Experiment and theory

Combination of experiment and theory todetermine data and understanding on

reactions for application in combustion

1

Copyright ©2011 by Michael J Pilling. This material is the property of Michael J Pilling It is not to be sold, reproduced or distributed without theprior written permission of the owner.

Transition state theory

Q - partition function± indicates the transition state± indicates the transition state

r is the density of states (number of states per unitenergy rangeN± is the sum of states at the transition state fromenergy zero to EProperties of transition state (and reactants ifnecessary) determined from electronic structurecalculations

2

CH3 Vibrational energy levels / cm-1

quanta OOP bend deformation stretches

0 0 0 0

1 606 1396(2) 30043161(2)

1. Stretch , 3004 (A1’) 2. Out of plane bend 606 (A2’’)

3. stretch, 3161 (E’) 4. deformation, 1396 (E’)

3161(2)

2 1212 2792(3)

3 1818 3988(4)

4 2424

5 3030

6 3636

E = hwc1000 cm-1 11.96 kJ mol-1

3

Sums and densities of states for CH3

Energy range/cm-1

Density /500cm-1 Sum of states

0 -499 1 1500 - 999 1 2

1000 - 1499 3 51000 - 1499 3 51500 - 1999 1 62000 - 2499 1 72500 - 2999 4 113499 - 3499 4 153500 - 3999 5 20

4

Klippenstein p11

5

Klippenstein p13

Last lecture – determination ofdata for calculation of Qs fromspectroscopy and electronicstructure calcs

At 300 KkT/hc = 208 cm-1

6

Klippenstein p24

7

Radical + radical reactionse.g. CH3 + H, CH3 + CH3

No barrier on surface. Transition statesNo barrier on surface. Transition statesdetermined variationally

8

9

Correlation of reactant and product modes for CH3+H

Vibrational frequencies / cm-1

CH3 CH4

10

Methyl and Ethane frequencies

CH3 C2H6

11

CH3 + CH3

Slagle et al.J. Phys. Chem. 1988, 92, 2455-2462• Laser flash photolysis +

photionization massspectrometry (PIMS) atlow pressures andabsorption spectroscopy(AS) at high pressures.

• Reaction is second orderin radical – soin radical – soabsolute, notrelative, concentrationneeded. Use aborptioncross section for AS (seeJ. Phys. Chem.1985, 89, 2268-2274) andcalibration forPIMS, against loss ofprecursor. 12

Rate coefficient vs pressure

13

Theory – Wagner and Wardlaw,J. Phys. Chem. 1988, 92, 2462-2471

• Applied flexible transition state theory to calculatemicrocanonical rate constants, k(E,J) with a RRKMmodel:

• Two adjustable parameters linked to (i) efficiency ofcollisional energy transfer and (ii)the evolution of thetransitional modes.

• Obtained best fit to experimental data and thenfitted to the Troe parameterisation.

14

15

More recent calculations, based on ab intio surfacesHarding et al Phys. Chem. Chem. Phys., 2008, 9,4055

• k depends sensitively onpotential energy, V, asradicals approach.

• Vcalc depends on the levelof theory used.

• Calculated k(T) varies• Calculated k(T) variesby > factor of 10 as levelof theory is changed.

• k(T)calc may be moreaccurate thank(T)expt, because thelatter depends onextrapolation

16

Klippenstein p122

17

Experimental determination of k (CH3 + H))

• Laser flash photolysisproducing H and CH3with [H]<<[CH3]

• H by resonancefluorescence, CH3 byabsorption. Needabsolute [CH ], sinceabsorption. Needabsolute [CH3], sincek’(H) = k[CH3]

• Brouard et al. J. Phys.Chem. 1989, 93, 4047-4059

18

Experimental results for CH3 + H

CH3 absorption analysed via

Where D(t)=DI/I0

H fluorescence analysed via

• Where k2 refers to CH3 +CH3 and k3 to other 1st

order loss processes for H

• Plot show rate coefficentsvs p at 300, 400, 500, 600K.

19

CH3 + H. Parameterisation and determination of k

• Parameterisation using Troe method (see earlier)

20

Optimum k obtained from uncorrelated mVRRKM-master equation analvsis (10-10 cm3 molecule-1 s-1

300 K: 4.7 400 K: 4.5500 K: 4.6 600 K: 4.4

Klippenstein p99

Positive T dependence for k, : contrast –ve dependencefor CH3+CH3

21

Su and Michael, Proc Comb Inst 2002, 29, 1219

Shock tube study of the thermaldecomposition of C2D5I/CH3I/Kr mixtureswhich generated D atoms and CH3 radicals.[H] and [D] were monitored by ARAS. A rateconstant of 2.20·10-10 cm3 molecule-1 s-1 wasmeasured for the reaction CH + D CH D +measured for the reaction CH3 + D CH2D +H. This rate constant was converted to thehigh pressure limit for CH3 + H CH4 usingthe theoretical ratio of 1.6 determinedtheoretically by Klippenstein, Georgieskii, andHarding. (Proc. Comb. Inst. 2002, 29, 1229.)

22

Klippenstein p106

Gorin model (D M Golden)Excluded angles of approach

23

%

Klippenstein p137

24

25

OH + C2H4

26

27

E. E. Greenwald, S. W. North, Y. Georgievskii and S. J. Klippenstein,J. Phys. Chem. A, 2005, 109, 6031–6044.

Fits to available dataslight adjustment of inner TS energy

28

Contrast OH + C2H2 (yesterday)

5.0x10-13

6.0x10-13

7.0x10-13

8.0x10-13

9.0x10-13

mole

cu

les-1

s-1)

373K, He298K, He253K, He253K, N

2

233K, He210K, He

29

0.0 5.0x1018

1.0x1019

1.5x1019

2.0x1019

2.5x1019

-1.0x10-13

0.0

1.0x10-13

2.0x10-13

3.0x10-13

4.0x10-13

5.0x10-13

k(c

m3

mole

cu

les

[M] molecules cm-3

210K, He

Modelling dissociation and association reactions –master equation analysis

A+B

Dissociation and association

Collisional energy transfer between grains

AB

Energy grains -Bundles of energylevels

– Set up rate equation for concentrationin each grain.

– Express as matrix equation:dr/dt = Mr

– Time dependent grain concentrationsdepend on initial concentrations and oneigenvalues and eigenvectors of M

– Eigenvalue of smallest magnitude is thenegative of the dissociation rateconstant.

30

Master equation for dissociation

Solution:

31

Association reaction

32

Structure of M for an isomerisation reaction

33

More complex reactions.

A + B

A+B C DCompetitionbetween relaxationand reaction

E+F

• Similar approach to dissociationproblem

• Numerically smallest eigenvaluesrelated to phenomenological rateconstants (chemically significanteigenvalues)

CD

E+F

34

Master equation code

MESMER

Master Equation Solver for Multi-Energy WellReactions), 2008; an object oriented C++ program forcarrying out ME calculations and eigenvalue-carrying out ME calculations and eigenvalue-eigenvector analysis on arbitrary multiple wellsystems.

http://sourceforge.net/projects/mesmer

35

OH + C2H4 at low TOH + C2H4 HOC2H4

36

OH + C2H4 (Cleary et al, Phys. Chem. Chem.

Phys., 2007, 8, 5633–5642) Data fitted using masterequation, with k(E) for dissociation of HOC2H4 obtainedby inverse Laplace transformation

8.0x10-12

1.0x10-11

1.2x10-11

mole

cule

-1s

-1)

37

0.0 5.0x1018

1.0x1019

1.5x1019

2.0x1019

2.5x1019

0.0

2.0x10-12

4.0x10-12

6.0x10-12

8.0x10-12

kR

1/(c

m3

mole

cule

[M] / (molecule cm-3)

200K, He260K, He295K, N

2

295K, He400K, He

Inverse Laplace transform and association ratecoefficients

• Inverting this relationship allows k(E) to bedetermined from the high pressure limiting rateconstant. Most effectively performed using theassociation rate constant.

• Davies et al. Chem Phys Letters, 1986, 126, 373–

379. 38

Microcanonical dissociation rate constants frominverse Laplace transform of canonical association

rate constantb = 1/RT Q(b) is the rovibronic partition function, K(b) is the

equilibrium constant and N(E) is the rovibronic density of

states of the association complex. Np is the convoluteddensities of states of the reactant species

A + B C

39

Comparison of master equation fits with theoryof Greenwald et al.

40

High temperature, OH + C2H4

Hanson group (Vasu et al. J. Phys. Chem. A 2010, 114, 11529–11537)

• OH radicals were producedby shock-heating t-butylhydroperoxide, Me3COOH, and monitored by laserabsorption near 306.7 nm

• 890 -1366 K, 2.3 atm

1201 K

890 -1366 K, 2.3 atm

41

OH + C2H4 (Vasu et al.)

42

Uncertainty contributions in the determinationof OH + C2H4

• Contributions from uncertainty in rate coefficients:

CH3COCH3 + OH (fractional uncertainty 0.3) 0.1%

CH3 + OH 3CH2 + H2O (factor 2) 3.9%

CH3 + OH CH3OH (factor of 2) 1.5%

CH3 + CH3 C2H= (Factor of 2) 1.5%CH3 + CH3 C2H= (Factor of 2) 1.5%

Also contributions from temperature, fittingprocess, OH abosorption coefficient, mixtureconcentration, wavemeter reading

Overall uncertainty: 22.8%

43

Product yields – contributionfrom theory

• Senosiaian et al, J. Phys. Chem.A 2006, 110, 6960-6970

• Slight tuning of surface(~0.4 kcal mol-1) byreference toexperimental data.experimental data.

• Note formation of vinylalcohol >800 K, Confirmedby Taatjes et al.

• Srinivasan et al. Phys. Chem.Chem. Phys., 2007, 9, 4155-4163

44

Master equationChemically significant eigenvalues

45

More complex reactions.

A + B

A+B C DCompetitionbetween relaxationand reaction

E+F

• Similar approach to dissociationproblem

• Numerically smallest eigenvaluesrelated to phenomenological rateconstants (chemically significanteigenvalues)

CD

E+F

ReminderDissociation: Eigenvalueof smallest magnitude isthe negative of thedissociation rate constant.

46

Chemically significanteigenvalues forisomerisation

Two species, two CSEs

System is conservative,so l1 = 0

Reaction systemrelaxes to equilibriumstate . Relaxation rateconstant =|l2| = kf + kr

Relaxation time = t

t = (kf + kr)-1

47

Effect of sulfur oxides on fuel oxidationPeter Glarborg Hidden interactions—Trace species governing combustion and

emissions. 31st Symposium

• SO2 + H (+M) HOSO (+M) (R1)

• HOSO + H SO + H2O (R2)

• SO + O2 SO2 + O (R3)

• How do we provide rate data for• How do we provide rate data forreactions of this sort?

• Are there hidden complexities in asimple association reaction like (R1)?

48

H + SO2

experiment + theory

50

100

150

200

250

300

TS4TS2

TS1

OH+SO

HSO2

H+SO2

Ere

l/k

Jm

ol-

1

Experimental decays trace for H + SO2

Gives k at selected p and T.

k vs p at T = 295,363 and 423 K

TS3

• Potential energy surface for H +SO2, from electronic structurecalcs

• Approach: Experimentalinvestigation using vuv LIF for H

• Master equationanalysis, constrained toexperimental data

0

50

HOSO

200 400 600 800 1000 1200 1400 1600 180010

-13

10-11

10-9

10-7

10-5

10-3

10-1

101

103

105

107

109

||

T/KBlitz et al, J. Phys. Chem. A 2006, 110, 2996-3009

Experimental decays trace for H + SO2

Gives k at selected p and T.

Eigenvaluesfrom MEanalysis.Red – TS1Blue TS2Green TS3

49

Determination of individualphenomenological rate constantsfrom eigenvalues / eigenvectors

Total number of eigenvalues is equal to thetotal number of grains.The 3 eigenvalues of smallest magnituderelate to the phenomenological eigenvaluesof the macroscopic chemical system(chemically significant eigenvalues)H + SO2 HSO2 (1)H + SO HOSO (2)

200 400 600 800 1000 1200 140010

-10

10-7

10-4

10-1

102

105

108

|2|

k2[SO

2]+k

-2

k2k

-1/k

1

k2[SO

2]

k-2

|2|/s

-1

T/K

dc/dt =

H + SO2 HOSO (2)H + SO2 OH + SO (3)H SO2 HOSO (4)HSO2 OH + SO (5)HOSO OH + SO (6)

[SO2] >> [H] – pseudo first order conditions 50

Experimental characterisation of the TS2 and TS3regions of the surface

• TS2 is significant in the 400 –800 K region.

• Difficult to studyexperimentally using LFP.

• ?Characterise using flowreactor methods?

• TS3 is even more difficult toinvestigate. Use the reversereaction, OH + SO, viadetailed balance

109 -10.25

0.001 0.002 0.003 0.004

mole

cule

-1s

-1)

200 400 600 800 1000 1200 1400 1600 180010

-13

10-11

10-9

10-7

10-5

10-3

10-1

101

103

105

107

10

||

T/K

-11.25

-10.25

K / T

log

10

(kR

1/1

0-1

1cm

3m

ole

cule

Blitz et al. Proc Comb Inst

Use to determine rate constants,k(E) for the reverse reactionsH + SO2 SO + OHHOSO SO + OH

51

Issues – Overlap of chemicallysignificant eigenvalues withenergy relaxation eigenvalues:can lead to problems in definingrate constants (e.g. Tsang et al,Robertson et al in alkyl radicaldecomposition.

– Use of OH + SO to calculateforward ks using detailedbalance. Does detailed balancealways apply – are the forward-3

10-1

101

103

105

107

109

|

always apply – are the forwardand reverse rate constantsalways related through theequilibrium constant? (Millerand Klippenstein, Miller et al.Phys. Chem. Chem. Phys., 2009,11, 1128–1137

– Important issue in combustion– e.g. CHEMKIN generallyintroduces forward and reversereactions, linked viathermodynamics.

200 400 600 800 1000 1200 1400 1600 180010

-13

10-11

10-9

10-7

10-5

10-3|

T/K

HSO2 H + SO2

52

Detailed balance in multiple-well chemical reactionsPhys. Chem. Chem. Phys., 2009, 11, 1128–1137

• ‘In this Perspective we address the issue ofwhether or not (and to what extent) detailedbalance is satisfied by rate constants obtainedfrom solutions [of the master equation forfrom solutions [of the master equation formultiple well systems] ……...It is extremelyunlikely that the rate constants of interestsatisfy detailed balance exactly (there is noreason to believe that they do). However, thediscrepancies are expected to be vanishinglysmall, as observed in practice.’

53

Low T (<1000 K) R1,R-1,R2, R-2 dominate

H + SO2 HSO2 (1)

H + SO2 HOSO (2)

System conservative: l1=0

54

High T (>1000 K), k-1 >>k1[SO2]: [HSO2] ~0

H + SO2 HOSO (2)

H + SO2 OH + SO (3)

HOSO OH + SO (6)

|l3|is now very large andthe associated timescale ismuch less than theexperimental timescale.The system reduces to 2species (H, HOSO) withspecies (H, HOSO) withOH + SO as a sink.Solution has same form asbefore, and gives:

55

l3

1 atm

56

1 atm

l2

571 atm 0.001 atm

l1H + SO2 OH + SO (3)HOSO OH + SO (6)

0

50

100

150

200

250

300

TS4TS2

TS1

OH+SO

HOSO

HSO2

H+SO2

Ere

l/k

Jm

ol-

1

58

1 atm 106 atm

Eigenpair analysis to return macroscopic rate constants

Macroscopic rate-coefficients are combinations ofthe Chemically Significant eigenvalues and vectors ofthe collision matrix

• J. T. Bartis and B. Widom, J. Chem. Phys., 1974, 60,3474

• J. A. Miller and S. J. Klippenstein, J. Phys. Chem. A,• J. A. Miller and S. J. Klippenstein, J. Phys. Chem. A,2006, 110, 10528, J. A. Miller and S. J. Klippenstein,J. Phys. Chem. A, 2002 106, 9267, J. A. Miller and S.J. Klippenstein, J. Phys. Chem. A, 2003, 107, 2680.

• Robertson et al. Phys. Chem. Chem. Phys., 2007, 9,4085–4097

59

1,2-Pentyl isomerisation and dissociation

60

1,2 pentyl isomerisation and dissociationRate coefficients extracted with Bartis Widom analysis,

400 K

600 K

61

Behaviour at high temperatures: overlap of CS andrelaxation eigenvalues

62

1000 torr

Binomial expansion of quadratic solution for l2

• full diamonds: ratio of l 2

from full quadratic solutionto l 2 from the ME.

• Open triangles: ratio of l

Low T

• Open triangles: ratio of l 2

from Eq. full quadraticsolution to l 2 from equationabove (full expression. )

• Open squares: ratio of -l 2

from full quadraticexpression to (k7 + k-7).

63

Binomial expansion of quadratic solution for l1

• Full triangles: ratio of l1 from the full quadratic solution to l1

from the ME.

• Open squares: ratio of l1 from the full quadratic solution to l1

from above approximation

64

Comparison of the time dependence of the molefraction of the 1- and 2-pentyl isomers using thesummed grain populations from the ME and using the

phenomenological rate coefficients from the ME in abiexponential representation: (a) 600 K; (b) 1000 K.

a b65

Conclusions

• All wells can contribute to all sink channelsirrespective of whether they are directly connectedto the transition state that leads to a given set ofproducts.

• ‘Well-skipping’ is significant and is characterized bynon-standard fall-off curves which exhibit a declinein rate coefficient with increasing pressure,indicative of the competition between collisionalindicative of the competition between collisionalrelaxation and reaction.

• Product yields are very sensitive to the difference indissociation energies for 1- and 2-pentyl. Thecalculations give a difference of only 4 kJ mol-1, andancillary experiments are essential to define thesystem more accurately. Because of the complexity ofthe system, the experiments must be interpretedwith a master equation analysis. 66

Autoignition chemistry

OH

RH

R

RO2

O2O2

Smaller radical (R1) + Alkene (A1)

HO2 + Alkene (A2)

Termination

2

QOOH

O2QOOH

O2

OH + R'OOH

Products + OH

R'O + OH

Propagation

Branching67

Determination of product yields in C2H5 + O2

• Taatjes et al. (J. Phys. Chem. A

104 (2000) 11549 – 11560)

observed the formation of OHand HO2, determining thefractional yields. Used 100%yield of HO2 from CH2OH + O2

to calibrate the system.to calibrate the system.

• HO2 yield as T and p

• Two timescales at higher T

• OH yield is small.

• Theoretical interpretation andrelevance to autoignitionchemistry will be discussedlater

C2H5 + O2 C2H5O2*C2H5O2* + M C2H5O2 + MC2H5O2* C2H4 + HO2

C2H5O2 + M C2H4 + HO268

C2H5, C3H7+ O2

69

Master equation analysis: Miller and Klippenstein,Int J Chem Kinet 33: 654–668, 2001

• 3regimes, low, transition, highT.

• In transition region, thermalrate constant jumps from oneeigenvalue to the other – thetwo eigenvalues are mixed inthis region.

• At high T, the reaction• At high T, the reactionexclusively forms HO2 via alargely thermalised RO2. k is,in practical terms,independent of p.

• At low T, reaction involves thepressure dependent formationof RO2 and direct formationof HO2

70

Cyclohexyl + O2Fernandes et al. Phys Chem. Chem. Phys., 2009, 11, 1302 - 1307

71

Time dependence of OH formation

72

Importance of formally direct route to OH

73

Evidence forchain branchingat lower T

74

Dimethyl ether: CH3OCH2 + O2Eskola et al.

75

CH3OCH2 + O2: major mechanism

CH3OCH2

+O2

IM2QOOH

TS1

TS2TS3(c,t)

CH2O...CH2OOH

TS4

TS5

IM1, RO2

QOOH

2CH2O+OHOH+c-OCOC

IM3, R'O

TS6

H+R"CHO

CBS-QB//mpw1k/avtz + ZPE

76

Species profiles, 550 K, 1 bar

0.01

0.1

1

1.00E-11 1.00E-10 1.00E-09 1.00E-08 1.00E-07 1.00E-06 1.00E-05 1.00E-04 1.00E-03 1.00E-02 1.00E-01

1E-06

1E-05

0.0001

0.001

CH3OCH2

IM1

IM2

OH-1

77

Master equation: rate constant analysis

I1 = RO2

I2 = QOOH

R (+O2)

I1I2

78

Phenomenological rate ceoefficients from a BartisWidom analysis

1.00E+05

1.00E+06

1.00E+07

1.00E+08

1.00E+09

1.00E+10

k1

k2

k3

k4k/s-1

1.00E+00

1.00E+01

1.00E+02

1.00E+03

1.00E+04

1.00E+05

550 600 650 700 750 800 850

k5

k6

k7

k8

k9

k/s

T/K79

Routes to branching: CH3OCH2 + O2 (+ O2)

• Anderson and Carter: Molecular Physics 2008, 106, 367–39680

Excited electronic states in combustionChemistry of methylene (CH2)

– CH2 exists as a triplet (3CH2) and a singlet(1CH2), separated in energy by ~ 9 kcal mol-1.

– The upper state (singlet) is much more reactive. Itis involved, e.g., in the production of C3H3, a sootprecursor and in the chemistry of Titan.

– The singlet is deactivated to the triplet on collision– The singlet is deactivated to the triplet on collisionwith unreactive (and reactive) gases.

– Our understanding of the mechanism of deactivationin reactive systems is limited, especially atcombustion temperatures

81

Methodology– Laser flash photolysisCH2CO at (308 nm).

– Detection 1CH2 byLIF, e.g. line from 312

state in a1A1 (0,0,0) at589.21 nm.

– Pressure 1 - 10 Torr.Rapid initial rotationrelaxation of

15

20

Sig

na

lrelaxation of1CH2(0,0,0).

– Collision inducedintersystem crossing(CIISC) and reactionsinvestigated forrotationally relaxed 1CH2

(0,0,0)

0 20 40 60 80 1000

5

10

Sig

na

l

time (s)

82

1CH2 + M - CIISC

j

iWSO

krot

k

En

ergy

20

30

40

xR

ate

coef

fici

ent

/cm

3m

ole

cule

s-1

s-1

HeNeArKrXeN

2

SF6

kil

kll’l’

k

l

321 vvvX~

En

ergy

000a~

100 200 300 400 500 600 700 8000

10

10

-12

xR

ate

coef

fici

ent

/cm

Temperature (K)

83

1CH2 + C2H2 C3H4* C3H3 + H1CH2 + C2H2

3CH2 + C2H2

1. Kinetics from decay of CH2

– the overall rate constantdecreases as T .

2. If same mechanism fordeactivation as for Ar, thenreactive channel becomes 2.0

2.5

3.0

3.5

4.0

To

talflu

ore

sce

nce

sig

na

l/

arb

itra

ryu

nits

Hreactive channel becomesunimportant at higher T???

3. Monitor H using VUV LIF;growth shows same kineticsas 1CH2 decay

4. Calibrate H signal todetermine what fraction ofthe 1CH2 loss occurs byreaction and what fractionby deactivation.

-5 0 5 10 15 200.0

0.5

1.0

1.5

2.0

To

talflu

ore

sce

nce

sig

na

l/

arb

itra

ryu

nits

Time / s

1CH2

H

84

CH2 + C2H2

85

200 300 400 500 600 700 8000

1

2

31

010

xR

ate

co

effic

ient

/cm

3m

ole

cu

le-1

s-1

Temperature / K

1CH2 + C3H6

C2H2

C2H4

200 250 300 350 400 450 500

0.0

6.0x10-11

1.2x10-10

1.8x10-10

2.4x10-10

Ra

teco

eff

icie

nt/

cm

-3m

ole

cule

-1s

-1

Temperature / K

1CH2 + C2H2

ReactionDeactivation

Rate coefficients for reactionAnd deactivation

Rate coefficient fordeactivation to the tripletnow decreases with T.Doesn’t fit in with thebehaviour found for inertgases. What is themechanism?

Temperature / K

Singlet surfaceTriplet surfaceLook at a simpler system

Surface crossing

86

1CH2 + H2 CH4* CH3 +H

T / K1010 × kH2 /

cm3 molecules-1

s-1

1011 × kD2 /cm3

molecules-1

s-1

195 1.030 ± 0.021 5.77 ± 0.27

298 1.094 ± 0.064 6.39 ± 0.47

398 1.054 ± 0.044 5.77 ± 0.36

0.000E+00

5.000E-11

1.000E-10

1.500E-10

2.000E-10

2.500E-10

3.000E-10

3.500E-10

0 200 400 600 800 1000 1200

Temperature/K

k/c

m3

mo

lec

ule

-1s

-1

CH2 + H2 Theory

CH2 + D2 theory

CH2 + H2 Expt

CH2 + D2 Expt

Theory: Klippensteinand Harding

398 1.054 ± 0.044 5.77 ± 0.36

498 1.072 ± 0.045 6.49 ± 0.52

598 1.087 ± 0.073 6.45 ± 0.44

698 1.024 ± 0.093 5.91 ± 0.22

798 1.098 ± 0.080 6.14 ± 0.35

200 300 400 500 600 700 800

8

10

12

14

16

Temperature / K

10

11

xk

H2

/cm

3m

ole

cu

les

-1s

-1

1CH2 + H2

Hancock et alWagenerLeeds

87

Absolute H and D atom yields from 1CH2 + H2, D2

– kCIISC again increasesas T decreases.Similar behaviour forboth collisionpartners.

– H vs D yields dependon dissociation ofCH2D2*. Theory gives

0.2

0.4

0.6

0.8

1.0

Flu

ore

scen

ce

sig

na

l/a

rbitra

ryu

nits

H from 1CH2 + H2

H and D from 1CH + DCH2D2*. Theory givesa lower H:D ratio(~1.3 vs 1.6 – 2) 0 10 20 30 40 50

0.0Flu

ore

scen

ce

sig

na

l/a

rbitra

ryu

nits

Time / s

T / K1CH2 + H2

1CH2 + D2

αH αH αD αH + αD

195 0.71 ± 0.07 0.49 ± 0.07 0.24 ± 0.09 0.73 ± 0.12

298 0.85 ±0.08 0.47 ± 0.05 0.28 ± 0.09 0.75 ± 0.10

398 0.92 ± 0.08 0.55 ± 0.07 0.34 ± 0.04 0.89 ± 0.10

H and D from 1CH2 + D2

88

Mechanism of 1CH2 3CH2

deactivation in reactivesystems

– The triplet reacts with H2on a repulsivesurface, while that for thesinglet is attractive – anintersection occurs whereisc may occur

– Harding calcs show theintersection occurs at largeintersection occurs at largedistances and at a smallinteraction energy

– Can the T dependence ofISC be explained in termsof Landau Zener theory?

– What is the role of themixed states – if any?

– Do we include both thereaction and deactivationprocesses in the capturerate calculations?

Larry Harding

89