Excited States + Terms & States

Photochemistry

Chemistry initiated by light.

Electronic Transition

When an electron moves from one molecular orbital to another.

Chromophores

Molecules which absorb light.

Photophysics

The non-reactive decay of excited states.

Photochemistry

The reactive decay of excited states.

Ground State

The state which most molecules occupy, where electrons usually occupy bonding and non-bonding MOs.

Excited State

When a molecule absorbs a photon, causing an electron to transition to a higher energy MO.

How do you name an excited state?

Names after the orbitals with one electron

Eg. π,π*

The full name includes the multiplicity

Eg. ¹(π,π*) or ³(π,π*)

What is the equation for multiplicity?

2S+1

Where S is the total spin quantum number, given by:

1/2(no. of e- with positive spin) - 1/2(no. of e- with negative spin)

Hund’s Rule

Unpaired electrons in orbitals have the same spin - hence a triplet state is lower in energy than the equivalent singlet state

Born-Oppenheimer Approximation

Total wavefunction is the product of the electronic, vibrational, and rotational wavefunctions.

ψ_total = ψ_e ∙ ψ_v ∙ ψ_r

E_total = E_e + E_v + E_r

What are the transitions labelled by the arrows?

Overall Selection Rule Equation

Demonstrates that in order to excite an electron, there must be a displacement of charge which gives a transition dipole moment.

What are the three selection rules?

Spin, orbital, vibrational

Spin Selection Rule

A transition is spin disallowed if there is a change in state multiplicity.

How can the spin selection rule be defined in terms of ∆S?

∆S is the change in multiplicity:

If ∆S = 0, the transition is S₀ —> S₁, so spin allowed

If ∆S ≠ 0, the transition is S₀ —> T₁, so spin disallowed

What impact does the presence of heavy atoms have on the spin selection rule?

Spin flip transition are less disallowed in the presence of heavy atoms (in the molecule or solvent).

This is because there is increased spin-orbit coupling.

This means that the transfer of spin angular momentum to orbit angular momentum is more likely, so these transitions are more likely.

Orbital Selection Rule - Symmetry component

If any one of the three direct products has A1/Ag (highest symmetry of the point group) then it is allowed.

What is the symmetry of a spin state with all electrons paired?

Totally symmetric - A₁ or A_g

(highest symmetry of point group)

What is the symmetry of a spin state with unpaired electrons?

The product of the symmetries of the unpaired electron orbitals

(symmetries of orbitals for this given in this course)

What is the equation to give the 3 symmetry products in the orbital selection rule?

Г_i x Г_x,y,z x Г_f

How do you find Г_x,y,z ?

Find x, y or z in the right hand column of the point group

What does this mean and what can be said about this transition?

This transition is symmetry allowed.

It is polarised along the z axis.

Spatial Component of Orbital Selection Rule

Dictates the magnitude of the orbital component based on the spatial overlap of orbitals.

Good overlap gives a larger integral (aka spatially allowed)

Vibrational Selection Rule

The magnitude of a transition will be larger for transitions with large vibrational overlap integrals.

How does the S₁ equilibrium bond length differ from that of S₀ and why?

Often longer because an electron has been promoted to an antibonding orbital, which weakens the bonds

What does it mean in terms of vibrational overlap integrals if r_e(S₁) = r_e(S₀)

If the equilibrium bond lengths are the same for S1 and S0 then the highest intensity transition will be the v”=0 —> v’=0

Franck-Condon Principle

The position of the atoms is unchanged during the transition because electrons move faster than nuclei.

Therefore, any change in geometry occurs after the electronic transition

Oscillator Strength (f)

Represents the probability of a transition.

Comprised of spin and orbital (symmetry and spatial) components

An f value of 1 denotes a fully allowed transition

Which selection rule has the largest impact on oscillator strength (probability of transition)?

Spin

Fluorescence

A radiative transition to a state of the same multiplicity (S1→S0).

What are the similarities and differences between an absorption spectrum and a fluorescence spectrum?

Similarities:

• Both show vibrational fine structure

• Both absorption and fluorescence mostly occur from the lowest vibrational energy level (due to Boltzman and vibrational relaxation)

  Differences:

• Absorption spectra show the fine structure of the excited states vibrational levels, fluorescence spectra show the fine structure of the ground state

How can you observe fluorescence from v’>0 states?

Record the spectra of the compound in the gas phase.

There’s fewer collisions so the rate of vibrational relaxation is lower

Why is the wavelength of absorbance and fluorescence spectra slightly different?

The S₁/S₀ energy gap becomes smaller in the excited state.

The solvent reorganises to stabilise the excited state, which slightly destabilises the ground state

Phosphorescence

A radiative transition between states of different multiplicity (T1 → S0).

(By definition, spin disallowed - slow)

How does a phosphorescence spectrum compare to a fluorescence spectrum?

They both show excited state v’=0 —> transitions, but phosphorescence spectra are at longer wavelengths.

This is because the triplet state is lower in energy due to Hund’s rule (unpaired electrons favour having the same spin)

Vibrational Relaxation (vr)

Excess vibrational energy is given to surrounding molecules by collisions.

What is the rate of vibrational relaxation dependent on?

The rate of collision

(very fast, occurs before anything else)

Internal Conversion (ic)

A non-radiative transition between states of the same multiplicity.

Draw a diagram to depict internal conversion

Kasha's Rule

vr and ic happen so rapidly between (different) excited states that fluorescence only occurs from the S1 state.

Eg. S3 —> S2 —> S1 very rapid,

S1 —> S0 slower (due to larger energy gap) so fluorescence can occur

Intersystem Crossing (isc)

A non-radiative transition between states of different multiplicity.

Explain why T1 states can be fairly long lived

isc is spin disallowed, but isc’ is even slower due to the large T1/S0 energy gap

Jablonski Diagrams

Energy states displayed as stacks, with energy as the vertical axis.

Chemiluminescence

Excitation caused by a chemical reaction.

Quantum Yield

The number of molecules undergoing a process / the number of photons absorbed.

OR

Write the general equation for the quantum yield of fluorescence?

Quantum Efficiency

The quantum yield of transitions from the T1 state

Lifetimes

When [A*] falls to 1/e of its initial value.

What is the equation for lifetime?

τ = 1/k

What impact does temperature have on photophysical processes?

Temperature doesn’t impact photophysical rates.

It can impact competing processes, such as isomerisation

Draw a diagram to depict how Q can act as an electron acceptor in exciplexes

Draw a diagram to depict how Q can act as an electron donor in exciplexes

Quenchers

Substances in solution that collide and cause T1 states to decay.

How do you decrease the impact of quenchers? What impact does this have?

Turn the solution into a rigid matrix (solid).

This stops the quencher from being able to diffuse to collide.

Therefore, photophysical decay dominates and phosphorescence is more visible.

Heavy Atom Effect

The presence of heavy atoms in a molecule increases the rate of all ‘spin-flip’ processes.

This is due to an increase in spin-orbit coupling.

What are the two types of experimental methods?

Steady-state techniques (measuring the wavelength of emission/absorbance upon irradiation (at 90 degrees))

Time-resolved techniques (light pulse)

Photochemistry

The reactive decay of excited states

How does excitation change the reactivity of a molecule?

• Changes electronic configuration

• Gain of energy to overcome activation barriers

• Formation of long-lived T₁ states which can then react

Photodissociation (give equation)

When a molecule dissociates upon excitation.

AB + hv → AB* → A + B

What is the dissociation limit? Draw a diagram

When the absorbance of a wavelength above a certain value causes the molecule to dissociate.

Above this limit, there is no vibrational fine structure in the absorbance spectrum because the absorbance becomes continuous

What is the difference between photodissociation in the gas phase and in solution/liquid phase?

In the gas phase, the fragments move freely apart upon dissociation.

In the liquid phase (/solution), the fragments may be held together long enough by the solvent cage to recombine.

Photopredissociation

Excitation causes a vibrationally excited state to form, which internally converts rapidly into a dissociative state.

Vibrational fine structure is lost in the absorbance spectrum at the wavelength which rapidly converts into the dissociative state

Photoisomerisation (give equation)

When a molecule changes structure (eg. isomerises) upon excitation.

AB + hv → AB* → AB’

Describe photoisomerism in alkenes

Excitation causes the alkene to form its twisted structure.

This can then decay into either the cis or trans isomer.

If you only irradiate with the wavelength which excites one of the isomers, you can get up to 100% conversion into the other.

The balance of isomers produced under irradiation is called the photostationary state.

Photochromism

A change in color upon excitation.

Generally caused by isomerisation (cis/trans) or ring opening/closing.

Excimers (give equation)

A system which produces a dimer in the excited state.

When does excimer fluorescence occur?

When [M] is high

How can you identify excimer fluorescence experimentally?

An excimer fluorescence peak will be at lower energy and won’t show vibrational fine structure

Recording fluorescence spectra at different [M] - The excimer peak will decrease in intensity at lower [M]

How does the emission intensity of a monomer over time compare to that of an excimer?

A monomer will decrease over time after excitation.

An excimer will increase initially as the excimer forms, then begin to decay

Exciplexes (give equation)

A system which forms a complex upon excitation.

Draw a diagram to depict monomer and exciplex/excimer emission and the cause of them being at different wavelengths

What is the main difference between excimers and exciplexes?

In exciplexes, there is a significant degree of charge transfer between M and Q

What is τ⁰_obs in the Stern-Volmer equation?

The observed lifetime without a quencher

Diffusion Controlled Limit

The rate of quenching is controlled by the rate of diffusion of the quencher to the molecule.

What is the rate of diffusion dependent on?

Temperature: higher temperature = faster diffusion

Viscosity: higher viscosity = slower diffusion

Electron transfer

Quenching via an electron transfer between M* and Q

Draw a diagram to depict Q acting as an electron acceptor in electron transfer quenching. What type of quenching is this?

Draw a diagram to depict Q acting as an electron donor in electron transfer quenching. What type of quenching is this?

What impact does solvent polarity have on electron transfer quenching?

In a low polarity solvent, the exciplex is more energetically stable.

In a high polarity solvent, the ion products are energetically favoured because they are stabilised by the solvent

Energy Transfer

The transfer of electronic excitation energy from a donor to an acceptor molecule.

Any further reaction of the acceptor is called ‘sensitised’

What are the 3 mechanisms of energy transfer?

• Radiative

• Non-radiative: long-range Coulombic, short-range electron exchange

Write an equation to depict radiative energy transfer

D* —> D + hv

A + hv —> A*

When does radiative energy transfer dominate?

When the solutions are in low concentration,

or when the molecules are far apart eg. Sun —> Earth

Long-Range Coulombic Energy Transfer

Energy transfer by a dipole-dipole interaction between D* and A, no contact or photon emission involved.

Draw a diagram to depict long-range Coulombic energy transfer

What are the requirements for long-range Coulombic energy transfer?

• D/D* and A/A* energy gaps must be the same

• D* and A must be 2-10nm apart

Short-Range Electron Exchange Energy Transfer

Energy transfer by the exchange of electrons between D* and A, no photon emission involved.

Draw a diagram to depict short-range electron exchange

What are the requirements for short range electron exchange?

• D/D* and A/A* energy gap must be the same

• D* and A must be about 1 nm apart

Photosensitisation (give equation)

Triplet states can be produced by triplet-triplet electron exchange

T₁ + S₀ —> S₀ + T₁

What is the equation for spin-orbit coupling?

J = L + S

How do electrons interact?

The orbital angular momentum of the two electrons are coupled because they repel each other.

The strength of this interaction is measured through the Racah parameter (B)

What is the general form of a term symbol?

^2S+1L

What are the letters given for these L values?

A) L = 0

B) L = 1

C) L = 2

D) L = 3

A) S

B) P

C) D

D) F

What are the mL and mS values for these microstates?

Draw the ground state for an element with p² valence electrons. Explain why this is the ground state.

Hund’s rules state that the ground state has maximum spin and orbital angular momentum

What are the steps to determining the term symbols for an electronic configuration?

1) Find the ground state term symbol