55:42,720 --> 00:55:44,010
Yeah?

1227
00:55:44,010 --> 00:55:45,660
It's like pumping hydro.

1228
00:55:45,660 --> 00:55:48,030
Hydro pumping is one of
the best technologies

1229
00:55:48,030 --> 00:55:50,460
we know of to store energy.

1230
00:55:50,460 --> 00:55:53,910
It's even creating a little
stir here in the third row,

1231
00:55:53,910 --> 00:55:56,593
because he has read
the reports, and he

1232
00:55:56,593 --> 00:55:58,260
knows that there are
certain areas where

1233
00:55:58,260 --> 00:56:00,300
that's the only
game in town, pumped

1234
00:56:00,300 --> 00:56:03,840
hydro, a beautiful technology.

1235
00:56:03,840 --> 00:56:04,830
It works.

1236
00:56:04,830 --> 00:56:06,540
You pump water up a hill.

1237
00:56:06,540 --> 00:56:08,400
When you got too much
energy, and you let

1238
00:56:08,400 --> 00:56:10,050
it roll back down
when you need it.

1239
00:56:10,050 --> 00:56:10,680
Right?

1240
00:56:10,680 --> 00:56:12,870
Now, that's all we're
doing with electrons.

1241
00:56:12,870 --> 00:56:13,410
That's it.

1242
00:56:13,410 --> 00:56:14,910
It's the same exact thing.

1243
00:56:14,910 --> 00:56:17,360
We're pumping
electrons up a hill.

1244
00:56:17,360 --> 00:56:19,340
We're using light to do it here.

1245
00:56:19,340 --> 00:56:21,530
For a battery, when you
plug your electric car

1246
00:56:21,530 --> 00:56:26,180
in, you're using current
and electrons, potential,

1247
00:56:26,180 --> 00:56:30,515
voltage to do it, but you're
driving electrons up the hill.

1248
00:56:30,515 --> 00:56:32,390
And then you're trying
to keep them up there,

1249
00:56:32,390 --> 00:56:34,748
and then let them come
back when you need them,

1250
00:56:34,748 --> 00:56:36,290
when you need them
to release energy.

1251
00:56:36,290 --> 00:56:38,260
OK?

1252
00:56:38,260 --> 00:56:40,600
Now, if my gap is
really low, you

1253
00:56:40,600 --> 00:56:44,410
see, the hill, it's never
going to get to the top.

1254
00:56:44,410 --> 00:56:47,060
Here's my hill.

1255
00:56:47,060 --> 00:56:49,220
OK?

1256
00:56:49,220 --> 00:56:52,340
If my gap is only
this much in energy,

1257
00:56:52,340 --> 00:56:54,410
then I'm just going
to roll around here,

1258
00:56:54,410 --> 00:56:57,750
and I'm never going to
get any amount of storage.

1259
00:56:57,750 --> 00:56:58,250
Right?

1260
00:56:58,250 --> 00:57:02,870
So you want this to be
as large as possible,

1261
00:57:02,870 --> 00:57:06,370
because that's how
much energy you store.

1262
00:57:06,370 --> 00:57:09,580
But the gap can't be
any smaller than this,

1263
00:57:09,580 --> 00:57:12,310
or you're not going to give
those electrons enough energy

1264
00:57:12,310 --> 00:57:15,250
to get up the hill to go there,
so the material can go there.

1265
00:57:15,250 --> 00:57:16,350
Yeah?

1266
00:57:16,350 --> 00:57:18,790
AUDIENCE: So let's see
you have some material

1267
00:57:18,790 --> 00:57:22,870
with some small
gap, and you just

1268
00:57:22,870 --> 00:57:27,490
have it exposed to sunlight
and then compare it

1269
00:57:27,490 --> 00:57:29,950
with some material
with a large gap.

1270
00:57:29,950 --> 00:57:33,400
Wouldn't they both on average
collect the same number

1271
00:57:33,400 --> 00:57:35,300
of high-energy photons anyway?

1272
00:57:35,300 --> 00:57:36,485
JEFFREY C. GROSSMAN: Yes.

1273
00:57:36,485 --> 00:57:38,110
AUDIENCE: So with
the low-gap material,

1274
00:57:38,110 --> 00:57:41,260
you'd get some with height
that collect higher--

1275
00:57:41,260 --> 00:57:42,760
JEFFREY C. GROSSMAN:
Great question.

1276
00:57:42,760 --> 00:57:45,490
AUDIENCE: High energy
photons, and then they

1277
00:57:45,490 --> 00:57:47,920
have some excited state.

1278
00:57:47,920 --> 00:57:49,593
And then the ones
with the high gap

1279
00:57:49,593 --> 00:57:51,010
will also have
that excited state,

1280
00:57:51,010 --> 00:57:52,330
but the ones with
the low gap will also

1281
00:57:52,330 --> 00:57:53,530
have these lower,
excited states.

1282
00:57:53,530 --> 00:57:54,280
JEFFREY C. GROSSMAN: Yes.

1283
00:57:54,280 --> 00:57:54,580
Yes.

1284
00:57:54,580 --> 00:57:55,240
AUDIENCE: On top of that?

1285
00:57:55,240 --> 00:57:56,220
JEFFREY C. GROSSMAN:
It's a great question,

1286
00:57:56,220 --> 00:57:59,020
and what you're talking
about is such a cool idea

1287
00:57:59,020 --> 00:58:01,690
in solar PV called hot carrier.

1288
00:58:01,690 --> 00:58:04,120
What you'd like to do is get
those excited, really high

1289
00:58:04,120 --> 00:58:07,860
energy electrons
out in solar cells,

1290
00:58:07,860 --> 00:58:10,740
before they come back down.

1291
00:58:10,740 --> 00:58:15,360
In this case, they
come back down.

1292
00:58:15,360 --> 00:58:18,420
See in this case,
they thermalize,

1293
00:58:18,420 --> 00:58:21,000
and the reaction happens in
the lowest excited state.

1294
00:58:24,230 --> 00:58:25,700
But it also happens
in solar cells,

1295
00:58:25,700 --> 00:58:27,825
because there are no hot
carrier solar cells today.

1296
00:58:27,825 --> 00:58:28,850
It's a great theory.

1297
00:58:28,850 --> 00:58:30,390
It's a great idea.

1298
00:58:30,390 --> 00:58:33,408
So this is the idea, and
there's a lot of active research

1299
00:58:33,408 --> 00:58:33,950
in this area.

1300
00:58:36,800 --> 00:58:39,420
And it's basically the
idea of multijunction cells

1301
00:58:39,420 --> 00:58:42,170
which are cells that work, and
in fact, the highest efficiency

1302
00:58:42,170 --> 00:58:44,570
solar cells to date
are multijunction,

1303
00:58:44,570 --> 00:58:46,200
triple-junction solar cells.

1304
00:58:46,200 --> 00:58:49,550
Where basically, you have
different band gaps together,

1305
00:58:49,550 --> 00:58:51,950
and those different band
gaps do exactly what you say.

1306
00:58:51,950 --> 00:58:52,460
OK?

1307
00:58:52,460 --> 00:58:55,670
They let you take some
electrons out here,

1308
00:58:55,670 --> 00:58:58,460
and then you have another
material with a higher gap,

1309
00:58:58,460 --> 00:59:00,110
and you can take them out here.

1310
00:59:00,110 --> 00:59:01,880
And then you have
another material

1311
00:59:01,880 --> 00:59:04,910
with an even higher gap, and
you can take those electrons out

1312
00:59:04,910 --> 00:59:05,870
there.

1313
00:59:05,870 --> 00:59:06,560
OK?

1314
00:59:06,560 --> 00:59:08,990
And see because
otherwise, what happens?

1315
00:59:08,990 --> 00:59:12,110
Otherwise, all the electrons
will-- in each case--

1316
00:59:12,110 --> 00:59:14,630
all the electrons
cascade down to here.

1317
00:59:14,630 --> 00:59:17,630
They all wind up in that
conduction band or that LUMO

1318
00:59:17,630 --> 00:59:19,130
state, if it's a molecule.

1319
00:59:19,130 --> 00:59:23,240
No matter what, that's just
the dramatic and traumatic loss

1320
00:59:23,240 --> 00:59:26,280
of solar materials.

1321
00:59:26,280 --> 00:59:27,120
Right?

1322
00:59:27,120 --> 00:59:31,320
Solar conversion, solar capture,
those electrons thermalize,

1323
00:59:31,320 --> 00:59:33,720
because that process
of thermalization

1324
00:59:33,720 --> 00:59:37,650
is so fast, that it's
very hard to beat.

1325
00:59:37,650 --> 00:59:40,110
The way you beat it in
multijunction solar cells--

1326
00:59:40,110 --> 00:59:44,250
42% maybe is the record,
something like that.

1327
00:59:44,250 --> 00:59:48,150
The way you beat it
is you literally just

1328
00:59:48,150 --> 00:59:50,040
stick a level in there.

1329
00:59:50,040 --> 00:59:52,200
So it's sort of a
cheat, but that's

1330
00:59:52,200 --> 00:59:55,200
the only way to do it that we
know technologically today.

1331
00:59:55,200 --> 00:59:57,870
If there were other ways
of extracting electrons out

1332
00:59:57,870 --> 01:00:00,540
at their higher energies,
you could do wonders

1333
01:00:00,540 --> 01:00:02,910
in solar capture and storage.

1334
01:00:02,910 --> 01:00:07,800
In the molecule, the
electron thermalizes down,

1335
01:00:07,800 --> 01:00:10,690
and the reaction goes in
that lowest excited state.

1336
01:00:10,690 --> 01:00:14,460
So that gap has to be
bigger than delta H. OK?

1337
01:00:14,460 --> 01:00:17,347
Does everybody see that?

1338
01:00:17,347 --> 01:00:18,430
It's a very good question.

1339
01:00:21,830 --> 01:00:23,770
So it's this
beautiful, constrained

1340
01:00:23,770 --> 01:00:25,000
optimization problem.

1341
01:00:25,000 --> 01:00:27,940
I love those, because
constrained optimization

1342
01:00:27,940 --> 01:00:30,040
problems, I want this
to be really big,

1343
01:00:30,040 --> 01:00:33,280
but I want this to stay not
less than an electron volt.

1344
01:00:33,280 --> 01:00:35,170
But then if this
is really big, I

1345
01:00:35,170 --> 01:00:37,070
can't absorb any of the light.

1346
01:00:37,070 --> 01:00:37,570
Right?

1347
01:00:37,570 --> 01:00:42,260
If I made delta H
huge, then I'd have

1348
01:00:42,260 --> 01:00:44,660
to have a gap that
was like here,

1349
01:00:44,660 --> 01:00:47,430
and I'd get almost
no solar efficiency.

1350
01:00:47,430 --> 01:00:49,850
These are beautiful problems
for materials design

1351
01:00:49,850 --> 01:00:53,480
and for computation,
because they're constrained,

1352
01:00:53,480 --> 01:00:54,980
but they're not
that constrained.

1353
01:00:54,980 --> 01:00:58,070
And using computers,
you can get your way out

1354
01:00:58,070 --> 01:00:59,870
of that, those
constraints, sometimes.

1355
01:00:59,870 --> 01:01:01,220
OK?

1356
01:01:01,220 --> 01:01:03,170
And that's what's, I
think, really exciting.

1357
01:01:03,170 --> 01:01:05,930
That's what your homework
is going to be about, and so

1358
01:01:05,930 --> 01:01:07,190
let's calculate one of these.

1359
01:01:07,190 --> 01:01:07,690
OK?

1360
01:01:07,690 --> 01:01:15,180
Because that is the key
to the optical efficiency.

1361
01:01:15,180 --> 01:01:16,140
Yeah?

1362
01:01:16,140 --> 01:01:20,506
AUDIENCE: So is the gas thinner
than the just delta H or delta

1363
01:01:20,506 --> 01:01:23,362
H plus the base?

1364
01:01:23,362 --> 01:01:25,733
JEFFREY C. GROSSMAN: That's
a very good question, and--

1365
01:01:25,733 --> 01:01:26,900
AUDIENCE: He told me to ask.

1366
01:01:26,900 --> 01:01:27,290
JEFFREY C. GROSSMAN: Yeah.

1367
01:01:27,290 --> 01:01:27,790
Yeah.

1368
01:01:27,790 --> 01:01:29,810
It's a very good question.

1369
01:01:29,810 --> 01:01:33,230
So in general,
most of these kinds

1370
01:01:33,230 --> 01:01:34,760
of photoactive molecules--

1371
01:01:34,760 --> 01:01:39,410
I've already talked to a
chemist, so I'm well armed.

1372
01:01:39,410 --> 01:01:43,260
Most of these
photoactive molecules

1373
01:01:43,260 --> 01:01:45,180
need the gap plus the
activation barrier,

1374
01:01:45,180 --> 01:01:50,040
because in the excited state,
you'll get a similar barrier.

1375
01:01:50,040 --> 01:01:52,110
It's not clear that's
always true though,

1376
01:01:52,110 --> 01:01:56,240
and so that puts more
constraints on this.

1377
01:01:56,240 --> 01:01:58,700
So it's even less of the
spectrum you can absorb,

1378
01:01:58,700 --> 01:01:59,210
basically.

1379
01:01:59,210 --> 01:01:59,960
Right?

1380
01:01:59,960 --> 01:02:01,910
If you want to store
1 1/2 electron volts,

1381
01:02:01,910 --> 01:02:04,280
and you need an electron volt
of an activation barrier,

1382
01:02:04,280 --> 01:02:07,220
that's a 2 1/2 v-gap minimum.

1383
01:02:07,220 --> 01:02:10,550
Which means you're closing
in on the UV, which

1384
01:02:10,550 --> 01:02:14,540
means your optical efficiency
is probably at most 5%, 8%, 10%,

1385
01:02:14,540 --> 01:02:15,650
at most.

1386
01:02:15,650 --> 01:02:16,220
Right?

1387
01:02:16,220 --> 01:02:19,170
That doesn't mean it's
a deal breaker at all.

1388
01:02:19,170 --> 01:02:21,622
But there are also
cases where you

1389
01:02:21,622 --> 01:02:23,455
do change the barrier
in the exciting state,

1390
01:02:23,455 --> 01:02:26,580
and so we're looking into that.

1391
01:02:26,580 --> 01:02:30,380
Now, I want another concept
here to come across which

1392
01:02:30,380 --> 01:02:31,580
is really important.

1393
01:02:31,580 --> 01:02:32,300
OK?

1394
01:02:32,300 --> 01:02:38,000
And that is nothing more than
these levels smoothed out,

1395
01:02:38,000 --> 01:02:40,320
and it's called the
density of states.

1396
01:02:40,320 --> 01:02:42,100
OK?

1397
01:02:42,100 --> 01:02:49,140
So if you do a calculation
of one of these molecules--

1398
01:02:49,140 --> 01:02:51,690
let me go back to here.

1399
01:02:51,690 --> 01:02:54,600
Oh, yeah.

1400
01:02:54,600 --> 01:02:55,990
You know we love this.

1401
01:02:55,990 --> 01:02:59,670
Have you all rated this
say a 10 out of 10?

1402
01:02:59,670 --> 01:03:02,450
Come on.

1403
01:03:02,450 --> 01:03:06,320
You know it's a 10 experience.

1404
01:03:06,320 --> 01:03:08,350
AUDIENCE: Someone gave it a 9.5?

1405
01:03:08,350 --> 01:03:09,350
JEFFREY C. GROSSMAN: No.

1406
01:03:09,350 --> 01:03:10,300
That's an average.

1407
01:03:10,300 --> 01:03:11,830
OK.

1408
01:03:11,830 --> 01:03:13,623
I want to start using--

1409
01:03:13,623 --> 01:03:16,040
we're going to use a different
tool for our next homework.

1410
01:03:16,040 --> 01:03:18,310
We're going to use DFT
for solids, surfaces,

1411
01:03:18,310 --> 01:03:19,210
and molecules.

1412
01:03:19,210 --> 01:03:20,110
It's called SIESTA.

1413
01:03:20,110 --> 01:03:24,520
It's another free software
that you can download.

1414
01:03:24,520 --> 01:03:26,740
And it's solving
the same equations,

1415
01:03:26,740 --> 01:03:29,950
but it uses different
approximations, different basis

1416
01:03:29,950 --> 01:03:31,050
sets, and so forth.

1417
01:03:31,050 --> 01:03:31,780
OK?

1418
01:03:31,780 --> 01:03:33,888
But here, and you
see that basis sets

1419
01:03:33,888 --> 01:03:35,680
are called different
things, but I've still

1420
01:03:35,680 --> 01:03:39,670
tried to help by saying really
bad, mediocre, and OK, in terms

1421
01:03:39,670 --> 01:03:40,840
of the quality.

1422
01:03:40,840 --> 01:03:42,520
OK?

1423
01:03:42,520 --> 01:03:46,030
Again, that's not the
focus in this class.

1424
01:03:46,030 --> 01:03:48,710
Let's look at it, and we're
going to do a molecule here--

1425
01:03:48,710 --> 01:03:50,410
Uh-oh, there we go--

1426
01:03:50,410 --> 01:03:52,030
a molecule.

1427
01:03:52,030 --> 01:03:56,080
And I'm going to upload one,
and you're going to get these.

1428
01:03:56,080 --> 01:03:58,037
We'll give these
with the homeworks.

1429
01:03:58,037 --> 01:03:59,120
We'll put them on Steller.

1430
01:03:59,120 --> 01:04:01,600
So here's a trans state.

1431
01:04:01,600 --> 01:04:03,810
Let's do the phenyl.

1432
01:04:03,810 --> 01:04:04,890
Here's a trans state.

1433
01:04:04,890 --> 01:04:08,010
We're going to upload
it and simulate.

1434
01:04:08,010 --> 01:04:08,620
OK?

1435
01:04:08,620 --> 01:04:11,310
And this is doing just
what the other code does.

1436
01:04:11,310 --> 01:04:14,490
It's doing this self-consistent
cycle, where it's

1437
01:04:14,490 --> 01:04:16,300
solving for the wave function.

1438
01:04:16,300 --> 01:04:17,922
OK?

1439
01:04:17,922 --> 01:04:19,380
And it's getting
the wave functions

1440
01:04:19,380 --> 01:04:24,280
of all these levels for the
molecule I just entered.

1441
01:04:24,280 --> 01:04:26,490
So it's going to give
me all these levels.

1442
01:04:26,490 --> 01:04:28,170
That's what I want.

1443
01:04:28,170 --> 01:04:31,950
Now, the way this plots
it though is in something

1444
01:04:31,950 --> 01:04:33,570
called the density
of states, and all

1445
01:04:33,570 --> 01:04:36,870
that is, as we'll see in a
minute, is you take these,

1446
01:04:36,870 --> 01:04:39,240
and you turn it on the side.

1447
01:04:39,240 --> 01:04:39,960
OK?

1448
01:04:39,960 --> 01:04:42,750
So let's take a look.

1449
01:04:42,750 --> 01:04:44,040
Is it done?

1450
01:04:44,040 --> 01:04:45,990
Yes.

1451
01:04:45,990 --> 01:04:46,670
There it is.

1452
01:04:46,670 --> 01:04:48,510
Oh, this is a
beautiful solar fuel.

1453
01:04:48,510 --> 01:04:52,140
It's actually got two
photo-switchable molecules

1454
01:04:52,140 --> 01:04:53,820
hanging off the same
azobenzene ring.

1455
01:04:57,560 --> 01:05:00,690
But anyway, and this--

1456
01:05:00,690 --> 01:05:02,760
where is the-- there we go.

1457
01:05:02,760 --> 01:05:03,330
OK.

1458
01:05:03,330 --> 01:05:07,380
So the key outputs, so
it tells you some things,

1459
01:05:07,380 --> 01:05:09,690
and then you can go
to Density of States,

1460
01:05:09,690 --> 01:05:16,070
and this is a very
important property.

1461
01:05:16,070 --> 01:05:16,850
OK?

1462
01:05:16,850 --> 01:05:21,930
This is the way that we like
to look at energy levels,

1463
01:05:21,930 --> 01:05:23,962
especially in solids.

1464
01:05:23,962 --> 01:05:25,670
So we're going to be
looking at DOS plots

1465
01:05:25,670 --> 01:05:27,030
when we get to solids.

1466
01:05:27,030 --> 01:05:27,770
OK?

1467
01:05:27,770 --> 01:05:30,050
But in molecules, you
can look at the DOS plot

1468
01:05:30,050 --> 01:05:32,660
as well, and
basically, what it is

1469
01:05:32,660 --> 01:05:35,000
it's just these levels
turned on their side.

1470
01:05:35,000 --> 01:05:38,780
So if there's a bunch of
levels near each other,

1471
01:05:38,780 --> 01:05:43,490
you'll get a higher
peak in the DOS.

1472
01:05:43,490 --> 01:05:46,910
You want to think about
it as averaging over

1473
01:05:46,910 --> 01:05:51,910
the likelihood of finding
states at these energies.

1474
01:05:51,910 --> 01:05:53,860
Has anybody seen a DOS plot?

1475
01:05:53,860 --> 01:05:56,890
How many of you have seen a
DOS plot, a density of states?

1476
01:05:56,890 --> 01:05:58,130
One or two?

1477
01:05:58,130 --> 01:05:58,780
That's OK.

1478
01:05:58,780 --> 01:06:01,730
They're energy levels
turned on their side.

1479
01:06:01,730 --> 01:06:02,380
Right?

1480
01:06:02,380 --> 01:06:06,388
Now, when we do solids,
it gets really fun.

1481
01:06:06,388 --> 01:06:07,930
It gets really fun
when we do solids,

1482
01:06:07,930 --> 01:06:09,555
because when we do
solids, like I said,

1483
01:06:09,555 --> 01:06:13,415
these things go like this in
a space yet to be determined.

1484
01:06:13,415 --> 01:06:15,040
And then you turn
those on their sides,

1485
01:06:15,040 --> 01:06:17,740
and you still get the
same kind of DOS plot.

1486
01:06:17,740 --> 01:06:21,455
But for molecules, this is
what it would look like.

1487
01:06:21,455 --> 01:06:23,080
So there's a little
smoothing going on,

1488
01:06:23,080 --> 01:06:25,480
but you're also
representing how many states

1489
01:06:25,480 --> 01:06:26,720
you have near these energies.

1490
01:06:26,720 --> 01:06:28,720
So that's why it's called
the density of states.

1491
01:06:28,720 --> 01:06:31,420
Right?

1492
01:06:31,420 --> 01:06:33,280
Gesundheit.

1493
01:06:33,280 --> 01:06:35,980
Does everybody see that
this is that energy gap?

1494
01:06:35,980 --> 01:06:37,090
This is it.

1495
01:06:37,090 --> 01:06:38,860
That's the energy
gap, but there's

1496
01:06:38,860 --> 01:06:40,280
more in the density of states.

1497
01:06:40,280 --> 01:06:40,780
OK?

1498
01:06:40,780 --> 01:06:42,850
So the energy gap, now I can--

1499
01:06:42,850 --> 01:06:45,820
watch this-- I can go
back, and I can magically

1500
01:06:45,820 --> 01:06:53,650
put on some functional groups
and go to the amino benzene

1501
01:06:53,650 --> 01:07:00,300
case, and I can do
that simulation.

1502
01:07:03,600 --> 01:07:06,060
How many people really want
to hear about hydrogen storage

1503
01:07:06,060 --> 01:07:07,740
or don't care?

1504
01:07:07,740 --> 01:07:08,880
Be honest.

1505
01:07:08,880 --> 01:07:11,920
Really want to hear
about hydrogen storage?

1506
01:07:11,920 --> 01:07:12,730
In the back.

1507
01:07:16,210 --> 01:07:19,420
Because I really want to make
this point, because also,

1508
01:07:19,420 --> 01:07:21,400
this will be the basis
of your homework.

1509
01:07:21,400 --> 01:07:25,340
But I can also take the
first 10 minutes of Thursday

1510
01:07:25,340 --> 01:07:27,257
and talk about hydrogen storage.

1511
01:07:27,257 --> 01:07:29,840
Hydrogen storage, nobody cares
about hydrogen storage anymore,

1512
01:07:29,840 --> 01:07:30,950
do they?

1513
01:07:30,950 --> 01:07:35,660
In the back, we have
one hydrogen storage.

1514
01:07:35,660 --> 01:07:40,170
The hydrogen economy,
it was a big myth.

1515
01:07:40,170 --> 01:07:44,730
Well, it's not a myth,
but it's a long way off.

1516
01:07:44,730 --> 01:07:46,965
That we'd all be--

1517
01:07:46,965 --> 01:07:48,840
I'm not sure I would
use that-- that we'd all

1518
01:07:48,840 --> 01:07:51,570
be driving hydrogen-powered
cars in this decade

1519
01:07:51,570 --> 01:07:55,120
was a little bit of an
exaggeration, to say the least.

1520
01:07:55,120 --> 01:07:55,920
So here's this guy.

1521
01:07:55,920 --> 01:08:00,630
Now, what I did
is I decorated it.

1522
01:08:00,630 --> 01:08:03,730
I did some, like I
thought-- oh, by the way,

1523
01:08:03,730 --> 01:08:06,780
your computation is only
as good as what's up here.

1524
01:08:06,780 --> 01:08:07,440
Right?

1525
01:08:07,440 --> 01:08:09,810
So you need to think about
what you want to simulate,

1526
01:08:09,810 --> 01:08:13,390
and here, we thought,
well, we had this one.

1527
01:08:13,390 --> 01:08:13,890
OK?

1528
01:08:13,890 --> 01:08:17,310
We had this one, and it's
not quite the same angle,

1529
01:08:17,310 --> 01:08:18,250
but it's close.

1530
01:08:18,250 --> 01:08:18,750
OK?

1531
01:08:18,750 --> 01:08:20,100
So these guys are
going to switch,

1532
01:08:20,100 --> 01:08:22,183
when the sun shines on
them, and store some energy

1533
01:08:22,183 --> 01:08:22,950
and switch back.

1534
01:08:22,950 --> 01:08:25,529
But I decided that I wanted
to try to do something

1535
01:08:25,529 --> 01:08:30,260
about the strain in this state.

1536
01:08:30,260 --> 01:08:35,399
Again, you're trying
to lower, remember--

1537
01:08:35,399 --> 01:08:37,680
you're trying to
lower these states,

1538
01:08:37,680 --> 01:08:40,210
or change them, figure
out how to tune them.

1539
01:08:40,210 --> 01:08:40,710
Right?

1540
01:08:40,710 --> 01:08:44,000
So what I did is we
put a group in there.

1541
01:08:44,000 --> 01:08:45,750
You can see, you put
a group in here which

1542
01:08:45,750 --> 01:08:49,140
is going to cause some bonding,
when it's in the trans state.

1543
01:08:49,140 --> 01:08:50,640
And you put another
group here which

1544
01:08:50,640 --> 01:08:53,310
causes some bonding
between those OH

1545
01:08:53,310 --> 01:08:56,490
groups and the nitrogen,
and that adds to the energy.

1546
01:08:56,490 --> 01:08:57,420
It lowers the energy.

1547
01:08:57,420 --> 01:08:58,200
Right?

1548
01:08:58,200 --> 01:09:01,300
Now, as I said, we do that
with quantum mechanics,

1549
01:09:01,300 --> 01:09:03,300
because it's actually not
that big of a problem,

1550
01:09:03,300 --> 01:09:05,550
but that doesn't
tell me whether--

1551
01:09:05,550 --> 01:09:07,800
I may have made this a great
solar thermal fuel that

1552
01:09:07,800 --> 01:09:09,300
can never absorb light.

1553
01:09:09,300 --> 01:09:12,960
And so you got to go, and you've
got to look at these things,

1554
01:09:12,960 --> 01:09:14,330
like the density of states.

1555
01:09:14,330 --> 01:09:14,910
OK?

1556
01:09:14,910 --> 01:09:21,770
And so here they are together,
and you can see that in--

1557
01:09:21,770 --> 01:09:22,420
so that's one.

1558
01:09:22,420 --> 01:09:22,920
OK.

1559
01:09:22,920 --> 01:09:26,510
So one is now bold, and you can
see that my modifications have

1560
01:09:26,510 --> 01:09:28,850
done some interesting things.

1561
01:09:28,850 --> 01:09:30,770
My chemical
modifications have really

1562
01:09:30,770 --> 01:09:34,899
changed where those
energy levels are.

1563
01:09:34,899 --> 01:09:38,135
Now, remember, they're
getting filled from here.

1564
01:09:38,135 --> 01:09:39,010
Remember the filling.

1565
01:09:39,010 --> 01:09:39,510
Right?

1566
01:09:39,510 --> 01:09:43,390
You draw from the bottom, the
most energy favorable ones,

1567
01:09:43,390 --> 01:09:45,279
all the way up, and
then you fill them up,

1568
01:09:45,279 --> 01:09:47,180
and you stop filling here.

1569
01:09:47,180 --> 01:09:47,680
Right?

1570
01:09:47,680 --> 01:09:49,970
You stop filling here,
and that's your gap,

1571
01:09:49,970 --> 01:09:54,000
and you can see that the gap
has changed considerably.

1572
01:09:54,000 --> 01:09:55,500
So the gap has
changed considerably,

1573
01:09:55,500 --> 01:09:57,830
and that changes
what kind of sunlight

1574
01:09:57,830 --> 01:10:00,980
that molecule can absorb.

1575
01:10:00,980 --> 01:10:04,820
Now, what's nice about
having the density of states

1576
01:10:04,820 --> 01:10:07,010
is that, you see,
I'm getting-- in all

1577
01:10:07,010 --> 01:10:12,340
of the energy levels-- is I'm
getting more than just the gap.

1578
01:10:12,340 --> 01:10:12,840
Right?

1579
01:10:12,840 --> 01:10:14,340
I'm getting other things.

1580
01:10:14,340 --> 01:10:16,870
I'm getting shapes and peaks,
and here's a double peak.

1581
01:10:16,870 --> 01:10:18,030
There's a single peak.

1582
01:10:18,030 --> 01:10:20,850
Here's a little narrow peak,
but there's a really broad thing

1583
01:10:20,850 --> 01:10:23,670
with like three
peaks and a shoulder.

1584
01:10:23,670 --> 01:10:25,460
Right?

1585
01:10:25,460 --> 01:10:27,440
That matters too.

1586
01:10:27,440 --> 01:10:29,320
That matters a whole lot.

1587
01:10:29,320 --> 01:10:30,380
OK?

1588
01:10:30,380 --> 01:10:36,900
And the reason is that to a
very, very crude approximation,

1589
01:10:36,900 --> 01:10:40,920
you can consider these peaks in
where the states are in energy

1590
01:10:40,920 --> 01:10:43,350
as the places where
this molecule will

1591
01:10:43,350 --> 01:10:46,580
be able to absorb light.

1592
01:10:46,580 --> 01:10:48,090
OK?

1593
01:10:48,090 --> 01:10:53,060
And so you can match this
up with the solar spectrum.

1594
01:10:53,060 --> 01:10:53,560
Right?

1595
01:10:53,560 --> 01:10:56,110
Because what you want
is for the molecules

1596
01:10:56,110 --> 01:10:59,230
to be able to absorb light,
where there's a lot of light.

1597
01:10:59,230 --> 01:11:01,875
And you don't really care
about them absorbing light.

1598
01:11:01,875 --> 01:11:04,000
You don't necessarily need
them to have huge peaks,

1599
01:11:04,000 --> 01:11:05,330
where there's no sunlight.

1600
01:11:05,330 --> 01:11:05,830
Right?

1601
01:11:05,830 --> 01:11:08,740
So now, you have an
interesting comparison

1602
01:11:08,740 --> 01:11:12,100
of where these molecules
tend to absorb light

1603
01:11:12,100 --> 01:11:13,910
and where the light is.

1604
01:11:13,910 --> 01:11:14,650
OK?

1605
01:11:14,650 --> 01:11:18,650
So let's go back
to this and make

1606
01:11:18,650 --> 01:11:23,020
sure we know where I'm going.

1607
01:11:23,020 --> 01:11:23,590
OK?

1608
01:11:23,590 --> 01:11:29,620
So see, we talked about--

1609
01:11:29,620 --> 01:11:31,600
just another five
minutes or so I think

1610
01:11:31,600 --> 01:11:36,180
to finish this discussion.

1611
01:11:36,180 --> 01:11:38,730
We talked about how,
well, you don't want--

1612
01:11:41,340 --> 01:11:44,940
there are constraints on just
thinking about how big of a gap

1613
01:11:44,940 --> 01:11:45,480
you want.

1614
01:11:45,480 --> 01:11:47,700
Because it's a
constrained optimization

1615
01:11:47,700 --> 01:11:50,010
problem with this thing and
this thing and this stuff.

1616
01:11:50,010 --> 01:11:50,820
Right?

1617
01:11:50,820 --> 01:11:52,140
We just talked about that.

1618
01:11:52,140 --> 01:11:56,330
Now, I'm going to tell you
there's another problem,

1619
01:11:56,330 --> 01:12:02,110
and that is that this
state is also photoactive.

1620
01:12:02,110 --> 01:12:08,750
So this state can absorb
light which makes it go back.

1621
01:12:08,750 --> 01:12:09,920
Well, that's a bummer.

1622
01:12:09,920 --> 01:12:10,940
Right?

1623
01:12:10,940 --> 01:12:13,040
That is a bummer.

1624
01:12:13,040 --> 01:12:15,470
Now, what that
means is that, when

1625
01:12:15,470 --> 01:12:18,140
I shine light on
this material, I

1626
01:12:18,140 --> 01:12:21,240
will never get it
all to convert.

1627
01:12:21,240 --> 01:12:23,430
I will never charge
all of the material

1628
01:12:23,430 --> 01:12:26,350
and make it all go
from here to here,

1629
01:12:26,350 --> 01:12:30,130
because there's constantly
a competition at play.

1630
01:12:30,130 --> 01:12:32,410
Some of it will be going
this way, and some of it

1631
01:12:32,410 --> 01:12:33,730
will be going that way.

1632
01:12:33,730 --> 01:12:37,450
And what holds the key to
determining how much of which

1633
01:12:37,450 --> 01:12:41,570
one is made?

1634
01:12:41,570 --> 01:12:44,428
What holds the key?

1635
01:12:44,428 --> 01:12:47,423
AUDIENCE: The ratio
of delta H plus EA.

1636
01:12:47,423 --> 01:12:49,590
JEFFREY C. GROSSMAN: Well,
actually, but the delta H

1637
01:12:49,590 --> 01:12:52,320
and EA are out of
the picture for now,

1638
01:12:52,320 --> 01:12:56,430
because I'm only talking about
the absorption efficiency.

1639
01:12:59,130 --> 01:13:02,010
What type of photons it
could absorb and what else?

1640
01:13:04,520 --> 01:13:07,430
What type of photons
it can absorb and?

1641
01:13:07,430 --> 01:13:08,843
Yeah?

1642
01:13:08,843 --> 01:13:10,760
AUDIENCE: How many of
those types of photons--

1643
01:13:10,760 --> 01:13:11,300
JEFFREY C. GROSSMAN: Exactly.

1644
01:13:11,300 --> 01:13:12,383
AUDIENCE: Your solar cell.

1645
01:13:12,383 --> 01:13:15,670
JEFFREY C. GROSSMAN:
Exactly, and this.

1646
01:13:15,670 --> 01:13:16,750
Right?

1647
01:13:16,750 --> 01:13:20,650
So you're given this much
photons on planet Earth.

1648
01:13:20,650 --> 01:13:23,780
You're give given the yellow,
if you go up a little bit.

1649
01:13:23,780 --> 01:13:24,320
Right?

1650
01:13:24,320 --> 01:13:26,610
We're not going to charge
our fuels in space.

1651
01:13:26,610 --> 01:13:29,330
So this is what you
got, the red, and that's

1652
01:13:29,330 --> 01:13:33,260
where the photons are in
energy, in wavelength energy,

1653
01:13:33,260 --> 01:13:34,530
same thing.

1654
01:13:34,530 --> 01:13:41,450
Now, I'm giving you the
fact that some molecules--

1655
01:13:41,450 --> 01:13:42,410
let's go back here.

1656
01:13:46,070 --> 01:13:48,380
I can't just delete one, can I?

1657
01:13:48,380 --> 01:13:53,870
I'm going to do one more
simulation while I talk.

1658
01:13:53,870 --> 01:13:58,400
I wish it wouldn't show
my picture everywhere.

1659
01:13:58,400 --> 01:14:00,410
I'm going to do the cis state.

1660
01:14:00,410 --> 01:14:00,910
OK?

1661
01:14:05,300 --> 01:14:13,500
You see, some molecules
in their cis state,

1662
01:14:13,500 --> 01:14:16,650
they're still photoactive,
which means they go back here,

1663
01:14:16,650 --> 01:14:18,430
when you shine light on them.

1664
01:14:18,430 --> 01:14:23,490
What that means is that there's
going to be a stationary state.

1665
01:14:23,490 --> 01:14:26,070
When I hold the
fuel out in the sun,

1666
01:14:26,070 --> 01:14:30,420
the light is converting this
into this, as well as this

1667
01:14:30,420 --> 01:14:33,660
into this with some
efficiency in both directions.

1668
01:14:33,660 --> 01:14:35,400
And there will be
a stationary state

1669
01:14:35,400 --> 01:14:38,370
that gives me a
percentage, or a yield,

1670
01:14:38,370 --> 01:14:39,960
or as it's called
in the literature

1671
01:14:39,960 --> 01:14:44,410
a quantum yield, of
charged material.

1672
01:14:44,410 --> 01:14:45,130
How much is it?

1673
01:14:45,130 --> 01:14:48,280
Well, in isolated azobenzene,
when you don't do anything

1674
01:14:48,280 --> 01:14:49,900
to it, it's 25%.

1675
01:14:49,900 --> 01:14:54,020
I can only charge
25% of this stuff

1676
01:14:54,020 --> 01:14:59,210
in the photo-stationary state,
when I hold it out in the sun.

1677
01:14:59,210 --> 01:15:02,360
And you can see why this
is such an important part

1678
01:15:02,360 --> 01:15:04,790
of the problem, I
will remind you,

1679
01:15:04,790 --> 01:15:07,850
a purely quantum mechanical
part of the problem.

1680
01:15:07,850 --> 01:15:11,630
Because if I increase this, I
work so hard to increase this

1681
01:15:11,630 --> 01:15:14,727
by a factor of three
or four, and then I

1682
01:15:14,727 --> 01:15:16,310
can only charge a
fourth of it, that's

1683
01:15:16,310 --> 01:15:17,760
a whole factor of four hit.

1684
01:15:17,760 --> 01:15:19,760
If you can only charge a
fourth of it at a time,

1685
01:15:19,760 --> 01:15:21,930
it's four times less useful.

1686
01:15:21,930 --> 01:15:25,170
So it's effectively changing
this by four times back.

1687
01:15:25,170 --> 01:15:25,670
Right?

1688
01:15:25,670 --> 01:15:27,630
So this is critical.

1689
01:15:27,630 --> 01:15:29,390
How much of this can you charge?

1690
01:15:29,390 --> 01:15:30,020
Right?

1691
01:15:30,020 --> 01:15:31,770
And that comes from
the quantum mechanics.

1692
01:15:31,770 --> 01:15:36,560
Now, the way that you
get it is by looking at--

1693
01:15:36,560 --> 01:15:37,937
and I'll go through
the equations

1694
01:15:37,937 --> 01:15:39,020
on the next line a minute.

1695
01:15:41,600 --> 01:15:44,660
So here it is now in
the charged state.

1696
01:15:44,660 --> 01:15:45,290
OK?

1697
01:15:45,290 --> 01:15:46,220
So it's flipped.

1698
01:15:46,220 --> 01:15:47,180
It's done its flip.

1699
01:15:47,180 --> 01:15:50,000
You can see, it's rotated
those nitrogen bonds.

1700
01:15:50,000 --> 01:15:54,230
It's a beautiful thing, kind of
an emotional moment in a way.

1701
01:15:54,230 --> 01:15:58,010
And you go back to here,
and you look at your DOS,

1702
01:15:58,010 --> 01:15:59,520
and now this is
kind of hard to see.

1703
01:15:59,520 --> 01:16:00,020
Isn't it?

1704
01:16:02,600 --> 01:16:06,170
One of these is the cis
state that I just mentioned,

1705
01:16:06,170 --> 01:16:07,662
and it's different.

1706
01:16:07,662 --> 01:16:09,245
I can't see, because
there's two trans

1707
01:16:09,245 --> 01:16:12,680
states here and one cis state.

1708
01:16:12,680 --> 01:16:15,710
I don't think there's any
way to just do simulations

1709
01:16:15,710 --> 01:16:19,020
two and three, but I think you
know what I'm talking about.

1710
01:16:19,020 --> 01:16:22,280
There's a density of
states for the trans.

1711
01:16:22,280 --> 01:16:27,337
These levels here
turn on their side,

1712
01:16:27,337 --> 01:16:29,420
and there's a density of
states for the cis state.

1713
01:16:29,420 --> 01:16:32,060
And matching that
with the solar flux

1714
01:16:32,060 --> 01:16:34,610
is what will give you the
photo-stationary state.

1715
01:16:34,610 --> 01:16:37,620
It will give you the quantum
yield of the material.

1716
01:16:37,620 --> 01:16:38,120
OK?

1717
01:16:38,120 --> 01:16:40,700
That will be your
second homework.

1718
01:16:40,700 --> 01:16:50,670
So this, let's see, this is
two ways that you could do it.

1719
01:16:50,670 --> 01:16:52,600
OK?

1720
01:16:52,600 --> 01:17:00,290
One way is you could just assume
that all of the photons higher

1721
01:17:00,290 --> 01:17:05,400
in energy than the gap are
absorbed and lead to a switch.

1722
01:17:05,400 --> 01:17:08,030
And if you do that, then the
fraction of the molecules

1723
01:17:08,030 --> 01:17:11,190
in the cis state, if
you let them be x,

1724
01:17:11,190 --> 01:17:12,980
you can show that
it's just going

1725
01:17:12,980 --> 01:17:15,740
to be a simple integral
over the solar spectrum,

1726
01:17:15,740 --> 01:17:20,728
that this I function,
up to the gap times x.

1727
01:17:20,728 --> 01:17:22,270
That's how many are
in the cis state.

1728
01:17:22,270 --> 01:17:23,940
Gesundheit.

1729
01:17:23,940 --> 01:17:28,260
[NON-ENGLISH] Equals the number
that are in the trans state,

1730
01:17:28,260 --> 01:17:32,850
1 minus x, times the integral
over the number of photons that

1731
01:17:32,850 --> 01:17:36,770
convert the trans.

1732
01:17:36,770 --> 01:17:37,390
OK?

1733
01:17:37,390 --> 01:17:39,640
That's just
stationary-- that's just

1734
01:17:39,640 --> 01:17:42,190
telling you that the change
in the concentration of cis

1735
01:17:42,190 --> 01:17:42,850
is the same.

1736
01:17:42,850 --> 01:17:47,060
It's like a reaction
kinetics equation,

1737
01:17:47,060 --> 01:17:51,040
the rate of going from
one state to another times

1738
01:17:51,040 --> 01:17:53,950
the number in that state equals
the same as the other way.

1739
01:17:53,950 --> 01:17:55,180
That's all we've done here.

1740
01:17:55,180 --> 01:17:58,570
But it gets more interesting if
you use the density of states,

1741
01:17:58,570 --> 01:18:02,550
because now, you
have the absorption--

1742
01:18:02,550 --> 01:18:03,960
what I'm calling the absorption.

1743
01:18:03,960 --> 01:18:05,970
Again, it's a
crude approximation

1744
01:18:05,970 --> 01:18:08,620
for the absorption, but
let's just call it that--

1745
01:18:08,620 --> 01:18:15,160
of the cis state as a
function of the wavelength,

1746
01:18:15,160 --> 01:18:20,280
convoluted with, or
times, the solar spectrum.

1747
01:18:20,280 --> 01:18:23,550
Where you have states in
both is where it matters.

1748
01:18:23,550 --> 01:18:24,510
Right?

1749
01:18:24,510 --> 01:18:28,200
Where you have states in both
is where you hit the integral,

1750
01:18:28,200 --> 01:18:30,030
and it's when those
are taken together

1751
01:18:30,030 --> 01:18:33,150
that you can calculate
more accurately than just

1752
01:18:33,150 --> 01:18:34,440
using the gap.

1753
01:18:34,440 --> 01:18:38,700
You can calculate the
photo-stationary yield,

1754
01:18:38,700 --> 01:18:41,070
and you get this all
from those energy levels,

1755
01:18:41,070 --> 01:18:44,010
those beautiful energy
levels that we started

1756
01:18:44,010 --> 01:18:45,840
this lecture talking about.

1757
01:18:45,840 --> 01:18:46,350
OK?

1758
01:18:46,350 --> 01:18:52,050
That yield is so important,
because it can kill your--

1759
01:18:52,050 --> 01:18:53,880
great idea for improving
delta H can get

1760
01:18:53,880 --> 01:18:55,450
killed if the yield isn't good.

1761
01:18:55,450 --> 01:18:55,950
OK?

1762
01:18:59,280 --> 01:19:01,710
Maybe I'll spend 10 minutes
on hydrogen storage.

1763
01:19:01,710 --> 01:19:05,190
Nobody raised their hands,
but we'll do another poll.

1764
01:19:05,190 --> 01:19:07,590
And we're going to start
moving now-- you'll

1765
01:19:07,590 --> 01:19:09,660
have a homework on this.

1766
01:19:09,660 --> 01:19:12,240
It'll be lots of fun, and
then on Thursday, we're

1767
01:19:12,240 --> 01:19:14,360
going to move into solids.