To match my own.

Yes accomplishment of the book was a
welcome of the Guardian around the country

with an ordinarily distinguished and
worship pile of scientists.

That's what I mean the cardinals
the rock of West in addition

to being an excellent scientist the making
a very vigorous academic career for

Basheer an associate dean thirty years now

going back to being the Jewish
university professor of art of energy.

Recently he has developed at least
relatively recently an interest in

trying to develop technologies for
the exploitation of every energy and

novel ways of doing it his fundamental
interests are in fundamental political

process using now wants to stretch to
use too narrow a scale structure and

function and when I'm right.

Mark Mark was a little before you go.

He says I was just what I would wish for
myself.

So it's just too violent for the means
that if you walk in these interactions

of collections of molecules and certainly
nano scale is that and understand

the fundamental molecular process
has been treating patients for life.

In addition to me and
an extraordinary scientist he has

I see you to see the world expert route or

at least attempts to apprentice
progress and I have a suspicion that

kind of like going greats like you always
trying to catch the next bigger fish

are these are members national carrier
science the American Academy of Arts and

Sciences International Academy one
of the comics in the world English.

Science has received the langar award
from the American Chemical Society.

I mean the Warriors honorary doctors.

I mean he is also in addition to all of
the author of signs you saw what were two

experts on on tax and he used to
publish the number of non-technical.

Knowledge which is extremely important
science scientists can actually

tell the market here.

Send money so we would look

on today's going to be talking to us about
a particular you and interesting and on

solved problem which is a molecular tree
and we're junctions some mysteries and

some Thank you Jeff.

My mother will love that.

I really do feel like an imposter right.

Systems Biology.

It's like.

I know a code word for
science of which I have no knowledge.

But precious conic is very understanding
and when I said that he said it's OK

yeah well I will try to
enlighten everybody right.

That's what work in turn this around.

And having apologized for
being an impostor.

At least I'm an impostor with a number
of wonderful friends in the world and so

I think I can get bailed out
if it gets too terrible.

OK so what I want to talk about today
is work done by a number of people.

Once in purple are ones who
are Northwestern associated

what to say these these
three folks were postdocs

in the group they're all remarkable he is
now a professor in Warrick in England and

both of them are in faculty members
in Copenhagen actually Chris is a is

a graduate student who's working with me
on a number of the topics I'll talk about

and who's really an off
scale wonderful guy.

The three collaborators.

You got Schleifer is a biomedical
engineer at Northwestern he used to be

a chemical engineer and
before that he was a chemist.

So I think next he's going
to become a philosopher but

he's he's really an expert in assembled
films and at the very end of one talk

about something that's not published yet
but has to do with assembled films and

dynamics and
those as a long time collaborate.

He's from Venezuela.

He's now a faculty member at
Arizona State University.

It was a tragedy to see him leave
because he brings a joy to science.

That's pretty unusual and maybe that's on
his a large print here because there might

be a better theorist on earth but if there
is I don't know who it is what worked for

them for twenty five years we
publish sixty papers together and

I continue to learn from and
now that Skype exists.

I think all I really need to do to do
science is just use my Skype account and

talk to him because he's
he's a remarkable guy.

I didn't know about the bee.

But I've discovered that
the bee is omnipresent so.

It's a pleasure to be here.

Georgia Tech and.

Jeff.

I've known for a very very long time he
sort of moves around the country in a.

Cycloid kind of fashion and
winds up in Georgia Tech which

is really neat and again I apologize for
the systems biology is let's talk

about what I do think I want to talk
about was like trying to answer.

Now if you think about an important
process in the chemical and

biological sciences.

It's a little hard to think of one that's
more on the present or important than

electron transfer it digests our food it
makes our energy it powers our lights it

arises from the fundamental Klown dynamics
of electrons in condensed face systems.

And it's been studied in various ways
by various people in the places and

traces the thing is because
what I'd like to do is to

talk about three different limits
of the electron transfer phenomena.

The first two of which are pretty
broadly published the third one is is

a little bit newer and
a little bit different and

they have to do in EFI case with
geometry with the nature of the space.

But the molecules or the crystals or the
surfaces or the electrons can experience.

So let's start with this.

This is sort of.

Pretty standard stuff in the molecular
electron transfer business.

We have a donor on one end you have
an accept around the other and you felt.

Which site one of them in that
photo excited said an electron can

move to the other.

OK So there's a donor intellect and
scepter and you can photo excite and

watch electron move from one side and
then back.

This was Emily Weiss his Ph D. work.

I'm sure was a joint student
with Mike was a Lucy.

Mike and she made these molecules and
measured them and

then we did modeling to try to understand
in this particular case the dependence on

the length of that bridging benzene
chain and there's a transition

in which she goes from tunneling to
hopping transport and she saw that.

But this is standard stuff in the sense
that the theory to understand it

goes back to the one nine hundred fifty S.
to really Marcus.

Joshua George and the idea that
they came up with is pretty simple

electron moves fast nuclei move slowly.

Because the electron moves fast.

It basically sees static nuclei and
you can take into

account the motion of the nuclei by
putting in front condom factors.

So that D W F C thing means density of
states weighted from common factor but

the way to think about it is.

I'm a system in the reactant
potential energy well.

I want to go to the product potential
energy well in order to do that.

Two things have to happen I
have to conserve energy and

I have to worry about the fact
that when I don't enter G.

from the system this Delta you
think it has to go someplace.

And the someplace it has to go is the
polarization of the environment so that

was Marcus is fundamental understanding in
this is the rate constant expression and

if you can calculate
the tunneling matrix element.

And Professor brother has done a great
deal of that we've done some two and

you can calculate the front common factor
that actually calculate the rate cuts and

that works well for
systems of the kind I just talked about.

So there's a synthesis aspect to it and
then there is a.

Sort of analysis and
measurement aspect to it so

that standard electron transfer and
it's hugely important.

Hugely important.

And I want talk about something
different for a while now and

talk about a system where.

Instead of polarizing the in.

Vironment.

Well let Tron tunnels from a band of
electrons on one end to a band of

electrons on the other and so it's band
to band transport when that happens.

Everything changes and one could ask
the question how does current flow through

single molecules and
you can draw cartoons of this kind.

And it's important to recognize
that this is a cartoon.

This is Powerpoint science
it's not real science.

It doesn't look like that.

We don't know what it does look like.

Which address goes in northwestern try
to figure out what it looks like but

we don't know what it looks like there's
a cartoon people draw this cartoon.

So it's believe the cartoon for
just a moment this molecule or

that molecule sit between two
electrodes and I put a voltage across.

And current goes through the molecule and
the simplest question you could ask is

how does current flow
through single molecules.

I didn't draw this cartoon Heiko
of a bridge with this cartoon.

He also makes these and measures these but
the question can still be asked and

does this fit with that Marcus
approach where everything goes from

parabola to rubble and everything is
determined by vibrations and polarization.

The answer is no.

And that was discovered.

Not by somebody in a university but
by somebody working for I.B.M..

And his name was Rauf Landauer and
back in the one nine hundred fifty S.

He was interested in moving charge in
hetero structures solid state structures

from gallium arsenide gallium
aluminum arsenide for example and

his argument was that because it
was locked arms are moving so fast.

We don't have time to talk to
the polarization of the five patients and

the simplest way to think about
transport conductance now

is that it's the atomic unit of
conductance which is east quit over age

times the probability that if I
throw an electron from the left.

It's going to come through and
make it through T. is transmission and T.

is one when it makes it through and T.
is their own it doesn't make it through.

What are offline are said
was OK figure out.

All the different ways it can
make it through here some or

all of those that give you a number.

That number multiplied by a squared
over it gives you a conductor.

But it's two things one
the conductance is quantized and

if you think about Ohms law
that doesn't work right.

Ohms law says that equals I.R. resistance
inverse of conductance is continuous.

But it's not quantized and in fact not
only was it predicted to be quantized it's

been measured to be quantized
in lots of different systems so

conductance is quantized.

And he wasn't thing about molecules.

Molecules are a little bit different but
this behavior is completely different

from the behavior that characterizes that.

And the reason for that is that where
the electrons are going is different.

So there are both electron transfer
reactions but they're totally different

from one another but one that I talked
about first is about electrons tunneling

from place to place the energy goes into
a vibrant sink in other words in it goes

into polarizations things begin to
wobble because the electron is moved and

normally structures are don't accept a
bridge and the markers form the describes

it and the important observable is the
rate cuts and how fast does this happen.

If I go over to the The Wire
junction everything is different.

Except the electron tunneling right.

The fiber optic sync
where the energy goes.

This was a line that was another point
the energy goes into the electrons

of what he called the leads.

So got a nano scopic
structure single molecule.

And I got this huge hunk of metal and the
electrons go into that hunk of metal and

disperse their energy
in the hunk of metal.

There's an interface here.

There's a don't accept a bridge
structure and what Emily did but

there's an interface there and

the measurement now is by a conductance
measurement you don't measure a rate

constant anymore you measure
conductance as a function of voltage.

So the concepts are quite different.

This is the second kind of electron
transfer since it's much less well known.

I want to talk a little bit.

About it.

We can ask the question again.

How does kind of flow
through a single molecule.

Now we've gone from power point science
to real science because the thing

on the right is a measurement.

In fact a multiple measurements on that
lower molecule the asymmetric molecule and

you can see that both the current
in red in the conductance which

is its derivative in blue.

There are several lines because
the experiment was done several times and

you can see that there fluctuations but
there's behaviors and

we'd like to be able to
understand these behaviors.

How can we relate the structure of
a single molecule brake junction

to its transport.

And it.

It really it depends on
different energy space

right in the molecule the energy spacings
or orbital energies and we know about

homos and Lumos and slow motion and slew
modes and all of these molecular overland.

In the metal bands are continuous
they're characterized by

a momentum K. and so
we know when we construct this entity

that little molecule looks out its
environment knows about two things.

It knows about the band
structure in the metal and

it knows that it's coupled to
the metal with a gamma and

the gamma describes the coupling
between the molecule and the electrode.

There's I change the geometry at that
interface I will change gamma so

this is the simplest way to think about
it a better way to think about it is

to remember that the molecule is
not innocent molecule as all kinds

of things that it cares about and so it's
thinking about its molecular orbitals and

thinking about the energies
of its molecular.

It's thinking about the fact that
electrons repel the first in the second

Dinah's ation energies are not the same.

It's also thinking about
the fact that there's vibrational

coupling on the molecule we're back
to Marcus these couples vibrations

will will change the transport.

So this is really a nice problem.

They're not parameters here to keep you
busy until you're retired right because

in addition to these parameters of course
there's temperature which is an external

pressure and
structure which I haven't talked about.

OK So this this very broad range
of possibilities gives you.

Huge number of mechanisms for

the simplest mechanism is that Linderman
ism which is the last stick tunnelling.

Now it's not like

conduction in the classical Ohms Law
thing where the metal heats up right.

The toaster heats up when
you pass current through it.

You don't heat up when
you pass current through.

Because it's the last it tonally.

Round our set.

It's elastic so these guys.

Turned that formulation into something
that can actually become computed and

then up doing two things One is this gamma
that mixing at the interface the other

is a Green's function G. That's
a propagating the greens function tells me

how the electron or the whole I will
do that again from there to there.

That's the G. the propagator.

So I've got to propagate to move it back
and forth and then I've got interfaces.

And.

That's what you need to calculate
now the calculation is not simple.

It's normally done these days with
density functional theory and

roughly here is what you do.

First you have to guess a geometry.

And I say guess the geometry and

guess the geometry because when
the current is flowing this is in

an equilibrium system it's pretty
hard to calculate the jump tree.

So normally people do is assume no
current calculate that geometry and

assume it doesn't change
which is probably wrong.

So you assume a geometry if you know
the geometry can calculate electronic

properties of the molecule
then the ingredients of

the calculation are as follows.

First thing you have to do
is calculate a cup Ling V.

between the molecule and
the electrode that coupling.

And that's done by methods very similar
to the ones that professor brought out is

used to look at bandwidths and behaviors
in conducting polymers very similar.

But you have to calculate this gamma.

Which is the coupling between the molecule
me electrode and that the pins on

the local density of states which you
also need to know when you put all that

stuff together and calculate the greens
function using some kind of comp.

Technique.

I should say that this is
not a norm calculation.

It's not a model of chemistry yet
we don't yet

know what method you should use to get a
particular accuracy it's not that good get

not sure it will give or
get that good for different reasons.

And there are lots of
people who've done this.

And there are a bunch of names on there
and there are a number of other people.

So it just tests this the simplest
possible thing I'm going to tunnel

electrons through a barrier.

So if you take quantum mechanics in the
physics department this is the second day

of quantum mechanics right you build this
barrier and you calculate the tunneling

probability to go through the barrier and
we know that it falls off exponentially.

And if the chemist thinks about this is
a rate constant the rate constitute go

through this dies off exponentially
with the width of the barrier.

And that beta term the way it falls off
depends on the mass of the electron and

depends on the shape of
the potential that's really simple.

We'll come back to that in a minute but
that's what you should get so

in simple systems that's
what you expect to get.

Well it's a simple system and

alkane is a simple system wise Now can a
simple system know do localized electrons

very simple stuff spaced very broadly
nowhere near optical absorption.

So that's the first measurements
that were any good.

They were done about six years
ago by the group at NIST and

by Mark Reed's group at Yale.

And so they they see exponential decay.

Just like we expected should fall
off exponentially it falls off

exponentially and
these are actually different voltages and

you see different behaviors
at different voltages.

This is an octane file or
a hex of that infile stuck

onto a gold surface is what the actual
structures look like out of which

the measurements are made this is the
simplest system if you can't get this one.

You're in trouble.

So we a lot of other people try to
calculate this one and that actually works

out pretty well this is done using
semi-commercial code called trans C.S.

they're now called F..

The company has gone out
of business twice and

has reached reappeared again in Denmark.

And.

Is this combination of
density functional theory and

these non equilibrium Green's function
methods and what we used it for

was to calculate the length the pendants
for going through the molecular wire and

noticed there's a lot of gold in this
calculation and not much molecule.

The reason for

that is the gold tells you about the band
struck shift at the band structure right.

So it actually isn't quite this there's
a continuum of goal Latham's around this

which you build in in order to give
you the correct and structure and

then you can calculate this guy and and
the points agree with the measurements and

everything is fine but pretty factor
right now that it falls off exponentially

with length we calculate
this fall off parameter B.

day it agrees with experiment very well
we don't calculate the tree factor.

And the reason for that is that prefecture
is incredibly geometry dependent right.

So if I if I took the molecule and

moved it say a tenth of
a nanometer away from the surface.

The Prefect will change tremendously
because the electron has to tunnel through

that that.

And since we don't know the geometry
we can't calculate the prefect.

So we're happy that we got this and

we did a few other things
other people did other things.

So we understand these out Keynes
really quite well we should they're not

very interesting.

They're tunneling barriers.

Let's talk about geometry for
just a moment.

These are published papers from extremely
good groups doing molecular like

Tronics doing this kind of transport and
all the website locations and

you know that they're looking at
simple molecules more complicated

molecules very complicated molecules
switching molecules biomolecules.

There's no science in these pictures
right they're all power points.

You know a Power Point because
you can't see anything.

Let me show you.

This isn't a C.M. image.

This is real.

Where is the molecule.

It's there.

Can you see it.

No you can't see it.

It's probably there because maybe
there isn't a molecule there.

Maybe there are three molecules there.

Maybe their face that way maybe their
face this way maybe they've even

undergone a reaction.

Probably not.

So it's.

Like the bad old days when you were doing
bio physics without knowing anything about

the structure of the entity or
study doesn't mean you can't do good work.

You can't.
But the geometry is a huge problem.

And I think it's going to remain a huge
problem because only indirect method

like Raman spectroscopy actually allow
you to say anything about it but

what else we know that when you get really
little there are fluctuations fluctuations

go like one over the square and when N.
is one there are big fluctuations.

Let's Telegraph noise This is from
a really good group in Japan.

And you see these Telegraph noises and
basically what we think is going on.

This is pent the scene which
is a molecule of substantial

local interest at Georgia Tech what's
happening here is the motel's wobbling in

the in the interface and that's the
molecule wobbles you see it's changes and

these kinds of fluctuations spectra
characteristic of single molecule

spectroscopy this is
a single molecule transport.

So the same thing.

It has to do with fluctuations
in the geometry we think and

that actually fits the models reasonably
well these are some calculations done by

a wonderful group in Denmark Christian
to use and there's a really good guy.

What he did was to just make one tiny
little change he's going to move

the molecule in its geometry between
the golds take it from above

to the middle to below.

What you see here are measurements
of conductance and

calculations of energy for going through
there you see these fluctuations they

are about a factor of three.

So roughly he's geometry changes these
wiggling changes as a moves around

give you a factor of two or
three in the prefecture.

So when they're all Bash was with
me he did some calculations.

This guy's a vice president for
research at a university in Israel and

he really want to get away so he came and
spent a year and a half with us.

Chad you know.

You published a little bit with.

So so these are some of Harold
calculations and basically what

you see is if you move the sulfur from a
top group to a three foot bridge in group.

You see a change of about two point four
And that's the magnitude of the changes

that we saw before and
many experiments that show the same.

I think so.

The geometry seems to be OK.

So this work actually goes back
to two thousand and three or so.

So we've been working at this for
a long time and and about a year and

a half ago I was ready to give this up.

In the sense that we weren't
finding anything new.

It was a matter of Smith
his measure conductance of

a certain molecule will calculate
that Jones has done different one

will turn out not terribly enlightening.

And then one of the wonderful things
that sometimes happens to faculty

members happened to me I went
to a conference I was gone for

seven days I came home there
was a paper on my desk.

That was written by these people.

Jem I mentioned she's a faculty
member in Copenhagen now David

is actually working for think tank in D.C.
Randi is post docking with the Wiemer.

Josh is about to go post that was
Steve Leonean Thorsten is also

a faculty member in Copenhagen and
we came up with something new.

Based on simple chemistry and this
actually might have something to do with.

Systems Biology.

So that's a group meaning.

Let's see.

I remember when this is now there's
a group meeting in July in Chicago.

So we try to get away once and
once or twice a year.

Got the house and the other.

That guy right there in the back row so.

So the work was done in this particular
David and Thorsten and Gemma and what

they did was to go back and think about
the state of the art in this business.

The first thing was wonderful synthesis
had been done a really amazing synthesis

by Jim tourist group at Rice.

By my colleague Fraser Stoddard's group
making these kinds of molecules so

Lindsay had measured carotene and people
had made specific says Randy Goldsmiths

working making these complicated
trip to see in molecules to look for

something that didn't happen but

you know all these things had been
done wonderful synthetic were.

Couldn't measurements and it would all be
explained by this incredibly trivial model

from the one nine hundred sixty S.
developed actually by Simmons that says.

All these things are just tunneling.

You give me the height of the tunneling
barrier the with the telling bear and

I will tell you what your current is so
you're wasting your time and you can see

these these are collaboration's you know
collaboration with the Georgia Tech Group.

It works is very simple barrier telling
models explain most of the measurements

that people have seen and then there
are rules of thumb that you sort of expect

we know that conduction should die off
exponentially if it's coherent and

that's what you see this group on D.N.A.
and as you put more and

more eighty's in the middle of the G.C.
stack it falls off exponentially as work

at Georgia Tech a long time ago suggested
and as expected in this business.

It's also true that.

Conjugated molecules will do a better
job of moving electrons non-conscious

good ones.

So the Karata know it is
a better conductor than the Alex.

And that's not surprising either.

So these rules of thumb seem to work and
then there's this business about the gap

but the Home Alone gap
with the family level.

Affan but not always does a pretty
good job of describing these systems.

This is a work of Chad's that that
really I think is quite nice here and

tells you something about
the limitations of measurement.

They're just going to give you
the same simple behaviors.

So what changed.

Here's what changed.

Let's think about
the simplest possible system.

Ethylene PI system or H two.

And let's think about the simplest
theoretical model which is the one model

so no repulsions no interaction.

That happens is electrons can
move from one side to another.

So the Hamiltonian that describes this has
tunneling terms and side energy terms and

their molecular orbitals is a bonding
one of the anti bonding one and

the coupling is to the environment
the gamma is what will characterized

by this A That's the right one and
that's the left one of that's awesome.

Ready to go.

We can do all these calculations.

We can calculate this G. gamma G.
gamma thing we can compute T.

and then we can integrate that and
get the conductance and

you can do very sexy
Power Points to do this right.

So we got integrate that guy
over this voltage window.

So this is T. which is that.

And this is going to be
the the current i so.

As you start the integrals you pick up
this region that region and that region

and you can see that you get a current
voltage curve that looks like that and

that's what you expect.

That's fine.

Now it gets interesting.

When I do something simple.

First let's look at the transmission
have a small it will

transmit You see two peaks.

The reason for
the two peaks is the homeowner and

the limo transport through homeowner
builders transport through loom or

will they appear at different places in
between you get this to drip or drop.

And then take the same molecule exactly
the same molecule in turn on its side.

We turn on its side.

It looks like this and
now look what's happened.

We have these gigantic holes
in the transmission spectrum

the really gigantic This is logarithmic so

this goes down by a factor of ten
to the seventh and conductance.

Perhaps off by ten million by
doing this to the molecule.

Now remember the rules of thumb the rules
of thumb said it depends on the home

Alou mug at home or when we get has been
changed to the molecule and changed.

Length length hasn't changed because
the molecule hasn't actually only that's

changed is how we've put
this in the junction.

It's actually acting as a stub resonator.

And these guys come from interferences.

Quantum Mechanical interferences between
two pathways that the electron could take

through the molecule now.

I knew this paper but I had forgotten
it back in two thousand and three.

Marcel Maior and his his collaborators put
some measurements on these molecules and

if you look carefully the only
difference between the guy on top and

the bottom is the guy on top.

Has this metal linkage.

Where.
The bottom has a para linkage.

OK.

Para linkages should be extremely
metal but it's a should mix weakly.

And if you look at these curves
they look very very similar.

But if you look at the circled thing
you'll notice that this isn't my gramps

and that's and that all of these differ by
a factor one hundred forty in conduction

Now if you're not a chemist
if you don't love molecules.

You would look at this you know that those
are the same things molecule exactly

the same no difference as I move
this sulphur from there to there why

does it make any difference makes
a huge difference in this case they had

more than a factor of one hundred in
conductance Now what is going on here.

Well here's what's going
on organic chemists

knew all about this or did you know
all about this cross coupling.

Across conjugation says that if I have

a multiple bond there are multiple
on there are multiple man there.

If they're all conjugated together.

That's an end conjugated system like
beauty Dion hexa trying benzine

stuff like that.

But if there's one in-between which
is conjugated to each of those but

not true that those two
are conjugated with each other.

That is called a cross
conjugated molecule.

And from what Dietrich it has
done wonderful work on the optics

of these things to quince kid Alberta has
actually made them a whole bunch of them.

It's a little Sudbury of
organic chemistry but

it has these really interesting
phase properties and

it's the phase properties that the
theoretical chemists finds interesting.

OK so here is the transmission again for
a really simple

set of molecules one is cross conjugated
that guy has a little stub in the middle.

The other ones are N conjugated
there's a system a trans but

you see that the big a hole
in the Pike conduction

a great big hole in the production only
occurs in the cross country to molecule.

It only occurs in a small kill that
has this interference feature.

It's quantum mechanics.

It's really quantum mechanics
macroscopically scene.

Yes So if you are.

The great those and you get the current
You see that there's about a factor of

a hundred difference in the current in
these very very small molecules and

the reason for that is in one case the
electron just tunnels through the other

case the electron has two pathways they
interfere like the two slit experiment and

it looks different.

Now if you make them
bigger you amplify this.

So in this particular case there
are a bunch of molecules calculated

the interesting ones are the black ones
which are for cross conjugated systems and

you can see this giant hole again
really giant hole that's been eaten

in the transmission and
it's down by ten to the.

Eighth or so down by one hundred million
or so because of this interference.

So cross conservation can actually do
things we think in the calculations

suggest all kinds of things First
thing what happens here you

have to check that your
calculation makes sense right.

The right tool for the right job.

We're in a nano center and

I was toured around today and there are
a lot of the right tools around here for

the right out there is have
the right tools for the right jobs.

And you know one of these you'd really
like to be able to do would be to get

the right tool to agree with other things
that are more or less the right tool

with three different levels of calculation
trivial expensive and correct.

And you know that they all
agree with each other.

So that's good.

How about Wiggles we know that
molecules are doing this right.

And if the molecules are doing this and

it really depends on one of
those it's not going to work.

So this is a man Dave Eggers work should
say that this work was done while the guy

was actually working for this consulting
firm in D.C. So he's a good multitasker.

You see these transmissions
the differences in these are just we

let the thing vibrate in its
normal coordinates for a while and

then we stopped that and

did a calculation we did it again again
again you can see that there is fuzz.

But you can see this big
hole is still there.

So we think it's robust to
that kind of the phasing So

bottom lesson of this is that when
interference affects dominate.

All of those rules of thumb fail.

Conjugated molecules may have lower
conductance and saturated ones

because there's an interference
thing that cuts the geometry down.

Shorter molecules maybe much less
conductive the longer molecules

depending on how their number that
thing with the medical nectar that.

My R.C.N. and the home a limo stuff
is completely out the window.

It's got nothing to a home aluminum one.

So this is interesting and
sort of breaks the rules.

So what do you do when you run downstairs
to Mike was loose can say make

me a molecule and measure it and he did.

Well actually molecule synthesis
was done by a man named Mickle

this is not Joseph This is his nephew.

Who's an undergraduate E.T.H. and spent
the summer with us making molecules and

they made these guys and what you can see
is that the cross conjugated one up here.

Has the same charge separation rate

constant as he totally
Signum on that one there.

Whereas the non-trust conjugated one
here is about a factor of forty faster.

So there's a relationship between
conductance and trance and and

kinetics which I didn't talk about but
they map each other because they both

depend on tunneling and as expected
this cross conjugated guy is much

less conductive the electron
moves much less effectively.

Because of this interference phenomena.

I think that's kind of interesting.

And that's what's relatively
new in this transport business.

Because I said we talk about three
things First simple molecule don't or

accept or
second junctions third new stuff.

When this stuff has to do with a women
Sorry have to have pictures right.

So when we said that there
are resonances when there are resonances

there's an energy dependence of this
this interference only occur in

certain energy regime so
these are some pictures that Gemma made

over the tribes going through this
molecule this is the transmission and

this is the cartoon The cartoon
is looking for local currents.

There it's a way that you can
take that gamma G. gamma G.

formula and construct local currents.

So it'll.

Current through an alkane which is not
very interesting because the local

currents through a pair of bends
annoyed structure they come there one

goes there one goes there and
they come out they interfere positively.

So there's more current coming out than
going through either one of those branches

but let's look and see what happens with
the cross conjugated molecule because

that's what's interesting.

OK this is a cross conjugated
molecule it's a metal benzine

current comes in goes through there but
it goes through there.

The other way the blue arrows are pointed
the opposite way of the Red Arrows and

that's this interference phenomenon that
gives these deep cuts there there and

there and

it should be energy dependent than it
is so let's have a look at the energy

dependence what we're doing is coming
toward the residents way up above it.

It's going through both of those
this is the total current That's

the pipe current Now you can see we're
getting it's get really interesting see

the blue things coming up it's going
the other way and then turns off.

So that resonance occurs over a very
very small regime an energy and

that's what we think is responsible for
the cross coupling behavior.

OK now let's go to the third thing.

But first thing is when the poor little
molecule is trying to transport charge is

held in as tightly as people getting
pushed into the Tokyo subway right.

So so there's a self assembled monolayer
and on the ends of the molecules.

There are places where the electrons
can fit it can hop it can move as

all of the molecules that John
looked in his group of looked at

here could move a long way it's going to
move from molecule to molecule tomorrow.

But now it's in a situation where
the molecules are moving a little bit.

So the model that you can build for
this and this is work with the eagle and

Chris is that you have an self assembled
monolayer glued on to some surface.

You can prepare these by Langer Blodgett
techniques on the top of the molecule

the yellow guys.

The reduction groups in other words
they can accept an electron or

they can pass an electron and the way it's
drawn here there are a lot of them and

the blue top as.

And so it's a mixed model or one of which
can host electrons one of which cannot.

And the question you could ask is how do I
move electrons from one side of the other

through such an entity.

Now this relates vaguely to
Systems Biology in the sense that.

When I was your age I was
told that a cell is a bag of

water with an outside it's got a membrane
it's got water inside all these things.

That's entirely wrong.

The cell is as engineers as this building
is and so there are issues of free volume

inside the cell the entities can actually
move freely into These are controlled so.

One model for this kind of thing
is to make a crowded film and

see what the crowd filmed us and there is
a long tradition in statistical mechanics.

That actually studies this.

We want to combine that with
this charge transport so

it's a system like this as I said and
a whole bunch of things that

this actually could apply to Langer model
years by layers polymer now to raise.

NATHI honor athenæum structures all things
in which there's a dynamical motion

of a molecule.

There's also an electron motion.

It's a model that we make for

this is single molecules our single
molecule has four blobs on it.

The blob on the top can need to be
conductive or non-conductive the blob on

the bottom is constrained to move in
a plane so I have a plane molecules on it.

They're moving around.

First thing is what's there.

Geometry.

This is a great question as to the slow
mechanics you get wonderful names like

heck Sadek order parameters but
as I squeeze these things they want

to be hexagonal impact the more you
squeeze in the one hexagonal they ought to

be if you put a dipole on them
though they don't like that right.

Because if they are sad if the dipoles
would be like this they don't

like that they like to do this.

So there's a competition between
that I pull a direction that

says bend the knot that pull
it one which says stack up and

as you change the German trees these are
going to change because the calculation

has model layers that a thousand chain.

Moves occur.

It's more it's a Monte-Carlo
calculation actually so

we construct this monomer we allow it to
move we use potentials that are reasonable

potentials and we want to see what
the structure in the Namak Saar

this is the ecstatic order parameter I
was talking about the six means ecstatic.

It basically tells you if
you're a molecule like this.

How are your buddies around you.

Organized.

And if it's one.

It's a purely hexagonal structure.

There's an order premise that tells
you how exactly you ordered this.

And these are results just for
the phase behavior with no dipoles just

grease molecules on top and you can
see that there are two regimes right.

There's this regime which is strongly
disordered this regime which is strongly

ordered right.

This is the density here of the density
is point six here the density is

point nine It's getting
really really tight and

you can see what happens there's a phase
transition here which is the heck.

Sadek ordering phase transition which
comes out in the Monte Carlo and

temperature dependence.

It's all fine.

It's two dimensional melting.

OK.

Now let's put the dipoles on.

So there's a competition now between
one force and another what we have here

is as we change the charge as we
change the magnitude of the dipole for

small dipoles it's almost consistent
across the sampling region.

That's a sex addict stuff
when that happens get bigger.

There's a competition and you begin to
see a much more gradated structure so

called tilt domains.

So the tips are different in the yellow
part than they are on the blue part.

So there's a sort of transition
in geometry from this to this

which is interesting for geometry.

Let's talk about transport.

So now we're going to

do is we're going to stick on the top
of these these conductive entities.

And really to change a fusion.

So you look at the change
themselves the future at the change

are not bolted to the ground.

They're allowed to move and they do and
you can look at this is a function of

density and
not surprisingly when the density is low.

They diffuse Well when the.

It's it gets bigger.

They diffuse less well and

then gets really big going to
fuse that all their stock.

And they do that.

So let's pull out from the top and
it gets interesting.

Art to remember these Dom's rough papers

back in the one nine hundred seventy S.
Dom's and rough.

Said Look under these conditions
the diffusion coefficient actually has

two components to it.

One for

computing the diffusion coefficient
is this strand which is moving.

If you're an electron you sit on
the strength the strength going to move

you're going to move.

And then there's another part which
is actually electron hopping and

what they suggested was that
this was a simple song.

So the trunk can either hitch a ride or
it can hop.

Let's see if that's right.

So the simulations are done.

Carlo don't want to waste time
with the nature of what we did and

you can some That's all fine.

But three properties that you care about.

There's the hopping rate the electron
hops from place to place exponentially

tunneled so can't Total very far but

you can change how far it can
tunnel by changing this parameter.

Then there's the density of ones that
have redux sites if there's only one

redux site it's not going anyplace.

And there's the overall chain
density the three parameters that

determine this transport.

This is very different from the first
two situations we talked about.

The intro molecular turn transfer
is fixed by tunneling and

vibrations the junctions are fixed by
tunneling and densities of states.

Now it's fixed by geometries
in the underlying system

is actually sort of interesting
something if you're at the high density.

Things are packed together
very tightly in the red right.

High Beta they can't go very far and
very low concentration of except yours

first but if you're going to fish and
is very small ten to minus five.

Second you can see that it
increases as the fraction of

tipped ones goes up which is what
you'd expect but it's much more.

Striking in the red which
is the high density thing

in the blue which is a low density thing.

So I think there's a simulation and
I hope it works.

Much in the US.

So we're great guys.

The electron right and
he's trying to move around.

He can't get away from his local area.

Why can't he get away
because this density is so

high that these things
are just jiggling in space and

the number of yellow ones which in
the except hers is relatively small.

So all he's doing is exploring
his little cluster there and

that's all that's going to go
on no matter how long you watch.

It's below the percolation threshold
if you like even though they're moving.

They're not changing very much.

And so it's going to sit there forever.

And if you take his trajectory and
plot it.

There it is it just moves around in this
local site and you can see that the mole

fraction of sites that can accept and
the gold topped ones.

There are very many gold topped ones and

he's stuck in his local region forever and
forever.

So how can we make a move.

Well one way to make him move.

Is to increase.

The ball fraction of places that he
can go now it's still relatively low

the conduction is still relatively low
because it's still high density and

he still has the wiggle.

But you can see in this case that
the trajectory is more extended

It's not local.

He's stuck it moves around from place to
place but it's not terribly efficient

over the time scale of the measurement it
hasn't to fuse from one end to the other.

So let's make it a little bit better.

So now notice that the.

Numbers in the little red circles have
gone up by a factor of a thousand this

guy can really move.

OK now it's not.

Localized the beta has become smaller so
can tunnel farther and

it's got a high density.

And you can see that in this
particular case the conduction is high.

There are no crossovers
everything is as expected right.

As you make the number of
carriers bigger and bigger and

bigger and the conduction gets bigger and
bigger and bigger.

And that's this one right there
aren't very many yellow guys but

they can move around a lot so he can
actually move long long distances and you

can see sometimes he actually doesn't even
go through anatomy just skips over one.

So there are a whole bunch of behaviors of
this kind of don't want to belabor this.

This is what happens
when there's low density.

Now they were moving around like this
they can flop around Dom's rough

would say should move fast.

There's a steep telling fall off but
there's no reduction and you can see here

these long jumps long jumps That's because
the only thing that they can do when they

look around is to look for the nearest
guy they can get to and they do that.

So as I said I don't want to belabor this
there are lots of them but the point is.

But these quasi Christly model layers
actually give you a percolation threshold.

When.

This fell off as quick another one
can only go to nearest neighbor.

You saw that was stuck couldn't get away.

As I relaxed that.

OK Two things can happen.

Long range hopping from its macroscopic
charge transfer they can time a long way

and if the model has become fluidic
then you have both hopping and

this physical chain displacement.

The only thing wrong with this Doms
rough theory which is older than most of

the people in this room is
that it's not a simple sum.

These two things are not separated
they actually work together and

we've done some analysis to do that.

Well over time.

So let's finish with this.

It's a great pleasure to be
back here I can tell you.

In the privacy of some other conversation
about my first visit to Georgia Tech which

was thirty nine years ago this
was quite a different place.

So it's nice to be back thirty nine
years later at a much nicer and

much more impressive and
much warmer place.

So thanks for much.

Questions.

Was.

I'm telling you that it will
change this and all the states.

You're going from apply kind of states
in the middle or on the molecules.

On the atoms.

OK so the metals are metals right.

The question was as you change the
molecule you change the local density of

states in the metal very very slightly
if you go all the way back to NEW And

Anderson one nine hundred fifty four.

They weren't about chemists or passion and

how do you change the states when
you chemist or been it onto a local.

They're pretty basins of course.

Right because you're changing
the local site energy.

So I didn't talk about this but
I actually have a student who's who's done

this analytically now in a tight binding
model and you can see that it heals.

Now the words the changes.

He'll into the crystal in one
dimension they never heal so

in one dimension the answer that
question is they're huge changes.

Not surprisingly in two dimensions
they heal after three layers

in three dimensions they heal after
one layer which is what you'd expect.

So there are changes but except in reduced
dimensionality they're not important

to good question and you might.

So Professor Margaret is one of the people
in this room who knows all about cross

conjugated molecules so
we're going to flip back to there.

That's correct.

Saturating the cross conjugate
are basically the same.

So I

want to go through.

Yes.

Not here.

Here you're using you know
if you have a great great.

Why you know what you're like

what you know I've got

me Paris

on the Yeah Yeah Yeah Yeah Yeah Yeah Yeah.

Well.

First a martyr says something you have
to listen because there are several

layers of meaning here and
it's a complicated question.

But but briefly put.

The reason sulfurous are used
is that people are lazy and

selfish form self assemble modelers
there are other measurements.

There are measurements with an means by
litho Venkataraman their measurements with

selenium as in various places.

It's almost always software because they
form a self a somewhat monolayer nicely

and most of these measurements are not
made by chemists I mean by physicists or

electrical engineers and
they buy the molecules.

So these the ones they buy those the ones
who measured you can do calculations on

these other ones and compare with the few
experiments that there are the conduction

is actually better through sulphur than it
is through Amien for reasons that markets

and as explained if you pretend
that you could build a direct bond

from the metal to a carbon that's
calculations has been done.

We've done it.

Other people and

yes it conducts much better because there
is a barrier that comes about because of

this sulfur it's only got one lone pair
Nowlan past a couple between the metal.

And the molecule is going
to depend on geometry.

So the answer your question is yes but

I think it's slightly different because
here we're isolating this entity.

So whatever goes on here is effectively
different I think than what goes on here.

So the way to think about that
in terms of this gamma G.

gamma G. formulation I talked about
is this is in G. that's gamma

that's the interface it's a pretty factor
in this conductance it does change that.

That's right.
But

it doesn't modify the behavior seen here
and you wouldn't expect that to actually

right because I

shot your ball conductance goes down but
that goes down.

Similarly in all of these.

There's actually work by Dan Frisbee who's
looked at a whole bunch of molecules and

extrapolated to zero length.

And he comes up with what he
calls a contact resistance and

the contact resistance is different for
files and it is for and

Means or selenium as you'd expect
because the overlaps are different but

again the the the theory
with that gamma G. gamma G.

suggests that this ought to happen should
be able to separate what goes on at

the interface for those on the molecule.

OK

So when

you're on these transport
residents have you guys

done enough different comic
to that you can articulate

rules for

these pieces of the Kurds guess with

as you're proposing to say do you have
rules for just asking a question.

About.

Can i Map a geometry onto
an interference pattern.

The answer in simple systems
is yes there's a guy named

Chu who published a paper in his
read about six years ago and

I got some sleighs we can talk about
it to Basically it's what you'd expect.

So you can define a phase angle and
the phase angle basically has to with

the geometry of the molecule in
the voltage that you're at and

that phase angle when it becomes
two pod there is a flip and

that's exactly where these
holes in the resonance.

That that's a really nice thing but

it would to be able to do it whether it
is constructive or destructive resonance.

It's a matter of whether it
comes by to Pyar PI right.

And yes that works fine but

only in very simple systems only in simple
systems where you can define this phase

independent of the tunneling energy or
it is not independent of it and

it shouldn't be independently energy but
but you'd expect that actually.

One thing that we haven't thought
about here is the phasing right.

And this is totally coherent and
inorganic molecules the phasing

always occurs in them and
trying to figure out how to put the D.

phasing into this and
that's one software talk later.

Getting exercise.

I mean yes.

If the molecule is symmetric and the I.V.

characteristic be on
symmetrical What do you think.

I think.

Well suppose that the two linkages are
completely different suppose that one side

links snuggly to an electrode in the other
side there is a terrible thing in the way.

So the gamma is different on the two ends.

So I mean.

So you have a molecule and
bonded very strongly to one and

then very weakly to the other even
though the molecule itself is symmetric.

The bonding is on symmetrical.

And you can prove to yourself I think.

But low voltages you won't see any

rectification if you want but high voltage
as you will and it's basically because of

the way you couple into these
different coupling States.

So low ball to just totally symmetric
backward current same thing but

then as you get higher.

It actually changes the issue of
rectification is actually the issue that

started all this stuff back
thirty years ago about whether or

not molecules could be used as rectifiers
that's not the best way to do it.

There are better ways to do it but
that will do it.

So you will get on symmetrical behaviors.

If the gaps are different
on the two ends but

only a high voltage is
not it not zero fault.

But

what I was going to

talk about is something called inelastic
electron tunneling spectroscopy was what

happens at very very low voltages where
you actually see molecular vibrations.

That's the most successful
aspect of this whole

thing in the sense that the measurements
have been made the theories been done and

they fit incredibly well.

So at low voltages.

What's interesting is actually the
vibrational component of the voltage at

high voltage is you see these resonances
and you like to explain the resonances but

generally it will never be what John
pople called a model chemistry.

You're never going to get within a few
percent because of your uncertainty and

geometries but for
most simple molecules as I indicated these

rules of thumb work very well and you can
sort of guess what's going to happen.

There are interesting things the market
gets longer and longer and longer.

It does the thing and you do see
a transition from tunneling to hopping see

that change in the temperature dependence.

Distance dependence all the sort of
stuff the D.N.A. work suggests occurs in

a molecule section but a low voltage
regime is mostly interesting because

these vibrations tell you something about
where the molecules are in the circuit

and the R..

OK and the negative differential
resistance there were measurements

that show that as you increase
the voltage the current went down.

That's called negative difference
resistance it was very exciting in one

thousand nine hundred seven.

It was first seen the molecules in which
it was first seen Mark Read's molecules

probably aren't right because they switch
and we think it goes by switching but

negative differential resistance at
a small level is seen quite often

in the simplest argument is the molecule
geometry is changing just a little bit and

as it changes geometry
is going to change that.

That is reproducible measurements by Paul
Weiss in films where it goes like this and

goes like that and the feeling
flips on and off and on and off and

on and off as it changes the coupling.

So I think we sort of
understand where N.P.R.

comes from now it's mostly geometric

it

is possible or what is missing.

What is the key elements
which are missing protein and

try to figure out what
the other proteins so.

Now the question is about pathways of
electron transfer in protein systems and

this goes back to this really nice
work that para ten on you did

where they have suggested pathways for the
electrons based on it's a penalty model.

The things that I showed with
the arrows and moving around and

all that stuff that's
a local currents measurement.

It's not a pathways it's
a currents measurement.

We think that actually.

Well work.

We've looked at some of the kinds of
molecules that are of interest here for

example peise stack systems and
PIs tax systems that are staggered and

look at those those arrows and
where they go.

I think I think you can
learn a lot from this but

remember it's a different assumption.

Essentially the current is coming
in from interfaces with models and

that might work well in organic
transistor photovoltaics So

I think that the pathways
business is still out there.

Quantum mechanics tells you there
should be lots of pathways and

they should interfere and
that's what we saw so.

So how you interpret that as you
begin to deface and eco here and

go to a system where you magine
there'd be one dominant pathway.

That's something I don't know stand.

That's a really good question

and it kind of in the device right.

Well it depends on which part of my N.S.F.
proposal you read.

Now seriously I think that the place that
this does work and it really does work.

Is by absorption conductive sensing but

there are thousands of
other ways to do that but

you can you know the guys are pretty
have actually done this you can build

a molecular bridge like this and you can
sense iodine if you want to sense iodine.

It works fine.

You build yourself a little bridge as
apply system that it comes down forms of

Moloch and type don't accept a complex
conduction changes by a factor of five and

you can see it so it works for the first
most people don't want to sense iodine.

Secondly you don't want to send side
down the vapor phase where the.

This is done.

Thirdly you know there's a much better
way to do it just to spectroscopy see it.

It is very very sensitive in fact but it's
not selective and it doesn't scale and

our Janata would say you're wasting
your time and he'd be right.

So I don't think that's useful.

People will tell you
that these are useful for

other things too but I'm not persuaded.

I mean I think it's a different regime.

One of the most fundamental processes in
chemistry which electron transfer and

that's enough for me.

One more person a guy in France
whose name is Christian Shoshanna

who runs an A C N R S lab in Toulouse
he's convinced you can actually do logic

inside one molecule remember these
interfering pathways and stuff.

Well if you can control
the interference pathways

then maybe you can do untangle
ment within a molecule.

And maybe you can actually do data
processing within one molecule and

most people would say it won't
happen because of the phasing but

that hasn't stopped him and he's done some
really beautiful stuff actually suggesting

all sorts of manipulations logic and
arithmetic within a single molecule.

But it's so far it's theory
although he's got an enormous.

Now what is the nervous Has this been an
enormous amount of set up to actually make

measurements on these
molecules to see if it works

where you're seeing you electron
you know transported your personal

approach to properly action threshold in
the almost the future as you might Is

it Peter that one or something like
that for the collective path and

then there's a plateau and then it takes
off just simply a box and what happens

above the percolation threshold is
that regime collapses always to.

OK temperature.

I know to use in time T.
is time or OK OK OK OK Well the logical

of part that's the this business
about is this thing a sum or not.

So if you do Dommes rough and it's.

Some you should see two behaviors one is
the fusion goes like excrete goes like

the cells like to the one half and
the other is just lateral motion so X.

goes like the.

If you think of a very similar but
not identical problem which is called

either stirred percolation or dynamic
percolation in which you say there's

a percolating network but the little
guys move positions from time to time.

Then if you plot excoriate as
a function of the it looks like this

what happens within each one of these
is the guy fills his local cluster and

then has to wait for the relaxation
process and then he goes on.

So if you take your glasses off and put
a plow through there and he goes like X.

where but here it's going exponentially
actually sticking exponentially.

So that is a very similar model is
not quantum mechanical it's classical

The answer to the question is I don't
know because we haven't done it yet.

I think to do that this Monte Carlo has
the yield to molecular Namak Swilley have

to do a correct time approximation right.

Monoculture steps are not time steps
as you know better than anybody so

that remains to be done.

One of the question.

All of the biological question
people who study things like

the electron transport and
through synthetic reactions Yes.

Clausen Yes.

How far are the most fundamental tools
actually still use wars that follow

have you learned from the response to me
it's very similar your own was there.

I mean if you get about those who
are less a Linus used up a whole bunch

of protein you more or
less know where they are.

You're asking the wrong person
because there is a huge effort

worldwide especially around the corner
in memory to mix Molech killer

mechanics with quantum mechanics and try
to get these very very large systems and

obviously in systems biology
that's an important.

I don't do that stuff.

The particular case of photosynthesis.

There are all these new
things from shills lab and

Flemings lab where they see quantum
coherence this over long periods of time.

That's interesting.

Whether it's biologically relevant or
not I'm not in a position to judge but

it's very interesting that in a molecule
that large you actually see quantum

coherence as an energy transfer.

I don't think that the methods I talked
about today are the methods that I

would use to work on that problem.

I think that problem is
probably better for Q M M M.

But you can learn something
by looking at these currents

connection with that question
that was asked before.

With more.