•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 m 1 v 1 2 = ½ m 2 v 2 2 = ½ m 3 v 3 2 •The arrival time at the detector, t, depends only on v: t i ≈ L/v i •Hence singly charged ions are separated according to their mass.

Mass Determination

Using a known mass to predict an unknown mass: V = dt m 1 = m 2 ( ) 2 2 4.12 μs = OH 4.24 μs = OH 2 Time-of-flight (μs)

Arrival time Identification of Rh n and Rh n CO 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., O 3 → or → O 2 O 2 (X 3 S) + O ( 3 P) (a 1 D) + O ( 1 D) Y.T. Lee et al. J.C.P. 1980 O 2 (a 1 D) + O ( 1 D) O 3 O 2 (X 3 S) + O ( 3 P) 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: n 0 at rest n 0 n n v v n = n = n 0 1- v/c n 0 1+ v/c

Blue

-shift

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 CF 2 from 246 nm photodissociation of CBr 2 F 2 (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: Δ E Δ t ≥ ħ This has dramatic implications: If a system has a short lifetime ( the system ( Δ E large).

Δ t small) then there must be a correspondingly large uncertainty in the energy of e.g., if a particular energy level lives for 1 ps there is an uncertainty in its energy of: Δ E ≥ ħ/{1 x 10 -12 }, i.e., Δ E ≥ 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 (H 2 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 ~10 15 molec cm -3 •“collision free” •Need large (£££) vacuum pumps

Effect of supersonic cooling: 2+1 REMPI spectrum of H 2 O 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

V

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: R 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?

Dissociative potentials

Consider the H 2 + The 1 σ 1 molecule: , bonding configuration gives rise to a bound potential {X-state} The 2σ 1 (or 1σ* 1 ) antibonding configuration gives a purely repulsive potential {A-state} A state {2σ 1 } E(1sσ*) E (1s) E(1sσ)

H-atom

σ* σ

H-atom

X state {1σ 1 }

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., H 2 O A-State, H-X A-state (X=F, Cl, Br) fragments

E.g.,The first absorption band of H

2

O (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.

absorption λ

Aside: Transition Intensities

Governed by the square of the transition dipole moment, μ AB : (μ AB ) 2 = [  Ψ * B Ψ A d τ ] 2 where , the dipole moment operator, =  i er i Applying the Born-Oppenheimer approximation, Ψ A = Ψ

Vib

A Ψ el A μ 2 AB = [  Ψ *

Vib

B Ψ A

Vib

d τ ] 2 [  Ψ *el B μ AB Ψ A

el

d τ ] 2 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.

fragments Overlap: 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 H 2 O

Sharp lines

: long lifetimes

Diffuse lines

due to short lifetimes arising from rapid predissociation

C. Vibrationally mediated photodissociation

A Vibrationally mediated photodissociation

E UV E

X

OH + H

IR pump (state-selective)

R HO----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: reaction in real time as it proceeds. + Prepare the reactants and then watch the 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:

ν

= 1 2π k μ or 

e

= 1 2π

c

k μ e.g., for HCl, a strong single bond; ω e (m = 1.614 x 10 -27 kg, k = 512 Nm -1 ) = 2990 cm -1 , hence ν = 8.96 x 10 13 Hz Hence the period of vibration is 1/ν = 1.12 x 10 -14 motion occurring at speeds of 1-10 km s -1 .

or 11.2 fs with atomic

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

probe CN* (A) ICN

→

pump I-CN* → I + CN (X) •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 λ 2 (= 388.5 nm, on-resonance ) the production of CN (x 2 S ) is detected via the CN (B fluorescence.

← X) What happens though if the probe wavelength is tuned? Suddenly the experiment is “sensitive to different bond-lengths”.

ICN (cont.) λ 2 = 389.8 nm 388.9 nm 390.4 nm 391.4 nm deconvoluted

D C B A D C B A

Leads to a very classical picture if we think of wavepackets…

The fs laser pulses do not excite individual “stationary states”, ψ a , ψ b but rather “coherent superpositions” of states: Ψ coh (

t

) = a(t)ψ a + b(t)ψ b + c(t)ψ 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 .

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 + + I PE a 1/R PE Na + I R 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 Na + + I covalent Na + 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 + + 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.

Probe using LIF:

Different probe wavelengths, λ 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) Na* + I Na + + I Na + I

II.

Probing [Na—I]* 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 1 vibrational period

* * * * * *

Large signals when wavepacket back at inner turning point

Effect of tuning pump wavelength (exciting to different points on excited surface)

λ pump /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:

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.

λ pump /nm 300 nm 295 nm 290 nm 284 nm

Tuning λ

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: Detection window

Chemist as a sleuth: e.g., High Rydberg time-of flight (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: E int,AB + hν → D 0 (AB) + E int,A n.b., A, B not necessarily atomic fragments + E int,B + KE

Consider the left hand side, i.e., reactants:

E int, 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

E int,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 hν A (A) + B (X) A (X) + B (A) Vib n - rot n A (X) + B (X) levels Different dissociation “channels” How can we identify the different channels?

The key lies in the fact that D

0

(AB), E

int,A

, E

int,B

and the kinetic energy release, are related…

E int,AB + hν → D 0 (AB) + E int, A + E int,B + KE (1) In the dissociation, momentum must also be conserved. So, in the centre of mass frame: And m A v A = m B v B KE = ½ m A v A 2 + ½ m B v B 2 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) hν E int, AB A (X) + B (X) 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 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 > 100 μs) neutral states:

High Rydberg states: Production of H*

n

∞ 3 2 IP Excitation is 2-stage: Ly a e xcites n = 1 → n = 2 Ly a 13.6 eV Then another photon from dye laser 1 n = 2 → n > 80 Ly a has energy R y = ¾ x 13.6eV

=10.2 eV i.e., λ = 121.6 nm {1/1 2 – 1/2 2 }

Production of Lyman-alpha radiation:

121.6 nm (82 259 cm χ 3 (see lecture 1).

-1 ) is generated by frequency tripling in a gas cell of Kr which has large non-linear susceptibility, 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:

detector Known flight length, L H* H* Atoms are field ionized upon passing through a biased grid directly before detector.

Photodissociation Laser pulse (t=0) “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 m H v H 2 But m H v H = m X v X + ½ m X Substituting, TKER = ½ m H {1 + m H /m X }v H 2 But v H = L / t H where t H is the H* arrival time.

v X 2 TKER = 1 2

m H

   1 

m H m X

     

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..

E int,HX

0

+ hν → jet-cooling known D o (HX) + E int,X

0

+ E int,H + TKER No internal excitation measure Unique solutions for each channel TKER = 1 2

m H

  1 

m H m X

   

L t H

  2

e.g., Ly-

a

photodissociation of H

2

S

121.6 nm is so high in energy that several channels are open: H 2 S + 121.6 nm → → → → ( → ( → ( → H + SH (X 2 Π) KE < 6.3 eV H + SH (A 2 Σ) KE < 2.5 eV H + H + S ( 3 P) KE < 2.6 eV H + H + S ( 1 D) KE < 1.4 eV H 2 H 2 H 2 + S ( + S ( + S ( 3 1 1 P) D) S) 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 H

2

S

TKER = 1 2

m H

  1 

m H m X

   

L t H

  2 Time, t H /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 H

2

S

Alternative fragmentation channels: Main channel Almost no ground state products

Major Results:

Primary fragment channels are: H + SH (A 2 Σ) H + H + S ( 1 D) 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 ω e and ω e x e for A-state if not already known.

•Generation of SH (X •H + SH (A 2 2 Π) represents a very minor channel Σ) total kinetic •Added to the known SH X-A spacing this yields an H dissociation energy of 3.903  energy determined to be 2.47 eV 2 S ground state 0.005 eV (very precise and accurate)

Which tells us what?

Ground state H 2 S + hν yields an excited 1 A 1 selection rules) – the B-state state (by There are 3 possible fragmentation pathways: • Transfer to H products.

2 S X-state dissociation continuum via conical intersection (non-adiabatic) – would yield ground state •Transfer to the dissociative H 2 S 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.

Comparison with H

2

O dynamics

H 2 O Combination of OH (X) in high rot. states and some OH (A) H 2 S

H

2

O / H

2

S comparison

H 2 O

Dominant products Vibrational / rotational distributions Implied dominant mechanism 90% OH (X) state 10% OH (A) state Both X and A state fragments formed vibrationally cold .

High rotational excitation Most fragmentation follows from crossing onto the X surface via a conical intersection

H 2 S

Almost all SH (A) state Some H + H + S Mainly SH A(v=0) with large rot excitation (up to D 0 ) Some higher v with lower rot excitation Primary fragmentation takes place on the excited B state 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 A 2 S (v=0) - X 2 Π(v=0) band is observed in LIF as a series of sharp peaks whilst the OH A 2 S (v=1) - X 2 Π(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) c) 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.