Lecture 4: Crossed-beam reactive
scattering experiments
Getting a collision by collision
picture of a chemical reaction
© 2014 D.J. Auerbach – All rights reserved
How do we obtain information about the PES

Through many methods:
– Energy Requirements: Looking at what promotes a
reaction: translation, vibration, rotation
– Energy Disposal: Looking at the energy content of
reaction products - are they vibrationally, rotationally,
or translationally excited
– Scattering Experiments: The most useful and
definitive method has turned out to be scattering
experiments


Sept. 25, 2014
define the initial state of reactants
measure the angular, energy, and quantum state
distributions of products and compare to theory
Lecture 4 -- Chemical Dynamics at Surfaces -- Dalian 2014
2
Rutherford Experiment
The power of scattering experiments
Sept. 25, 2014
Lecture 4 -- Chemical Dynamics at Surfaces -- Dalian 2014
3
Discovery of the electron
Sept. 25, 2014
Lecture 4 -- Chemical Dynamics at Surfaces -- Dalian 2014
4
Plum Pudding Model and Plum Pudding
Sept. 25, 2014
Lecture 4 -- Chemical Dynamics at Surfaces -- Dalian 2014
5
Plum Pudding Model Prediction
Sept. 25, 2014
Lecture 4 -- Chemical Dynamics at Surfaces -- Dalian 2014
6
Rutherford, Geiger, Marsden Experiment
Ernest Rutherford
Sept. 25, 2014
Hans Geiger
Ernest Marsden
Lecture 4 -- Chemical Dynamics at Surfaces -- Dalian 2014
7
Geiger – Marsden Apparatus
Geiger-Marsden apparatus photo"
by Original work: Hans GeigerDepiction: Joachim Grehn - Metzler Physik. Licensed under Fair use
of copyrighted material in the context of Geiger–Marsden experiment via Wikipedia http://en.wikipedia.org/wiki/File:Geiger-Marsden_apparatus_photo.jpg#mediaviewer/File:GeigerMarsden_apparatus_photo.jpg
Sept. 25, 2014
Lecture 4 -- Chemical Dynamics at Surfaces -- Dalian 2014
8
Results




Most of the  particles (He+)
went straight through.
Occasionally, however one
was deflected to large angles
Very occasionally, an 
particle bounced back
Rutherford said “It was as if you shot a 15 inch shell and
a piece of tissue paper and it came back and hit you.”
Sept. 25, 2014
Lecture 4 -- Chemical Dynamics at Surfaces -- Dalian 2014
9
Discovery of the Nucleus

The positive and the vast
majority (>99.9%) of the
mass of the atom was
concentrated in an
extremely tiny nucleus

Knowing the energy of the
 particle (7.7 MeV),
Rutherford could place an
upper limit on the size of
the nucleus of 3.6x10-14 m
Sept. 25, 2014
Lecture 4 -- Chemical Dynamics at Surfaces -- Dalian 2014
10
Stripping, Direct Rebound and Complex forming reactions
being examples
SCATTERING METHODS
ALLOW US TO CLASSIFY
REACTION TYPES
Sept. 25, 2014
Lecture 4 -- Chemical Dynamics at Surfaces -- Dalian 2014
11
Scattering methods allow us to
classify reaction types
Stripping, Direct Rebound and
Complex forming reactions being
examples
© 2014 D.J. Auerbach – All rights reserved
Impact parameter
What YT Lee liked to call ‘the aiming
error’
Sept. 25, 2014
Lecture 4 -- Chemical Dynamics at Surfaces -- Dalian 2014
13
Geometric parameters of a molecular Collision
 consider scattering of two spherical particles
 sit on B so it appears to be at rest
b impact parameter
 scattering angle
vrel initial relative velocity
v´rel final relative velocity
Note how an attractive potential can steer molecules together.
There is an orbital angular momentum L perpendicular to the plane of the
collision of magnitude
L = vrel b
Sept. 25, 2014
Lecture 4 -- Chemical Dynamics at Surfaces -- Dalian 2014
14
Relation of scattering angle to impact
parameter
Sept. 25, 2014
Lecture 4 -- Chemical Dynamics at Surfaces -- Dalian 2014
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Relation of scattering angle to impact
parameter
Sept. 25, 2014
Lecture 4 -- Chemical Dynamics at Surfaces -- Dalian 2014
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Relation of scattering angle to impact
parameter
Sept. 25, 2014
Lecture 4 -- Chemical Dynamics at Surfaces -- Dalian 2014
17
Opacity function
Back-scattering
1,2
1,2
1,0
1,0
P(b)
P(b)
0,8
Arb. units
0,8
Arb. units
Forward scattering
0,6
0,6
0,4
0,4
0,2
0,2
0,0
0,0
-4
-2
0
2
4
-4
-2
impact parameter (b)
Sept. 25, 2014
Lecture 4 -- Chemical Dynamics at Surfaces -- Dalian 2014
0
2
4
impact parameter (b)
18
Scattering and the impact parameter, b
Example of a stripping reaction
K
b large
I
I
Sept. 25, 2014
Lecture 4 -- Chemical Dynamics at Surfaces -- Dalian 2014
19
Scattering and the impact parameter, b
Example of a stripping reaction
K
K
I
b large
b large
I
Reaction cross section
(assuming every collision
within ‘b’ reacts)
 ~ b
Sept. 25, 2014
I
I
2
Lecture 4 -- Chemical Dynamics at Surfaces -- Dalian 2014
20
Stripping reactions in molecular
beam scattering Experiments
 Stripping
reaction
– Forward scattering in CM
frame
– usually attractive PES,
early barrier;
– direct reaction;
– large impact parameters, b;
– short lived TS.
Sept. 25, 2014
Lecture 4 -- Chemical Dynamics at Surfaces -- Dalian 2014
21
A Closer look
We represent results by
polar plots of velocities of
products in Center of
mass frame:
Scattering angle is angle
between reagent and
product relative velocity
vectors.
Distance from CM
represents product
speed.
Sept. 25, 2014
In this example - Angular
distributions is forward
scattered with respect to the
original direction of the K
atom
Lecture 4 -- Chemical Dynamics at Surfaces -- Dalian 2014
22
Rebound reaction
Initial Conditions
vrelative  vF  vH 2
F
vF
b small
vH2
H-H
Collision Occurs
Sept. 25, 2014
Lecture 4 -- Chemical Dynamics at Surfaces -- Dalian 2014
23
Rebound reaction
Initial Conditions
vrelative  vF  vH 2
vHF
F
F vF H
b small
vH2
HH - vH
H
Linear momentum conserved


mHF vHF  mH vH
Sept. 25, 2014
Lecture 4 -- Chemical Dynamics at Surfaces -- Dalian 2014
24
Rebound reactions in molecular
beam scattering Experiments
 Rebound
reaction
– Backward scattering
in CM frame;
– Can be early or late
barrier
vD2
vF
– small b
– direct reaction;
– short lived TS.
Sept. 25, 2014
Lecture 4 -- Chemical Dynamics at Surfaces -- Dalian 2014
25
Complex Forming Reaction
H
vO
O
vH2
1
O( D)
Sept. 25, 2014
H
+ H2  OH + H
Lecture 4 -- Chemical Dynamics at Surfaces -- Dalian 2014
26
Complex Forming Reaction
vO
HH
O
O
vH2
1
O( D)
Sept. 25, 2014
HH
+ H2  OH + H
Lecture 4 -- Chemical Dynamics at Surfaces -- Dalian 2014
27
Complex Forming Reaction
vO
O
O HHH
O
HH H
vH2
Dissociation in all possible directions
Memory of original direction forgotten
1
O( D)
Sept. 25, 2014
+ H2  OH + H
Lecture 4 -- Chemical Dynamics at Surfaces -- Dalian 2014
28
Complex forming reaction in
molecular beam scattering
Experiments
 Forward/backward
scattering;
 long-lived
complex
(lifetime of many ps);
 Deep
binding well on
PES.
Sept. 25, 2014
Lecture 4 -- Chemical Dynamics at Surfaces -- Dalian 2014
29
A good homework problem (optional – extra credit)
WHY FORWARD-BACKWARD
SCATTERING AND NOT
ISOTROPIC
Sept. 25, 2014
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30
Reaction rate in terms of opacity function
 P(b)
is the so-called
‘opacity function’
– It is a function of impact
parameter, b
– This function may be
different at different
values of the relative  (vrel ) ~
velocity
 The
thermal rate
constant
– is the thermal average
of the cross section
times the velocity
Sept. 25, 2014
 P(b; v
rel
) 2 b db
k (T )    (vrel ) vrel PMB (v; T ) dvrel
k (T )   (v) v
Lecture 4 -- Chemical Dynamics at Surfaces -- Dalian 2014
thermal
31
Opacity function for some reactions is
independent of impact parameter
1.4
1.2
Arb. units
1.0
0.8
0.6
0.4
0.2
0.0
-4
-2
0
2
4
impact parameter
The influence of the opacity function can be dramatic
Determining the magnitude of the reaction cross section and
Reaction rate constant
Sept. 25, 2014
Lecture 4 -- Chemical Dynamics at Surfaces -- Dalian 2014
32
Maximum reaction rate

This occurs when the opacity function is unity over a
wide range of impact parameters.

Long range interactions attract reactants.

Once they get close to one another they react with 100%
efficiency
– E.g. Electron transfer reactions
k (T )    (v) v PMB (v; T ) dv
Sept. 25, 2014
3
𝑐𝑚
𝑘𝑚𝑎𝑥 ~10−10
𝑠
Lecture 4 -- Chemical Dynamics at Surfaces -- Dalian 2014
33
Crossed-beam reactive scattering
experiments
Getting a collision by collision
picture of a chemical reaction
© 2014 D.J. Auerbach – All rights reserved
Last Modified 29.10.2010
34
10-6 Torr
Molecular beam expansion
10-8 Torr
0.1-5 bar
10-4 Torr
Sept. 25, 2014
Lecture 4 -- Chemical Dynamics at Surfaces -- Dalian 2014
35
Molecular beam expansion
10-4 Torr
Sept. 25, 2014
Lecture 4 -- Chemical Dynamics at Surfaces -- Dalian 2014
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Properties of the molecular beam expansions

Velocities are large
For pure gases
vmost probable 
2C p Tstag
m
5kT
For monoatomics vmost probable 
m
He 1800 m/s at 300K
7kT
vmost probable 
m
H2 2900 m/s at 300K
For Diatomics
Sept. 25, 2014
Lecture 4 -- Chemical Dynamics at Surfaces -- Dalian 2014
37
Further properties of molecular beam
expansions: “seeded beams”

If you have a dilute mixture of heavy gas in a light gas.
You get very high translational energies
– e.g. I2 in H2
– mI2 = 254
vH2 = 2900 m/s
– EI2 =11.5 eV
vmost probable 
Sept. 25, 2014
2C p Tstag
m
Lecture 4 -- Chemical Dynamics at Surfaces -- Dalian 2014
38
Number of collisions required for
significant energy transfer
Sept. 25, 2014
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39
Translation is strongly cooled

Dv/vMP = 0.05 is routine

Dv/vMP = 0.005 is possible

Production of He2 – weakest bound species –
demonstrated in molecular beams
Sept. 25, 2014
Lecture 4 -- Chemical Dynamics at Surfaces -- Dalian 2014
40
Rotation is strongly cooled
 Spectroscopy
shows
J=0 is dominant
state in an HCl beam
– (seeded in H2)
– Rotational Temperature
is 20K
Ran, Q., et al., An advanced
molecule-surface scattering
instrument for study of vibrational
energy transfer in gas-solid
collisions. Review of Scientific
Instruments, 2007. 78(10).
Sept. 25, 2014
Lecture 4 -- Chemical Dynamics at Surfaces -- Dalian 2014
41
Rotation is strongly cooled
 Spectroscopy
shows
J=0 is dominant
state in an HCl beam
– (seeded in H2)
– Rotational Temperature
is 20K
Ran, Q., et al., An advanced
molecule-surface scattering
instrument for study of vibrational
energy transfer in gas-solid
collisions. Review of Scientific
Instruments, 2007. 78(10).
Sept. 25, 2014
Lecture 4 -- Chemical Dynamics at Surfaces -- Dalian 2014
42
Crossed beams reactive
scattering in F+H2
An instructive example
Sept. 25, 2014
Lecture 4 -- Chemical Dynamics at Surfaces -- Dalian 2014
43
Scattering using crossed beams

Two beam sources and a
rotatable detector
– Detector is a mass
spectrometer or laser based
state specific detector
– Study angular scattering of
reaction products in the lab
frame
– Time-of-flight to measure
product speed

To understand the collision
dynamics, examine
scattering in the centre-ofmass frame.

Scattering distributions depend sensitively on the
topography and nature of the PES
Sept. 25, 2014
Lecture 4 -- Chemical Dynamics at Surfaces -- Dalian 2014
44
Crossed Molecular Beams Reactive Scattering
Features
 A beam of F atoms is
introduced

Normal to a beam of H2
molecules

A velocity selector is
used to narrow the F
atom velocity spread

Reaction Products are
observed by a rotatable
mass spectrometer
– Angular distributions and
– TOF distributions using a
choppper
Sept. 25, 2014
Experimental arrangement
Neumark, D.M., et al., Journal of
Chemical Physics, 1985. 82(7):
p. 3045-3066.
Lecture 4 -- Chemical Dynamics at Surfaces -- Dalian 2014
45
Basic information on F+H2
Thermochemistry
 Highly exothermic

Energetics of the F+H2
reaction
Tendency to produce
vibrationally excited
products. – See Pimentel
chemical laser
A small reaction barrier is
located in the entrance
channel of the reaction
coordinate
Sept. 25, 2014
Lecture 4 -- Chemical Dynamics at Surfaces -- Dalian 2014
46
More on the experiment
Lee, Y.T., et al., MOLECULAR BEAM REACTIVE SCATTERING
APPARATUS WITH ELECTRON BOMBARDMENT DETECTOR.
Review of Scientific Instruments, 1969. 40(11): p. 1402-1408.
Nobel Prize
in Chemistry
1986
Experimental Overview
 An electron
bombardment ionizer
provides “universal
detection”
– Ion fragmentation must be
sorted out.

Sept. 25, 2014
Rotatable triple chamber
design is crucial to
reduce background
Lecture 4 -- Chemical Dynamics at Surfaces -- Dalian 2014
47
Newton Diagrams
Center of Mass Demo Video - MIT
Last Modified 29.10.2010
48
Newton Diagrams
Center of Mass Demo Video - MIT
Last Modified 29.10.2010
49
Newton diagrams for reactive scattering
Newton diagrams show the relationship between the LAB and CM frames
Lab frame
CM frame
vA
lab velocity of A
urel
relative vel. of A + BC
vBC
lab velocity of BC
urel'
relative vel. of AB + C
vAB
lab velocity of AB
uA
relative velocity of A
vC
lab velocity of C
uBC
relative velocity of BC
U
velocity of CM
uAB
relative velocity of AB
uC
relative velocity of C

CM scattering angle

Sept. 25, 2014
lab scattering angle
Lecture 4 -- Chemical Dynamics at Surfaces -- Dalian 2014
50
Vector Addition in Newton Diagrams

vF

vCM
Sept. 25, 2014

 
vrel  vF  vH 2


mF vF  mH 2vH 2

mF  mH 2
Lecture 4 -- Chemical Dynamics at Surfaces -- Dalian 2014

vH 2
51
Some reminders
Translational Energy of
Incidence

 
vrel  vF  vH 2

1 
Ecollision   vrel  vrel
2
mF mH 2

mF  mH 2
Sept. 25, 2014
Transformation from Lab to CM
frame

vCM

vCM

vCM


mF v F  mH 2 v H 2

mF  mH 2


 u F  vF


 u H 2  vH 2
Lecture 4 -- Chemical Dynamics at Surfaces -- Dalian 2014
52
Vector Addition in Newton Diagrams:
Transformation from CM to Lab frame

vF

vCM

vCM

vCM
Sept. 25, 2014

uF

uH 2


mF v F  mH 2 v H 2

mF  mH 2


 u F  vF


 u H 2  vH 2
Lecture 4 -- Chemical Dynamics at Surfaces -- Dalian 2014

vH 2
53
Each vibrational channel has its own Newton
Circle
Ereleased
Ereleased

vF


 
1
1
 mHF u HF  u HF  mH u H  u H
2
2
0K
 DH reaction
 Ecollision  Erovibrational energy of the products

u HF
So, HF formed in different
vibrational states has
different translational
energy release and a
different Newton Circle

vH 2
Sept. 25, 2014
Lecture 4 -- Chemical Dynamics at Surfaces -- Dalian 2014
54
Each vibrational channel has its own Newton
Circle
Ereleased
Ereleased

vF
Sept. 25, 2014


 
1
1
 mHF u HF  u HF  mH u H  u H
2
2
By the way, The H atom is
0K
 DH reaction  Ecollision momentum
Erovibrationalmatched
with
HF
energy of the
products

u HF
And carries most of the kinetic
energy
So, HF formed in different
mvibrational
u HF has
states
H u H  mHF
different translational
1energy release
1and a
2
2
mH u H  mHF u HF
different
Newton
2
2 Circle




mH E H  mHF E HF
EH
mHF

 20
E HF
mH
Lecture 4 -- Chemical Dynamics at Surfaces -- Dalian 2014

vH 2
55
A side note

Actually every quantum state of HF produced in this
reaction gives rise to its own Newton Circle.

Every different rotational state of HF also has a different
translational energy release.

The tricky part is: Can you do an experiment to resolve
them

We will show later that this is possible.
Sept. 25, 2014
Lecture 4 -- Chemical Dynamics at Surfaces -- Dalian 2014
56
Newton Circles in the F+H2 reaction
Things to Notice
 The CM angle is indicated

The signal drops abruptly
at 8°, 26° and 55°

These are the edges of
the Newton Circles for
HF(v=3) and HF(v=2)
formation
Sept. 25, 2014
Experimental Angular
distributions
Lecture 4 -- Chemical Dynamics at Surfaces -- Dalian 2014
57
TOF data allows you to see a cut along
one angle.
Sample Data – TOF
distributions
Sept. 25, 2014
Newton Circles
Lecture 4 -- Chemical Dynamics at Surfaces -- Dalian 2014
58
TOF and Angular Distributions
TOF data at various
angles
Sept. 25, 2014
Angular distribution data
Lecture 4 -- Chemical Dynamics at Surfaces -- Dalian 2014
59
The experimentally derived product flux
distribution
Summary of Results
Vibrationally state resolved
angular distributions
V=1,2
backward scattered
vH2
V=3
forward scattered
Something fishy going on
here. We will return to this
Originally attributed to a
reaction resonance – Long
lived complex that can
appear on a potential
surface where there is no
well
Sept. 25, 2014
Lecture 4 -- Chemical Dynamics at Surfaces -- Dalian 2014
vF
60
Chemical Dynamics: Experimentally
testing the standard model

Striving for 1st principles understanding of
chemical reactivity

Approach
– Measure angle and speed resolved scattering with as
complete as possible control and characterization of
initial and final quantum state
Experimental Signatures:
derive mechanisms from
“signatures” and how they vary
with incidence conditions.
Sept. 25, 2014
Benchmarks for Theory:
Compare measurements with
theory to develop fundamental
understanding.
Lecture 4 -- Chemical Dynamics at Surfaces -- Dalian 2014
61
The Ultimate Goals of the field of
Chemical Dynamics

Compare first principles calculations to the best possible
experiments and derive the PES quantitatively

Demonstrate reliable first principles theoretical modeling
of chemical reactivity

Predict new chemistry from a computer keyboard using
established theoretical methods.
25.09.2014
62
Let’s look at the H+H2 system in
more detail
Sept. 25, 2014
Lecture 4 -- Chemical Dynamics at Surfaces -- Dalian 2014
63
The first attempt to calculate a potential
energy surface
Henry Eyring
Michael
Polanyi
English translation in: World Scientific Series in 20th Century Chemistry - Vol.
8,“Über
Quantum
Chemistry
Classic Scientific
Papers,
Hinne Hettema,
Imperial
einfache
Gasreaktionen”,
H. Eyring
and M.byPolanyi,
Sonderdruck
aus Z.
College
Press. Abt. B 12, Heft 4 (1931).
Phys.
Chem.,
Sept. 25, 2014
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64
Some comments about Eyring and
Polanyi’s calculation

The calculation was drastically simplified
– The H atoms were restricted to move on a line: the co-linear
approximation
– The electronic Schrödinger equation was solved semi-empirically

The computer had not yet been invented

We must consider the PES only qualitatively correct.
– In fact there are some qualitative problems with the PES
Sept. 25, 2014
Lecture 4 -- Chemical Dynamics at Surfaces -- Dalian 2014
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A closer look
H1-H2
H3
(Products)
H1
H2-H3
(Reactants)
Transition State region
Reaction Path
Sept. 25, 2014
Lecture 4 -- Chemical Dynamics at Surfaces -- Dalian 2014
66
Experimental efforts to reveal the nature
of the H3 PES
Crossed beam reactive
scattering

DI was photolyzed by a
polarized laser.

A collimated D-atom
beam was formed.

This beam was crossed
at 90° with an H2 beam

A rotatable mass
spectrometer detected
scattered HD products at
m/z=3
Continetti et al. 1990
Sept. 25, 2014
Lecture 4 -- Chemical Dynamics at Surfaces -- Dalian 2014
67
Energy Diagram for the Continetti experiment

Two Collision energies
simultaneously: DI
photolysis leads to two
products
– D+I(2P3/2); Etrans,D= 1.01 eV
– D+I(2P1/2); Etrans,D= 0.53 eV
Sept. 25, 2014

Threshold energy is
higher than 0.43 eV due
to zero point energy
correction

HD(v=0,1,2) are
accessible
Lecture 4 -- Chemical Dynamics at Surfaces -- Dalian 2014
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Experimental detail: D-atom TOF
 The
laser is fired and
the signal at m/z=2
(D+) is detected as a
function time using a
multichannel scaler.
 Ions
are counted
using a Daly style
detector
• Continetti et al. 1990
Sept. 25, 2014
Lecture 4 -- Chemical Dynamics at Surfaces -- Dalian 2014
69
The Newton Diagram for D+H2 reaction according to
Continetti
vH2
vD
Sept. 25, 2014
Lecture 4 -- Chemical Dynamics at Surfaces -- Dalian 2014
70
The Newton Diagram for D+H2 reaction according to
Continetti
vH2
vD
HD
Backward
Sept. 25, 2014
HD
Forward
Lecture 4 -- Chemical Dynamics at Surfaces -- Dalian 2014
71
TOF measurements of the reaction products
 Angles
are
measured with
respect to the
direction of the D
atom beam
 Collision
energy was
1.01 eV
Continetti et al. 1990
Sept. 25, 2014
Lecture 4 -- Chemical Dynamics at Surfaces -- Dalian 2014
72
Angle resolved reactive flux map
 HD
is seen to be
scattered roughly
back in the direction
from which the D
atom came.
significant
‘sideways scattering’
is also seen. This is
also seen in the
theoretical flux map
Exp
 But
Theory
Continetti et al. 1990
Sept. 25, 2014
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73
H-atom Rydberg Atom Tagging
Extremely high resolution velocity
measurements
Sept. 25, 2014
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74
Rydberg atom tagging: Lifetimes of Rydberg
states in H
Karl Welge
Uni Bielefeld
Yang Xueming
Dalian Institute
of Chemical
Physics
Schnieder, L., et al., Hydrogen-exchange reaction h + d2 in crossed beams.
Faraday Discussions, 1991. 91: p. 259-269.
Sept. 25, 2014
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75
Field Ionization of high Rydberg states
• Application of a small
external field leads to
emission of the electron.
A Rydberg state 2.5 cm-1 below ionization
• Hence the Rydberg may fly
as a neutral and encounter
a grid with an applied
potential and be ionized
with 100% efficiency
• Notice the spatial extent of
the wave function 5 m
A Rydberg state 25 cm-1 below ionization with
a 10V/cm external field
• And the ease with which
field ionization can be
implemented
Sept. 25, 2014
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76
Lets think about TOF resolution
t
Definition
R  ; of TOF resolution
t
t  l / v and t  l / v
so,
t
l /v
l
R 

t l / v l
Sept. 25, 2014

For an H atom of one
velocity, the uncertainty
in the flight time is
determined by the
uncertainty in the flight
distance

For electron
bombardment ionization
(e.g. continetti) the size
of the electron cloud

For Rydberg tagging,
the size of the focused
laser beam
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Energy Resolution – Homework problem

Calculate the energy resolution of a Rydberg Atom
Tagging experiment and compare to the energy spacing
of rovibrational states of the product molecule.

Parameters
–
–
–
–
Sept. 25, 2014
Reaction D + H2  HD + H
Flight path for Rydberg atoms = 0.5 m
Tagging laser beam diameter 1 mm
Tagging laser beam energy spread 0.5 cm-1.
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Isotope selective
 lH=
1 21.5668237310
nm
 l D=
1 21.533755495 nm
 Separated
 Bandwidth
~0.5 cm-1
Sept. 25, 2014
by 22 cm-1
of laser
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The Lyman- line is a doublet due to spin
orbit splitting in the 2p state

2P state splits into
– 2P3/2
– 2P1/2

Sept. 25, 2014
This can be used to
interrogate the M state
populations in the
ground state.
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From Schnieder, L., et al., HYDROGENEXCHANGE REACTION H + D2 IN CROSSED
BEAMS. Faraday Discussions, 1991. 91: p. 259269.
Sept. 25, 2014
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Rydberg state lifetimes can be dramatically
lengthened
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82
Generation of Lyman-
 Two
photon
resonance enhanced
four wave mixing in
Krypton.
 Argon
added to
improve phase
matching
J / pulse are
produced from YAG
pumped ns lasers
 10-100
Sept. 25, 2014
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83
Extra Credit Homework Problem: Calculate
the excitation probability
 H-Atom
Lyman-
 Laser
properties
– trad= 1.6 ns
– Pulse energy:10 J
– l = 121.6 nm
– Pulse duration: 5 ns
– Spot size: 1 mm circular
– Line-width: 0.2 cm-1
Sept. 25, 2014
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Advantages of Rydberg atom tagging

High sensitivity:
– You are utilizing the 1s-2p transition in H atom. There is no
stronger transition in nature.
– Detection Efficiency of high Rydberg states is close to 100%
using field ionization
– Essentially no Background

High Resolution Time of Flight
– By focusing the laser spot the uncertainty in the flight distance
can be much less than one mm
– Flight distances can be anywhere from 0.25 to 1 meter
– No space charge effects
Sept. 25, 2014
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85
One more advantage: Detection of the
H-atom is ‘kinematically’ favorable
High (the highest) translational
energy resolution is obtained
© 2014 D.J. Auerbach – All rights reserved
Previously we pointed out that the TOF
resolution was limited this equation
l
R
l
But actually that is too simple
Sept. 25, 2014
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87
Other factors can degrade resolution

Consider F+H2

Due to spreads in the F
and H2 beam velocities,
the CM velocity vector is
blurred


Even though ℓ 𝛿ℓ can be
large. The results are
blurred in velocity space to
start with ….
We say “you have to
average over many similar
but different Newton
Diagrams”
Sept. 25, 2014
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The spreading of the Vcm has little
influence on the spread in uH
Since the H atom speed is so
high, the Vcm blurring is a
smaller fraction of its magnitude
uH
uHF
mH uH  mHF uHF
Due to momentum
conservation
uH>>uHF
Sept. 25, 2014
We call this a kinematic
advantage
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89
Carrying out the crossed beam scattering
experiment
•
•
•
Parallel beam geometry: D2 beam crosses photolytic H-atom beam
Photodissociation of molecular beam cooled HI creates a nearly
mono-energetic H-atom beam
Rydberg tagging in the collision volume probes D-atom product
Sept. 25, 2014
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90
First RAT data obtained by Welge in
Bielefeld (@1990-1991)
D atom Kinetic energy
distribution
D atom TOF data
The reaction of H+D2HD(v) + D
Individual vibrational states of HD resolved
Sept. 25, 2014
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91
Within a few years Rotational resolution was
achieved

In the H+D2 reaction one
produces D + HD(v,J)

HD(v, J) has two quantum
numbers that determine
the internal energy of the
system
– We neglect nuclear spin
states

Rydberg tagging allows
each ro-vibrational
channel to be resolved.
And its angular scattering
distribution to be observed
Sept. 25, 2014
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Theoretical approach to the H+H2 reaction

Adiabatic potential energy surface is calculated from ab
initio quantum theory of electrons in the presence of fixed
nuclei.
– Born-Oppenheimer Approximation employed
– Large basis sets used to account as accurately as possible for
electron correlation
– 10-50 ab initio points calculated for each degree of freedom. Total
number of points (10-50)3 that is, 103-5 points
– Points fit to an analytical function with high accuracy

The Schrödinger equation for the motion of the nuclei on
the PES must be solved.
– Alternatively one can carry out classical trajectory calculations
Sept. 25, 2014
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93
Comparison to the standard model
Dashed line
is classical
approximation
Solid and
dotted lines
quantum with
two different
PES
Not surprisingly, classical mechanics doesn’t work that well
But Quantum dynamics gives outstanding agreement with experiment
and comparison of two potential surfaces is possible.
Sept. 25, 2014
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The current master of this technique
Yang Xueming
Dalian Institute
of Chemical
Physics
Dalian Rydberg Tagging instrument
Sept. 25, 2014
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Sept. 25, 2014
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Chemical Dynamics: an example
Playing (Quantum) Billiards with Atoms
H + H-D → H-H + D
H
Experiment
Theory
Yang and Skodje, Journal of Chemical Physics, 117 (18) 8341 -8361 (2002)
Sept. 25, 2014
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With this level of agreement we
can state without qualms that the
standard model of chemical
reactivity works
At least for the H+H2 system
Sept. 25, 2014
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End of Lecture 4
Crossed-beam reactive scattering
experiments
Getting a collision by collision
picture of a chemical reaction
Sept. 25, 2014
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Extra Slides
Sept. 25, 2014
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100
The 4He Dimer: The World‘s Weakest Bound and
Largest Ground State Molecule
Butterfly of molecules. Like catching
a butterfly, measuring the delicate
molecule formed by two helium atoms
requires a light touch.
Since <R> is much greater than Rout the
<R> dimer is a classically forbidden molecule
Eb
Expt.
Theory
Eb 1.1 0.2 1.62  0.03 mK
R  52  4 47.1  0.05 Å
Scatt
High
cross
SR sect
Sept. 25, 2014
H2 molecule: <R> = 0.74Å
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101
“Simple” experiment

Make a really strong expansion
– High backing pressure
– Low stagnation temperature

Then you get some He clusters including the dimer

But how do you detect it with breaking it apart?
Sept. 25, 2014
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Atom-Wave Diffraction
(including Atom-Grating vdW Interaction)
Using a grating
He is a wave. At
constant velocity
He2 is a wave of
half the
wavelength
ξ
z
Sept. 25, 2014
2
Re[]
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103
Electron Microscope Picture of the SiNx Transmission Gratings
100 nm period
50 nm slit width
View of the chip
before the Si base
is etched away
App
Sept. 25, 2014
Courtesy of Prof. H. Smith and Dr. Tim Savas ,M. I. T.
Lecture 4 -- Chemical Dynamics at Surfaces -- Dalian 2014
Courtesy of JP Toennie
104
Nano-Structure Gratings
1 um
Sept. 25, 2014
Lecture 4 -- Chemical Dynamics at Surfaces -- Dalian 2014
Courtesy of JP Toennie
105
Transmission Grating Diffraction Apparatus
S1 and S2 =5 microns
S3= 20 microns
Can discriminate against atoms
with mass spectrometer set at mass 8 and larger
Sept. 25, 2014
Lecture 4 -- Chemical Dynamics at Surfaces -- Dalian 2014
Courtesy of JP Toennie
106
Sept. 25, 2014
Lecture 4 -- Chemical Dynamics at Surfaces -- Dalian 2014
Courtesy of JP Toennie
107
Decreasing Source Temperature
Slit fct
Courtesy
of JP Toennies
Sept. 25, 2014
Kornilov and Toennies.
Europhysics News 38, 22 (2007)
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He-He Scattering Cross Section is Huge
  8 a
2
T→0
where a  2 R
a  100 Å
2
Å
  250,000
Large cross section explains extreme cooling
and sharp velocities of He atom beams
Sept. 25, 2014
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Measured Cross Sections as a Fct. of Velocity
 R 
Expect   2 
  3900 Å2
 2 
2
  2  atom cross sec tion
Magic nos
Sept. 25, 2014
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Measured Cross Sections as a Fct. of Velocity
 R 
Expect   2 
  3900 Å2
 2 
2
  2  atom cross sec tion
The Kr atom can pass through
the middle of the molecule
without its being affected
Magic nos
Sept. 25, 2014
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111
The deflection angle gives you the mass
Electron
bombardment
ionization
destroys all
clusters. All
species are
detected as He+
Sept. 25, 2014
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He diffraction through a multislit grating

Top Panel: The
angular distribution of
He: many diffraction
orders seen

Middle panel: P0
raised T0 lowered: two
peaks between the He
n=0 and 1 orders seen

Lower panel: P0 raised
T0 lowered further:
Three peaks seen.
Sept. 25, 2014
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