Photochem Flashcards
How do you find the allowed transition of symm polyatomics?
Find term of gs (totally symm) and es (direct product table)
Then test es terms with μ, which transforms via x,y,z in term table
TDM must be non-zero (so totally symm)
What occurs to BO approx in polyatomics?
Two or more vib modes can be excited simultaneously with elec
Means nuclear and elec motion is no longer separable
How can selec rules be determined for polyatomic molecules?
Determined by multiplying representations for each mode (elec and vib)
What is a chromophore?
Excitation which is a small group of atoms
Occurs when little/no symm overall in the molecule
What is internal conversion?
Non-radiative transition between states of same spin multiplicity
e.g. S1 -> S0
From vib g.s of the elec e.s -> vib e.s of elec g.s
What steps are there in internal conversion (IC)?
1) Excitation - elec gs to es
2) Vib relaxation - fast, lowers to vib gs of elec es
3) Internal Conversion - vib gs of elec es -> vib es of elec gs
4) Vib relaxation - prevents system going back
What is intersystem crossing?
Non-radiative transition from es to close in energy state with diff spin multiplicity
e.g. S -> T
Then vib relaxation
What occurs in fluorescence?
Radiative transition to lower energy state of same spin
Followed by VR
What occurs in phosphorescence?
Radiative transition from triplet to singlet state
T1 -> S0
What is a Jablonski diagram?
Summarises all transitions
How fast are the different radiative transitions?
elec excitation - fs
fluorescence - ns
phosphorescence (slow) - ms
How fast are non-radiative transitions?
vib relaxation (fast) - ps
internal conversion - fs/ns
intersystem crossing - ns/μs
When does the BO break down?
When ΔEel ~ ΔEvib
What does the Franck-Condon principle assume?
e- move faster than nulcei
What occurs to excited molecules in gas and liquid phase?
Gas - remains at same energy until collision, then loses vib and maybe el energy
Liquid - VR occurs rapidly, exchanges E fast with solvent
What occurs in reverse intersystem crossing?
Goes T1 -> S1
opposite to standard and leads to delayed fluorescence
Why is T1 lower in energy than S1?
Less repulsion
How does the frequency of fluorescence and phosphorescence compare?
Phosphorescence lower frequency and slower
How does fluorescence compare in rate to inter-system crossing?
ISC is around same speed of fluorescence
ISC fast as not highly excited vib state so FC overlap integral is large
How does absorption and fluorescence freq compare to 0 <-> 0 transition?
Absorption - higher freq
Fluorescence - slower freq
What is the Beer-Lambert Law?
It = I0 - Iabs = I0 exp(-αcl) = I0 10-εcl
where:
It,0,abs = intensity of transmitted, initial, and absorbed respectively
α - natural absorption coeff
ε - decadic absorption coeff
What is assumed for the Beer-Lambert Law?
Monochromatic light
Path length fixed
Absorption only - no scattering due to dust, bubbles, etc.
Conc fixed - homogeneous
What are the approx of the Beer-Lambert Law?
Weak field - absorption doesnt effect population of absorbing state (all molecules in gs)
Absorbers independent
What occurs to the Beer-Lambert Law at low conc?
Linear regime abs prop to conc:
It = I0 exp(-αcl) ~ I0 (1-αcl)
Iabs~ I0(αcl) = I0(εcl x ln10)
What is flux?
Rate at which energy flows
What is the SI quantity of intensity?
Energy flux per unit area per unit time
Not same as intensity of kinetics (photons absorbed per second)
What is the effect of light on quantum states?
Light mixes initial and final elec state
kfi = (2π/hbar) ∫ |ψf*H^ψi| 2
What is Fermi’s Golden Rule?
Formula describing transition rate from one energy eigenstate to another as a result of weak perturbation
Where is Fermi’s Golden rule derived from?
From time-dependent perturbation theory
Don’t learn
How does light interact with charges in a molecule?
Electric vector of light E interacts with charges in a molecule
H^' = -Σ qi E.ri
Sum extends over all charges, e- and nuclei, and related to dipole moment:
H^' = - E.μ
How is BO separation used for μ?
Dipole moment separated into sum over e- and nuclei
Overlap integral of nuclear-elec states approx 0 as for fixed nuclei the elec states are approx orthogonal
Molec wavefn separated into product of elec and nuclear
How is the electronic wavefn separated?
Separated into orbital and spin components
What is the rate of absorption proportional to?
kfi α
|χf*χidτN|2
|φf* μe φedτe|2
|<σf|σi>|2
1st term: Franck-Condon factor
2nd term: Elec matrix element, gives orbtial selection rule
3rd term: spin selection rule
What are the equations for Einstein coeffcients B (2-photon) and A (spontaneous emmision)?
Bfi = |μfi|2/6ε0hbar2
Afi = 8πhv3|μfi|2/6ε0hbar2c3
When large v (such as UV or Vis) is relevant to emission rates
What does absorption coefficient depend on?
Depends on frequency
Integral of absorption = πvNa|μfi|2/3cε0hbar
What is a mirror image spectrum?
Elec absorption is approx mirror image of fluorescence spectrum
with the 0<->0 overlapping in the middle
Where are absorption & fluorescence wrt 0<->0 transition?
Absorption: transition @ low λ as go to S1 excited state
Fluorescence: transition @ higher λ as S1 gs to es S0
What is required for a mirror image spectrum to occur?
ΔE between vib levels similar & transition prob therefore similar
Condensed phase - geometry of es similar to gs
Solvent relaxation occurs faster than fluorescence so all emission occurs from v=0
Why are mirror spectra observed?
Frank-Condon principle states nuclei stationary on elec timescale
Vib overlap occurs quickly so all emmision from S1 v=0
When are mirror image spectra not observed?
Not observed when:
change in geometry
es may transfer phenol
es may dissociate
several singlet states may appear in absorption (normally only lowest in fluorescence)
What is Kasha’s Rule?
Photon emission (fluorescence/phosphorescece) occurs only from lowest excited state of a given multiplicity
What is the bathochromic shift?
0 <-> 0 band shows shift towards red (smaller λ) due to quick VR before emmission
Why do phenol and biphenyl not have mirror spectra?
Phenol - es transfers proton
Biphenyl - change in geometry, S0 is twisted with low barrier and S1 is planar
Why do quinine and azomethane not exhibit mirror spectra?
Quinine - several singlet states in absorption, and only lowest in fluorescence
Azomethane - excited state may dissociate
What is the lifetime equation?
τ = 1 / k
where k is rate const
What is the rough lifetime of phosph/fluor?
Phosphorescence: τ in ms/s
Fluorescence: τ in ~10 ns
What processes compete to remove S1 state?
Fluorescence
Inter-system crossing
Internal conversion
What are the kinetics for removal of S1 state?
[S1] = [S1]0 exp(- (kf + kISC + kIC)t)
still first order
What is fluorescence lifetime?
τf = 1/(kf + kISC + kIC + …)
i.e. sum of the removal processes
What is the equation for quatum yield, φ, in terms of molecules?
φ = (# molecules undergoing a process) / (# of photons absorbed) = kfτf = kf/(kf + kISC + kIC + …)
How can # of photons be quantised?
[S1]0
What is a branching ratio?
Simple 1st order competition of different processes
What is the triplet yield?
φT = 1 - φf
What is the phosphorescence yield?
φph = φT kph/(kph+kisc’) = φT kph τph
where kisc’ is reverse intersystem crossing
When can a quantum yield be larger than 1?
Chain reaction
or
Produces gas
Quantum yield may depend on conc if competing 2nd order process
What is steady-state illumination?
S1 in a true steady state
Iabs = (kf + kisc+ …)[S1]SS
[S1]SS = Iabs/(kf + kisc+ …)
What is a quencher and how do they work?
S1 + Q -> S0 + Q
Quencher dissipates elec energy via vibrations to give heat
Pseudo-first order as quencher in XS and not destroyed
What is the fluorescence yield when a quencher present?
φf = kf/(kf + kisc + kQ[Q])
Use a straight line plot for ratios of rate const
1/φf = 1 + (kisc/kf) + (kQ[Q]/kf)
What is dynamic quenching?
Requires encounters and is diffusion controlled
Decreases lifetime (stern-volmer)
What is static quenching?
Rigid matrix, quenching occurs immediately if quencher in range
φf reduced but not τ
How can you measure # of photons absorbed indirectly?
Indirect chemical standards used - where the quantum yields known
Why can intramolecular energy transfer (transitions beteween elec states without change in E) occur?
Small terms in hamiltonian which mix elec states
Treat them as perturbation via Golden Rule
What is spin-orbit coupling hamiltonian in the orbital selection rule?
H^’ = Σξs^.l^
HSO is Rx,y,z in char tables
Rotations are rarely totally symm
So if ψintial and ψfinal have same symm the elec matrix element = 0
Rate enhanced by heavy atoms as SO coupling depends on it
What is El Sayed’s rule?
ISC slow unless accompanied by change of e- config
(between S1 and T1)
Why does ISC crossing occur in aromatic ketones?
Close nπ* and ππ* states
S1 to T2 occurs
(follows by fast IC from T2 -> T1)
Why does ISC occur more with heavy atoms?
SO coupling depends on Z4
Therefore as mass increases the rate of ISC increases (which will also increase rate of phos)
What is e-type delayed fluorescence?
Delayed fluorescence, same rate of phosphorescence when does start
Due to heavy atoms and so processes like ISC occur
What energy terms are involved for internal conversion?
Sum of nuclear KE
Vibration, Rk, must have correct symm to mix the states
What energy terms are involved for internal conversion?
Sum of nuclear KE
Vibration, Rk, must have correct symm to mix the states
How does the FC factor increase with V?
@ high they go to classical turning points
How does overlap of FC change as the bond length increases in change?
How does overlap of FC change as the bond length increases in change?
What is the energy gap law?
Rate of energy transfer decreases with increasing energy gap
S1-T1 < S0-T1 < S0-S1
What causes the energy gap law?
From FC overlap
What does the energy gap law favour?
Intersystem over internal conversion
How does rate of ISC change with deuteration?
As deuteration increases then kISC lower τp increases
As they have lower freq and so elec energy gap requires high vib excitation
(poorer overlap - more nodes)
What is Kasha’s rule?
Fluorescence from lowest excited singlet state
Phosphorescence from lowest triplet state
What is a conical intersection?
Intersection of two conical surfaces representing individual wavefn
If occurs then v fast IC can occur
How does azulene break Kasha’s rule?
Fluroescence from S2
Small energy gap between S1 and S0 meaning interconversion, extremely fast IC
What is radiative transfer?
Fluorescence of D* absorbed by A
Long range
Normal selec rules
D fl must overlap with A ab
What occurs in collisional transfer?
D* + A -> [D*A] -> [DA*] -> D + A*
Intramolec transfer within collision complex - golden rule with some perturbation
Franck-Condon principle ensures energy gap small - little energy degraded as translation
What occurs in resonant energy transfer?
Spectra must overlap - energy conservation
What occurs in Forster energy transfer?
Elec interaction between dipoles
Follows fermi golden rule
Has its own rate const
What is the rate of energy transfer?
kT = (1/τ)(r06/r6)
where r0 is distance at which ET rate = spont decay rate
What is short range energy transfer?
What occurs wrt spin when energy transfer occurs (between D and A)?
Resultant spin of reactants conserved in complex and products
What are the wigner spin correlation rules for energy transfer?
What is triplet sensitisation?
Use a T1 state compound easily accesible to make an S0 compound (which is difficult to make into a triplet )
What happens to reaction between two triplet state molecules (in ET)?
Leads to two singlets (S0 and S1)
This is a type of delayed fluorescence (p-type)
What causes p-type delayed fluorescence?
Triplet annihilation occurs to give two singlet states
What is an excimer?
Excited dimer
What is an exiplex and main characteristic?
Excited complex between different species
Emission at longer λ than monomer fluorescence
How does an exiplex form?
es bound and gs repulsive
Exciplex emission broad spectrum
Population inversion leads to laser action
Does photoexcitation effect acid/base properties?
Yes
Phenol S1 more acidic
Aniline S1 less basic
Carboxylic acids less acidic as reduced delocalisation
Do excited aromatic states react differently?
React with nucleophiles (opposite direction to normal)
Why are reactions in excited state different?
Nucleophile usually interacts with LUMO of compound
In photo-reaction then nuc interacts with HOMO
How does oxn state change in excited species?
e.s. easier to oxidise and reduce than gs
What is channel 3?
Internal Conversion
What are the valence isomers of benzene?
What occurs when you excite benzene?
Small amount of isomerisation to valence isomers in the S1 and S2 state
What is geminate recombination?
Recombination of fragments of a dissociated molecule
Where the fragments are made in same event
What is diffusion control?
Atoms diffuse and recombine on encounter
In solution the solvent hinders separation
What is the yield of escape from geminate recombination on time?
Decreases as t increases
Escapes at Ω=0.5
What does the yield of escape from geminant recombination dependent on?
Wavelength: as decreases the yield of escape increases
(more energy to more likely to escape)
Viscosity: as increases the yield of escape decreases
What is Ω, yield of escape with respect to intial distance between fragments?
Ω = 1 - a/r0
where a is a const and r0 is intial distance between fragments
What occurs during photoionization and dissociative photoionization?
Photo: AB + hv -> AB+ + e-
Photo diss: AB + hv -> A + B+ + e-
What occurs during autoionization and field ionization?
Auto:
AB + hv -> AB* (E>1) -> AB+ + e-
Field:
AB + hv -> AB* (E<1) -> apply field -> AB+ + e-
What is the process of double ionization?
AB + hv -> AB2+ + 2e- -> A+ + B+
What are the selection rules for single photoionization?
Any elec state of cation can be produced if can be accesed by removal of one electron from neutral (without further electron rearrangement)
Why is there no resonant condition for single photoionization?
Energy of the outgoing electron is not quantised (as a free electron)
What is done for photoelectron spec?
Ionization of a sample of molecules with hv > Ionisation energy
Produces ions with distribution of internal energies and hence a distribution of KEs
What is seen on PES?
Each progression is from removal of e- from a different orbital
Progression structure represents vib energy levels of each state
What is Koopman’s theorem?
In closed-shell the first IE of a molecular system is equal to the negative of orbital energy of HOMO
IE + Eion = -ε (orbital energy)
What is a large progression on PES?
Extensive vib structure
Means removal of e- from this MO which causes a sig change in bonding
What is required for photodissociation?
Requires excitation directly/indirectly to state above dissociation limit
When is vertical excitation favoured?
Franck-Condon factors
Strong overlap when higher vib states in excited state
What occurs to absorption spectrum at short wavelengths?
Becomes continuous as hv crosses dissociation threshold
What occurs in predissociation?
Molecule excited to bound state - vibrates for a few periods then undergoes curve crossing and dissociates on repulsive PE curve
Then will dissociates
Franck-Condon determines if occurs
What is a stationary state?
No time dependence
What is the main assumption of Franck-Condon principle?
Nuclei are stationary on tiome scale of elec motion
Nuc wavefn unchange on es
What causes more than non-0 linewidths?
Es has a non-zero lifetime
Homogeneous linewidth is a common feature of all molecules
