CH405 Dynamics of Chemical Reactions: Introduction to Modern Experimental Methods

1
CH405Dynamics of Chemical ReactionsIntroductio
n to Modern Experimental Methods
2
Assessment methods
Type of assessment

Length

weighting
Examinations


1.5
Hours

80

Oral Presentation


20

• Oral presentation
• 5th December
• 905 1155
• B209

3
Assessment methods
ORAL PRESENTATION FOR CH405You have been given
a research article or letter relating to material
ortechniques covered in the module. You are
required to critically readthe article and
prepare a 10 minutes presentation for a non
specialistaudience, containing the following
elements (in any order you deemappropriate)1)
The context of the article is explained2) The
main findings are described3) The methodology
used by the investigators is outlined3-4
minutes of discussion (based on questions asked
to you by lecturers or other students) will
follow your presentation. You should be able to
provide clarification on any aspect you decided
to include in the presentation.
4
5 lectures VGS

• The LASER and its properties
• Laser based techniques
• Examples of modern techniques through pioneering
  studies
• Photodissociation
• Femtochemistry
• High Rydberg Time of Flight

5
The LASER

• Reminder
• Light
• Electromagnetic radiation
• Sinusoidally oscillating electric and magnetic
  fields

6
LASER light Special properties
Light Amplification by the Stimulated Emission of
Radiation

• High directionality
• High intensity
• Can be highly monochromatic
• Can be continuous or very short pulsed
• Highly polarised (all E vectors aligned)

7
Interaction of light / matter
E2

• Absorption

n2

• Photon lost
• Sample absorbs energy

E1
n1
Rate of absorption ? ?(?)n1
Rate of absorption B12?(?)n1
B12 is the Einstein coefficient for absorption
8
Interaction of light / matter

• Spontaneous Emission

n2

• Photon created
• Sample emits (loses) energy

n1
Rate of spontaneous emission ? n2
Rate of spontaneous emission A21n2
A21 is the Einstein coefficient for spontaneous
emission
9
Interaction of light / matter

• Stimulated Emission

E2
n2

• Photon created
• Sample emits (loses) energy
• The stimulated emission is monochromatic and in
  phase with the same polarization as the
  stimulating photon

E1
n1
Rate of stimulated emission ? ?(?)n2
Rate of stimulated emission B21?(?)n2
B21 is the Einstein coefficient for stimulated
emission
10
Einstein coefficients

• It can be shown that actually there is only one
  independent Einstein coefficient

At eqm, rate absn rate st. em rate sp. em
B12?(?)n1 B21?(?)n2 A21n2 i.e., ?(?)
A21
n2
Recall
e-?E/kt
n1
B12 eh?/kt - B21
?(?) 8ph?3 . 1
Yet Plancks law states
eh ? /kt -1
c3
i.e., B21 B12 CA21
LASER radiation is dominated by stimulated
emission
11
Conditions for LASER Action

• Stimulated emission to dominate spontaneous
  emission
• Want more photons out than are absorbed
• Feedback
• Amplification in a fixed direction

12
These impose requirements

• A) If stim. Emission is to dominate absorption,
  we need
• rate of stim. Emission gtgt rate of absorption
• i.e.,

B21?(?)n2
n2
gtgt 1
gtgt 1 i.e.,
n1
B12?(?)n1
But for systems in equilibrium, n2/n1 is given by
the Boltzmann Law
which for all temperatures gives n2 lt n1. In
other words we require population inversion
13
Other requirements

• B) If Stim. Emission is to dominate spontaneous
  emission, we need
• rate of stim. Emission gtgt rate of spont.
  emission
• i.e.,

B21?(?)n2
B21
?(?)
gtgt 1 i.e.,
gtgt 1
A21n2
A21
We require the radiation intensity to be as large
as possible.
14
Typical LASER cavity
100 Reflective mirror
Partial mirror
Lasing medium (gas, crystal etc.)
15
Schematic LASER Action
1 Pump system to excited levels
100 Reflective mirror
Partial mirror
16
Schematic LASER Action
2 Initial spontaneous emission
100 Reflective mirror
Partial mirror
17
Schematic LASER Action
3 Followed by stimulated emission
100 Reflective mirror
Partial mirror
18
Schematic LASER Action
4 Feedback produces amplification light leaks
out of the partial mirror each trip
100 Reflective mirror
Partial mirror
19
Specific Examples of lasers

• Different Lasers have
• Different lasing media
• Different, often sophisticated methods of
  generating population inversion
• Some are fixed wavelength others tuneable.

20
A. The Helium Neon Laser

• Very common
• A gas laser (medium a mixture of He and Ne)
• The first continuous wave (cw) laser
• Lasing occurs in excited Ne atoms
• Most common wavelength 632.8nm (RED)

21
HeNe
He
Ne
Discharge creates metastable, He He Ne ? Ne
He Creates population inversion in Ne
22
B.The excimer / exciplex laser

• Gas lasers
• Electric discharge creates ions which recombine
  to give exotic species (excited dimers)
• Usually high energy pulsed lasers (up to 1J/10ns)
• Almost always generate ultraviolet light
• Common versions include
• ArF (193nm) produces O3 in lab-pungent
• KrF (248nm)
• XeCl (308nm) Very common

23
Excimers
collision

• Discharge ionizes gas mix
• Ar and F- recombine on excited ionic surface
• Upon charge transfer the system drop to the
  covalent surface which is dissociative always
  population inversion

Discharge / reaction
24
C. The NdYAG LASER

• Solid state laser (crystalline rods)
• Nd3 ions doped in a Yttrium Aluminium Garnate
  crystal
• Population inversion achieved by external pumping
  with flashlamps
• Can be cw or pulsed
• Lases at 1064 nm (near IR) but frequency doubling
  generates harmonics at 532 nm or 355 nm.

25
Tuneable Lasers Dye Lasers

• Use large organic molecules as lasing medium
• Population inversion is created by pumping with a
  fixed wavelength laser (e.g., excimer / NdYAG)
• Each dye has a tuning window determined by its
  fluorescence spectrum.
• Dye has a lifetime. Need to replace every so
  often (Rhodium 6G very popular-Red).

26
Schematic dye laser
27
Common dye Rhodamine 6G
LASE
PUMP
28
Different dyes cover IR-UV
29
Ultrafast lasers
fs 10-15 s
ps 10-12 s
ns 10-9 s
time
30
Generating ultrafast laser pulses
Mode locking-Revision
This technique can produce pulses of picosecond
(1 ps 1 x 10-12 Sec) duration and less. The
laser radiates at a number of different
frequencies depending on (a) the medium and (b)
the number of half wavelengths trapped between
the mirrors (resonant modes)
n Integer L Length of cavity
1
n x ? L
2
Locking the phases of the different frequencies
together, interference leads to a series of sharp
peaks (pulse duration).
31
Generating ultrafast laser pulses
Resonant modes (there are N of these)
Doppler profile of gain medium
??
Intensity
Full width half maximum (FWHM) N(7) x ??
Frequency (?)
By locking the phases of the modes and allowing
them to interfere, the point of constructive
interference corresponds to the laser pulse
output. The more nodes present, the shorter the
pulse in time (frequency-time uncertainty).
32
Generating ultrafast laser pulses
The resonant modes differ in frequency (?) by
c
c speed of light
?v
2 x L
1
?t
N resonant modes
N x ??
For example, for a FWHM of 200 cm-1 and a 1 meter
length cavity, this leads to 40000 resonant modes
and a pulse duration of 0.17 ps or 170
femtoseconds (1 fs 10-15 Sec).
33
Generating ultrafast laser pulses
The example given is for equal mode amplitudes.
In reality, this is not true. For example, a
laser producing pulses with a Gaussian temporal
shape gives
0.441
?t
N resonant modes
N x ??
Therefore, for a FWHM of 200 cm-1 and a 1 meter
length cavity, the pulse duration becomes 0.07 ps
or 73.5 fs
34
Generating ultrafast laser pulses
Active mode locking
Involves the periodic modulation of the cavity
loss or the round trip phase change with an
acousto-optic modulator. If the modulation is
synchronized with the cavity round trips, this
leads to generation of ultrafast pulses, normally
picosecond duration.
Passive mode locking
Involves the generation of much shorter pulses
(femtoseconds) and relies on the optical Kerr
effect in which the refractive index of the gain
medium (say Ti-Sapphire) changes when exposed to
intense electric fields. The cavity loss is
modulated much faster than with an electronic
modulator (e.g. acousto-optic).
35
Example Spitfire XP
Seed laser
Amplifier
36
Outline

• Background on regenerative amplification
• Intro
• Comparison Multipass vs Regen
• Spitfire Pro features and performances
• Optical layout
• Stretcher/compressor
• Regen cavity

37
Regenerative Amplification

• Goal amplify ultra-short pulses (20fs-100ps, nJ,
  tens of MHz) up to the milli Joule level
• Motivation need for ultra-short, high peak
  power, frequency tunable pulses for
• Scientific research (spectroscopy, pump-probe,
  non linear physics)
• Industrial and scientific micro/nano-machining
• Gain medium Titanium Sapphire (TiSapphire)
• Large gain bandwidth (650-1100) supports ultra
  short pulses down to 10fs, large tunability
  throughout the gain range
• High thermal conductivity facilitates rod thermal
  management at high pump power

38
Regenerative Amplification
Amplify
12 ns
Time (µs)
82 MHz seed (from modelocked output) amplified at
1 kHz (typically) in a regenerative amplifier
39
Regenerative Amplification

• General scheme
• Trap seed pulse in an optical cavity
• Pass pulse multiple times through TiSapphire rod
  until amplified to desired energy level
• Switch pulse out
• But with short high energy pulses there is risk
  of damage and self-focusing in the TiSapphire
  rod.
• Need to maintain a low peak power in critical
  components of the system.

Chirped Pulse Amplification(CPA)
40
Chirped Pulse Amplification

• Stretch in time Chirp introduce GVD
• Frequencies are
• spread in time (x104)
• safely amplified at different times in the rod
• Recombined to form a short amplified pulse

Output Pulse from Spitfire A few 10s fs
Pulse from seed laser (Tsunami or Mai Tai) A few
10s fs
Stretched pulse A few 100ps
Amplified Pulse
stretcher
amplifier
compressor
41
The system layout (DNL)
PD
Faraday isolator
M
M
Iris
Iris
M
M
M
M
M
M
M
Stretcher grating
Compressor grating
M
CM
M
PC2
PC1
TFP
M
M
M
M
M
TiSapphire Rod
L
L
M
M
PD
M
M
M
M
M
L
L
42
Enhanced Spitfire XP Regen Cavity (DNL)
Patented single Pockels cell cavity design
? less material dispersion ? shorter pulse width
? normal incidence rod ? higher power and better
mode
The Spitfire Pro XP is specified at lt35fs and
gt3.5W
Intra-cavity components M1, M2 End mirrors
Rod TiSapphire rod WP ¼ Waveplate TFP
Thin Film Polarizer PC2 Pockels Cell
43
Enhanced Spitfire XP Regen Cavity (DNL)
Regen Operation Before Injection
Only the pulse to be amplified enters the cavity
Intra-cavity components M1, M2 End mirrors
Rod TiSapphire rod WP ¼ Waveplate TFP
Thin Film Polarizer PC2 Pockels Cell
44
Enhanced Spitfire XP Regen Cavity (DNL)
Regen Operation PULSE Injection
Pulse is injected using the external Pockels cell
PC1.
Pulse is trapped using the internal Pockels cell
PC2.
V1Vl/2
V2Vl/4
Intra-cavity components M1, M2 End mirrors
Rod TiSapphire rod WP ¼ Waveplate TFP
Thin Film Polarizer PC2 Pockels Cell
45
Enhanced Spitfire XP Regen Cavity (DNL)
Regen Operation Pulse AMPLIFICATION
V2Vl/4
Intra-cavity components M1, M2 End mirrors
Rod TiSapphire rod WP ¼ Waveplate TFP
Thin Film Polarizer PC2 Pockels Cell
46
Enhanced Spitfire XP Regen Cavity (DNL)
Regen Operation Pulse EJECTION
Internal Pockels cell PC2 is turned off
V2Vl/4
V20
Intra-cavity components M1, M2 End mirrors
Rod TiSapphire rod WP ¼ Waveplate TFP
Thin Film Polarizer PC2 Pockels Cell
47
Enhanced Spitfire XP Regen Cavity (DNL)
Patented single Pockels cell cavity design
? less material dispersion ? shorter pulse width
? normal incidence rod ? higher power and better
mode
The Spitfire Pro XP is specified at lt35fs and
gt3.5W
Intra-cavity components M1, M2 End mirrors
Rod TiSapphire rod WP ¼ Waveplate TFP
Thin Film Polarizer PC2 Pockels Cell
48
Switching out cavity
Without switching
With switching
49
Frequency doubling
As e-m radiation passes through a medium it sets
up a polarization in the medium, P given by the
series P e0(?(1) E ?(2) E2 ?(3) E3
) where ?(i) is the ith order susceptibility
and E is the electric field. Most optical
phenomena (e.g. reflection) can be understood in
terms of ?(1). However, at high electric field
intensities, the non-linear terms (?(2) and ?(3))
become significant. Consider a light wave of the
form
E E0sin(?t)
50
Frequency doubling cont.
The polarization thus becomes
P e0?(1)E0sin(?t) e0?(2)E02sin2(?t)
e0?(3)E03sin3(?t) )
P e0?(1)E0sin(?t) (e0?(2)/2)E02 (1-cos(2?t))
(e0?(3)/4)E03(3sin(?t) - sin(3?t) )
2 x orig frequency (SHG)
SHG achieved in crystals with no center of
symmetry
l1
l1
l1/2
51
Other (non-laser) light sources
Optical parametric oscillators use non-linear
optics in a different way to split high energy
(e.g., UV) photons into two lower energy photons
(one visible, one infra-red) subject to
conservation of energy.
l2
l1
l3
Synchrotron sources are national facilities
producing enormously tuneable (and very high
energy) radiation generated by the acceleration
of charged particles, e.g., electrons, around
enormous storage rings. They produce weak
fluences but are the most common sources of
tuneable hard X-ray and XUV.
52
LASER Applications in Chemical Physics
Reading Gardner Miller, J. Chem. Phys. 121,
5920, (2004)
53
By way of illustration we will concentrate on two
types of application
A. Determining Quantum state distributions of a
sample Laser Induced Fluorescence
(LIF) Resonance Enhanced Multiphoton Ionization
(REMPI) B. Determining kinetic energy (or
mass/velocity) distributions of a sample Laser
Ionization Time Of Flight Mass-Spec (LI TOFMS)
There are, of course a plethora of other laser
applications but these will prove useful later
when we examine real examples.
54
So how does one determine the quantum state
distribution of a sample?
Almost always by some form of spectroscopy
i.e., exciting transitions between
different electronic, X, A, B, S,
? vibrational, v, or (v1, v2, v3) And
rotational, J, or JKa,Kc quantum
states And why would one want to? The quantum
state distribution gives us information on the
internal energy of the molecules in a sample
(i.e., large amounts of electronic and/or
vibrational and/or rotational excitation).
55
A. Laser Induced Fluorescence (LIF)
A system in an electronically excited state can
decay back to a lower lying state by emitting a
photon. Detection of the photons can be used to
infer information on the state distribution.

• Excite sample with a pulsed tuneable (UV) laser.
• Photons emitted only when the laser is resonant
  with a transition from an occupied level to an
  excited level.
• Can achieve rotational resolution for small
  molecules, vibrational resolution for larger
  molecules

simple (1 - photon) spectra, large signals,
lifetime information - Not all states fluoresce
(not universal), collection efficiency poor, need
to know excited states
56
2 variants of LIF Total Fluorescence

• Total Fluorescence
• (or fluorescence excitation)
• Collect all light emitted as a function of
  excitation ?.
• Info on excited states from line positions and
• Info on ground state populations from spectral
  intensities.

scan
57
Fluorescence excitation spectrum of jet-cooled
(5K) toluene
E?
58
Vibrations of ground state benzene
 Selected Freq.
 Approximate 
 No 
 Sym. 
 Value (cm-1)
 type of mode 
 Species 
3062
CH str
1
a1g
992
Ring str
2
a1g
1326
CH bend
3
a2g
673
CH bend
4
a2u
3068
CH str
5
b1u
1010
Ring deform
6
b1u
995
CH bend
7
b2g
703
Ring deform
8
b2g
1310
Ring str
9
b2u
1150
CH bend
10
b2u
849
CH bend
11
e1g
3063
CH str
12
e1u
3063
CH str
12
e1u
1486
Ring str deform
13
e1u
1038
CH bend
14
e1u
3047
CH str
15
e2g
1596
Ring str
16
e2g
1596
Ring str
16
e2g
1178
CH bend
17
e2g
606
Ring deform
18
e2g
975
CH bend
19
e2u
410
Ring deform
20
e2u
410
Ring deform
20
e2u
59
HS fragments produced in 248nm photodissociation
of H2S
Rotational Resolution A 2S(v0, J)?X 2?(v0, J)
P
21
Q
19/2
1/2
11
P
R
15/2
1/2
3/2
11
11
Q
15/2
21
R
1/2
12
Q
21/2
22
Intensity / arbitrary units
P
22
13/2
3/2
Q
1/2
R
13/2
12
21
P
15/2
15/2
3/2
12
7/2
R
1/2
15/2
22
13/2
1/2
30400
30600
30800
31000
-1
Wavenumber / cm
60
Vibrationally excited HCO produced in the O (3P)
C2H4 ? HCO CH3 reaction
B?X transition (v1, v2, v3)
v1 C-H stretch v2 v3
Mixed bending and C-O stretch
Gardner Miller, J. Chem. Phys. 121,5920, (2004)

61
Dispersed Fluorescence

• Fix excitation ? to excite a single
  (ro)vibrational transition
• Disperse the fluorescence (using a monochromator)
  to determine the individual wavelength
  components.
• Learn about ground state levels

62
Fluorescence excitation spectrum of ethoxy radical
Dispersed Fluorescence (from 1003)
63
B. Resonance Enhanced Multiphoton Ionization
(REMPI)
Instead of trying to detect photons (which are
emitted in all directions and can only be
detected with 10 efficiency) it is more
efficient (although harder) to detect ions
produced by photoionization of the sample
molecules. Typical small molecule ionization
energy 10 eV i.e., require a photon of ? lt 125
nm (deep UV) - very difficult to generate in the
laboratory. Instead use simultaneous absorption
of several photons to ionize the
atom/molecule/cluster.
64
REMPI (cont.)
Take advantage of the fact that the probability
of ionization is enormously enhanced if the
photons are resonant at the n photon level with
an excited state AB.

• Excite with tuneable pulsed laser
• AB??AB?AB e-
• Detect ions only when laser is resonant with
  excited state

AB e-
IP
AB
energy
100 efficient ion detection, ionization is
universal, can access unusual states, high
species selectivity - Need powerful lasers (),
complicated selection rules, intermediates often
not characterised
21 REMPI
AB
65
REMPI of N2 from 193nm dissociation of N2O
57 excess energy appears in rotation
193 nm
N2 X 1Sg ?? a 1Sg(v0, J )? N2
N2O ? N2 O
66
Mass / Kinetic Energy Determination
Laser ionization time-of-flight (TOF) mass
spectrometry
E
Flight distance, L
m3
m2
detector



m1
m1
m2
m3
0 V
HV
time
m2 lt
m3
m1 lt

• Laser pulse ionizes sample (t0), ions are
  accelerated in electric field (to HV/2 if laser
  hits the centre)
• All ions leave with the same kinetic energy ½
  m1v12 ½ m2v22 ½ m3v32
• The arrival time at the detector, t, depends only
  on v ti L/vi
• Hence singly charged ions are separated according
  to their mass.

67
Mass Determination
Using a known mass to predict an unknown mass
d
V
t
? (4.24µs)
? (4.12µs)
4.12 µs OH 4.24 µs OH2
H (1µs)
Intensity (arb. units)
Time-of-flight (µs)
68
Identification of Rhn and RhnCO clusters by laser
ionization time of flight
Arrival time
Meijer et al. J. Phys. Chem. B., 108,14591, 2004
69
Metal cluster source
70
TOF for Kinetic Energy Analysis
e.g., O3 ? O2 (X 3S) O (3P)
Y.T. Lee et al. J.C.P. 1980
or ? O2 (a 1D) O (1D)
O2 (a 1D) O (1D)
O signal
266 nm
O2 (X 3S) O (3P)
O3
Different channels identified by different KE
release
71
Spectral Broadening
Lines in any form of spectrum are not infinitely
sharp due to a range of phenomena some of which
can themselves be used to infer further
information. Examples include
Instrumentation Broadening Clearly if an
instrument has an inherent resolution (e.g., a
laser linewidth of 1 cm-1) then no line can be
observed narrower than this. However, if known,
this can be deconvoluted from real data. Doppler
Broadening (see below) Uncertainty, or lifetime
Broadening (see below)
72
Doppler Broadening
The very narrow linewidth of lasers can be used
to determine the velocity spread in a sample of
rapidly moving molecules by measuring the small
Doppler shifts in known transitions
Transition observed at frequency
n0
at rest
n0
n
v
n0
Blue-shift
n
1- v/c
n0
n
v
Red-shift
n
1 v/c
73
Doppler Broadening
Laser linewidth 0.1 cm-1 Obs. linewidth 0.2
cm-1 Infer Kinetic Energy release of 24 kJ mol-1
LIF spectrum of CF2 from 246 nm photodissociation
of CBr2F2 (Kable et al PCCP, 2000)
74
Lifetime Broadening
Heisenbergs uncertainty principle, ?x?p h/2,
relates the uncertainty in a systems position
with the uncertainty in its momentum and
indicates that we cannot know both to arbitrary
precision. There is an analogous relationship
between energy, E, and time which, in SI units,
can be expressed ?E?t h This has
dramatic implications If a system has a short
lifetime (?t small) then there must be a
correspondingly large uncertainty in the energy
of the system (?E large). e.g., if a particular
energy level lives for 1 ps there is an
uncertainty in its energy of ?E h/1 x
10-12, i.e., ?E 1 x 10-22 J( 5.3
cm-1) This is trivially measurable with a pulsed
dye laser (linewidth lt 0.1 cm-1)
75
Molecular Beams
In order to study molecules/clusters/reactions in
isolation we require a collision-free
environment. This is achieved using a supersonic
expansion into vacuum creating a molecular beam

• Joule Thomson cooling
• All random trans. motion converted through
  collision into motion in the same direction
• Creates high speed supersonic beam (H2 2800
  ms-1, He 1800 ms-1)
• seed sample in carrier gas, e.g., He, Ar.
• Internal energy reduced to lt 5 K
• Different temperatures for different degrees of
  freedom
• High density 1015 molec cm-3
• collision free
• Need large () vacuum pumps

High pressure (0.5 - 30 atm)
vacuum
76
Effect of supersonic cooling
21 REMPI spectrum of H2O via the C(000)
vibrational level
77
Examples of modern experimental methods in
chemical physicsPhotodissociation
Reading Zewail, J. Phys. Chem. 104, 5660, (2000)
78
Photodissociation (or photolysis)
Definition The dissociation of a molecule by the
absorption of electromagnetic radiation
(photons) i.e., bond breaking by light We will
consider three types of photodissociation Direc
t dissociation Predissociation Vibrationally
mediated photodissociation
79
A. Direct dissociation
We are familiar by now with bound potential
energy curves representing the potential energy
of a molecule in a particular electronic state
(configuration) as a function of internuclear
separation
Such curves represent bonds arising from
bonding orbitals and are stable in the sense that
the potential energy of the system is lower than
that for isolated atoms / fragments. What about
the potential energy curves for anti-bonding
orbitals?
V
R
80
Dissociative potentials
Consider the H2 molecule The 1s1 , bonding
configuration gives rise to a bound potential
X-state The 2s1 (or 1s1) antibonding
configuration gives a purely repulsive potential
A-state
A state 2s1
E(1ss)
s
E (1s)
Potential Energy
s
H-atom
H-atom
E(1ss)
X state 1s1
81
Direct dissociation
Occurs when a molecule is excited directly to a
dissociative potential (or the repulsive wall of
a bound potential above its dissociation
energy). The absorption is governed by
Franck-Condon overlap between the ground state
wavefunction and the continuum wavefunctions

• Characterised by
• Smooth , structureless absorption spectrum
• Energetic fragments
• e.g., H2O A-State, H-X A-state (XF, Cl, Br)

fragments
82
E.g.,The first absorption band of H2O (A ? X)
Determined using LIF detection of the OH radical
detected
Smooth and featureless!
83
Aside Continuum Wavefunctions
Recall vibrational wavefunctions
As v increases we approach the form of the
continuum wavefunction (bound in only one
direction) away from the repulsive wall is the
simple sine function of a unrestricted particle.
84
The Reflection Principle
We can understand the smooth featureless
absorption spectrum as a reflection of the ground
state wavefunction in the excited potential. This
is due to the Franck-Condon overlap of the
ground-state wavefunction and the continuum
functions.
?
absorption
85
Aside Transition Intensities
Governed by the square of the transition dipole
moment, µAB


2
ò
å
ˆ

2

t
?
µ
?

er
ˆ
d


operator,

moment

dipole

the

,

where
)
(
µ
µ
i
AB
A
B
i
el
Applying the Born-Oppenheimer approximation,
Vib
?
?

?

A
A
A
2
2




ò
ò

Vib
2
t
µAB
Vib
t
?
?

d
d
µ
A
B
AB
Franck-Condon Factor the strength of the
transition is dependent on the square of the
overlap integral Good overlap strong transition
86
B. Predissociation
Excitation to a bound level which is nevertheless
coupled to a dissociative state.
Degree of predissociation is dependent on the
degree of mixing of the two states. This, in turn
is dependent on the degree of overlap of the
relevant wavefunctions.
Overlap
Poor
87
Manifestations
A vibrational level that suffers from
predissociation will have a reduced lifetime.
Hence in the spectrum of this level the lines
will appear diffuse due to lifetime broadening.
e.g., 21 REMPI spectrum of jet cooled H2O
Sharp lines long lifetimes
Diffuse lines due to short lifetimes arising from
rapid predissociation
88
C. Vibrationally mediated photodissociation
F.F.Crim et al., J.C.P., 94, 1859 (1991)
Leicester, Nov 04
89
Strategies in Chemical Physics
Traditional Chemist as a sleuth Know as much
as possible about the reactants, allow the
reaction to proceed and then characterise the
products as fully as possible. The science
comes in trying to figure out how the system got
from one to the other. Well established
methodology (relatively cheap) - Intellectually
challenging Modern alternative Chemist as a
voyeur Prepare the reactants and then watch the
reaction in real time as it proceeds. Data
relatively simple to interpret - More modern
sophisticated techniques () required
90
Watching Reactions Proceed
So how fast does a chemical reaction take?
It depends what you mean by a reaction electrons
move essentially instantaneously, nuclei much
more slowly. So what constitutes making/breaking
bonds? A traditional view is that breaking a
bond is equivalent to a half collision (i.e., the
two fragments set out as if on a vibration but
never come back). Which is how long? Recall
classical oscillation frequency
e.g., for HCl, a strong single bond ?e 2990
cm-1, hence ? 8.96 x 1013 Hz (m 1.614 x 10-27
kg, k 512 Nm-1) Hence the period of vibration
is 1/? 1.12 x 10-14 or 11.2 fs with atomic
motion occurring at speeds of 1-10 km s-1.
91
So
in order to actually observe reactions taking
place (or at least the nuclear rearrangements
which signify the electronic change) we need to
be probing on a timescale faster that this. For
this reason this area of chemistry is known as
ultrafast chemistry or femtochemistry. Its
birth, as with so many advances in this general
area was heralded by the invention of ultrafast
pulsed lasers. The Nobel Prize in 1999 was
awarded to Prof. Ahmed Zewail of Caltech For
his studies of the transition states of chemical
reactions using femtosecond spectroscopy.for his
pioneering investigation of fundamental chemical
reactions, using ultra-short laser flashes, on
the time scale on which the reactions actually
occur. Professor Zewails contributions have
brought about a revolution in chemistry and
adjacent sciences, since this type of
investigation allows us to understand and predict
important reactions. To illustrate what is
possible in femtochemistry we will study some of
the milestone experiments
92
Pump-probe experiments
All femtochemistry studies comprise pump-probe
methodologies A pump pulse (or clocking pulse)
at t0 initiates a change. The system is then
monitored by a second, probe pulse and changes
detected as a function of time after the pump
pulse.

• Detection is usually by LIF or REMPI
• Close control of time delay of two pulses is
  performed by moving mirrors

10 µm path length 33 fs
93
1985 Photodissociation of ICN
CN (A)
probe
388 nm
306 nm
ICN ? I-CN ? I CN (X)
pump

• Use 400 fs laser pulses
• Detect photons emitted as a function of the
  pump-probe delay

J. Chem. Phys. 89 5141 (1985)
94
Results I
Laser overlap determined by REMPI
t
From the deconvolution of the two pulses it was
inferred that it took around 600 fs to break the
bond (or pass through the transition state). Is
it possible to measure the transition state
itself?
95
ICN, 1988 -Transition state spectroscopy
As laser pulses got shorter more and more detail
began to be revealed
With the probe laser tuned at ?2 ( 388.5 nm,
on-resonance) the production of CN (x 2S) is
detected via the CN (B ? X) fluorescence. What
happens though if the probe wavelength is tuned?
Suddenly the experiment is sensitive to
different bond-lengths.
96
ICN (cont.)
deconvoluted
?2 389.8 nm
388.9 nm
390.4 nm
391.4 nm
97
A
D
A
C
B
B
C
D
98
Leads to a very classical picture if we think of
wavepackets
The fs laser pulses do not excite individual
stationary states, ?a, ?b but rather coherent
superpositions of states ?coh(t) a(t)?a
b(t)?b c(t)?c . where the coefficients, a(t)
are time dependent. Think of the pump pulse
creating a wavepacket on the excited state
which behaves in some senses like a classical
particle, i.e., a localised object in space.
99
The NaI system Probing transition states
The potential energy curves The ground, X-state
is ionic in character with a deep minimum and 1/R
potential leading to ionic fragments
PE
Na I
R
The first excited state is a weakly bound
covalent state with a shallow minimum and atomic
fragments.
100
The non-crossing rule
According to Wigner and von Neumann potential
energy curves with the same symmetry cannot
cross. The best wavefunctions for the system are
mixtures of the two curves. At the crossing point
the two potentials repel and new adiabatic
surfaces result
Na I-
ionic
Na I
covalent
Avoided crossing
ionic
Adiabatic states are mixtures of simple MO or
valence bond structures
101
Behaviour of nuclei at avoided crossings
If the nuclei move slowly into the region of an
avoided crossing then they will follow the
adiabatic path (i.e., stay on the same adiabatic
potential energy surface).
If, however ,they have enough momentum, the
Born-Oppenheimer approximation fails and the
system can hop onto the other adiabatic surface
effectively ignoring the gap. This is known as
non-adiabatic behaviour better modelled using the
diabatic curves.
102
So, the NaI femtochemistry

• The wavepacket is launched on the repulsive wall
  of the excited surface.
• As it undertakes motion on this surface it
  encounters the avoided crossing at 6.93 ?. At
  this point some molecules will take either path
• Some fragmenting to atomic products
• The remainder hopping onto the ionic potential up
  to the turning point and then coming back down to
  start all over again.

103
To visualise
Na I-
Na I
The wavepacket continues sloshing about on the
excited surface with a small fraction leaking out
each time the avoided crossing is encountered
left to right.
104
Probe using LIF
Different probe wavelengths, ?2, probe different
internuclear separations as before.
I. Probing Na atom products Steps in the
production of Na as more of the wavepacket leaks
out each vibration into the Na I channel. Each
step smaller than last (because fewer molecules
left)
105
II. Probing NaI

• At the inner turning point
• Signal at t0
• Oscillations as the wavepacket sloshes out of
  and back into the detection window.
• Peak separation gives the vibrational period
  (1200 fs)
• first peak sharpest

Large signals when wavepacket back at inner
turning point
106
Effect of tuning pump wavelength (exciting to
different points on excited surface)
?pump/nm
300
311
321
Different periods indicative of anharmonic
potential
339
J.C.P., 91, 7415, (1989)
107
At short pump wavelengths few oscillations are
seen
?pump/nm
Reason At shorter pump wavelengths the
wavepacket is launched from higher on the excited
surface and thus the nuclei have more kinetic
energy when they encounter the avoided crossing.
Hence a larger fraction (nearly all) go straight
through the crossing and fall apart into atomic
fragments.
300 nm
295 nm
290 nm
284 nm
108
Tuning ?probe
Different probe wavelengths are sensitive to the
wavepacket at different internuclear separations.
Away from the turning points double peaks appear
as the wavepacket passes through in both
directions
?time
Detection window
R?
109
Chemist as a sleuthe.g., High Rydberg
time-of-flight(photofragment translational
spectroscopy)
Reading Ashfold, J. Chem. Phys. 92, 7027, (1990)
110
A traditional form of experiment..
Essentially consists of reacting
well-characterised reactants, measuring the
outcome in terms of the products created, their
quantum states and the kinetic energy released
and then inferring the likely reactant pathway
from the results. Consider the photodissociation
reaction AB ? A B
Clearly, from a simple consideration of
conservation of energy Eint,AB h? ?
D0(AB) Eint,A Eint,B KE
n.b., A, B not necessarily atomic fragments
111
Consider the left hand side, i.e., reactants
Eint, AB h? We can clearly control the photon
energy used to dissociate the molecule (subject
to the energy levels and Franck-Condon factors of
the molecule itself). But what about Eint,AB,
the internal energy of the molecule? We could
prepare an individual quantum state
spectroscopically. However, it is usual to simply
cool the molecule to its lowest quantum state by
seeding it within a supersonic expansion (i.e.,
within a molecular beam).
112
..and the products..
Simply measuring the fragment quantum states will
not characterize the dissociation event we
really need correlated fragment distributions and
the kinetic energy released simultaneously
A (A) B (X)
Different dissociation channels
A (X) B (A)
Vibn- rotn levels
A (X) B (X)
h?
How can we identify the different channels?
113
The key lies in the fact that D0(AB), Eint,A,
Eint,B and the kinetic energy release, are
related
Eint,AB h? ? D0(AB) Eint,A
Eint,B KE (1) In the dissociation,
momentum must also be conserved. So, in the
centre of mass frame mAvA mBvB And
KE ½ mAvA2 ½ mBvB2 Not only this but the
internal energy of the fragments is encoded in
the kinetic energy release according to (1)
114
Photofragment translational spectroscopy
A (A) B (X)
A (X) B (A)
A (X) B (X)
h?
Production of each unique fragment quantum states
is accompanied by a signature kinetic energy
release. Inverted, measurement of the KER
identifies the quantum states produced. Due to
conservation of momentum it is only necessary to
measure the KE of one fragment.
Eint, AB
115
H-atom time of flight
The experiment is usually performed with
hydrides, looking at the H atom kinetic energy
because it, being the lightest fragment, develops
most kinetic energy. Detection Early
experiments used direct time of flight ionizing
the H-atoms directly. However such schemes suffer
from space-charge effects arising from mutual
repulsion of H spoiling the kinetic energy
resolution. Modern methods use high-n Rydberg
states which are highly excited but meta-stable
(t gt 100 µs) neutral states
116
High Rydberg states Production of H
n
8
IP
Excitation is 2-stage Ly-a excites n 1 ? n
2 Then another photon from dye laser n 2 ? n
gt 80
3
2
13.6 eV
Ly -a
1
Ly-a has energy Ry 1/12 1/22 ¾ x
13.6eV 10.2 eV i.e., ? 121.6 nm
117
Production of Lyman-alpha radiation
121.6 nm (82 259 cm-1) is generated by frequency
tripling in a gas cell of Kr which has large
non-linear susceptibility, ?3 (see lecture 1).
364.68 nm
364.68 nm
121.6 nm
Lens 2 (Li F)
Lens 1
Very inefficient process but one of very few ways
of generating Ly-a
118
The experiment is based on neutral atom time of
flight
detector
Atoms are field ionized upon passing through a
biased grid directly before detector.
H
Known flight length, L
H
Tag of H-atom fragments resulting (Ly-a h?)
Photodissociation Laser pulse (t0)
119
Measure H-atom arrival times.
E.g., for X-H dissociation Total kinetic energy
release ½ mHvH2 ½ mXvX2 But mHvH
mXvX Substituting, TKER ½ mH1
mH/mXvH2 But vH L / tH where tH is the H
arrival time.
So measuring the arrival time of just one
fragment, the H atom, is enough to determine the
channel and the KE release, too.
120
So..
Eint,HX h? ? Do(HX) Eint,X
Eint,H TKER
measure
121
e.g., Ly-a photodissociation of H2S
121.6 nm is so high in energy that several
channels are open H2S 121.6 nm ? H
SH (X 2?) KE lt 6.3 eV ? H SH (A
2S) KE lt 2.5 eV ? H H S
(3P) KE lt 2.6 eV ? H H S (1D)
KE lt 1.4 eV (? H2 S (3P) KE lt 7.1
eV ) (? H2 S (1D) KE lt 5.9 eV) (?
H2 S (1S) KE lt 4.3 eV) H-atom TOF (or High
Rydberg time of flight HRTOF) is only sensitive
to the first 4 channels since the others would
not liberate H atoms.
122
Results 121.6 nm photolysis of H2S
Time, tH /µs
Each peak corresponds to fragmentation into a
different rovibronic channel.
TKER / eV
Ashfold et al., J. Chem. Phys., 92, 7027, (1990)
123
Results 121.6 nm photolysis of H2S
Alternative fragmentation channels
Main channel
Almost no ground state products
124
Major Results

• Primary fragment channels are H SH (A 2S)
• H H S (1D)
• By fitting the SH rovibrational structure we can
  deduce
• Most A- state SH is formed in v0 with rotational
  excitation extending all the way to the
  dissociation limit.
• Evidence of small vibrational excitation up to
  v4, allowing accurate determination of ?e and
  ?exe for A-state if not already known.
• Generation of SH (X 2?) represents a very minor
  channel
• H SH (A 2S) total kinetic energy determined
  to be 2.47 eV
• Added to the known SH X-A spacing this yields an
  H2S ground state dissociation energy of 3.903 ?
  0.005 eV (very precise and accurate)

125
Which tells us what?

• Ground state H2S h? yields an excited 1A1 state
  (by selection rules) the B-state
• There are 3 possible fragmentation pathways
• Transfer to H2S X-state dissociation continuum
  via conical intersection (non-adiabatic) would
  yield ground state products.
• Transfer to the dissociative H2S A-state via the
  linear H-S-H geometry which would also yield
  ground state fragments
• Dissociation on the B-state surface yielding SH
  (A) H
• Clearly the third dominates the dissociation
  dynamics.

126
Comparison with H2O dynamics
H2O
H2S
Combination of OH (X) in high rot. states and
some OH (A)
127
H2O / H2S comparison
H2O H2S
Dominant products 90 OH (X) state 10 OH (A) state Almost all SH (A) state Some H H S
Vibrational / rotational distributions Both X and A state fragments formed vibrationally cold. High rotational excitation Mainly SH A(v0) with large rot excitation (up to D0) Some higher v with lower rot excitation
Implied dominant mechanism Most fragmentation follows from crossing onto the X surface via a conical intersection Primary fragmentation takes place on the excited B-state surface without surface hopping.
i.e., significant differences from seemingly
similar systems
128
CH405 part I Conclusions
Hopefully this module has give you an insight
into the some of the technologies and
methodologies used in modern Chemical Physics.
It goes without saying that we have hardly
touched the surface but maybe you can now
appreciate the level of detail it is possible to
extract from these sophisticated
experiments. This is a difficult module to
assess all I can do is recommend that you do as
many past papers as possible and the model
questions attached. These will form the basis for
an examples class in Week 20.
129
CH405 part I Example Questions
1) Answer both parts a) In terms of a single
photon and a two level system, explain the
different ways in which light can interact with
matter. Explain what is meant by population
inversion and why it is a necessary condition for
laser action. How is this population inversion
effected in the gas phase Helium-Neon
laser? What properties of laser radiation
distinguish it from light produced by other
means? 50 b) In a High Rydberg Time of
Flight (HRTOF) experiment, an ArF (193 nm)
excimer laser is used to photodissociate
jet-cooled water in its first absorption band.
The fastest H atom produced had a kinetic energy
of 10870 cm-1. Calculate the dissociation energy
of water. 50
130
2) Describe one method with which it is possible
determine the quantum state distribution of a
sample of gaseous molecules. 30 What
factors contribute to the width of spectral
lines? 20 Explain the following i) In
absorption the spectrum of water in the region
130 190 nm is smooth and featureless. ii) 248
nm light is not absorbed by gaseous water
molecules. The same light is however absorbed if
the water molecules are subjected to an intense
infra-red laser just before the 248nm light
pulse. iii) The OH A2?(v0) - X2?(v0) band is
observed in LIF as a series of sharp peaks whilst
the OH A2?(v1) - X2?(v0) band consists of much
more diffuse peaks. 50
131

• 3)
• Zewail has pioneered the technique of
  femtochemistry by which it is possible to follow
  simple chemical reactions in real time. The most
  famous example is his study of the NaI system.
• a) Draw the potential energy curves involved in
  this system and account for the difference in
  their form. 25
• b) Explain briefly how the experiment is
  performed including the detection method used and
  how it can be used to differentiate different
  bond lengths. 40
• Sketch the form of the results obtained
  indicating the type of information obtained from
  them. 35
• You should also attempt the exam questions from
  2000 2007 inclusive.

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