CH405
Dynamics of Chemical
Reactions:
Introduction to Modern
Experimental Methods
Assessment methods
Type of assessment
Examinations
Oral Presentation
• Oral presentation
5th December
9:05 – 11:55
B209
Length
1.5 Hours
% weighting
80
20
Assessment methods
ORAL PRESENTATION FOR CH405
You have been given a research article or letter relating to material or
techniques covered in the module. You are required to critically read
the article and prepare a 10 minutes presentation for a non specialist
audience, containing the following elements (in any order you deem
appropriate):
1) The context of the article is explained
2) The main findings are described
3) The methodology used by the investigators is outlined
3-4 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.
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
The LASER
Reminder
Light:
•Electromagnetic radiation
•Sinusoidally oscillating
electric and magnetic fields
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)
Interaction of light / matter
Absorption
E2
n2
E1
n1
•Photon lost
•Sample absorbs energy
Rate of absorption  ρ(ν)n1
Rate of absorption = B12ρ(ν)n1
B12 is the Einstein coefficient for absorption
Interaction of light / matter
Spontaneous Emission E2
n2
•Photon created
•Sample emits (loses) energy
E1
n1
Rate of spontaneous emission  n2
Rate of spontaneous emission = A21n2
A21 is the Einstein coefficient for spontaneous emission
Interaction of light / matter
Stimulated Emission
•Photon created
•Sample emits (loses) energy
•The stimulated emission is
monochromatic and in phase with
the same polarization as the
stimulating photon
E2
n2
E1
n1
Rate of stimulated emission  ρ(ν)n2
Rate of stimulated emission = B21ρ(ν)n2
B21 is the Einstein coefficient for stimulated emission
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
B12ρ(ν)n1 = B21ρ(ν)n2 + A21n2
i.e., ρ(ν) =
A21
B12 ehν/kt - B21
n2
-ΔE/kt
Recall
=
e
n1
1
Yet Planck’s law states ρ(ν) = 8πhν3 .
eh ν /kt -1
c3
i.e., B21 = B12 = CA21
LASER radiation is dominated by stimulated emission
Conditions for LASER Action
• Stimulated emission to dominate
spontaneous emission
• Want more photons out than are
absorbed
• Feedback
• Amplification in a fixed direction
These impose requirements :
A) If stim. Emission is to dominate absorption, we need
rate of stim. Emission >> rate of absorption
B21ρ(ν)n2
>> 1
B12ρ(ν)n1
i.e.,
n2
>> 1
n1
But for systems in equilibrium,
n2/n1 is given by the Boltzmann Law:
which for all temperatures gives n2 < n1.
( kt
n2 g2
e
=
n1 g1
In other words we require population inversion
-ΔE
(
i.e.,
Other requirements :
B) If Stim. Emission is to dominate spontaneous emission,
we need
rate of stim. Emission >> rate of spont. emission
i.e.,
B21ρ(ν)n2
>> 1
A21n2
i.e.,
B21
ρ(ν) >> 1
A21
We require the radiation intensity to be as large as
possible.
Partial mirror
100%
Reflective mirror
Typical LASER cavity
Lasing medium (gas, crystal etc.)
Schematic LASER Action
Partial mirror
100%
Reflective mirror
1: Pump system to excited levels
Schematic LASER Action
Partial mirror
100%
Reflective mirror
2: Initial spontaneous emission
Schematic LASER Action
Partial mirror
100%
Reflective mirror
3: Followed by stimulated emission
Schematic LASER Action
Partial mirror
100%
Reflective mirror
4: Feedback produces amplification – light
leaks out of the partial mirror each trip
Specific Examples of lasers
Different Lasers have:
•Different lasing media
•Different, often sophisticated methods of
generating population inversion
Some are fixed wavelength – others tuneable.
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)
HeNe
Discharge
creates
metastable,
He*
He* +Ne 
Ne* + He
Creates
population
inversion in Ne
He
Ne
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
•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
Excimers
C. The Nd:YAG 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.
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).
Schematic dye laser
Pump laser
Partial
mirror
q
Diffraction
grating
Organic
Dye solution
Common dye: Rhodamine 6G
LASE
PUMP
Different dyes cover IR-UV
Ultrafast lasers
ps
ns
10-9 s
10-12 s
time
fs
10-15
s
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)
nx 1 λ = L
2
n = Integer
L = Length of cavity
Locking the phases of the different frequencies together,
interference leads to a series of sharp peaks (pulse duration).
Intensity
Generating ultrafast laser pulses
Doppler profile of
gain medium
Δν
Resonant modes
(there are N of these)
Full width half maximum
(FWHM) ~ N(7) x Δν
Frequency (ν)
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).
Generating ultrafast laser pulses
The resonant modes differ in frequency (ν) by
c
Δv =
2xL
Δt =
c = speed of light
1
N = resonant modes
N x Δν
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).
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
N = resonant modes
Δt =
N x Δν
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
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 TiSapphire) changes when exposed to intense electric
fields. The cavity loss is modulated much faster than
with an electronic modulator (e.g. acousto-optic).
Example: Spitfire® XP
‘Seed’ laser
Amplifier
Outline
• Background on regenerative amplification
– Intro
– Comparison Multipass vs Regen
• Spitfire Pro features and performances
– Optical layout
– Stretcher/compressor
– Regen cavity
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 (Ti:Sapphire)
– 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
Regenerative Amplification
Amplify
~12 ns
Time (μs)
82 MHz seed (from modelocked output) amplified at 1 kHz
(typically) in a regenerative amplifier
Regenerative Amplification
General scheme:
1. Trap seed pulse in an optical cavity
2. Pass pulse multiple times through Ti:Sapphire
rod until amplified to desired energy level
3. Switch pulse out
–
–
But with short high energy pulses there is risk of damage
and self-focusing in the Ti:Sapphire rod.
Need to maintain a low peak power in critical components
of the system.
Chirped Pulse Amplification
(CPA)
Chirped Pulse Amplification
Stretch in time = Chirp = introduce GVD
Frequencies are:
1. spread in time (x104)
2. safely amplified at different times in the
rod
3. Recombined to form a short amplified pulse
Pulse from seed laser
(Tsunami or Mai Tai)
A few 10s fs
stretcher
Stretched pulse
A few 100ps
Output Pulse from
Spitfire
A few 10s fs
Amplified Pulse
amplifier
compressor
The system layout (DNL)
M
PD
Faraday isolator
M
Iris
Iris
M
M
M
M
M
M
Stretcher
grating
Compressor
grating
M
CM
PC2
M
M
PD
L
L
M
L
M
M
Ti:Sapphire Rod
M
M
PC1
TFP
M
M
M
M
L
M
M
M
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 <35fs and >3.5W
M1
Rod
Intra-cavity components:
M1, M2 : End mirrors
Rod : Ti:Sapphire rod
WP
: ¼ Waveplate
TFP : Thin Film Polarizer
PC2
: Pockels Cell
TFP
Enhanced Spitfire XP Regen Cavity (DNL)
Regen Operation: Before Injection
Only the pulse to be amplified enters the cavity
Seed input
M1
TFP
Rod
Intra-cavity components:
M1, M2 : End mirrors
Rod : Ti:Sapphire rod
WP
: ¼ Waveplate
TFP : Thin Film Polarizer
PC2
: Pockels Cell
TFP
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.
Seed input
M1
TFP
Rod
V1=Vl/2
TFP
V2=Vl/4
Intra-cavity components:
M1, M2 : End mirrors
Rod : Ti:Sapphire rod
WP
: ¼ Waveplate
TFP : Thin Film Polarizer
PC2
: Pockels Cell
Enhanced Spitfire XP Regen Cavity (DNL)
Regen Operation: Pulse AMPLIFICATION
Seed input
M1
TFP
Rod
TFP
V2=Vl/4
Intra-cavity components:
M1, M2 : End mirrors
Rod : Ti:Sapphire rod
WP
: ¼ Waveplate
TFP : Thin Film Polarizer
PC2
: Pockels Cell
Enhanced Spitfire XP Regen Cavity (DNL)
Regen Operation: Pulse EJECTION
Internal Pockels cell PC2 is turned off
output
Seed input
M1
TFP
Rod
TFP
V2=Vl/4
V2=0
Intra-cavity components:
M1, M2 : End mirrors
Rod : Ti:Sapphire rod
WP
: ¼ Waveplate
TFP : Thin Film Polarizer
PC2
: Pockels Cell
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 <35fs and >3.5W
M1
Rod
Intra-cavity components:
M1, M2 : End mirrors
Rod : Ti:Sapphire rod
WP
: ¼ Waveplate
TFP : Thin Film Polarizer
PC2
: Pockels Cell
TFP
Switching out cavity
Without switching
With switching
Frequency doubling
As e-m radiation passes through a medium it sets up a
polarization in the medium, P given by the series:
P = ε0(χ(1) E + χ(2) E2 + χ(3) E3 + …)
where χ(i) is the ith order susceptibility and E is the electric
field. Most optical phenomena (e.g. reflection) can be
understood in terms of χ(1). However, at high electric field
intensities, the non-linear terms (χ(2) and χ(3)) become
significant. Consider a light wave of the form:
E = E0sin(ωt)
Frequency doubling cont.
The polarization thus becomes:
P = ε0χ(1)E0sin(ωt) + ε0χ(2)E02sin2(ωt)
+ ε0χ(3)E03sin3(ωt) + …)
P = ε0χ(1)E0sin(ωt) + (ε0χ(2)/2)E02 (1-cos(2ωt))
+ (ε0χ(3)/4)E03(3sin(ωt) - sin(3ωt) + …)
2 x orig frequency (SHG)
SHG achieved in crystals with no center of symmetry
l1
l1
l1/2
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.
LASER Applications in
Chemical Physics
Reading: Gardner & Miller, J. Chem. Phys. 121, 5920, (2004)
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.
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:
And
electronic, X, A, B, Σ, Π
vibrational, v, or (v1, v2, v3)
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).
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
2 variants of LIF: Total Fluorescence
Total Fluorescence
(or fluorescence excitation)
detector
scan
l
•Collect all light emitted as a
function of excitation λ.
•Info on excited states from line
positions and
•Info on ground state populations
from spectral intensities.
Fluorescence excitation spectrum of jet-cooled (5K) toluene
E→
Vibrations of ground state benzene
Sym.
Species
a1g
a1g
a2g
a2u
b1u
b1u
b2g
b2g
b2u
b2u
e1g
e1u
e1u
e1u
e1u
e2g
e2g
e2g
e2g
e2g
e2u
e2u
e2u
No
Approximate
type of mode
1
2
3
4
5
6
7
8
9
10
11
12
12
13
14
15
16
16
17
18
19
20
20
CH str
Ring str
CH bend
CH bend
CH str
Ring deform
CH bend
Ring deform
Ring str
CH bend
CH bend
CH str
CH str
Ring str + deform
CH bend
CH str
Ring str
Ring str
CH bend
Ring deform
CH bend
Ring deform
Ring deform
Selected Freq.
Value (cm-1)
3062
992
1326
673
3068
1010
995
703
1310
1150
849
3063
3063
1486
1038
3047
1596
1596
1178
606
975
410
410
HS fragments produced in 248nm photodissociation of H2S
Rotational Resolution
A 2Σ(v=0, J)←X 2Π(v=0, J)
P21
Intensity / arbitrary units
19/2
P11
1/2
15/2
1/2
Q11
3/2
15/2
R12
Q22
13/2
13/2
7/2
R11
Q21
1/2
21/2
P22
3/2
1/2
Q12
P12
R21
3/2
1/2
R22
1/2
30400
15/2
15/2
13/2
30600
Wavenumber / cm
30800
-1
31000
Vibrationally excited HCO produced in
the O (3P) + C2H4 → HCO + CH3 reaction
B←X transition
(v1, v2, v3)
v1= C-H stretch
v2 Mixed bending
v3 and C-O stretch
Gardner & Miller, J. Chem. Phys. 121,5920, (2004)
Dispersed Fluorescence
•Fix excitation λ to excite a single
(ro)vibrational transition
•Disperse the fluorescence (using
a monochromator) to determine
the individual wavelength
components.
• Learn about ground state levels
Fluorescence excitation
spectrum of ethoxy radical
Dispersed
Fluorescence
(from 1003)
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 λ < 125 nm (deep UV) - very
difficult to generate in the laboratory.
Instead use simultaneous absorption of several photons to
ionize the atom/molecule/cluster.
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*.
energy
IP
AB+
+
e-
AB*
2+1 REMPI
AB
•Excite with tuneable pulsed laser
•AB→→AB*→AB+ + e•Detect ions only when laser is
resonant with excited state
+ 100% efficient ion detection, ionization
is universal, can access unusual states,
high species selectivity
- Need powerful lasers (£££),
complicated selection rules, intermediates
often not characterised
REMPI of N2 from 193nm dissociation of N2O
57% excess energy
appears in rotation
N2O
193 nm
→
N2 + O
N2 X 1Σg+ →→ a’’ 1Σg+(v=0, J )→ N2+
Mass / Kinetic Energy Determination
E
Flight distance, L
+
m3
+ HV
0 V
+
m2
m1 < m2 <m3
+
m1
detector
Laser ionization time-of-flight (TOF) mass spectrometry
m2
m3
m1
time
•Laser pulse ionizes sample (t=0), 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.
Mass Determination
Using a known mass to predict an unknown mass:
Time-of-flight (μs)
? (4.24μs)
m1 = m2
? (4.12μs)
H (1μs)
Intensity
(arb. units)
d
V=
t
t1
t2
2
( )
4.12 μs = OH
4.24 μs = OH2
Arrival time
Identification of Rhn and
RhnCO clusters by laser
ionization time of flight
Meijer et al.
J. Phys. Chem. B., 108,14591, 2004
Metal cluster source
TOF for Kinetic Energy Analysis
e.g., O3 → O2 (X 3S) + O (3P)
→ O2 (a 1D) + O (1D)
266 nm
O2 (a 1D) + O (1D)
O+ signal
or
Y.T. Lee et al. J.C.P. 1980
O2 (X 3S) + O (3P)
O3
Different channels identified by different KE release
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)
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
n
n
at rest
v
v
n0
n0
n=
1- v/c
Blue-shift
n0
n=
1+ v/c
Red-shift
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)
Lifetime Broadening
Heisenberg’s uncertainty principle, ΔxΔp ≥ ħ/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:
ΔEΔt ≥ ħ
This has dramatic implications: If a system has a short lifetime (Δt small)
then there must be a correspondingly large uncertainty in the energy of
the system (ΔE large).
e.g., if a particular energy level lives for 1 ps there is an uncertainty in its
energy of:
ΔE ≥ ħ/{1 x 10-12},
i.e., ΔE ≥ 1 x 10-22 J(≥ 5.3 cm-1)
This is trivially measurable with a pulsed dye laser (linewidth < 0.1 cm-1)
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”:
High pressure
(0.5 - 30 atm)
vacuum
•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 < 5 K
•Different “temperatures” for
different degrees of freedom
•High density ~1015 molec cm-3
•“collision free”
•Need large (£££) vacuum pumps
Effect of supersonic cooling:
2+1 REMPI spectrum of H2O
via the C(000) vibrational level
Examples of modern
experimental methods in
chemical physics:
Photodissociation
Reading: Zewail, J. Phys. Chem. 104, 5660, (2000)
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:
Direct dissociation
Predissociation
Vibrationally mediated photodissociation
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.
V
R
What about the potential energy curves for
anti-bonding orbitals?
Dissociative potentials
Consider the H2+ molecule:
The 1σ1 , bonding configuration gives rise to a bound potential {X-state}
The 2σ1 (or 1σ*1) antibonding configuration gives a purely repulsive
potential {A-state}
E(1sσ*)
E (1s)
E(1sσ)
H-atom
A state {2σ1}
σ*
σ
H-atom
X state {1σ1}
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 (X=F, Cl,
Br)
fragments
E.g.,The first absorption band of H2O (A ← X)
Smooth and featureless!
Determined using LIF detection
of the OH radical detected
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.
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.
λ
absorption
Aside: Transition Intensities
Governed by the square of the transition dipole moment, μAB:
(μ AB ) =
2
[
]
Ψ B*ˆ
μ ΨA dτ
2
where ˆ
μ , the dipole moment operator, =  eri
i
el
Applying the Born-Oppenheimer approximation, ΨA = ΨVib
ΨA
A
But ˆ
μ only acts on the electronic part so we can write:
2
μ AB =
[Ψ
*Vib
B
] [ Ψ
2
ΨAVib dτ
]
2
el
*el
μ
Ψ
AB A dτ
B
Franck-Condon Factor: the strength of the transition is dependent on
the square of the overlap integral: Good overlap = strong transition
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:
fragments
Poor
Good
Poor
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., 2+1 REMPI spectrum of jet cooled H2O
Sharp lines : long lifetimes
Diffuse lines due to short lifetimes arising
from rapid predissociation
C.
Vibrationally mediated photodissociation
A
EUV
Vibrationally mediated
photodissociation
E
OH + H
X
IR pump
(state-selective)
RHO----H
absorbance
F.F.Crim et al., J.C.P., 94, 1859 (1991)
Leicester, Nov ‘04
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
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:
1 k
ν=
2π μ
or
1 k
e =
2πc μ
e.g., for HCl, a strong single bond; ωe = 2990 cm-1, hence ν = 8.96 x 1013 Hz
(m = 1.614 x 10-27 kg, k = 512 Nm-1)
Hence the period of vibration is 1/ν = 1.12 x 10-14 or 11.2 fs with atomic
motion occurring at speeds of 1-10 km s-1.
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 Zewail’s 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…
Pump-probe experiments
All femtochemistry studies comprise “pump-probe” methodologies:
A pump pulse (or clocking pulse) at t=0 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
1985: Photodissociation of ICN
388 nm
306 nm
CN* (A)
probe
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)
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?
ICN, 1988+ -Transition state spectroscopy
As laser pulses got shorter more and more detail began to be revealed…
With the probe laser tuned at λ2 (= 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”.
ICN (cont.)
deconvoluted
λ2=
389.8 nm
388.9 nm
390.4 nm
391.4 nm
D
A
C
B
A
B
C
D
Leads to a very classical picture if we
think of wavepackets…
The fs laser pulses do not excite
individual “stationary states”, ψa, ψb
but rather “coherent
superpositions” of states:
Ψcoh(t) = a(t)ψa + b(t)ψb + c(t)ψc +….
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.
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:
Na+ + IPE
a 1/R
R
PE
Na + I
R
The first excited state is a weakly
bound covalent state with a shallow
minimum and atomic fragments.
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:
ionic
covalent
Na++ INa + I
“Avoided crossing”
ionic
Adiabatic states are mixtures of
simple MO or valence bond structures
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.
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 Ǻ. 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.
To visualise:
Na++ INa + 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.
Probe using LIF:
Different probe wavelengths, λ2,
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)
Na* + I
Na++ INa + I
II.
Probing [Na—I]*
1 vibrational period
a) At the inner turning point:
Signal at t=0
Oscillations as the
wavepacket sloshes out of
and back into the detection
window.
Peak separation gives the
vibrational period (~1200 fs)
first peak sharpest
*
*
* *
*
signals when
* Large
wavepacket back at inner
turning point
Effect of tuning pump wavelength (exciting to
different points on excited surface)
λpump/nm
300
311
321
339
Different periods
indicative of
anharmonic potential
J.C.P., 91, 7415, (1989)
At short pump wavelengths few oscillations are seen:
λpump/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
Tuning λprobe
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:
Detection window
Chemist as a sleuth:
e.g., High Rydberg time-offlight
(photofragment translational
spectroscopy)
Reading: Ashfold, J. Chem. Phys. 92, 7027, (1990)
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 +
hν
→
D0(AB) + Eint,A + Eint,B + KE
n.b., A, B not necessarily atomic fragments
Consider the left hand side, i.e., reactants:
Eint, AB + hν
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).
..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)
A (X) + B (A)
hν
Vibn- rotn levels
A (X) + B (X)
Different dissociation
“channels”
How can we identify the different channels?
The key lies in the fact that D0(AB), Eint,A,
Eint,B and the kinetic energy release, are
related…
Eint,AB +
hν
→
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)
Photofragment translational spectroscopy
A (A) + B (X)
A (X) + B (A)
A (X) + B (X)
hν
Eint, AB
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.
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 Hatoms directly. However such schemes suffer from spacecharge 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 > 100 μs) neutral states:
High Rydberg states: Production of H*
n
∞
IP
3
Excitation is 2-stage:
2
Ly-a excites n = 1 → n = 2
13.6 eV
Ly -a
Then another photon from
dye laser
n = 2 → n > 80
1
Ly-a has energy Ry {1/12 – 1/22}
= ¾ x 13.6eV
=10.2 eV
i.e., λ = 121.6 nm
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,
χ3 (see lecture 1).
364.68 nm
364.68 nm
121.6 nm
Lens 1
Lens 2
(Li F)
Very inefficient process but one of very few ways of generating Ly-a
The experiment is based on neutral atom
time of flight:
Known flight
length,
L
Photodissociation
Laser pulse (t=0)
detector
H* Atoms are field ionized upon
passing through a biased grid
directly before detector.
H*
“Tag” of H-atom fragments
resulting (Ly-a + hν)
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 mH{1 + mH/mX}vH2
But vH = L / tH where tH is the H* arrival time.
TKER =

1
m 1 
2 H

mH
mX
 L

 t H



2
So measuring the arrival time of just one fragment, the H atom, is
enough to determine the channel and the KE release, too.
So..
0
Eint,HX + hν →
jet-cooling
Do(HX)
+
Eint,X +
0
Eint,H +
No internal
excitation
known
TKER
measure
Unique solutions
for each channel
 m  L 
TKER = 12 mH 1  H  
mX  t H 

2
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 2Π)
H + SH (A 2Σ)
H + H + S (3P)
H + H + S (1D)
H2 + S (3P)
H2 + S (1D)
H2 + S (1S)
KE < 6.3 eV
KE < 2.5 eV
KE < 2.6 eV
KE < 1.4 eV
KE < 7.1 eV )
KE < 5.9 eV)
KE < 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.
Results: 121.6 nm photolysis of H2S
TKER =

1
1 
m
2 H

mH
mX
 L

 t H



2
Time, tH /μs
Each peak corresponds to
fragmentation into a different
rovibronic channel.
TKER / eV
Ashfold et al., J. Chem. Phys., 92, 7027, (1990)
Results: 121.6 nm photolysis of H2S
Alternative fragmentation channels:
Main
channel
Almost no ground state products
Major Results:
Primary fragment channels are: H + SH (A 2Σ)
H + H + S (1D)
By fitting the SH rovibrational structure we can deduce:
•Most A- state SH is formed in v=0 with rotational
excitation extending all the way to the dissociation limit.
•Evidence of small vibrational excitation up to v=4, allowing
accurate determination of ωe and ωexe for A-state if not already
known.
•Generation of SH (X 2Π) represents a very minor channel
•H + SH (A 2Σ) 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)
Which tells us what?
Ground state H2S + hν 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 HS-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.
Comparison with H2O dynamics
H2O
Combination of OH
(X) in high rot. states
and some OH (A)
H2S
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(v=0) with large
rot excitation (up to D0)
Some higher v with lower rot
excitation
Implied dominant Most fragmentation
mechanism
follows from
crossing onto the X
surface via a conical
intersection
Primary fragmentation takes
place on the excited Bstate surface without
surface hopping.
i.e., significant differences from seemingly similar systems
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.
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%]
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 A2S(v=0) - X2Π(v=0) band is observed in LIF as a series of
sharp peaks whilst the OH A2S(v=1) - X2Π(v=0) band consists of
much more diffuse peaks.
[50]
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.
c)
[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.