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JEFFREY C GROSSMAN:
So we're here.

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00:00:29,430 --> 00:00:32,880
So we're in lecture four,
and this is really exciting

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00:00:32,880 --> 00:00:36,420
because we're going to be
talking about an application.

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00:00:36,420 --> 00:00:40,680
We sort of spent three lectures
introducing and building up

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00:00:40,680 --> 00:00:44,550
some of the framework
that the computer solves

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00:00:44,550 --> 00:00:46,710
to do quantum
mechanics, and now we're

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00:00:46,710 --> 00:00:48,490
going to actually look
at a real problem.

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00:00:48,490 --> 00:00:50,850
It's a really cool problem.

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00:00:50,850 --> 00:00:54,000
And then that'll sort of--
we'll follow up with this.

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00:00:54,000 --> 00:00:56,625
We might do a little bit more
of this to start on Tuesday,

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00:00:56,625 --> 00:00:58,500
and then we'll talk
about hydrogen storage is

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another problem.

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00:01:00,420 --> 00:01:03,690
We'll go back after that
to a little more formalism

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00:01:03,690 --> 00:01:06,660
to get to solids because
these are molecules so far,

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00:01:06,660 --> 00:01:08,470
and then we'll do
some more problems.

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00:01:08,470 --> 00:01:09,810
OK, so that's our plan.

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00:01:12,890 --> 00:01:15,800
What I want to do today is
I want to review a little.

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00:01:15,800 --> 00:01:21,200
Since I didn't-- so Michelle
came in and gave the lecture,

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00:01:21,200 --> 00:01:24,920
lecture number three, because
I was in San Francisco.

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00:01:28,120 --> 00:01:30,230
And so I'd like to review
some of the key points

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00:01:30,230 --> 00:01:31,332
from that lecture.

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00:01:31,332 --> 00:01:33,290
So we're going to review
a little bit to start.

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00:01:33,290 --> 00:01:36,140
And then I want to do some
interactive calculations

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00:01:36,140 --> 00:01:39,350
together because,
first of all, there's

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00:01:39,350 --> 00:01:40,910
no better way to
spend time, really,

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00:01:40,910 --> 00:01:43,340
with a person or
a class or any--

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00:01:43,340 --> 00:01:46,070
to compute together is
to know one another.

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00:01:46,070 --> 00:01:49,010
And through these interactive
calculations on the hydrogen

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00:01:49,010 --> 00:01:50,720
dimer, we will
pose some questions

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00:01:50,720 --> 00:01:53,150
and answer them
together, make sure

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00:01:53,150 --> 00:01:55,220
that we're kind of
collectively understanding

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00:01:55,220 --> 00:01:57,380
some of the key points of
the first three lectures.

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00:01:57,380 --> 00:02:02,870
Then I'll tell you about why
this is such a cool problem,

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00:02:02,870 --> 00:02:07,070
what solar thermal
fuels are, and why this

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00:02:07,070 --> 00:02:08,720
is such a cool energy problem.

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00:02:08,720 --> 00:02:11,000
And then we'll end with a
discussion and some more

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00:02:11,000 --> 00:02:13,340
interactive calculations
of the solar thermal fuels

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00:02:13,340 --> 00:02:16,370
and kind of talking about
why we need quantum mechanics

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00:02:16,370 --> 00:02:17,798
to tackle this problem.

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00:02:17,798 --> 00:02:18,590
So that's our plan.

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00:02:22,250 --> 00:02:24,620
Is anybody else-- yeah,
we're good with that?

49
00:02:24,620 --> 00:02:26,113
We got a thumbs up.

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00:02:26,113 --> 00:02:26,780
I'm ready to go.

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00:02:26,780 --> 00:02:27,380
I love it.

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00:02:27,380 --> 00:02:30,830
You can give me a little private
thumbs up like that any time,

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00:02:30,830 --> 00:02:32,540
and I love that
kind of feedback.

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00:02:32,540 --> 00:02:33,860
That's helpful.

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00:02:33,860 --> 00:02:36,320
And I was actually
thinking that you

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00:02:36,320 --> 00:02:39,410
were thinking of the Celtics
securing the division

57
00:02:39,410 --> 00:02:40,025
title anyway.

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00:02:44,160 --> 00:02:45,410
I think you talked about this.

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00:02:45,410 --> 00:02:46,785
This is sort of
where you started

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00:02:46,785 --> 00:02:48,660
because we had this kind
of quantum mechanics

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00:02:48,660 --> 00:02:49,618
that we couldn't solve.

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00:02:49,618 --> 00:02:52,350
And then we said, well, but
you can solve it analytically

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00:02:52,350 --> 00:02:54,450
for hydrogen, and we did.

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00:02:54,450 --> 00:02:58,050
And we said that that explained
the periodic table, amazingly,

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00:02:58,050 --> 00:03:01,410
if you only had one
electron and one proton.

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00:03:01,410 --> 00:03:03,730
Unfortunately everything
has a lot more than that,

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and what happens
is that when you

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00:03:06,900 --> 00:03:10,860
put more than one
quantum-mechanical particle--

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00:03:10,860 --> 00:03:11,940
by which I mean what?

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00:03:14,495 --> 00:03:15,870
AUDIENCE: More
than one electron.

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JEFFREY C GROSSMAN: Electrons.

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00:03:17,120 --> 00:03:19,260
For us, that's the
quantum-mechanical particle

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that we care about.

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00:03:20,152 --> 00:03:22,360
Of course there are more
quantum-mechanical particles

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than that in the world.

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Everything is
quantum mechanical,

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but those are the
things we really

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care about in this class.

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And if you put more than
one into the whole thing,

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then you've got to think about
how they talk to each other,

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and that's the killer.

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00:03:35,740 --> 00:03:38,220
So you can talk about
how they talk to the ion.

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00:03:38,220 --> 00:03:39,840
That's this 1 over r term--

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00:03:39,840 --> 00:03:42,060
how they talk to the
proton I mean, right?

85
00:03:42,060 --> 00:03:45,683
But talking to each other,
that's this many-body problem.

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00:03:45,683 --> 00:03:47,100
It's called the
many-body problem.

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00:03:47,100 --> 00:03:50,740
That's really hard, and
analytically it's a nightmare,

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00:03:50,740 --> 00:03:53,040
and that's where
computation comes in.

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00:03:53,040 --> 00:03:56,580
Unfortunately, so this
is sort of showing--

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00:03:56,580 --> 00:04:00,130
this is just all review for the
first little bit of this class.

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00:04:00,130 --> 00:04:01,350
I want to talk about review.

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00:04:01,350 --> 00:04:04,925
Those good-old days of
one electron are over.

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00:04:04,925 --> 00:04:05,550
They were good.

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00:04:05,550 --> 00:04:06,310
They were fun.

95
00:04:06,310 --> 00:04:09,580
We had a blast for one lecture,
and now we're moving on,

96
00:04:09,580 --> 00:04:13,213
and we're going to multibody,
many-body problems.

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00:04:13,213 --> 00:04:15,130
And that's the many-body
Schrodinger equation.

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00:04:15,130 --> 00:04:16,350
And you can see
that the thing goes

99
00:04:16,350 --> 00:04:18,392
from this where you get
those hydrogenic orbitals

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00:04:18,392 --> 00:04:19,899
and everything's
beautiful to this

101
00:04:19,899 --> 00:04:24,660
where it's just a complete
mathematical nightmare.

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00:04:24,660 --> 00:04:27,570
And this cannot be
solved analytically.

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00:04:27,570 --> 00:04:30,450
And so these are sums
over all of the ions,

104
00:04:30,450 --> 00:04:34,140
sums over all the electron-ion
interactions and sums

105
00:04:34,140 --> 00:04:36,500
over all the electron-electron
interactions.

106
00:04:36,500 --> 00:04:39,450
This is the killer right here.

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00:04:39,450 --> 00:04:40,798
We make some approximations.

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00:04:40,798 --> 00:04:42,840
That's how we get there
because as I talked about

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00:04:42,840 --> 00:04:46,890
in the beginning, even if
our computers were seriously

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00:04:46,890 --> 00:04:50,070
like 10 orders of magnitude
faster than they are today,

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00:04:50,070 --> 00:04:52,140
we still wouldn't be able
to solve this problem

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00:04:52,140 --> 00:04:53,760
in a straightforward way.

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00:04:53,760 --> 00:04:56,130
We cannot solve it
directly and exactly,

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00:04:56,130 --> 00:04:57,990
so we have to make
approximations.

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00:04:57,990 --> 00:05:00,000
One of the first
ones we make is--

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00:05:00,000 --> 00:05:01,740
oh, and that's just
those are the labels.

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00:05:01,740 --> 00:05:03,565
One of the first ones
we make are-- right,

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00:05:03,565 --> 00:05:04,440
there's the equation.

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00:05:04,440 --> 00:05:06,510
That's the
Schrodinger equation--

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00:05:06,510 --> 00:05:09,420
is this Born-Oppenheimer
approximation.

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00:05:09,420 --> 00:05:13,050
I think Michelle probably
showed you my tattoo.

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00:05:13,050 --> 00:05:15,390
Did you see the tattoo?

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00:05:15,390 --> 00:05:16,847
That was my--

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00:05:16,847 --> 00:05:18,930
I tried to find a good
image for Born-Oppenheimer,

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00:05:18,930 --> 00:05:20,370
and that came up first.

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00:05:20,370 --> 00:05:22,450
And then did she
talk about-- no?

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00:05:22,450 --> 00:05:26,177
So when I found the image,
I found it on a blog.

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00:05:26,177 --> 00:05:28,010
And that's a dangerous
thing because there's

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00:05:28,010 --> 00:05:30,200
a long trail of discussion.

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00:05:30,200 --> 00:05:33,140
And it was interesting that
the whole discussion was not

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00:05:33,140 --> 00:05:35,540
about computational
modeling and it was not

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00:05:35,540 --> 00:05:38,930
about physics, Schrodinger,
or Born-Oppenheimer.

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00:05:38,930 --> 00:05:41,150
It was entirely about
whether this guy was

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00:05:41,150 --> 00:05:44,450
going to be able to find
dates or not in his life.

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00:05:44,450 --> 00:05:47,720
And it was actually a
very engaging discussion,

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00:05:47,720 --> 00:05:49,520
and it came out--
it was like 50%

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00:05:49,520 --> 00:05:52,800
said definitely because of the
tattoo, and 50% said no way.

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00:05:52,800 --> 00:05:54,800
And so I don't know where that--

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00:05:54,800 --> 00:05:56,360
but anyway.

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00:05:56,360 --> 00:06:00,680
Now this is another
cartoon that just

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00:06:00,680 --> 00:06:05,070
shows that the
electrons are the flies,

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00:06:05,070 --> 00:06:07,560
and the protons, the
nucleus, are these cows.

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00:06:07,560 --> 00:06:11,040
And they move
really slow, bulls.

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00:06:11,040 --> 00:06:12,150
I didn't mean to dis.

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00:06:15,930 --> 00:06:18,420
These guys are
going really fast.

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00:06:18,420 --> 00:06:21,760
This guy's kind of slow,
and that's really the point.

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00:06:21,760 --> 00:06:25,860
Electrons are fast
and light, and so it's

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00:06:25,860 --> 00:06:27,570
a good approximation.

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00:06:27,570 --> 00:06:32,370
How much lighter are they than
the proton or the nucleus?

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00:06:32,370 --> 00:06:33,328
AUDIENCE: 1 over 2,000.

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00:06:33,328 --> 00:06:35,037
JEFFREY C GROSSMAN:
Yeah, it's a couple--

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00:06:35,037 --> 00:06:36,000
it's like 1,000, right?

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00:06:36,000 --> 00:06:40,320
So that's enough lighter that
you can say, you know what?

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00:06:40,320 --> 00:06:42,480
At any given time, it's
a good approximation

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00:06:42,480 --> 00:06:45,810
to say that this thing is
pretty stationary with respect

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00:06:45,810 --> 00:06:48,810
to these things buzzing around.

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00:06:48,810 --> 00:06:53,130
That's the Born-Oppenheimer
approximation in cow language--

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00:06:53,130 --> 00:06:54,390
OK, cow-fly language.

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00:06:59,620 --> 00:07:05,820
Actually, this is
more Google image art.

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00:07:08,910 --> 00:07:10,860
So this is the
approximation we make.

161
00:07:10,860 --> 00:07:13,970
What you can see is that we just
get rid of those nuclear terms.

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00:07:13,970 --> 00:07:15,900
We treat them as if
they're not moving

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00:07:15,900 --> 00:07:18,540
and they don't really matter
because at any given time what

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00:07:18,540 --> 00:07:25,340
we care about is the electronic
structure with the atoms fixed.

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00:07:25,340 --> 00:07:26,930
That's what we're
talking about here.

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00:07:26,930 --> 00:07:28,130
And you can solve for it.

167
00:07:28,130 --> 00:07:30,810
It's a really good
approximation in many cases.

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00:07:30,810 --> 00:07:33,110
There are some fields
where it matters,

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00:07:33,110 --> 00:07:35,340
where this approximation
actually can break down

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00:07:35,340 --> 00:07:36,590
like in superconductivity.

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00:07:36,590 --> 00:07:37,910
We're not going to go there.

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00:07:37,910 --> 00:07:40,820
For us and the things we
care about, that's sort of--

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00:07:40,820 --> 00:07:43,550
the positions of the
atoms are frozen,

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00:07:43,550 --> 00:07:45,290
and then we solve
for the electrons.

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00:07:45,290 --> 00:07:49,970
That's fine, and that's
a good approximation.

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00:07:49,970 --> 00:07:52,670
OK, so any questions
about Born-Oppenheimer,

177
00:07:52,670 --> 00:07:54,950
the Born-Oppenheimer surface?

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00:07:54,950 --> 00:07:58,160
You'll hear people say that,
the Born-Oppenheimer surface,

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00:07:58,160 --> 00:07:59,990
and now you know what they mean.

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00:07:59,990 --> 00:08:04,700
They mean the energy surface
where the electrons are always

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00:08:04,700 --> 00:08:07,550
in sort of their ground
state with respect

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00:08:07,550 --> 00:08:10,730
to the nuclei positions because
they always have enough time

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00:08:10,730 --> 00:08:14,332
to get there because they move
so much faster than the nuclei.

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00:08:14,332 --> 00:08:16,040
That's the Born-Oppenheimer
[INAUDIBLE]..

185
00:08:16,040 --> 00:08:19,450
You can pull that out
as well in conversation.

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00:08:19,450 --> 00:08:21,520
Now that's one approximation.

187
00:08:21,520 --> 00:08:23,170
That kind of helps.

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00:08:23,170 --> 00:08:25,010
It really doesn't
help the key problem,

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00:08:25,010 --> 00:08:28,270
which is that
many-body-interaction thing.

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00:08:28,270 --> 00:08:30,400
So that's like the real--

191
00:08:30,400 --> 00:08:32,030
that's the real issue here.

192
00:08:32,030 --> 00:08:37,140
How do we get over this
electron-electron interaction?

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00:08:37,140 --> 00:08:40,020
And don't even let me say it,
electron-electron-electron

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00:08:40,020 --> 00:08:43,620
interaction because you can
have like three-body effects.

195
00:08:43,620 --> 00:08:46,680
It's a many-body world,
but we can't do that.

196
00:08:46,680 --> 00:08:50,460
We can't do that on a computer
in a good-enough time scale

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00:08:50,460 --> 00:08:54,150
to be applicable to
materials, so we simplify.

198
00:08:54,150 --> 00:08:55,860
And you covered this, right?

199
00:08:55,860 --> 00:08:57,360
This is not-- but
we're getting back

200
00:08:57,360 --> 00:09:00,210
into our feeling
with this, right?

201
00:09:00,210 --> 00:09:01,920
But you did cover this.

202
00:09:01,920 --> 00:09:02,760
Am I correct?

203
00:09:02,760 --> 00:09:03,570
OK, good.

204
00:09:03,570 --> 00:09:05,550
One person got it.

205
00:09:05,550 --> 00:09:07,650
But thank you for
that in the back.

206
00:09:07,650 --> 00:09:12,900
Now, OK, there were basically
two paths because they saw this

207
00:09:12,900 --> 00:09:15,210
and they knew, they
being the people thinking

208
00:09:15,210 --> 00:09:19,440
about computational materials,
physics, and chemistry

209
00:09:19,440 --> 00:09:21,190
back in the 1940s.

210
00:09:21,190 --> 00:09:23,710
They knew they needed
to do something.

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00:09:23,710 --> 00:09:25,950
And so there were
essentially two paths.

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00:09:25,950 --> 00:09:28,680
There was a path that
most chemists took,

213
00:09:28,680 --> 00:09:30,840
and there was a path
that most physicists

214
00:09:30,840 --> 00:09:35,320
took starting in sort of
the '60s really, actually.

215
00:09:35,320 --> 00:09:42,700
The path that the chemists
took is to say, you know what?

216
00:09:42,700 --> 00:09:45,910
We're not going to mess
with the Hamiltonian.

217
00:09:45,910 --> 00:09:48,990
We are not going
to mess with this.

218
00:09:48,990 --> 00:09:50,620
This is right.

219
00:09:50,620 --> 00:09:52,570
The physics of this is
correct, so we don't

220
00:09:52,570 --> 00:09:54,430
want to play around with that.

221
00:09:54,430 --> 00:09:57,490
Most of what the chemists
did was to play around

222
00:09:57,490 --> 00:09:58,990
with the wave function.

223
00:09:58,990 --> 00:10:01,120
So what they did is--

224
00:10:01,120 --> 00:10:01,790
let me go back.

225
00:10:01,790 --> 00:10:04,000
Sorry.

226
00:10:04,000 --> 00:10:06,670
I think I had the
Schrodinger equation here.

227
00:10:06,670 --> 00:10:11,530
H-- remember Schrodinger
equation, H psi equals E psi.

228
00:10:11,530 --> 00:10:14,030
Well, they played with psi.

229
00:10:14,030 --> 00:10:16,550
So instead of saying
that psi can be complex

230
00:10:16,550 --> 00:10:20,760
as it needs to be with all the
freedom that it needs to have,

231
00:10:20,760 --> 00:10:24,890
they said no, we're going to
start to restrict that freedom.

232
00:10:24,890 --> 00:10:27,290
That's really how quantum
chemistry sort of began.

233
00:10:27,290 --> 00:10:29,082
I mean, there was some
perturbation theory,

234
00:10:29,082 --> 00:10:32,240
but a lot of the real
advances in quantum chemistry

235
00:10:32,240 --> 00:10:36,860
in the beginning happened in
making approximations for this,

236
00:10:36,860 --> 00:10:38,270
for the wave function.

237
00:10:38,270 --> 00:10:40,490
They said keep H, mess with psi.

238
00:10:40,490 --> 00:10:41,940
Make it simple.

239
00:10:41,940 --> 00:10:45,660
And if you make it simple, it
becomes a tractable problem,

240
00:10:45,660 --> 00:10:47,090
right?

241
00:10:47,090 --> 00:10:50,030
How many of you have heard
of a determinant, a Slater

242
00:10:50,030 --> 00:10:52,520
determinant?

243
00:10:52,520 --> 00:10:56,360
Slater was here at MIT, and
it was a really important

244
00:10:56,360 --> 00:10:58,010
contribution to
quantum chemistry

245
00:10:58,010 --> 00:11:02,568
was to be able to write psi,
keep the important properties

246
00:11:02,568 --> 00:11:04,610
that you need but to write
it in a much simpler--

247
00:11:04,610 --> 00:11:06,100
in a very simplified way.

248
00:11:06,100 --> 00:11:07,760
So you lose information.

249
00:11:07,760 --> 00:11:09,590
It's not the same
psi that you need.

250
00:11:09,590 --> 00:11:11,420
It's not the correct
psi, but it's

251
00:11:11,420 --> 00:11:13,233
sort of an approximate
version of it.

252
00:11:13,233 --> 00:11:14,900
That's kind of where
quantum chemistry--

253
00:11:14,900 --> 00:11:19,130
that's what Hartree-Fock
theory is based on.

254
00:11:19,130 --> 00:11:22,430
Then you have sort of the
physics world in the 1960s.

255
00:11:22,430 --> 00:11:25,430
And I've shown you the
picture of Walter Kohn, who

256
00:11:25,430 --> 00:11:28,440
is the only person to win a
Nobel Prize in computation,

257
00:11:28,440 --> 00:11:30,140
so far at least.

258
00:11:30,140 --> 00:11:31,908
And he won it for a
density function--

259
00:11:31,908 --> 00:11:33,950
for his development of
density functional theory.

260
00:11:33,950 --> 00:11:36,890
Now that is taking sort
of the opposite approach.

261
00:11:36,890 --> 00:11:42,980
What that is doing that
is saying, OK, ignore psi.

262
00:11:42,980 --> 00:11:44,450
Psi is just too hard.

263
00:11:44,450 --> 00:11:47,750
Even if you simplify it,
it's a really hard thing

264
00:11:47,750 --> 00:11:52,100
to write in a computer and to
represent accurately, and so

265
00:11:52,100 --> 00:11:56,150
let's just forget about that
and work only with the density.

266
00:11:56,150 --> 00:11:58,580
I take it you did talk
about this last week, right?

267
00:11:58,580 --> 00:12:01,970
So in density functional theory,
that's where it gets its name.

268
00:12:01,970 --> 00:12:04,430
You just get rid of psi
by not thinking about it

269
00:12:04,430 --> 00:12:10,160
and by solving the problem of
the density instead of the wave

270
00:12:10,160 --> 00:12:10,820
function.

271
00:12:10,820 --> 00:12:14,960
So it's the density of the
electrons instead of the wave

272
00:12:14,960 --> 00:12:16,670
function of the electrons.

273
00:12:16,670 --> 00:12:20,590
Now when you do that,
effectively-- and again,

274
00:12:20,590 --> 00:12:23,605
my goal here in this class is
not to go deep mathematics here

275
00:12:23,605 --> 00:12:25,730
because I know many of you
haven't had quantum yet,

276
00:12:25,730 --> 00:12:27,980
but I want you to come
away with an intuitive

277
00:12:27,980 --> 00:12:29,540
picture for what's happening.

278
00:12:29,540 --> 00:12:35,890
What happened in the 1960s when
these communities were really

279
00:12:35,890 --> 00:12:39,860
developing computational quantum
mechanics for the first time?

280
00:12:39,860 --> 00:12:42,670
And what this
does-- no, but stay.

281
00:12:42,670 --> 00:12:44,500
It's still going to be good.

282
00:12:44,500 --> 00:12:45,190
OK, go ahead.

283
00:12:47,920 --> 00:12:51,430
We'll fill you in
when you come back.

284
00:12:51,430 --> 00:12:53,290
What this does to
say that I want

285
00:12:53,290 --> 00:12:56,080
to think about the density
instead of the wave function

286
00:12:56,080 --> 00:13:01,850
is effectively it modifies H.
So now instead of modifying psi,

287
00:13:01,850 --> 00:13:05,430
you actually are
changing H considerably--

288
00:13:05,430 --> 00:13:07,440
considerably.

289
00:13:07,440 --> 00:13:09,540
But you hope that
you don't change it

290
00:13:09,540 --> 00:13:13,710
so much that it's wrong or
that it's unphysical, right?

291
00:13:13,710 --> 00:13:16,380
And density functional
theory effectively

292
00:13:16,380 --> 00:13:19,120
is a theory that simplifies
H, the Hamiltonian,

293
00:13:19,120 --> 00:13:20,940
the expression for the energy.

294
00:13:20,940 --> 00:13:25,290
You basically get rid of
those complex, many-particle

295
00:13:25,290 --> 00:13:31,710
interactions from H and you put
effective potentials into it.

296
00:13:31,710 --> 00:13:33,300
That's density
functional theory.

297
00:13:33,300 --> 00:13:37,050
Now, both of them get rid
of this many-body problem.

298
00:13:37,050 --> 00:13:40,890
Actually, see, what you do in
quantum chemistry is you change

299
00:13:40,890 --> 00:13:43,290
the wave function so it's
a single-particle wave

300
00:13:43,290 --> 00:13:46,890
function, which basically means
when you solve the equations,

301
00:13:46,890 --> 00:13:50,005
there are no more
many-body terms left.

302
00:13:50,005 --> 00:13:51,380
And in density
functional theory,

303
00:13:51,380 --> 00:13:54,530
you change the Hamiltonian so
that you explicitly get rid

304
00:13:54,530 --> 00:13:56,360
of the many-body interactions.

305
00:13:56,360 --> 00:13:59,950
Either way, you're left with
a single-particle picture.

306
00:13:59,950 --> 00:14:01,120
That's really the trick.

307
00:14:01,120 --> 00:14:04,060
In both communities,
what you end up with

308
00:14:04,060 --> 00:14:05,380
is a single-particle picture.

309
00:14:05,380 --> 00:14:08,440
Now that's something that you
can solve in less than the age

310
00:14:08,440 --> 00:14:12,810
of the universe on a
computer, and that's the key.

311
00:14:12,810 --> 00:14:14,838
You're left with these
single-particle pictures.

312
00:14:14,838 --> 00:14:16,380
What is this
single-particle picture?

313
00:14:16,380 --> 00:14:17,730
Who can tell me?

314
00:14:17,730 --> 00:14:19,720
Did you talk about that?

315
00:14:19,720 --> 00:14:25,220
You go from a many-body picture
to a single-particle picture.

316
00:14:25,220 --> 00:14:26,000
Take a guess.

317
00:14:30,190 --> 00:14:33,430
Yeah, I see that
you want to guess.

318
00:14:33,430 --> 00:14:36,010
Yeah, yeah, go ahead.

319
00:14:36,010 --> 00:14:39,970
AUDIENCE: It's one where all
the variables in your theory

320
00:14:39,970 --> 00:14:45,060
only sort of depend on--

321
00:14:45,060 --> 00:14:49,000
all the things in
your theory only

322
00:14:49,000 --> 00:14:53,530
depend on the variables
for one particle.

323
00:14:53,530 --> 00:14:55,240
JEFFREY C GROSSMAN:
Basically yes.

324
00:14:55,240 --> 00:14:56,800
I mean, that's
exactly it, right?

325
00:14:56,800 --> 00:14:59,560
So now my electrons--

326
00:14:59,560 --> 00:15:01,780
my electrons are like this.

327
00:15:01,780 --> 00:15:05,570
In my real system, here
are my electrons, all

328
00:15:05,570 --> 00:15:10,420
those E's, and there they are.

329
00:15:10,420 --> 00:15:12,610
But what I'm saying
is that this isn't--

330
00:15:12,610 --> 00:15:14,295
I can't describe
this because, look,

331
00:15:14,295 --> 00:15:16,420
that's when I have to take
into account these guys.

332
00:15:16,420 --> 00:15:20,050
Look, that's this term
here, the R minus r

333
00:15:20,050 --> 00:15:22,940
is the relative positions
of two electrons.

334
00:15:22,940 --> 00:15:24,640
And I even need
to take these guys

335
00:15:24,640 --> 00:15:28,030
and these guys and those guys,
and that's the many-body part.

336
00:15:28,030 --> 00:15:31,900
That's not solvable, basically,
not for computational material

337
00:15:31,900 --> 00:15:32,710
science.

338
00:15:32,710 --> 00:15:35,860
So what we need to do is--

339
00:15:35,860 --> 00:15:39,070
I mean, it's solvable in certain
ways, but it's very hard.

340
00:15:39,070 --> 00:15:41,410
I should put it that way.

341
00:15:41,410 --> 00:15:45,490
So the single-particle
picture is to say, sorry,

342
00:15:45,490 --> 00:15:48,820
but you're going to lose all
this individualness here,

343
00:15:48,820 --> 00:15:50,500
and each electron--

344
00:15:50,500 --> 00:15:52,600
I'm going to now map
this guy over here--

345
00:15:52,600 --> 00:15:55,960
is only going to feel
some potential field,

346
00:15:55,960 --> 00:16:01,060
some mean field, some
mean potential average

347
00:16:01,060 --> 00:16:02,800
of all of those other electrons.

348
00:16:02,800 --> 00:16:05,920
It swims in an
average potential now.

349
00:16:05,920 --> 00:16:08,770
And so I basically have
just eliminated the problem.

350
00:16:08,770 --> 00:16:10,650
The problem was this.

351
00:16:10,650 --> 00:16:13,840
It's too hard to solve on
the computer, certainly

352
00:16:13,840 --> 00:16:15,280
analytically but
also on computer.

353
00:16:15,280 --> 00:16:17,380
And so I've changed it to this.

354
00:16:17,380 --> 00:16:20,680
That's basically what
both of these things do.

355
00:16:20,680 --> 00:16:23,140
Quantum chemistry and
density functional theory

356
00:16:23,140 --> 00:16:26,720
both result in this picture,
this very simplified picture.

357
00:16:26,720 --> 00:16:30,040
It's called a mean-field
picture because each electron

358
00:16:30,040 --> 00:16:33,260
is in a mean field
of the rest of them.

359
00:16:33,260 --> 00:16:35,110
They do it in different ways.

360
00:16:35,110 --> 00:16:39,550
Quantum chemists do it by
simplifying the wave function,

361
00:16:39,550 --> 00:16:42,460
and the physicists
did it originally

362
00:16:42,460 --> 00:16:46,003
by simplifying the Hamiltonian.

363
00:16:46,003 --> 00:16:47,920
And there was a lot of
really interesting sort

364
00:16:47,920 --> 00:16:51,230
of discussion, to
put it lightly,

365
00:16:51,230 --> 00:16:53,450
about which path was better.

366
00:16:53,450 --> 00:16:55,640
And then I think now
both communities,

367
00:16:55,640 --> 00:16:57,607
I think, work in both ways.

368
00:16:57,607 --> 00:16:58,940
There's a lot of back and forth.

369
00:16:58,940 --> 00:17:01,040
But density functional
theory is definitely

370
00:17:01,040 --> 00:17:03,110
the one we're going to
work on with this class

371
00:17:03,110 --> 00:17:06,730
because it strikes a balance.

372
00:17:06,730 --> 00:17:10,930
It strikes a very nice
balance as a method that

373
00:17:10,930 --> 00:17:13,060
can capture enough accuracy.

374
00:17:13,060 --> 00:17:15,202
It sacrifices something.

375
00:17:15,202 --> 00:17:16,660
It definitely
sacrifices something.

376
00:17:16,660 --> 00:17:18,700
You approximate the Hamiltonian.

377
00:17:18,700 --> 00:17:22,450
But it doesn't sacrifice--
it still is pretty accurate,

378
00:17:22,450 --> 00:17:24,310
and it's been shown
to be pretty accurate

379
00:17:24,310 --> 00:17:28,690
for many, many, many problems.

380
00:17:28,690 --> 00:17:33,485
And you can see that it's also
right in this region here,

381
00:17:33,485 --> 00:17:35,110
which is a really
nice region to be in.

382
00:17:35,110 --> 00:17:37,660
Now why is this a nice region
to be in on the vertical axis?

383
00:17:43,287 --> 00:17:45,270
AUDIENCE: You can solve
for larger molecules.

384
00:17:45,270 --> 00:17:47,520
JEFFREY C GROSSMAN: You can
solve for large molecules,

385
00:17:47,520 --> 00:17:48,350
yeah.

386
00:17:48,350 --> 00:17:48,860
What else?

387
00:17:54,840 --> 00:17:55,890
Yeah?

388
00:17:55,890 --> 00:17:58,510
AUDIENCE: It's growing pretty
quickly, so in the future

389
00:17:58,510 --> 00:18:00,240
you'll be able to
do even more atoms.

390
00:18:00,240 --> 00:18:01,407
JEFFREY C GROSSMAN: Totally.

391
00:18:01,407 --> 00:18:04,830
Nice n-cubed scaling--
well, sorry, n-cubed scaling

392
00:18:04,830 --> 00:18:07,780
with the method with size but
also increase in the speed

393
00:18:07,780 --> 00:18:08,280
here.

394
00:18:11,500 --> 00:18:12,282
What else?

395
00:18:12,282 --> 00:18:13,990
What else might this
be a nice sweet spot

396
00:18:13,990 --> 00:18:15,820
for computational
materials design?

397
00:18:18,720 --> 00:18:22,620
1,000 to 10,000 atoms, sort of
where the limits of DFT are.

398
00:18:26,500 --> 00:18:30,060
Well, what are we solving for?

399
00:18:30,060 --> 00:18:31,065
Electrons, right?

400
00:18:31,065 --> 00:18:34,020
We're solving for those
properties of electrons.

401
00:18:34,020 --> 00:18:36,060
Now, why is this
a nice sweet spot?

402
00:18:44,050 --> 00:18:48,280
Well, when might I need less
or more atoms than that?

403
00:18:48,280 --> 00:18:50,290
OK, so let's say I'm in
coupled cluster, which

404
00:18:50,290 --> 00:18:54,380
is one of these ways of making
the wave function simpler.

405
00:18:54,380 --> 00:18:58,510
It's a very accurate method,
but you can only do today,

406
00:18:58,510 --> 00:19:04,763
I don't know, 15 atoms
accurately, maybe 20.

407
00:19:04,763 --> 00:19:06,180
What would be
limiting about that?

408
00:19:09,210 --> 00:19:10,380
Is 20 atoms enough?

409
00:19:10,380 --> 00:19:10,980
Yeah?

410
00:19:10,980 --> 00:19:12,260
AUDIENCE: If you're
trying to figure out, say,

411
00:19:12,260 --> 00:19:14,160
the electrical properties
of some material,

412
00:19:14,160 --> 00:19:16,560
you don't really
have enough space

413
00:19:16,560 --> 00:19:19,350
to take into account some
three-dimensional block

414
00:19:19,350 --> 00:19:20,017
of stuff.

415
00:19:20,017 --> 00:19:22,350
JEFFREY C GROSSMAN: And when
would you run out of space?

416
00:19:22,350 --> 00:19:22,892
What matters?

417
00:19:26,415 --> 00:19:28,540
AUDIENCE: Boundary conditions
and things like that.

418
00:19:28,540 --> 00:19:28,650
JEFFREY C GROSSMAN: Yeah.

419
00:19:28,650 --> 00:19:31,050
AUDIENCE: So if you're
talking quantum dots or things

420
00:19:31,050 --> 00:19:32,670
like that, you have
different sizes

421
00:19:32,670 --> 00:19:34,713
contributing to the
properties of the material.

422
00:19:34,713 --> 00:19:36,630
JEFFREY C GROSSMAN: Yeah,
and you can't really

423
00:19:36,630 --> 00:19:38,370
explore those with
just 20 atoms.

424
00:19:38,370 --> 00:19:39,660
Definitely a good point.

425
00:19:39,660 --> 00:19:40,460
Anything else?

426
00:19:45,590 --> 00:19:46,880
Why else might this--

427
00:19:46,880 --> 00:19:48,500
so it's not just--

428
00:19:48,500 --> 00:19:49,760
it's the size.

429
00:19:49,760 --> 00:19:53,120
When I hear it's the size of
the material you want to study

430
00:19:53,120 --> 00:19:55,730
and 1 to 10,000 is a
pretty good region,

431
00:19:55,730 --> 00:19:58,280
you can play a
lot-- welcome back.

432
00:19:58,280 --> 00:20:04,310
You can play a lot
with that size range.

433
00:20:04,310 --> 00:20:07,670
You can model a lot of
materials in that size range.

434
00:20:07,670 --> 00:20:10,670
But importantly, the
thing you're modeling

435
00:20:10,670 --> 00:20:12,090
are the electrons.

436
00:20:12,090 --> 00:20:15,080
And so what counts,
it's not just

437
00:20:15,080 --> 00:20:18,680
about how many atoms you can
put into your simulation.

438
00:20:18,680 --> 00:20:20,160
That's not what counts.

439
00:20:20,160 --> 00:20:24,470
You see these titles of papers
like million-atom simulation,

440
00:20:24,470 --> 00:20:27,980
billion-atom simulation,
trillion-atom simulation.

441
00:20:27,980 --> 00:20:28,822
OK, that's cool.

442
00:20:28,822 --> 00:20:29,780
You get a lot of atoms.

443
00:20:29,780 --> 00:20:30,560
Good for you.

444
00:20:30,560 --> 00:20:32,190
But what matters?

445
00:20:32,190 --> 00:20:36,350
What matters is did you need
those atoms for the property

446
00:20:36,350 --> 00:20:39,240
you care about?

447
00:20:39,240 --> 00:20:40,110
Did you need them?

448
00:20:40,110 --> 00:20:42,800
Now in some cases, maybe you do.

449
00:20:42,800 --> 00:20:46,870
But for electrons, very
often they're spread.

450
00:20:46,870 --> 00:20:52,110
What they want to do is
kind of more dominated

451
00:20:52,110 --> 00:20:54,360
by a few nearest-neighbor
distances,

452
00:20:54,360 --> 00:20:58,110
maybe 10-nearest-neighbor
distances in a crystal.

453
00:20:58,110 --> 00:21:02,170
In some cases they're very
spread out, like in a metal,

454
00:21:02,170 --> 00:21:04,530
and then we can use periodic
boundary conditions,

455
00:21:04,530 --> 00:21:07,890
and we can still
capture all the physics.

456
00:21:07,890 --> 00:21:11,340
But when you have interfaces
or roughness or molecules,

457
00:21:11,340 --> 00:21:13,570
the electrons aren't going to--

458
00:21:13,570 --> 00:21:16,850
even if you put a
million atoms in,

459
00:21:16,850 --> 00:21:19,790
you won't see anything different
than if you put a thousand

460
00:21:19,790 --> 00:21:21,110
atoms in.

461
00:21:21,110 --> 00:21:22,730
And that has--
for many problems.

462
00:21:22,730 --> 00:21:25,850
For many problems, not all, but
for many cool materials-design

463
00:21:25,850 --> 00:21:27,380
problems, that's the case.

464
00:21:27,380 --> 00:21:30,230
And that's why this is such
a nice sweet spot of a method

465
00:21:30,230 --> 00:21:33,950
because it hits in this range
where the stuff we care about,

466
00:21:33,950 --> 00:21:36,440
electrons, happen
to kind of play

467
00:21:36,440 --> 00:21:40,310
in this phase space of distance.

468
00:21:40,310 --> 00:21:41,930
That's where DFT is.

469
00:21:41,930 --> 00:21:43,840
That's why it's so powerful.

470
00:21:43,840 --> 00:21:47,660
Any questions?

471
00:21:47,660 --> 00:21:50,425
And right, I'm not
going to review.

472
00:21:50,425 --> 00:21:51,800
I just kind of
went through this.

473
00:21:51,800 --> 00:21:56,110
The approximation is to
work with the density,

474
00:21:56,110 --> 00:21:59,920
and you sort of throw everything
into a density formalism,

475
00:21:59,920 --> 00:22:04,630
and you punt on the exchange--
on this interaction term that's

476
00:22:04,630 --> 00:22:08,440
all about this V. So density
functional theory is about what

477
00:22:08,440 --> 00:22:13,000
functional you use to capture
these many-body effects

478
00:22:13,000 --> 00:22:15,670
in a single-particle way.

479
00:22:15,670 --> 00:22:19,600
That's really what
it comes down to.

480
00:22:19,600 --> 00:22:23,710
And this is all sort
of review, right?

481
00:22:23,710 --> 00:22:25,880
I kind of went through this.

482
00:22:25,880 --> 00:22:27,580
You will not be
tested on this math,

483
00:22:27,580 --> 00:22:29,663
but I think you went through
it already last week.

484
00:22:29,663 --> 00:22:30,610
Correct?

485
00:22:30,610 --> 00:22:31,870
Some nods.

486
00:22:31,870 --> 00:22:32,920
OK.

487
00:22:32,920 --> 00:22:42,120
And so you get
basically an equation

488
00:22:42,120 --> 00:22:45,450
where the potential
that I just showed you

489
00:22:45,450 --> 00:22:53,550
can be written as this potential
plus this exchange correlation

490
00:22:53,550 --> 00:22:58,200
functional, which is basically
a function only of this one

491
00:22:58,200 --> 00:22:59,100
electron.

492
00:22:59,100 --> 00:23:00,520
That's why it works so well.

493
00:23:00,520 --> 00:23:06,195
It's not a function anymore
of all these other electrons.

494
00:23:06,195 --> 00:23:08,670
I kind of want to make
sure we get the key points.

495
00:23:11,810 --> 00:23:15,170
Now the way you solve
this in a computer, which

496
00:23:15,170 --> 00:23:20,220
is what the nanoHUB does
for you when it works--

497
00:23:20,220 --> 00:23:22,684
I had some interesting crashes
last night on the nanoHUB--

498
00:23:25,410 --> 00:23:28,375
is basically you
have this equation.

499
00:23:28,375 --> 00:23:30,000
So what density
functional theory does,

500
00:23:30,000 --> 00:23:33,690
you see, this is
the beauty of it.

501
00:23:33,690 --> 00:23:35,460
What does that look like to you?

502
00:23:35,460 --> 00:23:39,870
I mean, that looks like
something that we did. ,

503
00:23:39,870 --> 00:23:41,700
That's definitely
your Hamiltonian,

504
00:23:41,700 --> 00:23:44,280
but this equation now--
remember the many-body,

505
00:23:44,280 --> 00:23:47,460
multiparticle mess that
we just showed you?

506
00:23:47,460 --> 00:23:49,740
Now we're back
from that to this.

507
00:23:49,740 --> 00:23:53,640
What does that look like,
it's reminiscent of,

508
00:23:53,640 --> 00:23:57,780
and for which material?

509
00:23:57,780 --> 00:24:00,140
It sort of looks back like
hydrogen almost, right?

510
00:24:00,140 --> 00:24:05,410
That's not as simple as hydrogen
because V is now more complex,

511
00:24:05,410 --> 00:24:07,350
but it basically
turned the problem back

512
00:24:07,350 --> 00:24:08,800
into a single-particle problem.

513
00:24:08,800 --> 00:24:10,500
So now that's the
equation we solve

514
00:24:10,500 --> 00:24:13,200
once we go through the
density functional theory

515
00:24:13,200 --> 00:24:15,930
approximation.

516
00:24:15,930 --> 00:24:18,210
And you have to
solve it in what's

517
00:24:18,210 --> 00:24:21,300
called a self-consistent
way, which

518
00:24:21,300 --> 00:24:26,910
is to say you have to start
with a guess for your density.

519
00:24:26,910 --> 00:24:29,880
You plug it into the
equation, and you get out

520
00:24:29,880 --> 00:24:32,527
these wave functions.

521
00:24:32,527 --> 00:24:34,860
So you do get wave functions
in density function theory,

522
00:24:34,860 --> 00:24:39,870
but they're essentially just
a basis for the density.

523
00:24:39,870 --> 00:24:42,580
The conceptual framework is
to work with the density.

524
00:24:42,580 --> 00:24:44,280
So you start with the density.

525
00:24:44,280 --> 00:24:46,303
You plug it into here,
and you solve this.

526
00:24:46,303 --> 00:24:48,720
The computer solves this, and
it gets you a wave function.

527
00:24:48,720 --> 00:24:51,960
And then from that wave function
you can get a new density

528
00:24:51,960 --> 00:24:53,670
because the density
is, after all, just

529
00:24:53,670 --> 00:24:55,380
this sum over these
things squared.

530
00:24:55,380 --> 00:24:58,620
We know that because we
talked about how that's what

531
00:24:58,620 --> 00:25:00,420
density is, electron density.

532
00:25:00,420 --> 00:25:03,930
So does everybody know
what I'm talking about?

533
00:25:03,930 --> 00:25:08,690
Probability-- electron
density is where it is.

534
00:25:08,690 --> 00:25:12,750
It's a probability distribution.

535
00:25:12,750 --> 00:25:14,750
And so that you get from that.

536
00:25:14,750 --> 00:25:15,750
You put it back in here.

537
00:25:15,750 --> 00:25:20,055
You do it again, and
basically you stop when what?

538
00:25:20,055 --> 00:25:20,937
AUDIENCE: [INAUDIBLE]

539
00:25:20,937 --> 00:25:22,770
JEFFREY C GROSSMAN:
When you're about right.

540
00:25:22,770 --> 00:25:24,390
I love that answer.

541
00:25:24,390 --> 00:25:26,430
Tell me more.

542
00:25:26,430 --> 00:25:27,210
When do you stop?

543
00:25:27,210 --> 00:25:30,660
If it's a self-consistent
loop, I guess for this.

544
00:25:30,660 --> 00:25:31,660
I put it in here.

545
00:25:31,660 --> 00:25:33,360
I get a new set of these.

546
00:25:33,360 --> 00:25:35,670
They give me a new this, and
I put that back in there,

547
00:25:35,670 --> 00:25:36,900
and I get a new set.

548
00:25:36,900 --> 00:25:39,120
When should I stop?

549
00:25:39,120 --> 00:25:40,250
AUDIENCE: [INAUDIBLE]

550
00:25:40,250 --> 00:25:42,478
JEFFREY C GROSSMAN: Yeah,
when it doesn't change,

551
00:25:42,478 --> 00:25:43,770
when the answer doesn't change.

552
00:25:43,770 --> 00:25:46,190
And so that's what this
is showing you here.

553
00:25:46,190 --> 00:25:49,790
Is it self-consistent means
it didn't change, basically.

554
00:25:49,790 --> 00:25:53,417
You did this loop,
and it didn't change.

555
00:25:53,417 --> 00:25:55,250
And that's what it'll
look like in the code.

556
00:25:55,250 --> 00:25:57,190
You'll see energies,
total energies

557
00:25:57,190 --> 00:25:59,140
coming out of the
system, and they'll

558
00:25:59,140 --> 00:26:01,707
be sort of converging
to a value.

559
00:26:01,707 --> 00:26:03,790
And then the code will
say, OK, it's close enough.

560
00:26:10,010 --> 00:26:13,760
Now the other key thing is
you have to write these phis.

561
00:26:13,760 --> 00:26:16,840
When you talk about a phi--

562
00:26:16,840 --> 00:26:20,330
so this is the
Schrodinger equation.

563
00:26:20,330 --> 00:26:25,270
And then you write the psi in
terms of some set of orbitals.

564
00:26:25,270 --> 00:26:28,360
But to write an orbital--

565
00:26:28,360 --> 00:26:31,840
I mean, if I want
to write anything--

566
00:26:31,840 --> 00:26:33,940
if I want to write anything
on a computer-- that's

567
00:26:33,940 --> 00:26:35,230
my electron density.

568
00:26:35,230 --> 00:26:36,520
It's my orbital.

569
00:26:36,520 --> 00:26:39,250
I need to represent it
mathematically somehow.

570
00:26:39,250 --> 00:26:42,520
The computer can't
just take that.

571
00:26:42,520 --> 00:26:44,860
So you need functions
to represent these,

572
00:26:44,860 --> 00:26:47,530
and those are called
basis functions.

573
00:26:47,530 --> 00:26:49,240
So those basis
functions-- and you

574
00:26:49,240 --> 00:26:51,580
can use different kinds
of basis functions.

575
00:26:51,580 --> 00:26:54,050
You can use Gaussians.

576
00:26:54,050 --> 00:26:55,120
You can just use--

577
00:26:55,120 --> 00:26:58,570
if I want Gaussians, I would put
a nice one there and then maybe

578
00:26:58,570 --> 00:27:00,530
some more ones here.

579
00:27:00,530 --> 00:27:01,813
Well, that wouldn't work.

580
00:27:01,813 --> 00:27:03,730
Anyway, you need a bunch
of Gaussians centered

581
00:27:03,730 --> 00:27:05,770
in different places,
and you add them up,

582
00:27:05,770 --> 00:27:09,070
and they'd give you that
function back, approximately.

583
00:27:09,070 --> 00:27:12,790
So we have to represent these
things with basis functions.

584
00:27:12,790 --> 00:27:17,860
You can use plane waves, which
are really good for solids.

585
00:27:17,860 --> 00:27:20,810
You can use plane waves
for atoms as well.

586
00:27:20,810 --> 00:27:21,370
They're nice.

587
00:27:21,370 --> 00:27:23,995
Plane waves are nice for solids
because they're periodic, which

588
00:27:23,995 --> 00:27:26,270
is what your wave function is.

589
00:27:26,270 --> 00:27:27,280
Gesundheit.

590
00:27:27,280 --> 00:27:28,060
Gesundheit.

591
00:27:28,060 --> 00:27:30,878
The double.

592
00:27:30,878 --> 00:27:32,920
You can use them for atoms
and molecules as well,

593
00:27:32,920 --> 00:27:36,750
but you have to be a little
careful because a plane

594
00:27:36,750 --> 00:27:40,150
wave goes through the whole
cell of the simulation,

595
00:27:40,150 --> 00:27:42,330
but your molecule only
takes up a small part of it.

596
00:27:42,330 --> 00:27:43,830
So with plane waves,
you're actually

597
00:27:43,830 --> 00:27:45,880
sort of wasting those functions.

598
00:27:45,880 --> 00:27:50,430
But if you do it in a
smart way, it's not so bad.

599
00:27:50,430 --> 00:27:52,410
All right, so that's sort of--

600
00:27:52,410 --> 00:27:54,180
I wanted to kind
of touch on that.

601
00:27:54,180 --> 00:27:58,440
This is a really cool
movie that Lynn found.

602
00:27:58,440 --> 00:27:59,500
Why do we care?

603
00:27:59,500 --> 00:28:01,080
Well, this is the
kind of thing you

604
00:28:01,080 --> 00:28:04,760
can do when you know
where these electrons are

605
00:28:04,760 --> 00:28:07,760
for complex systems.

606
00:28:07,760 --> 00:28:10,040
This is a porphyrin ring.

607
00:28:10,040 --> 00:28:14,300
I think it's got zinc in the
center from this group here.

608
00:28:14,300 --> 00:28:16,108
And you can actually show--

609
00:28:16,108 --> 00:28:17,900
this is a computation,
and you can actually

610
00:28:17,900 --> 00:28:19,850
show what happens
to the electrons--

611
00:28:19,850 --> 00:28:22,550
the density of electrons
when you shine lasers on it.

612
00:28:22,550 --> 00:28:25,042
Now it turns out that
this is-- and there it is.

613
00:28:25,042 --> 00:28:26,750
So now you're going
to push on the system

614
00:28:26,750 --> 00:28:30,020
with lasers, which
cause a resonance,

615
00:28:30,020 --> 00:28:31,790
and it causes these
electrons to start

616
00:28:31,790 --> 00:28:35,780
sloshing back and forth
as you pump this porphyrin

617
00:28:35,780 --> 00:28:36,620
ring with lasers.

618
00:28:36,620 --> 00:28:39,350
So you can see the
lasers down here.

619
00:28:39,350 --> 00:28:40,550
They're not actually real.

620
00:28:40,550 --> 00:28:42,020
It's a computation.

621
00:28:42,020 --> 00:28:45,428
But what you see
is very important.

622
00:28:45,428 --> 00:28:46,220
Look at that slosh.

623
00:28:46,220 --> 00:28:46,880
Look at that.

624
00:28:46,880 --> 00:28:49,220
Now that is really important.

625
00:28:49,220 --> 00:28:53,600
The sloshing of those electrons
is really, really important

626
00:28:53,600 --> 00:28:56,610
for how this molecule
absorbs light,

627
00:28:56,610 --> 00:29:00,690
and that's why it was studied
because this is what we're

628
00:29:00,690 --> 00:29:05,190
going to end with today is where
those electrons are determines

629
00:29:05,190 --> 00:29:07,380
the band gap of the
molecule, and it determines

630
00:29:07,380 --> 00:29:09,900
its optical properties,
what we talked

631
00:29:09,900 --> 00:29:11,970
about in the very beginning,
something we really

632
00:29:11,970 --> 00:29:16,830
need when we're talking
about photoactive materials

633
00:29:16,830 --> 00:29:17,760
like porphyrin.

634
00:29:17,760 --> 00:29:21,270
And porphyrin has many
important properties, right?

635
00:29:21,270 --> 00:29:22,880
It's a beautiful molecule.

636
00:29:22,880 --> 00:29:24,630
These are the kinds
of molecules and these

637
00:29:24,630 --> 00:29:26,910
are the kinds of
things you can get now

638
00:29:26,910 --> 00:29:28,740
using these approximations.

639
00:29:28,740 --> 00:29:33,000
You can get electron densities
and then correlate those

640
00:29:33,000 --> 00:29:34,490
to something really important.

641
00:29:34,490 --> 00:29:36,810
And that's what we're going
to do by the end of today

642
00:29:36,810 --> 00:29:39,150
and in our homeworks
for solar thermal fuels.

643
00:29:42,770 --> 00:29:46,160
Do you guys want me to post
these videos on Steller?

644
00:29:46,160 --> 00:29:47,870
Do you guys look at
the Stellar stuff?

645
00:29:47,870 --> 00:29:49,370
OK, I'll definitely
do that then.

646
00:29:49,370 --> 00:29:51,230
I wasn't sure if anybody--

647
00:29:51,230 --> 00:29:52,730
OK.

648
00:29:52,730 --> 00:29:53,490
So any questions?

649
00:29:53,490 --> 00:29:55,657
So that was sort of a little
review of where we are.

650
00:29:58,310 --> 00:29:59,860
Let's do a calculation.

651
00:29:59,860 --> 00:30:02,800
Actually, before we move
on, let's just do a calc--

652
00:30:02,800 --> 00:30:04,490
now that's a little
embarrassing.

653
00:30:04,490 --> 00:30:06,710
Let's put that over here.

654
00:30:06,710 --> 00:30:09,680
That was taken a few years ago.

655
00:30:09,680 --> 00:30:13,360
Now there's MIT.

656
00:30:13,360 --> 00:30:15,980
Oh yeah.

657
00:30:15,980 --> 00:30:17,526
It was out in Berkeley, yeah.

658
00:30:20,750 --> 00:30:22,290
Now let's see if this works.

659
00:30:22,290 --> 00:30:22,790
Aha!

660
00:30:25,760 --> 00:30:29,030
Now the two tools that
matter for quantum mechanics

661
00:30:29,030 --> 00:30:31,700
in this toolset are quantum
chemistry-- and this

662
00:30:31,700 --> 00:30:32,810
is doing just what I said.

663
00:30:32,810 --> 00:30:34,893
It's doing what those
quantum chemists like to do.

664
00:30:34,893 --> 00:30:37,010
It's messing with
the wave function.

665
00:30:37,010 --> 00:30:39,260
And this is the density
functional theory code

666
00:30:39,260 --> 00:30:42,490
we're going to use SIESTA,
which is a cool name.

667
00:30:42,490 --> 00:30:45,873
And this is actually
messing with the density.

668
00:30:45,873 --> 00:30:47,290
This is density
functional theory.

669
00:30:47,290 --> 00:30:49,180
Although this now, like I
said, the two communities

670
00:30:49,180 --> 00:30:49,990
have overlapped.

671
00:30:49,990 --> 00:30:53,545
This code now can also do
density functional theory.

672
00:30:53,545 --> 00:30:55,420
But these are the two
quantum-mechanics codes

673
00:30:55,420 --> 00:30:56,570
we're going to use.

674
00:30:56,570 --> 00:30:58,390
And if you go-- let's
say you go to here.

675
00:30:58,390 --> 00:31:01,660
I just want to just do one
little calculation together.

676
00:31:04,660 --> 00:31:08,900
And what I want to
do is the following.

677
00:31:08,900 --> 00:31:10,340
There's some inputs
here that are

678
00:31:10,340 --> 00:31:11,960
worth-- oh, you're kidding me.

679
00:31:11,960 --> 00:31:12,605
I can't scroll.

680
00:31:15,890 --> 00:31:16,840
Unbelievable.

681
00:31:21,370 --> 00:31:26,930
Well, that's really frustrating.

682
00:31:26,930 --> 00:31:30,160
So there's no way-- it
doesn't let me actually

683
00:31:30,160 --> 00:31:31,450
scroll down here.

684
00:31:31,450 --> 00:31:32,680
Oh, there.

685
00:31:32,680 --> 00:31:33,640
Thank you.

686
00:31:33,640 --> 00:31:36,190
OK, I'm good.

687
00:31:36,190 --> 00:31:40,297
So here you see it's got water,
and there are some things

688
00:31:40,297 --> 00:31:41,380
you can do-- that's right.

689
00:31:41,380 --> 00:31:44,080
So the cursor has to
actually be over there.

690
00:31:46,970 --> 00:31:48,410
And here are some inputs.

691
00:31:48,410 --> 00:31:50,960
So we'll work with water.

692
00:31:50,960 --> 00:31:52,520
That's the basis set.

693
00:31:52,520 --> 00:31:54,590
Low means like what?

694
00:31:54,590 --> 00:31:56,540
Do you think that's good or bad?

695
00:31:56,540 --> 00:31:58,220
Yeah, it's not very good.

696
00:31:58,220 --> 00:32:01,220
Medium and high, those
are the three options.

697
00:32:01,220 --> 00:32:03,500
Now G means Gaussians.

698
00:32:03,500 --> 00:32:06,800
The other person who won the
Nobel Prize together with Kohn

699
00:32:06,800 --> 00:32:11,140
that year was Pople,
and Pople won it

700
00:32:11,140 --> 00:32:13,330
for some really
important work that he

701
00:32:13,330 --> 00:32:16,730
did relating to these
basis sets, basically,

702
00:32:16,730 --> 00:32:19,580
and some important
chemistry work he'd done.

703
00:32:19,580 --> 00:32:23,300
But that G stands for
Gaussian, and the 3-21G

704
00:32:23,300 --> 00:32:26,260
is a set that he
made which became

705
00:32:26,260 --> 00:32:29,020
incredibly important to helping
quantum chemistry move forward.

706
00:32:29,020 --> 00:32:32,080
He made sets of basis sets.

707
00:32:32,080 --> 00:32:35,560
And if you google
"basis set order form,"

708
00:32:35,560 --> 00:32:37,750
there's a website where
you can enter any element,

709
00:32:37,750 --> 00:32:42,620
and there are hundreds and
hundreds and hundreds of basis

710
00:32:42,620 --> 00:32:45,610
sets that have been
developed and published,

711
00:32:45,610 --> 00:32:47,092
and these are some of them.

712
00:32:47,092 --> 00:32:48,550
And this is just--
you go from here

713
00:32:48,550 --> 00:32:49,450
to the next and the next one.

714
00:32:49,450 --> 00:32:51,320
You just add more
functions, basically,

715
00:32:51,320 --> 00:32:54,650
and so the calculation
gets longer.

716
00:32:54,650 --> 00:32:57,870
When is it enough?

717
00:32:57,870 --> 00:32:59,580
When do I have enough
of a basis set?

718
00:32:59,580 --> 00:33:01,330
That was one question
I wanted to discuss.

719
00:33:07,770 --> 00:33:09,740
10?

720
00:33:09,740 --> 00:33:10,990
Oh, I love that answer.

721
00:33:10,990 --> 00:33:13,790
I thought 10 was
pretty good too.

722
00:33:13,790 --> 00:33:15,410
It depends.

723
00:33:15,410 --> 00:33:16,700
That's the answer.

724
00:33:16,700 --> 00:33:18,820
Now what does it depend on?

725
00:33:18,820 --> 00:33:20,820
AUDIENCE: What kind of
calculation you're doing.

726
00:33:20,820 --> 00:33:21,420
JEFFREY C GROSSMAN: And?

727
00:33:21,420 --> 00:33:22,290
AUDIENCE: How accurate you
want the results to be.

728
00:33:22,290 --> 00:33:23,850
JEFFREY C GROSSMAN: How accurate
you want your results to be,

729
00:33:23,850 --> 00:33:25,410
what calculation you're doing.

730
00:33:25,410 --> 00:33:27,897
What do you mean by what
calculation you're doing?

731
00:33:27,897 --> 00:33:29,272
AUDIENCE: If you
just want energy

732
00:33:29,272 --> 00:33:31,860
or whether you want to get
properties [INAUDIBLE]..

733
00:33:31,860 --> 00:33:33,690
JEFFREY C GROSSMAN:
OK, so the property.

734
00:33:33,690 --> 00:33:37,010
It depends on the property
you're calculating.

735
00:33:37,010 --> 00:33:38,850
How do you know when to stop?

736
00:33:38,850 --> 00:33:42,410
So I'm going to do a
calculation with 3-21G,

737
00:33:42,410 --> 00:33:47,520
and I'm going to calculate
the water molecule using

738
00:33:47,520 --> 00:33:48,870
the formalism you just saw.

739
00:33:48,870 --> 00:33:50,448
That's what this code is doing.

740
00:33:50,448 --> 00:33:52,740
And you're going to see a
nice pretty picture of water.

741
00:33:52,740 --> 00:33:53,970
There it is.

742
00:33:53,970 --> 00:33:57,160
And then you have
these key outputs.

743
00:33:57,160 --> 00:33:59,050
And there's my total energy.

744
00:33:59,050 --> 00:34:01,360
My total energy of
this water molecule

745
00:34:01,360 --> 00:34:05,860
is 2,056.56 electronvolts.

746
00:34:05,860 --> 00:34:06,465
Yes?

747
00:34:06,465 --> 00:34:08,110
AUDIENCE: What's a basis set?

748
00:34:08,110 --> 00:34:09,152
JEFFREY C GROSSMAN: Yeah.

749
00:34:09,152 --> 00:34:12,429
So a basis set is
those functions

750
00:34:12,429 --> 00:34:17,480
that the computer needs to
represent the wave functions.

751
00:34:17,480 --> 00:34:20,440
So if this is your
wave function--

752
00:34:20,440 --> 00:34:23,440
if your wave function
looks like this--

753
00:34:27,150 --> 00:34:31,520
let's say this is phi versus r.

754
00:34:31,520 --> 00:34:34,120
By the way, does anybody know
which wave function this is?

755
00:34:34,120 --> 00:34:36,239
That is a wave function.

756
00:34:36,239 --> 00:34:37,739
I didn't just make it up.

757
00:34:37,739 --> 00:34:39,090
It belongs to an element.

758
00:34:42,600 --> 00:34:46,409
It's the 1s orbital of
hydrogen. You got it.

759
00:34:46,409 --> 00:34:48,900
That's the r dependence of
the 1s orbital of hydrogen.

760
00:34:48,900 --> 00:34:50,770
It looks like an exponential.

761
00:34:50,770 --> 00:34:53,370
So should I use an
exponential to represent

762
00:34:53,370 --> 00:34:55,239
this in a computer?

763
00:34:55,239 --> 00:34:58,900
You bet except
no, and the reason

764
00:34:58,900 --> 00:35:03,340
is that those are
slow to calculate.

765
00:35:03,340 --> 00:35:06,590
Exponentials are kind of
slow, exponential functions.

766
00:35:06,590 --> 00:35:09,230
So early on
exponentials were used,

767
00:35:09,230 --> 00:35:11,230
and then it was realized
that you could actually

768
00:35:11,230 --> 00:35:18,550
represent this pretty darn
well with Gaussians, like three

769
00:35:18,550 --> 00:35:20,930
or four Gaussians, and
you'd kind of get it right.

770
00:35:20,930 --> 00:35:22,330
You'd never get this part here.

771
00:35:22,330 --> 00:35:25,300
You can't get a finite slope
at zero with Gaussians,

772
00:35:25,300 --> 00:35:27,820
but you can come so close
that it doesn't matter.

773
00:35:27,820 --> 00:35:30,555
And so because Gaussians
have advantages--

774
00:35:30,555 --> 00:35:31,930
we won't go into
details, but I'm

775
00:35:31,930 --> 00:35:33,440
happy to talk to
anybody who wants.

776
00:35:33,440 --> 00:35:34,870
Gaussians have
advantages in terms

777
00:35:34,870 --> 00:35:37,470
of computing
integrals on computers

778
00:35:37,470 --> 00:35:41,850
so that you can actually use
some of the formalism that's

779
00:35:41,850 --> 00:35:44,160
been developed to do
integration with Gaussians

780
00:35:44,160 --> 00:35:45,800
and do it very quickly
and efficiently.

781
00:35:45,800 --> 00:35:48,000
You cannot do it
with exponentials.

782
00:35:48,000 --> 00:35:51,600
And because of that,
the chemists early on

783
00:35:51,600 --> 00:35:53,790
started using Gaussians
for their basic sets,

784
00:35:53,790 --> 00:35:56,820
and all these Pople sets,
those are all Gaussians.

785
00:35:56,820 --> 00:35:58,500
Now when you use
plane waves, that's

786
00:35:58,500 --> 00:35:59,760
a different kind of function.

787
00:35:59,760 --> 00:36:02,750
That's a sine and
cosine function.

788
00:36:02,750 --> 00:36:06,660
And so there you're
using functions like this

789
00:36:06,660 --> 00:36:09,270
to reproduce your psi.

790
00:36:09,270 --> 00:36:10,920
Either way, what
you're doing is you're

791
00:36:10,920 --> 00:36:12,330
going to add a
bunch of functions

792
00:36:12,330 --> 00:36:15,600
together to try to
make up your psi,

793
00:36:15,600 --> 00:36:17,845
and you've got to have
enough to do it justice.

794
00:36:17,845 --> 00:36:19,470
And that was the
question is how do you

795
00:36:19,470 --> 00:36:20,637
know when you've had enough?

796
00:36:20,637 --> 00:36:24,840
It's a very important part and
problem in quantum mechanics--

797
00:36:24,840 --> 00:36:26,400
in computing with
quantum mechanics

798
00:36:26,400 --> 00:36:30,060
that doesn't exist in
classical potentials, right?

799
00:36:30,060 --> 00:36:32,970
See, classical potentials, this
is not a convergence problem.

800
00:36:32,970 --> 00:36:34,920
You don't converge
your basis set.

801
00:36:34,920 --> 00:36:39,460
You just have a potential,
and you calculate it.

802
00:36:39,460 --> 00:36:42,340
Here you have to represent
psi mathematically somehow.

803
00:36:42,340 --> 00:36:43,840
Here you're doing
it with Gaussians.

804
00:36:43,840 --> 00:36:46,570
With SIESTA, actually
it's not plane waves.

805
00:36:46,570 --> 00:36:51,670
It's a different kind of
function like Gaussians.

806
00:36:51,670 --> 00:36:53,900
But in a way, it doesn't matter.

807
00:36:53,900 --> 00:36:57,053
They should all converge
to the same answer, right?

808
00:36:57,053 --> 00:36:58,720
You just have to
understand that this is

809
00:36:58,720 --> 00:37:00,230
what's going on under the hood.

810
00:37:00,230 --> 00:37:02,110
So again I ask,
when is it enough?

811
00:37:02,110 --> 00:37:04,228
When do I have enough
basis functions?

812
00:37:08,448 --> 00:37:10,990
AUDIENCE: When you approximate
your wave function well enough

813
00:37:10,990 --> 00:37:12,100
with your basis set.

814
00:37:12,100 --> 00:37:14,433
JEFFREY C GROSSMAN: And how
do I know if I've done that?

815
00:37:17,330 --> 00:37:19,700
AUDIENCE: When you check
for self-consistency.

816
00:37:19,700 --> 00:37:21,050
Is that [INAUDIBLE]?

817
00:37:21,050 --> 00:37:25,090
JEFFREY C GROSSMAN: That's
within a single calculation.

818
00:37:25,090 --> 00:37:28,920
How do I know I've used
a good-enough basis set?

819
00:37:28,920 --> 00:37:30,270
Well, let's go back.

820
00:37:30,270 --> 00:37:32,570
Let's go back a second
to what Sam said.

821
00:37:32,570 --> 00:37:34,530
It depends on the property.

822
00:37:34,530 --> 00:37:36,290
So now I'm going to
tell you a property.

823
00:37:36,290 --> 00:37:41,700
I want to know the binding
energy of a water molecule.

824
00:37:41,700 --> 00:37:44,247
How can I calculate that?

825
00:37:44,247 --> 00:37:45,830
Somebody tell me how
I calculate that.

826
00:37:45,830 --> 00:37:47,535
I have the energy of
the water molecule.

827
00:37:47,535 --> 00:37:48,660
Is that the binding energy?

828
00:37:48,660 --> 00:37:49,705
Yeah?

829
00:37:49,705 --> 00:37:51,580
AUDIENCE: The atoms that
are really far away,

830
00:37:51,580 --> 00:37:52,286
and then you
calculate the energy.

831
00:37:52,286 --> 00:37:54,273
And then if they
have energy with them

832
00:37:54,273 --> 00:37:56,690
close together minus the far
away, that will [INAUDIBLE]..

833
00:37:56,690 --> 00:37:57,857
JEFFREY C GROSSMAN: Exactly.

834
00:37:57,857 --> 00:38:02,720
So the energy-- so the
binding energy, E bind,

835
00:38:02,720 --> 00:38:08,247
is equal to the energy of the
molecule minus the energy sum

836
00:38:08,247 --> 00:38:09,455
over the energy of the atoms.

837
00:38:12,050 --> 00:38:14,030
So that's the property
I want to calculate.

838
00:38:14,030 --> 00:38:15,740
It could have been
another property.

839
00:38:15,740 --> 00:38:19,060
Could have been-- let's
say this is the gap.

840
00:38:19,060 --> 00:38:21,560
Yeah, it could have been the
electronic gap of the material.

841
00:38:24,750 --> 00:38:27,038
Now how do I know if I've
used enough basis functions?

842
00:38:27,038 --> 00:38:28,080
This is really important.

843
00:38:28,080 --> 00:38:29,783
Yeah?

844
00:38:29,783 --> 00:38:30,950
AUDIENCE: Experimental data.

845
00:38:30,950 --> 00:38:32,158
JEFFREY C GROSSMAN: OK, good.

846
00:38:32,158 --> 00:38:33,920
See if it matches
experimental data.

847
00:38:33,920 --> 00:38:37,110
Except there may
be other reasons

848
00:38:37,110 --> 00:38:43,530
it doesn't match experimental
data, not just the basis set.

849
00:38:43,530 --> 00:38:45,780
So how do I know if I've
just converged the basis set?

850
00:38:54,418 --> 00:38:56,210
AUDIENCE: Get the
lattice parameters of it.

851
00:38:56,210 --> 00:38:59,150
JEFFREY C GROSSMAN:
OK or along those

852
00:38:59,150 --> 00:39:02,020
lines, but that's still
comparing with experiment,

853
00:39:02,020 --> 00:39:06,740
which is always a good
thing to do when you can.

854
00:39:06,740 --> 00:39:08,480
Well, what if I just
do this calculation

855
00:39:08,480 --> 00:39:10,610
and then I do another one
with a higher basis set

856
00:39:10,610 --> 00:39:13,210
and it doesn't change?

857
00:39:13,210 --> 00:39:15,000
How about that?

858
00:39:15,000 --> 00:39:17,860
Well, it's the same as
the self-consistent thing.

859
00:39:17,860 --> 00:39:22,060
Once the answer doesn't
change, I've converged.

860
00:39:22,060 --> 00:39:24,192
But this isn't part of a
single calculation now.

861
00:39:24,192 --> 00:39:25,900
This is part of more
than one calculation

862
00:39:25,900 --> 00:39:26,733
that you have to do.

863
00:39:29,470 --> 00:39:33,010
So I'm going to go to a
larger basis set like medium

864
00:39:33,010 --> 00:39:35,500
and do simulate.

865
00:39:35,500 --> 00:39:37,330
And then it's going
to calculate this,

866
00:39:37,330 --> 00:39:38,560
and let's see what happened.

867
00:39:38,560 --> 00:39:40,540
The gap-- OK, there it is again.

868
00:39:40,540 --> 00:39:41,910
Thank you.

869
00:39:41,910 --> 00:39:43,810
The gap went to 19.

870
00:39:43,810 --> 00:39:44,550
Oh boy.

871
00:39:44,550 --> 00:39:47,160
So now my key output--

872
00:39:47,160 --> 00:39:52,190
let's see, is
2,068.6 electrons--

873
00:39:52,190 --> 00:39:55,220
electronvolts-- is the
energy with this basis set.

874
00:39:55,220 --> 00:39:56,490
Everything else is the same.

875
00:39:56,490 --> 00:40:00,770
And with the first basis set,
it's 2,056 electronvolts.

876
00:40:00,770 --> 00:40:03,170
Am I converged?

877
00:40:03,170 --> 00:40:06,240
Trick question.

878
00:40:06,240 --> 00:40:09,550
You still don't know.

879
00:40:09,550 --> 00:40:12,730
Well, except there's
something else to it

880
00:40:12,730 --> 00:40:15,200
that I'm trying to
get out of you guys.

881
00:40:15,200 --> 00:40:17,560
It's not an easy-- it's
not an easy thing to see,

882
00:40:17,560 --> 00:40:19,990
but it's really
important because we're

883
00:40:19,990 --> 00:40:22,210
talking about something
called convergence

884
00:40:22,210 --> 00:40:24,920
that you don't really have in
your classical force fields.

885
00:40:24,920 --> 00:40:26,560
You just have a
classical force field,

886
00:40:26,560 --> 00:40:29,500
and then you have another
one or another one, right?

887
00:40:29,500 --> 00:40:32,140
But here we're converging
within one calculation,

888
00:40:32,140 --> 00:40:34,520
one level of theory.

889
00:40:34,520 --> 00:40:35,940
And so what counts--

890
00:40:35,940 --> 00:40:39,350
you have to do this
when you do simulations.

891
00:40:39,350 --> 00:40:43,620
But what counts here is
not the total energy.

892
00:40:43,620 --> 00:40:44,120
Why?

893
00:40:44,120 --> 00:40:46,760
Because that's not the thing
I'm trying to converge.

894
00:40:46,760 --> 00:40:49,310
I'm trying to
converge this I said,

895
00:40:49,310 --> 00:40:53,340
the binding energy, which
is a difference of energies.

896
00:40:53,340 --> 00:40:58,700
And it very well may be that
the binding energy converges

897
00:40:58,700 --> 00:41:01,580
with a really bad
basis set right away

898
00:41:01,580 --> 00:41:05,987
and doesn't change when I get my
next basis set or my next one.

899
00:41:05,987 --> 00:41:07,820
Even though the total
energies are changing,

900
00:41:07,820 --> 00:41:10,040
they're changing in such a
way that the error cancels

901
00:41:10,040 --> 00:41:12,600
completely.

902
00:41:12,600 --> 00:41:14,430
This is the thing.

903
00:41:14,430 --> 00:41:17,680
It depends-- that's
why I love it depends.

904
00:41:17,680 --> 00:41:19,440
It depends is such
a great answer--

905
00:41:19,440 --> 00:41:22,950
on the property
you're simulating,

906
00:41:22,950 --> 00:41:25,650
and you have to do convergence
for the property you

907
00:41:25,650 --> 00:41:26,220
care about.

908
00:41:26,220 --> 00:41:27,600
It could have been the gap.

909
00:41:27,600 --> 00:41:33,600
20.7 was the low basis, and
the higher basis is 19.7.

910
00:41:33,600 --> 00:41:37,200
That's a whole EV difference
in the electronic gap.

911
00:41:37,200 --> 00:41:38,700
That's a lot of difference.

912
00:41:38,700 --> 00:41:40,020
That doesn't sound very good.

913
00:41:40,020 --> 00:41:42,353
Maybe we should go to-- let's
say we care about the gap.

914
00:41:42,353 --> 00:41:44,120
Let's go to one higher.

915
00:41:44,120 --> 00:41:46,810
Use a higher basis set.

916
00:41:46,810 --> 00:41:51,590
And we see here now the
gap, oh, it changed again.

917
00:41:51,590 --> 00:41:52,410
Uh oh.

918
00:41:56,510 --> 00:41:59,390
And so now it went to 18.

919
00:41:59,390 --> 00:42:02,060
So we had, with the
highest basis set,

920
00:42:02,060 --> 00:42:07,590
18, with the medium one, 19,
and with the lowest one, 20.

921
00:42:07,590 --> 00:42:09,273
So you can see it's
actually going down,

922
00:42:09,273 --> 00:42:10,940
which means the right
answer is probably

923
00:42:10,940 --> 00:42:13,108
going to be even lower.

924
00:42:13,108 --> 00:42:14,150
Does that look converged?

925
00:42:14,150 --> 00:42:15,080
Not to me.

926
00:42:15,080 --> 00:42:18,140
You actually need a
higher basis set still.

927
00:42:18,140 --> 00:42:21,547
This tool won't allow it because
it's not a very flexible tool,

928
00:42:21,547 --> 00:42:22,130
but that's OK.

929
00:42:22,130 --> 00:42:23,690
That's not the point.

930
00:42:23,690 --> 00:42:25,250
So does everybody
understand what

931
00:42:25,250 --> 00:42:26,990
I'm talking about when
I say convergence?

932
00:42:26,990 --> 00:42:29,300
We will come back
to convergence again

933
00:42:29,300 --> 00:42:32,330
when we do solids because
there's another thing in solids

934
00:42:32,330 --> 00:42:35,990
you have to converge, not just
your basis set but something

935
00:42:35,990 --> 00:42:37,850
else, which we'll
come back to and I'm

936
00:42:37,850 --> 00:42:43,150
going to save it as a surprise,
very exciting surprise.

937
00:42:43,150 --> 00:42:47,770
So we know that it can calculate
the binding energy of water.

938
00:42:47,770 --> 00:42:50,470
There's one more question I
want to ask you about, this spin

939
00:42:50,470 --> 00:42:51,850
thing here.

940
00:42:51,850 --> 00:42:56,030
Default-- default means
that it took a guess.

941
00:42:56,030 --> 00:42:58,700
And you can see that the
guess it made for water

942
00:42:58,700 --> 00:43:00,620
is that it's a spin singlet.

943
00:43:00,620 --> 00:43:03,990
Now we talked about
this in lecture two.

944
00:43:03,990 --> 00:43:07,390
Does everybody know what
a spin singlet means?

945
00:43:07,390 --> 00:43:11,050
So we're talking about
electrons filling orbitals.

946
00:43:11,050 --> 00:43:13,510
Remember, we're solving
for those electrons,

947
00:43:13,510 --> 00:43:16,730
and they fill
orbitals like this.

948
00:43:16,730 --> 00:43:22,250
Remember Pauli exclusion
and all that and filling--

949
00:43:22,250 --> 00:43:22,820
OK?

950
00:43:22,820 --> 00:43:27,290
Now if I-- this is the last
question I want to ask.

951
00:43:27,290 --> 00:43:30,230
Then we'll go back
to the lecture.

952
00:43:30,230 --> 00:43:32,300
Oxygen is 1s.

953
00:43:32,300 --> 00:43:36,962
Somebody tell me what else is
in oxygen. How many electrons?

954
00:43:39,680 --> 00:43:41,150
Three?

955
00:43:41,150 --> 00:43:42,320
Eight.

956
00:43:42,320 --> 00:43:46,715
So 1, 2, 3, 4, 5, 6, 7, 8.

957
00:43:46,715 --> 00:43:47,600
Right?

958
00:43:47,600 --> 00:43:48,200
Good.

959
00:43:48,200 --> 00:43:49,260
Very good.

960
00:43:49,260 --> 00:43:54,020
Now, is that a spin singlet?

961
00:43:54,020 --> 00:43:58,290
Does everybody remember what
singlet, doublet, triplet--

962
00:43:58,290 --> 00:44:01,380
so singlet, triplet,
doublet is very important

963
00:44:01,380 --> 00:44:05,810
because it tells the computer
how these electrons are

964
00:44:05,810 --> 00:44:07,550
filling these orbitals.

965
00:44:07,550 --> 00:44:09,350
So that's another
really important part

966
00:44:09,350 --> 00:44:10,340
of these simulations.

967
00:44:13,000 --> 00:44:16,300
A singlet means that
overall you have

968
00:44:16,300 --> 00:44:18,460
the same number of
spins pointing up

969
00:44:18,460 --> 00:44:20,410
as spins pointing down.

970
00:44:20,410 --> 00:44:22,230
Is that what I have for oxygen?

971
00:44:22,230 --> 00:44:25,230
Uh uh.

972
00:44:25,230 --> 00:44:31,470
So a doublet is when I have
one more pointing up or down,

973
00:44:31,470 --> 00:44:35,880
and a triplet is when I have
two extra electrons pointing

974
00:44:35,880 --> 00:44:37,140
up or down.

975
00:44:37,140 --> 00:44:39,030
Doesn't matter.

976
00:44:39,030 --> 00:44:45,580
So this is actually-- the
oxygen atom is a triplet.

977
00:44:45,580 --> 00:44:46,620
Now what about water?

978
00:44:46,620 --> 00:44:49,640
Well, it turns out
water is a singlet.

979
00:44:49,640 --> 00:44:52,620
So the default
guessed it correctly.

980
00:44:52,620 --> 00:44:55,530
Let's do the oxygen atom.

981
00:44:55,530 --> 00:44:59,270
Well, the code will do
whatever spin state you say.

982
00:44:59,270 --> 00:45:06,505
I'm going to say now that I just
want oxygen. So there it is.

983
00:45:06,505 --> 00:45:08,130
I'm going to do it
with the same basis.

984
00:45:14,140 --> 00:45:16,780
And now here it
is, and oh, that's

985
00:45:16,780 --> 00:45:21,880
a beautiful picture of oxygen.
And now you go to key outputs,

986
00:45:21,880 --> 00:45:22,990
and there's the energy.

987
00:45:22,990 --> 00:45:26,390
OK, so I'm going to do my
calculation of this binding

988
00:45:26,390 --> 00:45:26,890
energy.

989
00:45:26,890 --> 00:45:29,470
I just calculated the
energy of the atom.

990
00:45:29,470 --> 00:45:32,380
Can I use that?

991
00:45:32,380 --> 00:45:34,740
What's wrong with that?

992
00:45:34,740 --> 00:45:37,410
Look at the top line.

993
00:45:37,410 --> 00:45:41,670
No, second from the top line.

994
00:45:41,670 --> 00:45:44,380
What did it do?

995
00:45:44,380 --> 00:45:45,140
It did a singlet.

996
00:45:45,140 --> 00:45:46,180
Uh oh.

997
00:45:46,180 --> 00:45:47,230
It did this.

998
00:45:47,230 --> 00:45:48,970
It defaulted incorrectly.

999
00:45:48,970 --> 00:45:52,400
Never trust tools.

1000
00:45:52,400 --> 00:45:53,650
Always know what you're doing.

1001
00:45:53,650 --> 00:45:54,370
That's my point.

1002
00:45:54,370 --> 00:45:57,128
And these are the key
things you need to know.

1003
00:45:57,128 --> 00:45:58,920
You need to know that
the basis, and you've

1004
00:45:58,920 --> 00:46:00,320
got to know about spin.

1005
00:46:00,320 --> 00:46:03,050
You've got to know how those
electrons filled their levels.

1006
00:46:03,050 --> 00:46:09,280
And what this calculation
did is it did this.

1007
00:46:09,280 --> 00:46:10,210
Did it get an answer?

1008
00:46:10,210 --> 00:46:11,260
Sure.

1009
00:46:11,260 --> 00:46:13,350
Is it oxygen?

1010
00:46:13,350 --> 00:46:14,100
Well, yes.

1011
00:46:14,100 --> 00:46:18,000
in some very strange,
excited state of oxygen. But

1012
00:46:18,000 --> 00:46:20,530
that's not the right
state of oxygen.

1013
00:46:20,530 --> 00:46:23,190
And, in fact, you can
tell because remember

1014
00:46:23,190 --> 00:46:25,800
this energy, 2,032.1?

1015
00:46:25,800 --> 00:46:28,530
And now let's give it
the right spin state.

1016
00:46:28,530 --> 00:46:31,530
Let's make it a triplet,
which we know oxygen is,

1017
00:46:31,530 --> 00:46:35,520
and let's see what
the energy is.

1018
00:46:35,520 --> 00:46:36,660
OK, go away.

1019
00:46:36,660 --> 00:46:38,220
I know you're there.

1020
00:46:38,220 --> 00:46:41,240
Yes, that's the oxygen atom.

1021
00:46:41,240 --> 00:46:45,980
And now when I use the right
spin state, it's 2,035.6.

1022
00:46:45,980 --> 00:46:48,170
Do you see how much
lower the energy went?

1023
00:46:48,170 --> 00:46:54,720
Because, see, the right oxygen
is the way oxygen wants to be.

1024
00:46:54,720 --> 00:46:57,980
It's the ground
state of that atom.

1025
00:46:57,980 --> 00:47:02,300
If I compare it with
this excited state,

1026
00:47:02,300 --> 00:47:05,990
it's three electronvolts
higher in energy.

1027
00:47:05,990 --> 00:47:07,660
The more negative,
the more stable,

1028
00:47:07,660 --> 00:47:12,810
the more energy that has, the
more happy those electrons are.

1029
00:47:12,810 --> 00:47:14,895
So that means that the
electrons and oxygen really

1030
00:47:14,895 --> 00:47:16,770
want to be in a triplet
state, and you better

1031
00:47:16,770 --> 00:47:20,250
use that energy to do
things like calculate

1032
00:47:20,250 --> 00:47:21,360
the binding energy.

1033
00:47:21,360 --> 00:47:22,870
So you've got to think
about the spin state.

1034
00:47:22,870 --> 00:47:24,370
So that was the
other thing I wanted

1035
00:47:24,370 --> 00:47:28,965
to mention in doing this,
spin state and basis sets.

1036
00:47:28,965 --> 00:47:30,280
Any questions?

1037
00:47:33,750 --> 00:47:36,090
No questions?

1038
00:47:36,090 --> 00:47:40,425
In the last half hour or
so, I want to get to--

1039
00:47:40,425 --> 00:47:43,110
oh, 35 minutes even--

1040
00:47:43,110 --> 00:47:44,790
I want to get to this
first application

1041
00:47:44,790 --> 00:47:46,470
that I'm really excited about.

1042
00:47:46,470 --> 00:47:48,512
And I think you're kind
of now in a place where

1043
00:47:48,512 --> 00:47:50,220
we can actually think
about these-- think

1044
00:47:50,220 --> 00:47:55,260
about applications
for molecules.

1045
00:47:55,260 --> 00:47:56,490
And that's an area--

1046
00:47:56,490 --> 00:47:59,400
I want to introduce solar
chemical fuels to you,

1047
00:47:59,400 --> 00:48:02,610
and then we're going to talk
about why this kind of modeling

1048
00:48:02,610 --> 00:48:05,380
is so important here
and what we can do.

1049
00:48:05,380 --> 00:48:08,640
And then you'll have a
homework related to this.

1050
00:48:08,640 --> 00:48:10,560
OK, I love this.

1051
00:48:10,560 --> 00:48:12,840
I love that materials
are going to determine--

1052
00:48:12,840 --> 00:48:15,600
and then here we are down here.

1053
00:48:15,600 --> 00:48:16,590
I love this too.

1054
00:48:16,590 --> 00:48:18,480
I think I've shown
this to you, right,

1055
00:48:18,480 --> 00:48:20,550
but it never hurts
to show this again

1056
00:48:20,550 --> 00:48:23,730
because it's a cool picture,
and this is where we live.

1057
00:48:23,730 --> 00:48:25,020
We're past silicon, man.

1058
00:48:25,020 --> 00:48:25,680
That's old.

1059
00:48:25,680 --> 00:48:27,240
Never better against silicon.

1060
00:48:27,240 --> 00:48:27,990
Never.

1061
00:48:27,990 --> 00:48:29,910
It's still a really
important material.

1062
00:48:29,910 --> 00:48:32,640
But on the left, plastics.

1063
00:48:32,640 --> 00:48:35,640
Oh, what's that?

1064
00:48:35,640 --> 00:48:38,970
That is, I think, a
nanotube or a-- it's

1065
00:48:38,970 --> 00:48:41,820
either a nanotube or some
other sort of 2D material

1066
00:48:41,820 --> 00:48:48,930
wrapped up into like a gear that
I think has never been made.

1067
00:48:48,930 --> 00:48:52,770
Maybe it's not a good
picture, but it looked good,

1068
00:48:52,770 --> 00:48:57,270
and I grabbed it in five
seconds from Google.

1069
00:48:57,270 --> 00:49:01,440
Anyway, I'm going to skip this.

1070
00:49:01,440 --> 00:49:03,240
I'll talk about this later.

1071
00:49:03,240 --> 00:49:07,210
Solar, we get a
lot of it, right?

1072
00:49:07,210 --> 00:49:08,380
You guys have seen this.

1073
00:49:08,380 --> 00:49:10,270
How many of you have seen this?

1074
00:49:10,270 --> 00:49:12,340
There's a whole lot of solar.

1075
00:49:12,340 --> 00:49:14,240
So this is a cool comparison.

1076
00:49:14,240 --> 00:49:14,740
Look.

1077
00:49:14,740 --> 00:49:17,150
It beats coal.

1078
00:49:17,150 --> 00:49:18,800
I mean, forget
about like we know

1079
00:49:18,800 --> 00:49:20,330
the resource of
solar beats things

1080
00:49:20,330 --> 00:49:23,510
like tidal and tides,
waves, geothermal, hydro,

1081
00:49:23,510 --> 00:49:25,490
all the other
renewables combined.

1082
00:49:25,490 --> 00:49:27,130
But it beats coal.

1083
00:49:27,130 --> 00:49:30,240
That's pretty cool.

1084
00:49:30,240 --> 00:49:35,620
Well, biomass would be if
you take all the arable land.

1085
00:49:35,620 --> 00:49:37,620
You've got to remember,
these numbers-- and this

1086
00:49:37,620 --> 00:49:40,030
is the author of this
fairly recent study.

1087
00:49:40,030 --> 00:49:45,032
But those numbers have many
assumptions go into them,

1088
00:49:45,032 --> 00:49:46,740
and so there's a lot
of debate about what

1089
00:49:46,740 --> 00:49:47,760
the right numbers are.

1090
00:49:47,760 --> 00:49:50,640
To within a factor
of 2 to 10, these

1091
00:49:50,640 --> 00:49:53,920
are probably the right numbers.

1092
00:49:53,920 --> 00:49:56,430
But biomass, if you
take the arable land

1093
00:49:56,430 --> 00:49:59,670
where you're not going to
cause a huge famine in the area

1094
00:49:59,670 --> 00:50:02,640
and you kind of add
that up, you try

1095
00:50:02,640 --> 00:50:04,680
to consider water
resources and other things.

1096
00:50:04,680 --> 00:50:06,330
You can actually
compute using, say,

1097
00:50:06,330 --> 00:50:07,920
some crop or set of crops--

1098
00:50:07,920 --> 00:50:11,760
sugarcane, maybe other things,
switchgrass-- how much energy

1099
00:50:11,760 --> 00:50:14,790
could you generate in a year?

1100
00:50:14,790 --> 00:50:16,780
And that's about it.

1101
00:50:16,780 --> 00:50:18,120
I think-- and I don't remember.

1102
00:50:18,120 --> 00:50:20,790
There was a number with
biomass that was 11

1103
00:50:20,790 --> 00:50:22,380
that I saw for a
while in the study,

1104
00:50:22,380 --> 00:50:26,190
but that was if you literally
stop growing food for people

1105
00:50:26,190 --> 00:50:30,600
and you just take all land that
can be used to grow anything

1106
00:50:30,600 --> 00:50:34,885
and you make fuel, and you're
still at considerably less

1107
00:50:34,885 --> 00:50:35,760
than other resources.

1108
00:50:35,760 --> 00:50:39,210
I'm not saying biofuels isn't
a really important direction.

1109
00:50:39,210 --> 00:50:42,150
But I kind of like
these comparisons.

1110
00:50:42,150 --> 00:50:43,800
There we are.

1111
00:50:43,800 --> 00:50:47,230
We use not much compared to
how much we have in the sun.

1112
00:50:47,230 --> 00:50:50,110
These are the different
ways you can use the sun.

1113
00:50:50,110 --> 00:50:52,030
And I want to talk
about this one now.

1114
00:50:52,030 --> 00:50:53,690
So I think you know about this.

1115
00:50:53,690 --> 00:50:57,818
You take the sun, and
you make a lot of heat.

1116
00:50:57,818 --> 00:50:59,360
I'm going to actually
start with this

1117
00:50:59,360 --> 00:51:00,890
because it's related to this.

1118
00:51:00,890 --> 00:51:02,810
Here we take sun and
we make electrons.

1119
00:51:02,810 --> 00:51:06,470
That's going to be our next
homework-assignment example

1120
00:51:06,470 --> 00:51:09,920
that we'll talk about when we
do solids because from the band

1121
00:51:09,920 --> 00:51:12,470
structure of a solid--
and the band structure

1122
00:51:12,470 --> 00:51:16,640
is nothing more than
this for solids.

1123
00:51:16,640 --> 00:51:18,350
From the band
structure of a solid,

1124
00:51:18,350 --> 00:51:21,440
I can explain to you-- you
can explain to your friends

1125
00:51:21,440 --> 00:51:26,038
why silicon is so expensive--
why silicon is too expensive.

1126
00:51:26,038 --> 00:51:27,830
And then you can also
take the sun's energy

1127
00:51:27,830 --> 00:51:30,510
and just try to make
fuels directly out of it.

1128
00:51:30,510 --> 00:51:32,000
So what are solar thermal fuels?

1129
00:51:32,000 --> 00:51:33,833
Well, like I said, I
want to start with heat

1130
00:51:33,833 --> 00:51:34,565
because heat is--

1131
00:51:34,565 --> 00:51:37,370
and this will be a fairly
quick introduction.

1132
00:51:37,370 --> 00:51:39,680
But heat is something--
it's one of the oldest

1133
00:51:39,680 --> 00:51:42,952
technologies we know about in
terms of how to use the sun.

1134
00:51:42,952 --> 00:51:43,910
Paint the barrel black.

1135
00:51:43,910 --> 00:51:44,930
Put it on the roof.

1136
00:51:44,930 --> 00:51:45,650
Put water in it.

1137
00:51:45,650 --> 00:51:47,370
It gets hot.

1138
00:51:47,370 --> 00:51:49,290
It's a really simple technology.

1139
00:51:49,290 --> 00:51:53,380
It works really well, and
it's used all over the world.

1140
00:51:53,380 --> 00:51:55,810
You can also, if you want
higher temperatures because you

1141
00:51:55,810 --> 00:51:59,140
want to make electricity, you
can go to large-scale plants

1142
00:51:59,140 --> 00:52:01,750
because there you need
large scale because you

1143
00:52:01,750 --> 00:52:04,990
need to focus the sun's energy
to get much higher temperatures

1144
00:52:04,990 --> 00:52:07,990
like, say, 500 Celsius to
drive some sort of cycle

1145
00:52:07,990 --> 00:52:09,490
like a Stirling
engine or something.

1146
00:52:09,490 --> 00:52:11,380
If you do that, you
can make electricity.

1147
00:52:11,380 --> 00:52:15,550
Those are concentrated
solar power plants.

1148
00:52:15,550 --> 00:52:16,550
Here's the distribution.

1149
00:52:16,550 --> 00:52:18,050
That is actually
interesting, right?

1150
00:52:18,050 --> 00:52:21,260
This is how much-- there's
sort of capacity and produced.

1151
00:52:21,260 --> 00:52:26,290
But you can see that using
solar thermal as heat

1152
00:52:26,290 --> 00:52:28,720
is actually the
second-most-utilized renewable

1153
00:52:28,720 --> 00:52:29,920
resource in the world.

1154
00:52:32,353 --> 00:52:33,770
But that's the
painting the barrel

1155
00:52:33,770 --> 00:52:35,790
black and putting
it on your rooftop.

1156
00:52:35,790 --> 00:52:37,890
That's not making electricity.

1157
00:52:37,890 --> 00:52:41,270
So in the world this is actually
a very heavily used alternative

1158
00:52:41,270 --> 00:52:41,930
energy.

1159
00:52:41,930 --> 00:52:44,330
That is almost completely
unused in this country.

1160
00:52:44,330 --> 00:52:47,550
I think in terms of countries
that use the sun in this way,

1161
00:52:47,550 --> 00:52:50,362
we're like number 17.

1162
00:52:50,362 --> 00:52:52,820
There are some places that are
trying to make power with it

1163
00:52:52,820 --> 00:52:53,600
but very few.

1164
00:52:53,600 --> 00:52:55,640
It's a hard thing to do.

1165
00:52:55,640 --> 00:52:59,000
I think 15 of the 20 existing
CSP plants are in Spain.

1166
00:52:59,000 --> 00:53:00,455
The Spanish love this.

1167
00:53:00,455 --> 00:53:02,330
But you can just sort
of see where it stands.

1168
00:53:02,330 --> 00:53:06,530
Anyway, the point is there are
challenges with using the sun's

1169
00:53:06,530 --> 00:53:08,870
energy in the form of heat.

1170
00:53:08,870 --> 00:53:11,840
One of them is that you lose
the energy, reradiation.

1171
00:53:11,840 --> 00:53:15,090
As soon as you absorb heat,
it starts going out way,

1172
00:53:15,090 --> 00:53:17,052
so you've got to contain it.

1173
00:53:17,052 --> 00:53:18,260
And it's still going to leak.

1174
00:53:18,260 --> 00:53:20,720
So in some of these
plants, you actually

1175
00:53:20,720 --> 00:53:23,480
pump in
fossil-fuel-based energy.

1176
00:53:23,480 --> 00:53:26,720
So you use the sun to
concentrate on, say,

1177
00:53:26,720 --> 00:53:30,800
a molten salt in a tower, so
a phase change of material.

1178
00:53:30,800 --> 00:53:33,410
You get it up to really high
energy over the phase change.

1179
00:53:33,410 --> 00:53:35,420
You all took 3012.

1180
00:53:35,420 --> 00:53:36,980
Know many of you
did, so you know

1181
00:53:36,980 --> 00:53:38,522
about when I say
phase change, you're

1182
00:53:38,522 --> 00:53:41,660
going up this heat,
this latent heat,

1183
00:53:41,660 --> 00:53:44,210
and you're storing a
bunch of energy that way.

1184
00:53:44,210 --> 00:53:46,490
And then you want
to keep it up there.

1185
00:53:46,490 --> 00:53:48,373
So you actually pump
in fossil-fuel energy

1186
00:53:48,373 --> 00:53:50,540
because it's reradiating
heat out and losing energy,

1187
00:53:50,540 --> 00:53:52,207
and you don't want
it to slip back down.

1188
00:53:52,207 --> 00:53:53,780
That's not a good thing.

1189
00:53:53,780 --> 00:53:56,540
And really importantly is
this is not transportable.

1190
00:53:56,540 --> 00:54:01,070
So you can't use heat from the
sun except where you make it.

1191
00:54:01,070 --> 00:54:02,795
So that's where solar
chemical comes in.

1192
00:54:02,795 --> 00:54:04,170
Oh, there's that--
we're number--

1193
00:54:07,040 --> 00:54:10,460
well, we're after Macedonia.

1194
00:54:10,460 --> 00:54:12,500
Anyway, Albania.

1195
00:54:12,500 --> 00:54:14,000
We don't use solar
thermal this way,

1196
00:54:14,000 --> 00:54:15,125
and I don't understand why.

1197
00:54:15,125 --> 00:54:17,270
It's a very inexpensive
renewable resource.

1198
00:54:20,930 --> 00:54:24,130
Solar chemical-- so in
solar chemical, what you do

1199
00:54:24,130 --> 00:54:26,710
is you take a molecule-- in
this case, it's azobenzene.

1200
00:54:26,710 --> 00:54:31,300
And you shine a light on it, and
it goes into a different state.

1201
00:54:31,300 --> 00:54:34,270
Now the important thing is
that-- so that's the charging.

1202
00:54:34,270 --> 00:54:35,260
Charge it by the sun.

1203
00:54:35,260 --> 00:54:38,080
In this different state,
it's storing energy,

1204
00:54:38,080 --> 00:54:40,220
and that can be released.

1205
00:54:40,220 --> 00:54:42,200
It can be released
in the form of heat.

1206
00:54:42,200 --> 00:54:45,190
So you've got a
way of closed-cycle

1207
00:54:45,190 --> 00:54:47,620
capturing and storing
the sun's energy,

1208
00:54:47,620 --> 00:54:49,870
triggering this state
to release that energy

1209
00:54:49,870 --> 00:54:50,920
in the form of heat.

1210
00:54:50,920 --> 00:54:52,540
It's transportable.

1211
00:54:52,540 --> 00:54:56,600
It can be stored for
as long as you want.

1212
00:54:56,600 --> 00:54:57,440
It's renewable.

1213
00:54:57,440 --> 00:54:59,320
It's cheap, and
it's a closed cycle.

1214
00:54:59,320 --> 00:55:00,960
That's the dream.

1215
00:55:00,960 --> 00:55:06,100
Now this was very heavily
studied 30, 40 years ago.

1216
00:55:06,100 --> 00:55:08,250
And the reason as a
field it was abandoned

1217
00:55:08,250 --> 00:55:10,500
is because for
all the cases that

1218
00:55:10,500 --> 00:55:14,930
were studied in the 1970s
that do this closed loop,

1219
00:55:14,930 --> 00:55:16,670
they degrade.

1220
00:55:16,670 --> 00:55:18,110
So you get this cycle.

1221
00:55:18,110 --> 00:55:20,600
You charge up your
fuel from the sun.

1222
00:55:20,600 --> 00:55:22,580
You use it as heat somewhere.

1223
00:55:22,580 --> 00:55:23,360
You bring it back.

1224
00:55:23,360 --> 00:55:24,140
You charge it again.

1225
00:55:24,140 --> 00:55:24,848
You use it again.

1226
00:55:24,848 --> 00:55:29,452
And after 10 cycles, half
of your fuel is toluene.

1227
00:55:29,452 --> 00:55:30,160
That's a problem.

1228
00:55:33,120 --> 00:55:34,246
Some thoughts on that?

1229
00:55:34,246 --> 00:55:36,068
AUDIENCE: [INAUDIBLE]

1230
00:55:36,068 --> 00:55:37,110
JEFFREY C GROSSMAN: Yeah.

1231
00:55:37,110 --> 00:55:37,943
That was a good one.

1232
00:55:37,943 --> 00:55:40,860
It was actually well timed.

1233
00:55:40,860 --> 00:55:45,615
And I like that
kind of feedback.

1234
00:55:45,615 --> 00:55:47,610
The papers of the times
were saying things

1235
00:55:47,610 --> 00:55:51,315
like an energy-storage plant,
although technically feasible,

1236
00:55:51,315 --> 00:55:53,190
is not economically
justified because there's

1237
00:55:53,190 --> 00:55:54,990
an upfront cost for this fuel.

1238
00:55:54,990 --> 00:55:58,140
And if it doesn't cycle, if
it just degrades in 10 cycles,

1239
00:55:58,140 --> 00:55:59,580
you can't justify the cost.

1240
00:55:59,580 --> 00:56:01,970
So there's a lot
of work on this,

1241
00:56:01,970 --> 00:56:03,690
and those are the
degradation products.

1242
00:56:03,690 --> 00:56:06,480
I won't go into it, but
I'll leave it in your notes.

1243
00:56:06,480 --> 00:56:07,860
A lot of work was done.

1244
00:56:07,860 --> 00:56:10,470
Many papers were written,
and a lot of experiments

1245
00:56:10,470 --> 00:56:14,160
were done to fix this problem,
but no magic bullet was found.

1246
00:56:14,160 --> 00:56:17,220
So they would substitute
things into molecules.

1247
00:56:17,220 --> 00:56:19,260
They'd put metal atoms
into the molecules.

1248
00:56:19,260 --> 00:56:22,980
They'd do what are called
push-pull substitutions.

1249
00:56:22,980 --> 00:56:25,980
And no matter what they
did to these things,

1250
00:56:25,980 --> 00:56:29,010
if they made them
more cyclical, like 10

1251
00:56:29,010 --> 00:56:31,020
to the third cycles,
which isn't bad,

1252
00:56:31,020 --> 00:56:34,620
then they'd be terrible
in their energy density.

1253
00:56:34,620 --> 00:56:37,050
If they made them really
high energy density,

1254
00:56:37,050 --> 00:56:40,220
then maybe they were really
bad at absorbing sunlight.

1255
00:56:40,220 --> 00:56:44,390
So no matter what they did,
they couldn't fix this problem.

1256
00:56:44,390 --> 00:56:48,020
And this is where it's
just such a great time

1257
00:56:48,020 --> 00:56:50,420
to tackle it again.

1258
00:56:50,420 --> 00:56:53,690
The reason is that
if you wanted to do

1259
00:56:53,690 --> 00:56:59,360
100,000 calculations of
solids when this material was

1260
00:56:59,360 --> 00:57:01,520
being studied heavily--

1261
00:57:01,520 --> 00:57:04,430
if you wanted to screen
100,000 materials,

1262
00:57:04,430 --> 00:57:08,030
it would take you 30
years in 1980 to do that,

1263
00:57:08,030 --> 00:57:10,530
and today it takes a few days.

1264
00:57:10,530 --> 00:57:13,310
Not on the nanoHUB necessarily--

1265
00:57:13,310 --> 00:57:15,710
maybe they're back to 30 years.

1266
00:57:15,710 --> 00:57:17,063
AUDIENCE: [INAUDIBLE]

1267
00:57:17,063 --> 00:57:18,980
JEFFREY C GROSSMAN:
Depends where you compute.

1268
00:57:18,980 --> 00:57:23,210
But we're just a
whole generation

1269
00:57:23,210 --> 00:57:25,670
later in what we can tackle
with computational quantum

1270
00:57:25,670 --> 00:57:26,480
mechanics.

1271
00:57:26,480 --> 00:57:27,938
Now I'm going to
end by telling you

1272
00:57:27,938 --> 00:57:30,170
why you need quantum mechanics.

1273
00:57:30,170 --> 00:57:32,570
So this is a really cool
time to work on this problem,

1274
00:57:32,570 --> 00:57:34,400
and this wasn't
available back then when

1275
00:57:34,400 --> 00:57:36,030
it was such a big deal.

1276
00:57:36,030 --> 00:57:38,450
And then, of course,
there's the sort

1277
00:57:38,450 --> 00:57:41,990
of advances we've made on
the synthesis side, which

1278
00:57:41,990 --> 00:57:45,770
I won't talk about because
this is a class on computation.

1279
00:57:45,770 --> 00:57:47,780
So what we've done--

1280
00:57:47,780 --> 00:57:52,130
and this is research
that we're doing--

1281
00:57:52,130 --> 00:57:54,890
is we've shown that there
are new ways-- we've

1282
00:57:54,890 --> 00:57:57,890
shown computationally
that there are new ways

1283
00:57:57,890 --> 00:57:59,760
to tackle the problem.

1284
00:57:59,760 --> 00:58:04,140
We've shown that you
can take a molecule that

1285
00:58:04,140 --> 00:58:05,535
does this switch--

1286
00:58:05,535 --> 00:58:07,155
there are many
molecules that do this.

1287
00:58:07,155 --> 00:58:09,030
How many of you have
heard of photo switches?

1288
00:58:12,330 --> 00:58:15,780
What have you heard of
them being used for?

1289
00:58:15,780 --> 00:58:19,980
Have you heard of them
being used for anything?

1290
00:58:19,980 --> 00:58:23,247
Well, they have been studied
a lot but in what fields?

1291
00:58:23,247 --> 00:58:25,080
You have a molecule
that you shine light on,

1292
00:58:25,080 --> 00:58:27,300
and it goes like this.

1293
00:58:27,300 --> 00:58:28,800
And then you shine
a different light

1294
00:58:28,800 --> 00:58:31,955
on it or you just take the light
off maybe, and it goes back--

1295
00:58:31,955 --> 00:58:32,580
photo switches.

1296
00:58:35,510 --> 00:58:36,910
Where might that be useful?

1297
00:58:39,878 --> 00:58:42,003
AUDIENCE: It kind of reminds
me of like LCD screens

1298
00:58:42,003 --> 00:58:42,940
but it's a bit different.

1299
00:58:42,940 --> 00:58:43,982
JEFFREY C GROSSMAN: Yeah.

1300
00:58:43,982 --> 00:58:45,820
Well, actually
mechanical computing

1301
00:58:45,820 --> 00:58:49,600
is a big deal or
nanomechanical memory,

1302
00:58:49,600 --> 00:58:53,692
optomechanical functions.

1303
00:58:53,692 --> 00:58:55,150
There are actually
many areas where

1304
00:58:55,150 --> 00:58:56,890
these sorts of
switching molecules

1305
00:58:56,890 --> 00:59:01,330
like stilbene and
azobenzene and stuff

1306
00:59:01,330 --> 00:59:04,240
that the name is so long
I can't write it here--

1307
00:59:04,240 --> 00:59:06,160
spiropyran-- these
are very heavily

1308
00:59:06,160 --> 00:59:10,070
studied, these optically
activated switching, big deal.

1309
00:59:10,070 --> 00:59:12,160
But they're all terrible
solar thermal fuels.

1310
00:59:12,160 --> 00:59:13,153
They're terrible.

1311
00:59:13,153 --> 00:59:15,070
They don't store much
energy, and they go back

1312
00:59:15,070 --> 00:59:16,960
in a few minutes.

1313
00:59:16,960 --> 00:59:20,860
So what we've realized is that
you can actually turn them

1314
00:59:20,860 --> 00:59:23,710
into good ones, and the
way you do that is you

1315
00:59:23,710 --> 00:59:25,030
put them on a template.

1316
00:59:25,030 --> 00:59:28,540
So you take a molecule
that's one of these switches.

1317
00:59:28,540 --> 00:59:30,430
There are many switches.

1318
00:59:30,430 --> 00:59:32,010
You stick it on a
template, and what

1319
00:59:32,010 --> 00:59:33,760
happens is when you
stick it on a template

1320
00:59:33,760 --> 00:59:37,180
you have new chemistry
that you can do,

1321
00:59:37,180 --> 00:59:38,440
and that's really the key.

1322
00:59:38,440 --> 00:59:42,070
Now we're going to come back
to you in a few minutes is

1323
00:59:42,070 --> 00:59:44,320
this picture, so I wanted
to just tell you what it is.

1324
00:59:44,320 --> 00:59:46,470
This is what the molecule does.

1325
00:59:46,470 --> 00:59:48,000
This is a reaction pathway.

1326
00:59:48,000 --> 00:59:50,790
This is the energy
curve for the molecule.

1327
00:59:50,790 --> 00:59:52,740
So it's down here.

1328
00:59:52,740 --> 00:59:56,890
You shine light on it, and
it goes up over this barrier,

1329
00:59:56,890 --> 00:59:59,680
and it drops you down
here into a new state.

1330
00:59:59,680 --> 01:00:01,270
In this case, it's azobenzene.

1331
01:00:01,270 --> 01:00:05,740
It's going from trans to cis.

1332
01:00:05,740 --> 01:00:08,260
How many of you have heard
of trans/cis, trans and cis

1333
01:00:08,260 --> 01:00:09,070
isomers?

1334
01:00:09,070 --> 01:00:11,590
So you know about
photo switches then.

1335
01:00:11,590 --> 01:00:17,280
Not all trans/cis states are
photo accessible, but many are.

1336
01:00:17,280 --> 01:00:18,330
That's all this is doing.

1337
01:00:18,330 --> 01:00:20,130
And then when you want
to release the heat,

1338
01:00:20,130 --> 01:00:21,180
you trigger it.

1339
01:00:21,180 --> 01:00:24,210
And it goes over this barrier,
like say with a catalyst,

1340
01:00:24,210 --> 01:00:25,840
and it releases
this much energy.

1341
01:00:25,840 --> 01:00:27,890
So that's your storage energy.

1342
01:00:27,890 --> 01:00:30,240
That's how much energy
that molecule stored.

1343
01:00:30,240 --> 01:00:33,840
And this back-reaction barrier's
related to the lifetime

1344
01:00:33,840 --> 01:00:36,550
of the stored state.

1345
01:00:36,550 --> 01:00:39,040
We're going to
come back to this.

1346
01:00:39,040 --> 01:00:41,320
So these are-- what we
did is some work that

1347
01:00:41,320 --> 01:00:43,340
showed that you can put
these onto nanotubes

1348
01:00:43,340 --> 01:00:45,048
and you can make them
into good switches,

1349
01:00:45,048 --> 01:00:47,470
and I'm not going to
go into the details.

1350
01:00:47,470 --> 01:00:52,400
But basically you see
this is the advantage

1351
01:00:52,400 --> 01:00:55,940
of computational
quantum mechanics

1352
01:00:55,940 --> 01:01:00,450
today is that we
can do chemistry

1353
01:01:00,450 --> 01:01:03,990
in the computer on these
switches and screen

1354
01:01:03,990 --> 01:01:07,930
hundreds of ideas in a week.

1355
01:01:07,930 --> 01:01:11,760
And we can calculate the things
like how much energy they store

1356
01:01:11,760 --> 01:01:14,040
or how stable they
are in a matter

1357
01:01:14,040 --> 01:01:17,400
of an hour on a computer.

1358
01:01:17,400 --> 01:01:20,190
So this is the
perfect time to try

1359
01:01:20,190 --> 01:01:22,710
to tackle old problems like
this that weren't solved

1360
01:01:22,710 --> 01:01:25,950
a generation ago
but that you can

1361
01:01:25,950 --> 01:01:28,080
play with them with many
different directions

1362
01:01:28,080 --> 01:01:29,973
computationally.

1363
01:01:29,973 --> 01:01:31,140
And this is just an example.

1364
01:01:31,140 --> 01:01:33,000
And don't worry
about the details,

1365
01:01:33,000 --> 01:01:34,740
but this was that photo switch.

1366
01:01:34,740 --> 01:01:37,590
This is how much energy is
stored on its own, this line up

1367
01:01:37,590 --> 01:01:38,610
here.

1368
01:01:38,610 --> 01:01:41,850
And now we can tweak it by
putting it on this template

1369
01:01:41,850 --> 01:01:43,260
and doing different chemistries.

1370
01:01:43,260 --> 01:01:47,550
We can make it store three
times as much energy.

1371
01:01:47,550 --> 01:01:50,250
So we can triple the storage
energy of these molecules

1372
01:01:50,250 --> 01:01:53,700
just by playing with the
chemistry when you put them

1373
01:01:53,700 --> 01:01:54,690
on a rigid template.

1374
01:01:54,690 --> 01:01:56,130
That's the idea.

1375
01:01:56,130 --> 01:02:00,000
At the same time, we can
tune the barrier back,

1376
01:02:00,000 --> 01:02:01,950
and we can have
cases like this one

1377
01:02:01,950 --> 01:02:03,570
where you triple
the storage density

1378
01:02:03,570 --> 01:02:06,120
and you increase the
barrier to going back.

1379
01:02:06,120 --> 01:02:08,040
And that's really
important because you

1380
01:02:08,040 --> 01:02:09,998
want to be able to tune
those things separately

1381
01:02:09,998 --> 01:02:13,045
because the back barrier is
related to how long it stays

1382
01:02:13,045 --> 01:02:13,920
in the charged state.

1383
01:02:16,760 --> 01:02:19,730
So that's the key, and so
we've developed materials

1384
01:02:19,730 --> 01:02:24,045
like this that are very
competitive with the best

1385
01:02:24,045 --> 01:02:26,420
lithium-ion batteries in terms
of their energy densities.

1386
01:02:30,480 --> 01:02:31,955
Any questions about these?

1387
01:02:31,955 --> 01:02:33,580
I'm kind of going
through this quickly,

1388
01:02:33,580 --> 01:02:37,362
but I don't want to
get bogged down by too

1389
01:02:37,362 --> 01:02:38,195
much of the details.

1390
01:02:43,440 --> 01:02:45,530
So there are many
template materials

1391
01:02:45,530 --> 01:02:47,210
that you can put these on.

1392
01:02:47,210 --> 01:02:49,490
You have to use
a template or you

1393
01:02:49,490 --> 01:02:51,640
can't get this new chemistry.

1394
01:02:51,640 --> 01:02:53,920
And there are many
switches that let you

1395
01:02:53,920 --> 01:02:55,245
go back and forth like this.

1396
01:02:55,245 --> 01:02:56,620
And what we've
shown is that this

1397
01:02:56,620 --> 01:03:00,910
is sort of a large phase space.

1398
01:03:04,500 --> 01:03:07,860
And so they're sort of
a new chemistry platform

1399
01:03:07,860 --> 01:03:09,960
out here for making
these kinds of fuels.

1400
01:03:12,890 --> 01:03:18,510
When I went to the Sloan
class, Energy Ventures,

1401
01:03:18,510 --> 01:03:20,640
and talked about
this, my thought was--

1402
01:03:20,640 --> 01:03:22,595
this is last fall--

1403
01:03:22,595 --> 01:03:23,970
I have this really
cool material.

1404
01:03:23,970 --> 01:03:26,772
It's going to save the world.

1405
01:03:26,772 --> 01:03:28,230
We're going to
replace coal plants.

1406
01:03:28,230 --> 01:03:30,210
We're going to make
electricity this way.

1407
01:03:30,210 --> 01:03:32,520
Everything's going to
be heated this way.

1408
01:03:32,520 --> 01:03:35,460
And they did a study
on commercialization,

1409
01:03:35,460 --> 01:03:37,710
and they came back and
they said, no, you're

1410
01:03:37,710 --> 01:03:39,370
not going to do any of that.

1411
01:03:39,370 --> 01:03:42,420
What you're going to do is
you're going to deice windows.

1412
01:03:42,420 --> 01:03:45,750
And at first I was
actually not happy

1413
01:03:45,750 --> 01:03:48,460
because I wanted to solve
the world's energy problems.

1414
01:03:48,460 --> 01:03:50,460
They looked at all these
different applications.

1415
01:03:50,460 --> 01:03:51,960
There's lots of
ways to use heat.

1416
01:03:51,960 --> 01:03:54,400
If you can store
the sun's energy

1417
01:03:54,400 --> 01:03:58,470
and release it as heat on
demand, that's a big deal--

1418
01:03:58,470 --> 01:03:59,720
and do it over and over again.

1419
01:03:59,720 --> 01:04:01,040
There are many
places you can use.

1420
01:04:01,040 --> 01:04:03,040
But they said, no, this
is going to be the best.

1421
01:04:03,040 --> 01:04:05,768
So actually we started
looking at that.

1422
01:04:05,768 --> 01:04:07,310
Actually Sam started
looking at that,

1423
01:04:07,310 --> 01:04:09,390
and he built a whole
test apparatus.

1424
01:04:09,390 --> 01:04:13,670
And Sam, with our solar
fields when they're made,

1425
01:04:13,670 --> 01:04:17,960
he'll be able to deice a window
for you in about five seconds,

1426
01:04:17,960 --> 01:04:20,180
and that's pretty cool.

1427
01:04:20,180 --> 01:04:23,120
So you can embed this
stuff inside of glass

1428
01:04:23,120 --> 01:04:26,310
and have it passively absorb
the sun's energy during the day.

1429
01:04:26,310 --> 01:04:28,280
In the morning, trigger
it, and it gives you

1430
01:04:28,280 --> 01:04:31,580
300 Celsius inside the glass.

1431
01:04:31,580 --> 01:04:34,355
You don't need to melt much
ice to get it to fall off.

1432
01:04:34,355 --> 01:04:35,720
So a lot of people--

1433
01:04:35,720 --> 01:04:37,640
and they talked
with MBTA and others

1434
01:04:37,640 --> 01:04:39,230
who would pay a
whole lot of money

1435
01:04:39,230 --> 01:04:41,605
to get something like that
because there's a lot of money

1436
01:04:41,605 --> 01:04:42,510
wasted on deicing.

1437
01:04:42,510 --> 01:04:44,385
It actually turns out
to be very interesting.

1438
01:04:44,385 --> 01:04:47,150
We also built a solar
cooker in collaboration

1439
01:04:47,150 --> 01:04:50,792
with the Slocum group,
and that basically

1440
01:04:50,792 --> 01:04:52,250
lets you cook with
the sun's energy

1441
01:04:52,250 --> 01:04:54,920
when the sun's not out because,
again, you have this ability

1442
01:04:54,920 --> 01:04:57,050
to take the sun's
energy and release it

1443
01:04:57,050 --> 01:05:01,260
as heat when you want it and
then recharge it the next day.

1444
01:05:01,260 --> 01:05:03,445
So we're really
excited about this.

1445
01:05:03,445 --> 01:05:04,820
Oh, and there's
our solar cooker.

1446
01:05:04,820 --> 01:05:06,320
I love this.

1447
01:05:06,320 --> 01:05:11,980
I'm going to take the last
15 minutes to talk about what

1448
01:05:11,980 --> 01:05:15,250
we can do with what we can do.

1449
01:05:15,250 --> 01:05:18,250
But this is the last thing I'll
tell you about the solar fuels.

1450
01:05:18,250 --> 01:05:20,560
I love this picture.

1451
01:05:20,560 --> 01:05:23,020
So these kinds of
things are not good.

1452
01:05:23,020 --> 01:05:25,300
This is a big deal.

1453
01:05:25,300 --> 01:05:29,320
This causes more deaths in
the third world than malaria

1454
01:05:29,320 --> 01:05:32,440
and AIDS combined,
wood-fired stoves.

1455
01:05:32,440 --> 01:05:36,490
Women primarily and sometimes
children spend 20 hours a week

1456
01:05:36,490 --> 01:05:38,020
searching for wood.

1457
01:05:38,020 --> 01:05:40,240
20 hours a week
of their time goes

1458
01:05:40,240 --> 01:05:43,690
to getting wood for burning.

1459
01:05:43,690 --> 01:05:46,380
This is the alternative if you
want to use the sun to cooking.

1460
01:05:46,380 --> 01:05:49,890
And I love these because this
is a restaurant in India,

1461
01:05:49,890 --> 01:05:58,480
and you can see these come with
specialized goggles and gloves.

1462
01:05:58,480 --> 01:06:02,900
And you can see why because
he's inside the oven.

1463
01:06:02,900 --> 01:06:05,450
He's getting burned
when he's cooking

1464
01:06:05,450 --> 01:06:07,040
because you can
focus on a point,

1465
01:06:07,040 --> 01:06:08,550
but you're not
going to be perfect.

1466
01:06:08,550 --> 01:06:10,190
So there's a lot
of sun hitting him.

1467
01:06:10,190 --> 01:06:12,110
It's not a very
comfortable way to cook.

1468
01:06:12,110 --> 01:06:14,870
But also you can only
cook when the sun's out.

1469
01:06:14,870 --> 01:06:17,690
So solar cookers, I think, could
play a really big role if you

1470
01:06:17,690 --> 01:06:20,750
can get them low cost--
these are over $600--

1471
01:06:20,750 --> 01:06:23,270
and if you can get
them to be able to cook

1472
01:06:23,270 --> 01:06:25,300
when it's more convenient.

1473
01:06:25,300 --> 01:06:28,237
OK, so I won't go
into those details.

1474
01:06:28,237 --> 01:06:30,070
This is the kind of
thing we do in my group,

1475
01:06:30,070 --> 01:06:31,750
and I get so excited about it.

1476
01:06:31,750 --> 01:06:34,090
We design things in a computer.

1477
01:06:34,090 --> 01:06:36,940
We make them, and
we build prototypes,

1478
01:06:36,940 --> 01:06:39,520
and it's sort of
a full loop here

1479
01:06:39,520 --> 01:06:43,010
to try to impact
interesting energy problems.

1480
01:06:43,010 --> 01:06:45,830
Now this leaves me
on the last part,

1481
01:06:45,830 --> 01:06:48,970
which is what I want to
talk about in the last 10

1482
01:06:48,970 --> 01:06:50,240
minutes of class.

1483
01:06:50,240 --> 01:06:54,670
Which is, OK, that's a
really cool energy problem.

1484
01:06:54,670 --> 01:06:56,907
You have to agree with that.

1485
01:06:56,907 --> 01:06:58,490
OK, you don't have
to agree with that,

1486
01:06:58,490 --> 01:07:00,990
but I think it's really
cool energy problem.

1487
01:07:00,990 --> 01:07:06,050
Where does computational
quantum mechanics fit into this?

1488
01:07:06,050 --> 01:07:14,850
OK, so this is what it does.

1489
01:07:14,850 --> 01:07:17,190
The fuel goes from here to here.

1490
01:07:17,190 --> 01:07:18,690
This is the reaction coordinate.

1491
01:07:18,690 --> 01:07:20,940
It goes from a low-energy
state to a high-energy state

1492
01:07:20,940 --> 01:07:22,232
when you shine the light on it.

1493
01:07:26,380 --> 01:07:29,960
Could I calculate-- now this
is how much energy it's stored,

1494
01:07:29,960 --> 01:07:32,327
which is related to the
density of the fuel, the energy

1495
01:07:32,327 --> 01:07:33,160
density of the fuel.

1496
01:07:33,160 --> 01:07:35,050
Remember, that's something
we had to kind of hike up

1497
01:07:35,050 --> 01:07:36,310
by a factor of three or four.

1498
01:07:36,310 --> 01:07:39,200
It's not really that good.

1499
01:07:39,200 --> 01:07:41,330
Could I have done that
with classical potentials?

1500
01:07:41,330 --> 01:07:43,610
Can I calculate this with
classical potentials?

1501
01:07:43,610 --> 01:07:44,240
What is this?

1502
01:07:44,240 --> 01:07:45,260
How do I calculate this?

1503
01:07:56,950 --> 01:08:04,570
Here's my solar fuel, and
this is the trans state,

1504
01:08:04,570 --> 01:08:07,770
and this is the cis state.

1505
01:08:07,770 --> 01:08:09,120
What is this difference?

1506
01:08:09,120 --> 01:08:13,870
How would I calculate
this energy difference?

1507
01:08:13,870 --> 01:08:17,542
How would you do that
calculation in a computer?

1508
01:08:17,542 --> 01:08:18,420
AUDIENCE: [INAUDIBLE]

1509
01:08:18,420 --> 01:08:22,890
JEFFREY C GROSSMAN: No, no,
no, this is calculationally.

1510
01:08:22,890 --> 01:08:23,640
Is that a word?

1511
01:08:23,640 --> 01:08:25,380
Yeah.

1512
01:08:25,380 --> 01:08:26,130
Go ahead.

1513
01:08:26,130 --> 01:08:29,050
AUDIENCE: So they're
both sort of local minima

1514
01:08:29,050 --> 01:08:29,800
of the potentials.

1515
01:08:29,800 --> 01:08:30,842
JEFFREY C GROSSMAN: Yeah.

1516
01:08:30,842 --> 01:08:32,970
AUDIENCE: So you
could theoretically

1517
01:08:32,970 --> 01:08:36,920
run some DFT simulation on
your trans configuration

1518
01:08:36,920 --> 01:08:40,050
and run a DFT simulation
on your cis configuration

1519
01:08:40,050 --> 01:08:42,300
and then get out the sort
of ground-state energies

1520
01:08:42,300 --> 01:08:44,490
for the two and compare them.

1521
01:08:44,490 --> 01:08:50,210
JEFFREY C GROSSMAN:
E cis minus E trans.

1522
01:08:50,210 --> 01:08:51,470
You bet.

1523
01:08:51,470 --> 01:08:52,189
That's it.

1524
01:08:52,189 --> 01:08:53,569
That's all this is--

1525
01:08:53,569 --> 01:08:55,170
equals delta H.

1526
01:08:55,170 --> 01:08:57,410
Now tell me why you said DFT.

1527
01:08:57,410 --> 01:09:02,479
Can't I use reacts or a
Lennard-Jones potential

1528
01:09:02,479 --> 01:09:03,380
to calculate that?

1529
01:09:06,060 --> 01:09:08,667
Why not?

1530
01:09:08,667 --> 01:09:11,250
AUDIENCE: The trans and cis may
have different types of bonds,

1531
01:09:11,250 --> 01:09:12,600
so [INAUDIBLE] electrons.

1532
01:09:12,600 --> 01:09:13,975
JEFFREY C GROSSMAN:
What if I had

1533
01:09:13,975 --> 01:09:15,690
a super-duper good potential?

1534
01:09:15,690 --> 01:09:17,732
AUDIENCE: [INAUDIBLE] for
electrons [INAUDIBLE]..

1535
01:09:17,732 --> 01:09:19,357
JEFFREY C GROSSMAN:
But why do I need--

1536
01:09:19,357 --> 01:09:19,859
but hang on.

1537
01:09:19,859 --> 01:09:21,942
I mean, that would be true
with all the first part

1538
01:09:21,942 --> 01:09:22,859
of your class, right?

1539
01:09:22,859 --> 01:09:24,776
Everything you did in
the first part of class,

1540
01:09:24,776 --> 01:09:27,760
like straining wires and stuff,
captured energy of bonds.

1541
01:09:27,760 --> 01:09:28,560
Yeah?

1542
01:09:28,560 --> 01:09:31,319
AUDIENCE: You need to be given
the potential to use in order

1543
01:09:31,319 --> 01:09:34,229
to do a classical simulation.

1544
01:09:34,229 --> 01:09:36,029
So doing the quantum
simulation, you

1545
01:09:36,029 --> 01:09:39,880
just need to give the
configuration of atoms,

1546
01:09:39,880 --> 01:09:40,950
and then it--

1547
01:09:40,950 --> 01:09:41,609
JEFFREY C GROSSMAN:
Which is nice.

1548
01:09:41,609 --> 01:09:42,370
AUDIENCE: --find
the energy for you.

1549
01:09:42,370 --> 01:09:44,412
JEFFREY C GROSSMAN: Which
is certainly very nice,

1550
01:09:44,412 --> 01:09:46,649
but let's say I tell you
that I'm giving you a really

1551
01:09:46,649 --> 01:09:48,420
super-duper, really,
really, really,

1552
01:09:48,420 --> 01:09:51,050
honestly really good potential.

1553
01:09:51,050 --> 01:09:55,280
And that's what it's
called in the literature.

1554
01:09:55,280 --> 01:09:58,070
I put the word honest in it.

1555
01:09:58,070 --> 01:10:00,776
Could I calculate this
with classical potentials?

1556
01:10:04,880 --> 01:10:07,880
It's a difference of energies
between two molecules.

1557
01:10:07,880 --> 01:10:10,247
Can I calculate that with
a classical force field?

1558
01:10:16,450 --> 01:10:19,480
I'm seeing some of this and
I'm seeing some of this.

1559
01:10:19,480 --> 01:10:23,620
Well, actually yes.

1560
01:10:23,620 --> 01:10:25,540
You could calculate
the energy difference

1561
01:10:25,540 --> 01:10:28,090
between two molecules using
classical force fields.

1562
01:10:28,090 --> 01:10:30,160
What you have identified
is the challenge

1563
01:10:30,160 --> 01:10:33,400
of doing that, which
is that it's only going

1564
01:10:33,400 --> 01:10:35,200
to be as good as the potential.

1565
01:10:35,200 --> 01:10:38,560
Can the potential accurately
represent these two?

1566
01:10:38,560 --> 01:10:40,030
Well, you compare
with experiment.

1567
01:10:40,030 --> 01:10:42,610
You compare with higher-level
theories and you'll know.

1568
01:10:42,610 --> 01:10:44,350
But what if it can?

1569
01:10:44,350 --> 01:10:45,160
What if it can't?

1570
01:10:45,160 --> 01:10:47,440
Well, then this is
perfectly reasonable

1571
01:10:47,440 --> 01:10:51,850
to do with classical
force fields.

1572
01:10:51,850 --> 01:10:54,170
I don't need electrons
to calculate this.

1573
01:10:54,170 --> 01:10:58,975
I just need the right energies,
which is what classical force

1574
01:10:58,975 --> 01:11:02,280
fields are trying to capture.

1575
01:11:02,280 --> 01:11:04,890
Now, there's a key here though.

1576
01:11:04,890 --> 01:11:07,282
By the way, you could even
get this using a good--

1577
01:11:07,282 --> 01:11:09,240
if the classical force
fields were good enough,

1578
01:11:09,240 --> 01:11:12,330
you could get the back-reaction
barrier, the activation energy.

1579
01:11:15,290 --> 01:11:18,610
I want to make sure that
we understand context here.

1580
01:11:18,610 --> 01:11:21,380
When you do a
simulation, when you

1581
01:11:21,380 --> 01:11:26,540
do your computational
materials research,

1582
01:11:26,540 --> 01:11:30,110
it's not a one size
fits all kind of thing,

1583
01:11:30,110 --> 01:11:34,670
and it's not even a one problem,
one method kind of thing.

1584
01:11:34,670 --> 01:11:38,090
You can have one problem
with different properties

1585
01:11:38,090 --> 01:11:40,780
that require different methods.

1586
01:11:40,780 --> 01:11:43,510
And which is the
right method to use?

1587
01:11:43,510 --> 01:11:45,700
Well, very often
the answer to that

1588
01:11:45,700 --> 01:11:49,660
is whichever one is accurate
enough for the problem at hand

1589
01:11:49,660 --> 01:11:53,140
and fastest, and
so that's where you

1590
01:11:53,140 --> 01:11:55,700
have to know-- you have to
test and know where you sit

1591
01:11:55,700 --> 01:11:59,060
in accuracy phase space
with a given method,

1592
01:11:59,060 --> 01:12:00,840
and then you go ahead with it.

1593
01:12:00,840 --> 01:12:02,840
And if you can find a
classical potential that

1594
01:12:02,840 --> 01:12:05,450
seems to represent this
class of materials well

1595
01:12:05,450 --> 01:12:08,730
and you can validate that it's
getting this, by all means

1596
01:12:08,730 --> 01:12:13,600
use that because it's going to
be a whole lot faster than DFT.

1597
01:12:13,600 --> 01:12:18,130
However-- I should do that more
because it kind of felt good.

1598
01:12:18,130 --> 01:12:22,720
It actually kind of loosened my
shoulder, made me look silly.

1599
01:12:22,720 --> 01:12:26,170
There are things here I can't
do as classical potentials, not

1600
01:12:26,170 --> 01:12:30,390
even if I really, really
close my eyes and dreamt it.

1601
01:12:30,390 --> 01:12:31,688
They wouldn't happen.

1602
01:12:31,688 --> 01:12:32,480
What would that be?

1603
01:12:36,935 --> 01:12:39,748
AUDIENCE: [INAUDIBLE]

1604
01:12:39,748 --> 01:12:40,790
JEFFREY C GROSSMAN: Yeah.

1605
01:12:40,790 --> 01:12:42,440
So you're saying
there's a hint here.

1606
01:12:46,465 --> 01:12:49,110
This is what I'm
shining on the molecule.

1607
01:12:49,110 --> 01:12:51,710
Who's seen this before?

1608
01:12:51,710 --> 01:12:54,120
Yeah, you're feeling it.

1609
01:12:54,120 --> 01:12:55,850
This is the sun.

1610
01:12:55,850 --> 01:13:00,380
This is how much energy
comes to us from the sun.

1611
01:13:00,380 --> 01:13:02,620
And you can see that it's
dependent on the wavelength

1612
01:13:02,620 --> 01:13:03,940
of the light.

1613
01:13:03,940 --> 01:13:05,140
That's pretty cool, right?

1614
01:13:05,140 --> 01:13:07,540
And you know what's really
cool are these big, huge gaps.

1615
01:13:07,540 --> 01:13:09,915
See, this is if you go outside
of the earth's atmosphere,

1616
01:13:09,915 --> 01:13:12,170
you get this yellow line.

1617
01:13:12,170 --> 01:13:15,260
But on the planet, we
get this red curve.

1618
01:13:15,260 --> 01:13:17,540
We get all those
parts blocked out.

1619
01:13:17,540 --> 01:13:19,430
You just don't get
that frequency of light

1620
01:13:19,430 --> 01:13:20,030
on the earth.

1621
01:13:20,030 --> 01:13:22,130
And the reason is because
you have these molecules

1622
01:13:22,130 --> 01:13:25,100
in the atmosphere that are
blocking that part of the sun's

1623
01:13:25,100 --> 01:13:26,210
spectrum.

1624
01:13:26,210 --> 01:13:28,800
Isn't that pretty cool?

1625
01:13:28,800 --> 01:13:32,210
But this red is what
we get on the planet.

1626
01:13:32,210 --> 01:13:37,280
And the question is
how do these molecules

1627
01:13:37,280 --> 01:13:39,720
do in capturing that energy?

1628
01:13:39,720 --> 01:13:42,670
This is how we're
going to charge them.

1629
01:13:42,670 --> 01:13:45,770
This is how we're going
to charge them up.

1630
01:13:45,770 --> 01:13:49,620
Now that is related to
something else that's not here.

1631
01:13:49,620 --> 01:13:50,940
What might that be related to?

1632
01:13:55,450 --> 01:13:57,710
The band gap, exactly.

1633
01:13:57,710 --> 01:13:59,020
Exactly.

1634
01:13:59,020 --> 01:14:00,920
That is related.

1635
01:14:00,920 --> 01:14:05,980
So this all comes back to
where those electrons are.

1636
01:14:05,980 --> 01:14:09,420
So remember, we filled
these electrons up.

1637
01:14:09,420 --> 01:14:10,950
I'm just making them--

1638
01:14:10,950 --> 01:14:12,780
just for simplicity,
I'm not labeling

1639
01:14:12,780 --> 01:14:14,790
them s, p because
I'm not talking

1640
01:14:14,790 --> 01:14:16,680
about a particular thing here.

1641
01:14:16,680 --> 01:14:18,780
And then we filled them all up.

1642
01:14:18,780 --> 01:14:21,450
There were 10 electrons,
and we filled the levels

1643
01:14:21,450 --> 01:14:23,470
with those electrons,
and that was it.

1644
01:14:23,470 --> 01:14:25,710
But there's another
level up here,

1645
01:14:25,710 --> 01:14:27,420
and there's many
more levels up there

1646
01:14:27,420 --> 01:14:30,060
that don't have electrons.

1647
01:14:30,060 --> 01:14:34,140
And this distance here in energy
between the highest occupied

1648
01:14:34,140 --> 01:14:37,500
and lowest unoccupied
level, the HOMO/LUMOS,

1649
01:14:37,500 --> 01:14:39,055
that's called the band gap.

1650
01:14:41,910 --> 01:14:45,180
This is called the Highest
Occupied Molecular Orbital,

1651
01:14:45,180 --> 01:14:49,148
and this is the Lowest
Unoccupied Molecular Orbital.

1652
01:14:49,148 --> 01:14:50,940
And the difference
between them is the gap,

1653
01:14:50,940 --> 01:14:54,470
and that is so important
for optical properties

1654
01:14:54,470 --> 01:14:57,170
and electronic properties--
transport of electrons,

1655
01:14:57,170 --> 01:14:59,130
absorption of sun.

1656
01:14:59,130 --> 01:15:02,070
In this case, we care about the
absorption of the sun much more

1657
01:15:02,070 --> 01:15:03,900
than transport of electrons.

1658
01:15:06,500 --> 01:15:08,120
Now the reason
that's so important

1659
01:15:08,120 --> 01:15:12,290
is you see it goes back
to the hydrogen atom.

1660
01:15:15,500 --> 01:15:17,000
Somebody tell me
a weirdness thing

1661
01:15:17,000 --> 01:15:18,740
about looking out into space.

1662
01:15:18,740 --> 01:15:25,230
What do you see when you look
at the colors of hydrogen?

1663
01:15:25,230 --> 01:15:27,010
They're discrete.

1664
01:15:27,010 --> 01:15:28,786
Why?

1665
01:15:28,786 --> 01:15:30,215
AUDIENCE: [INAUDIBLE]

1666
01:15:30,215 --> 01:15:31,590
JEFFREY C GROSSMAN:
Yeah because,

1667
01:15:31,590 --> 01:15:35,010
remember, here's your electron.

1668
01:15:35,010 --> 01:15:39,750
It can only be in
these quantized levels.

1669
01:15:39,750 --> 01:15:44,860
It can only be in 1s or 2s,
and it cannot be in between.

1670
01:15:44,860 --> 01:15:47,720
Remember that?

1671
01:15:47,720 --> 01:15:50,600
How does that relate to
the absorption of sun

1672
01:15:50,600 --> 01:15:51,740
by a solar fuel?

1673
01:15:51,740 --> 01:15:53,740
Well, it's the same idea.

1674
01:15:53,740 --> 01:15:56,960
You see, when you
absorb sunlight--

1675
01:15:56,960 --> 01:15:58,070
see this H new?

1676
01:15:58,070 --> 01:16:00,800
Sunlight came into
this trans state,

1677
01:16:00,800 --> 01:16:03,950
and it made it go up onto
another energy surface.

1678
01:16:03,950 --> 01:16:06,170
That got it to twist.

1679
01:16:06,170 --> 01:16:10,190
Now when it absorbed the
sunlight, what really happened

1680
01:16:10,190 --> 01:16:13,610
is that the sun's energy
came into the molecule

1681
01:16:13,610 --> 01:16:17,940
and it kicked an electron
out of some happy place.

1682
01:16:17,940 --> 01:16:22,910
It's just hanging out with its
buddies, and a photon comes in,

1683
01:16:22,910 --> 01:16:28,070
and that photon kicks it up
here, and that's what does it.

1684
01:16:28,070 --> 01:16:31,340
That's what makes the
molecule change its shape,

1685
01:16:31,340 --> 01:16:35,900
that electron getting kicked up
into one of these other states.

1686
01:16:35,900 --> 01:16:37,460
Now the key here--

1687
01:16:37,460 --> 01:16:39,620
and this is what's related
to the hydrogen atom--

1688
01:16:39,620 --> 01:16:43,520
is that you see you
can't-- if you just shine--

1689
01:16:43,520 --> 01:16:47,030
so let me try to draw this
a little bit more clearly.

1690
01:16:47,030 --> 01:16:51,620
These are occupied levels, and
these are unoccupied levels,

1691
01:16:51,620 --> 01:16:54,450
and this is the gap.

1692
01:16:54,450 --> 01:16:58,990
So these would be
occupied, unoccupied.

1693
01:16:58,990 --> 01:17:00,550
You cannot shine light.

1694
01:17:00,550 --> 01:17:03,010
If I only have enough
energy from the photon

1695
01:17:03,010 --> 01:17:05,660
to take an electron
from here to here,

1696
01:17:05,660 --> 01:17:07,480
well, you're in no man's land.

1697
01:17:07,480 --> 01:17:10,240
You're just like that
electron in the hydrogen atom

1698
01:17:10,240 --> 01:17:13,480
trying to go in between
a 1s and a 2s orbital.

1699
01:17:13,480 --> 01:17:16,310
You can't do it.

1700
01:17:16,310 --> 01:17:18,050
There is no state here.

1701
01:17:18,050 --> 01:17:22,000
There's no wave function there
for the electron to be it.

1702
01:17:22,000 --> 01:17:23,890
And so there is a gap.

1703
01:17:23,890 --> 01:17:29,260
That is the minimum
energy it takes, right?

1704
01:17:29,260 --> 01:17:31,300
So how is that now
related to this?

1705
01:17:43,640 --> 01:17:45,530
Gap is related to
absorption how?

1706
01:17:48,980 --> 01:17:50,660
So this is actually wavelength.

1707
01:17:50,660 --> 01:17:54,300
So the energy gap goes
as 1 over this, right?

1708
01:17:57,153 --> 01:17:59,320
AUDIENCE: So for a molecule
only has a certain range

1709
01:17:59,320 --> 01:18:00,460
over which it can absorb light?

1710
01:18:00,460 --> 01:18:01,627
JEFFREY C GROSSMAN: Exactly.

1711
01:18:01,627 --> 01:18:06,660
Actually, for now we're just
saying it has a minimum energy

1712
01:18:06,660 --> 01:18:09,060
below which it cannot
absorb any light.

1713
01:18:09,060 --> 01:18:12,180
No photon below this
energy can do anything

1714
01:18:12,180 --> 01:18:14,580
in terms of exciting
these electrons up.

1715
01:18:14,580 --> 01:18:16,290
So the photons have
to be above that,

1716
01:18:16,290 --> 01:18:18,780
which means they have
to be-- if they have

1717
01:18:18,780 --> 01:18:21,540
to be above a certain
energy, then they have to be

1718
01:18:21,540 --> 01:18:23,270
below a certain wavelength.

1719
01:18:26,100 --> 01:18:27,660
So there's some--
does everybody see

1720
01:18:27,660 --> 01:18:32,068
there's some lambda
max where they're not

1721
01:18:32,068 --> 01:18:33,110
going to absorb any more?

1722
01:18:33,110 --> 01:18:38,480
So beyond some point here, they
can't take any of that sun.

1723
01:18:38,480 --> 01:18:39,440
That's it.

1724
01:18:39,440 --> 01:18:40,820
Does everybody see that?

1725
01:18:40,820 --> 01:18:43,190
They cannot absorb that sun.

1726
01:18:43,190 --> 01:18:46,820
Now would it be good-- if
lambda max were up here,

1727
01:18:46,820 --> 01:18:49,240
would that be OK?

1728
01:18:49,240 --> 01:18:51,400
Seems like it, but
there's a real problem

1729
01:18:51,400 --> 01:18:55,130
with that, which I'll come
back to probably next Tuesday.

1730
01:18:55,130 --> 01:18:57,220
But what would happen
if lambda max were here?

1731
01:18:59,527 --> 01:19:01,110
AUDIENCE: You're
missing out on a lot.

1732
01:19:01,110 --> 01:19:02,860
JEFFREY C GROSSMAN:
You're missing so much

1733
01:19:02,860 --> 01:19:04,080
of the sun's energy.

1734
01:19:04,080 --> 01:19:06,930
You just can't-- because
of quantum mechanics,

1735
01:19:06,930 --> 01:19:11,040
that darn quantum mechanics and
that electronic thing that you

1736
01:19:11,040 --> 01:19:13,140
cannot get from
classical potentials,

1737
01:19:13,140 --> 01:19:18,370
that electronic gap, you cannot
absorb light beyond the gap.

1738
01:19:18,370 --> 01:19:21,180
Which means if your
gap is here in energy,

1739
01:19:21,180 --> 01:19:25,760
all of this part of the
sunlight is completely wasted.

1740
01:19:25,760 --> 01:19:29,180
So I'm going to spend a
little time on this on Tuesday

1741
01:19:29,180 --> 01:19:34,010
because there's some really
cool questions about these photo

1742
01:19:34,010 --> 01:19:36,800
switches that we're going to
use quantum mechanics to model

1743
01:19:36,800 --> 01:19:37,623
in the homework.

1744
01:19:37,623 --> 01:19:40,040
And so I want to spend a little
more time on this Tuesday,

1745
01:19:40,040 --> 01:19:42,810
and then I'll talk a little
bit about hydrogen storage.

1746
01:19:42,810 --> 01:19:47,150
So we're going to pick up
with this picture on Tuesday.