Photochemistry

1
Photochemistry

• Lecture 2
• Fates of excited states of polyatomic molecules

2
Polyatomic molecule electronic states

• Use of group theory to define irreducible
  representations for MOs
• e.g., benzene

3
Benzene electronic excited states

• Ground state .(1a2u)2(1e1g)4 1A1g
• First excited configuration ...(1a2u)2(1e1g)3(
  1e2u)1
• Use direct product tables to generate the term
  symbols
• e1g x e2u B1u B2u E1u
• Resultant spin 1 or 0 (triplet/singlet)
• Lowest excited state is 3B1u
• Lowest singlet excited state 1B2u

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Selection rules for allowed electronic transitions

• ?(??) x ?(??) ? ?(Tx) and/or ?(Ty) and/or ?(Tz)
• For benzene (D6h) ?(Tx),?(Ty)? E1u , ?(Tz) ? A2u
• Transition to lowest excited state formally
  forbidden because
• A1g x B2u B2u

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Chromophores

• Larger molecules may have very few symmetry
  elements
• Excitation can often be traced to electrons
  belonging to a small group of atoms known as a
  chromophore
• Typically label excitation as e.g.,
• ? ? n (e.g., carbonyl group)
• ? ? ? (e.g., alkene or carbonyl)
• ? ??

n indicates a non-bonding electron usually
localised (e.g, lone pair on oxygen for carbonyl)
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Chromophores (cont)

• Likewise, excited states may be labelled e.g.,
  1(?,?) or 3(?,n) indicating which electrons are
  unpaired.
• ? ? ? transitions may lie deep into the
  ultraviolet (7 eV or ? 180 nm) for unconjugated
  double bonds, but shift towards visible as
  conjugation increases (cf particle in 1D box)
• ? ? n transitions in carbonyl group also in UV
  at around 290 nm (4 eV)

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Photochemical mechanism of vision ? ? ? of
11-cis retinal
Isomerization in 200 fs
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?? n transition is forbidden to first-order
approximation on grounds of symmetry (px ? py on
oxygen transition moments zero)
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Simplified nomenclature for polyatomic molecules

• S0 ground state
• S1 lowest excited singlet state (S0)
• T1 lowest triplet state (S1)

S2
T2
S1
T1
S0
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Vibrational modes of polyatomic molecules

• 3N-6 degrees of vibrational freedom (or 3N-5 for
  a linear molecule)
• Normal modes from group theory analysis e.g., for
  ammonia -

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Vibronically allowed transitions

• In benzene, transition to lowest excited state
  1B2u formally forbidden because it has
• A1g x B2u B2u
• whereas (Tx),?(Ty)? E1u , ?(Tz) ? A2u
• However, if an E2g vibration is simultaneously
  excited then overall symmetry of excited state is
• B2u x E2g E1u
• Hence excitation is weakly allowed, provided
  there is simultaneous excitation of vibration of
  appropriate symmetry mode.
• (distortion of symmetry causes mixing of excited
  electronic states)

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Potential energy surface

• Potential energy of molecule varies as a function
  of 3N-6 co-ordinates for polyatomic.
• PE surface, not just simple curve.
• Can represent a cut through this
  multi-dimensional surface by freezing all
  co-ordinates except one of interest e.g., for
  umbrella bending mode of ammonia

PE surface for triatomic bending angle fixed
(linear)
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Franck Condon principle as applied to polyatomic
molecules

• For those vibrational modes that are allowed by
  symmetry, whether a long or short progression is
  observed is determined by Franck Condon principle
• Need to consider whether there is a large change
  in geometry on excitation along the direction of
  the normal co-ordinate for the mode in question
• e.g., for NH3 molecule becomes more planar in
  excited states, hence a long progression in the
  umbrella bending mode is excited. For benzene the
  ring bond length increases, hence ring breathing
  mode is excited.

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Ring breathing mode vibrational progression of
Benzene
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Vibrational states of polyatomic molecules

• 3N-6 Normal modes of e.g., H2O
• Represent number of quanta in each mode as
  (v1,v2..) ? v1 quanta in mode ?1 etc.
• (0,0,0..) is the ground vibrational state.
• Energy, E is ? the sum of vibrational energies in
  each mode (harmonic approx).
• E (v1 ½) h?1 (v2½)h?2 .

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Density of vibrational states for hexafluorides

• Density of vibrational states defined as number
  of vibrational states per wavenumber
• Estimate from number of ways of distributing j
  quanta in s equivalent oscillators

106
101
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Jablonski diagram
Vibrational levels at high energy are
pseudo-continuous Levels of S1 are degenerate
with pseudo-continuum of high vibrational levels
of S0 and T1
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Fates of excited states III Polyatomic molecules
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Vibrational relaxation in solution

• Molecules excited to excited vibrational levels
  of S1 undergo rapid degradation to lowest
  vibrational level of S1.
• Energy is transferred to the solvent molecules
  (translation primarily) by collision i.e., V-T
• Subsequent processes begin from this lowest level
  and are thus independent of the vibrational level
  that is originally excited.

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Absorption spectrum determined by (a) vibronic
selection rules and (b) Franck-Condon
overlap Emission (fluorescence) or other
processes follow relaxation to lowest vibrational
level of S1
Energy transfer etc
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Intramolecular energy transfer

• Collision free radiationless process molecule
  evolves into different electronic state without
  loss or gain of energy
• Excess electronic energy transferred to
  vibrations, followed by fast relaxation.
• Represented by horizontal line on Jablonski
  Diagram

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Different intramolecular processes

• Internal Conversion (IC)
• No change of spin state e.g., S0 ? S1
• Intersystem Crossing (ISC)
• Change of spin state e.g., T1?S0 or S1?T1
• Intramolecular Vibrational Redistribution (IVR)
• No change of electronic state but change of
  vibrational state (more important in gas phase)
• S1(v1,v2,v3.) ? S1(v1,v2,v3)