Singlet Oxygen

1
Singlet Oxygen theRadical Triplet Pair
Mechanism

• Stuart Norman
• 26th February 2003

2
Photosynthetic RCs

• Irradiation, followed by a series of rapid
  electron transfers
• (BChl)2 dimer acts as e- donor (P)
• BPheo is 1o acceptor (I)
• Quinones (QA QB) are 2o acceptors

3
Photosynthetic RCs

• Normally, rapid removal of 1PI- occurs by e-
  transfer to Q
• If this pathway is blocked, and 1PI-
  sufficiently long lived, S-T mixing may occur ?
  3PI
• Magnetic field dependent step

4
Singlet Oxygen

• Molecular oxygen - GS is 3Sg- 1st ES is 1?g
• Formed in biosystems through triplet-triplet
  energy transfer from a photosensitizer
• (e.g. flavin, chlorophyll, porphyrin)
• P h? ? 1P ? 3P
• 3P 3O2 ? P 1O2

5
Photosynthetic RCs

• Bacteria have evolved systems to protect against
  1O2 damage
• Quinones quench 1PI- before S-T mixing occurs
• Carotenoids quench any 3PI formed
• Thus only expect to see significant 1O2
  production in mutant bacteria without quinones or
  carotenoids
• Quinones may also be removed by chemical
  reduction or intense illumination saturating the
  normal e- transfer pathway

6
Singlet Oxygen

• 1O2 can be detected
• through damage to cellular structures
• changes in P or 3P electronic absorption bands
  (vis/IR)
• directly by its phosphorescence at ? 1270nm
  using Ge-diode detector
• D20 solvent extends the radiative lifetime by a
  factor of 10

7
Triplet Pair Mechanism

• Possibility of MFE on triplet-triplet energy
  transfer reaction (spin-selective process )
• triplets collide, forming triplet-pair (TP),
  Stotal 0, 1, 2
• energy transfer allowed from Stotal 0 state,
  as singlet products (1P 1O2) formed (Sprod 0)
• Stotal 0 TPs removed. Remaining Stotal 1, 2
  TPs diffuse apart, undergo spin evolution and may
  re-encounter at later time.
• differences in local fields affect probability
  of recombination at re-encounter

8
Triplet Pair Mechanism

• In addition to hyperfine, exchange and dipolar
  couplings, TPs have intramolecular dipolar
  interactions (zero-field splittings)
• Anisotropic at high fields, but isotropic at low
  fields

9
Rotational Diffusion

• Diffusion equation dc/dt D.G.C(?)
• C(?) concn of molecules at orientation ? to
  lab axis
• D rotational diffusion coefficient
• G diffusion operator ( 1/sin ? ?/?? sin ?
  ?/??)
• Take discreet values - let zj cos ?j - and let
  molecules jump from zj ? zj1 or zj-1
• z takes n equal values between 0 (? ?/2) and 1
  (? 0) zj (i - 1)d where d 1/(n-1)

10
Rotational Diffusion

• Set up vector p pj C(zj) fraction of
  particles at each z
• Set up matrix W Wjk rates of diffusive jumps
  from zj ? zk
• Hence dp/dt W p
• W can be calculated, remembering that no.
  particles must remain constant - W11 and Wnn take
  this into account
• Wj,j1 D (1 d zi zi2) / d2 W1,1 D (-1 d
  z1 z12) / d2
• Wj,j 2D (-1 zi2) / d2 Wn,n D (-1- d zn
  zn2) / d2
• Wj,j-1 D (1 d zi zi2) / d2

11
Spin Evolution

• Evolution of density matrix ? (m x m) over time
• d?/dt - i ?, ?
• Convert to Liouville space
• ds/dt - i L s
• where L is defined as
• L ??1 1??T
• and s ?1,1, ?1,2, ?1,3, , ?m,m-1, ?m,m

12
Combining RD SE

• Combining Diffusion and Spin Evolution
• dp/dt W p and ds/dt - i L s ? df/dt A f
• Wjk is the m2 x m2 diagonal matrix with all
  elements Wjk
• -iLj is the m2 x m2 matrix iL appropriate for
  zj

13
EPR Triplet Spectrum

• ? Dcos2? sz2 sin2? sx2 sin?
  cos?(szsxsxsz) 2/31 ?0sz
• D is the dipolar coupling constant
• sx, sy, sz are spin matrices in T0, T, T- basis
• Calculate FID in Liouville space, assuming
• at t 0, that triplet has only magnetisation in
  x-y plane
• all orientations, zj, are equally likely
• Detect sx i sy during FID, then take FT to get
  spectrum

14
EPR Triplet Spectrum

• ?0 100, D 5000 s-1, D 2 x 106 s-1

15
EPR Triplet Spectrum

• n 40, ?0 100, D 2 x 106 s-1

16
Radical Triplet Pair

• Only one triplet (A) has significant zero-field
  splitting (DB 0)
• ? DAcos2? sAz2 sin2? sAx2 sin ? cos ?
  (sAzsAxsAxsAz) 2/31
• ?0(sAz sBz)
• Initial orientation of triplet A specified
• select one value of j J
• Recombination assume exponential model, rate
  constant, k
• ds/dt -iLs becomes ds/dt (-iL k1)s

17
Radical Triplet Pair

• Singlet projection operator, Ps, given by
• 2 vectors, Ps and f(0) defined
• Ps FlattenPs, FlattenPs, FlattenPs,
• i.e. a sequence of n-lots of the flattened
  operator, Ps
• f(0) 0,0,,0,0,, FlattenPs, 0,0,,0,0,
• i.e. a sequence of n-lots of length-m2
  zero-vectors, where the Jth zero-vector is
  replaced with the flattened Ps

18
Radical Triplet Pair

• Singlet yield is given by
• Fs - k Ps.A-1.f(0) 1
• A is a complex, symmetric, banded matrix, and
  most of the elements of f(0) are zero. Speed can
  be improved by solving simultaneous equations for
  f (fast Nag library routines)
• A.f f(0) 2
• Then Fs - k Ps.f 3
• Program runs 100x faster doing 2 3, rather
  than 1

19
Radical Triplet Pair

• RTPM program (rtpmband.f)
• n 16
• J 1,3,5,7,9,11,13,14,15,16
• D 2000 s-1
• D 3.94 cm-1
• Triplet-triplet program (t-plot.m)
• DA 3.94 cm-1
• ?A equiv. to J-values above
• DB 0, ?B 0

20
Radical Triplet Pair

• Spike present at ?-values close to Magic Angle
  (54º 44)
• At 0.955 rad ( 54º 41) the peak is at 2 x 106 G
  with Fs gt 0.6

21
Oxygen

• D(O2) 3.94 cm-1 7.42 x 1011 s-1 k 2.8 x
  107 s-1
• D 109, 1010, 1011, 1012, 1013 s-1 all ?
  values same to 3sf

22
Acknowledgements

• Thanks must go to
• Peter
• Chris
• Kevin