1
On the accuracy of collisional energy transfer parameters for reaction kinetics applications: detailed evaluation of data from direct experiments

Type: Object | Advantage: None | Novelty: New | ConceptID: Obj1

2
It is shown that the spread among the various “direct” experimental 〈ΔE〉 data in the literature, so unsatisfactory for their application in chemical kinetics, can be removed consistently.

Type: Result | Advantage: None | Novelty: None | ConceptID: Res1

3
Underlying agreement within very small uncertainties is demonstrated for the case of the much studied collisional relaxation of highly vibrationally excited azulene.

Type: Result | Advantage: None | Novelty: None | ConceptID: Res2

4
Benchmark experimental data for the collisional energy transfer of highly vibrationally excited azulene obtained by the method of “kinetically controlled selective ionization (KCSI)” (U. Hold, T. Lenzer, K. Luther and A. C. Symonds, J. Chem. Phys., 2003, 119, 11 192) are used for a detailed comparison with earlier measurements employing time-resolved ultraviolet absorption (UVA) and infrared fluorescence (IRF).

Type: Method | Advantage: None | Novelty: New | ConceptID: Met1

5
The experimental UVA and IRF traces are simulated by convolution of the transient vibrational distributions g(E) during relaxation obtained from KCSI measurements with the respective calibration curves of the UVA and IRF experiments.

Type: Method | Advantage: None | Novelty: New | ConceptID: Met2

6
The differences between such simulations and the experimental curves are traced back to non-negligible contributions of azulene self-collisions in the UVA and IRF data.

Type: Result | Advantage: None | Novelty: None | ConceptID: Res3

7
Astonishing quantitative agreement is reached when azulene/bath gas mixing ratios of the corresponding UVA/IRF experiments are fully accounted for in the KCSI simulations.

Type: Result | Advantage: None | Novelty: None | ConceptID: Res4

8
The influence of self-collisions is thus quantitatively assessed as an important source of error in addition to the well-known problem of calibration curve uncertainties in UVA and IRF detection as discussed earlier (T. Lenzer, K. Luther, K. Reihs and A. C. Symonds, J. Chem. Phys., 2000, 112, 4090).

Type: Conclusion | Advantage: None | Novelty: None | ConceptID: Con1

Introduction

9
Collisional energy transfer (CET) is a key process in a large variety of chemical reaction systems.1,2

Type: Background | Advantage: None | Novelty: None | ConceptID: Bac1

10
In cases like unimolecular or combination reactions, CET rates directly determine the total rates of the chemical reactions in the so-called “low pressure regime” and define the position of the fall-off range of diminishing pressure dependence at increasing densities.

Type: Background | Advantage: None | Novelty: None | ConceptID: Bac1

11
The analysis of such pressure dependent reactions or the extrapolation of restricted experimental data in the fall-off range towards limiting low and high pressure values k0 and k∞ is mostly done on the basis of well known analytical expressions from statistical rate theory.3,4

Type: Background | Advantage: None | Novelty: None | ConceptID: Bac1

12
In this approach, CET information is considered only in the form of a single collision efficiency parameter βc.

Type: Background | Advantage: None | Novelty: None | ConceptID: Bac1

13
An approximate analytical expression5 is mostly used to relate βc to 〈ΔE〉, the average amount of energy transferred per collision.

Type: Background | Advantage: None | Novelty: None | ConceptID: Bac1

14
A more general and better alternative consists in a numerical solution of the energy specific master equation of the reaction system, which needs as input data specific rate constants k(E) for the reactive steps and correspondingly kcoll(E) for inelastic collisions, usually quoted as 〈ΔE(E)〉 = kcoll(E)Z–1, with Z being the gas kinetic collision number.

Type: Background | Advantage: None | Novelty: None | ConceptID: Bac2

15
At chemically significant energies such CET data usually correspond to very large amounts of vibrational energy and densities of states.

Type: Background | Advantage: None | Novelty: None | ConceptID: Bac2

16
Analysis of pressure dependent data on reaction rates or yields from measurements in the fall-off range or under chemical activation conditions was the first method to derive 〈ΔE〉 values under such conditions and is still used today.

Type: Method | Advantage: None | Novelty: Old | ConceptID: Met3

17
However, the inherent disadvantages of this approach are well known: Due to the relation between βc and 〈ΔE〉, measurements of βc require a much higher precision to achieve the same level of accuracy as a corresponding direct determination of 〈ΔE〉.

Type: Method | Advantage: No | Novelty: Old | ConceptID: Met3

18
But more important, such data evaluation unavoidably includes the absolute value for a reaction rate in the measured product expression with an unknown error limit or a tacit assumption of quasi-infinite theoretical accuracy.

Type: Method | Advantage: No | Novelty: Old | ConceptID: Met3

19
The possibilities to clearly assign finer observed effects to either the energy transfer or the reactive properties are severely limited.

Type: Method | Advantage: No | Novelty: Old | ConceptID: Met3

20
In principle this dilemma was overcome with the advent of direct experiments to measure 〈ΔE〉 at chemically relevant energies independent from any knowledge on chemical reaction rates.

Type: Method | Advantage: None | Novelty: Old | ConceptID: Met4

21
Time-resolved infrared fluorescence (IRF)6 and “hot” ultraviolet absorption (UVA)7 became the most important techniques.

Type: Method | Advantage: None | Novelty: Old | ConceptID: Met4

22
However, the agreement between various measurements turned out to be much less than might be expected.

Type: Method | Advantage: No | Novelty: Old | ConceptID: Met4

23
This is very obvious for some frequently studied molecules, especially toluene and azulene, for which direct CET measurements with various techniques or even with the same have led to sometimes astonishing differences, see e.g. Figs. 1 and 2 and Fig. 22 in ref. 8 or Fig. 20 in .ref. 9

Type: Method | Advantage: No | Novelty: Old | ConceptID: Met4

24
As all these methods directly rely on the quality of a calibration curve for data evaluation, arguments on e.g. deficiencies in the quality of these reference curves have been exchanged mutually but the issue could not be settled.

Type: Method | Advantage: No | Novelty: Old | ConceptID: Met4

25
The considerable spread among reported “direct” 〈ΔE〉 values has led to a sort of common belief among users of 〈ΔE〉 data for chemical kinetics applications that the field of large molecule energy transfer at higher energies is still not really settled.

Type: Method | Advantage: No | Novelty: Old | ConceptID: Met4

26
Typically then, averages of the available first moment data are taken in the hope to arrive at what is believed to be the best value.

Type: Method | Advantage: None | Novelty: Old | ConceptID: Met4

27
And as a consequence 〈ΔE〉 values inferred from analysis of e.g. pressure dependent rate constants in the fall-off range are very generously called “reasonable”.

Type: Method | Advantage: No | Novelty: Old | ConceptID: Met4

28
Thus the impact hoped from directly measured 〈ΔE〉 values has not yet been achieved, namely to define much closer boundaries for the CET part in pressure dependent chemical rate data, with improved resulting possibilities to identify more detail in disagreement between chemical reaction rate models and reality.

Type: Motivation | Advantage: None | Novelty: None | ConceptID: Mot1

29
With the results from a second generation method, the kinetically controlled selective ionization (KCSI) this situation has changed.

Type: Method | Advantage: None | Novelty: Old | ConceptID: Met5

30
As the only technique so far available, KCSI can determine complete distributions of CET transition probabilities P(E′,E) even at quasi-continuous densities of states.

Type: Method | Advantage: Yes | Novelty: Old | ConceptID: Met5

31
This is done by monitoring the shape of the time dependent population distributions of highly vibrationally excited molecules, as they relax in the electronic ground state from a high initial energy.10

Type: Method | Advantage: None | Novelty: Old | ConceptID: Met5

32
The resulting 〈ΔE〉 data are of unprecedented accuracy, typically on the order of 2–7%.

Type: Method | Advantage: Yes | Novelty: Old | ConceptID: Met5

33
More important, KCSI data are widely and in favourable cases – like that of azulene treated in this paper – completely independent of external parameters of calibration data.

Type: Method | Advantage: Yes | Novelty: Old | ConceptID: Met5

34
Thus they provide a benchmark for reevaluation of earlier direct data.

Type: Method | Advantage: Yes | Novelty: Old | ConceptID: Met5

35
Already in the KCSI paper of toluene relaxation9 one example was shown, in which drastic discrepancies between an early UVA set of 〈ΔE〉 and new KCSI data was completely removed with a reconstruction of the experimental curve from time dependent KCSI population distributions and a very minor change in the most uncertain part of the calibration curve.

Type: Method | Advantage: None | Novelty: Old | ConceptID: Met5

36
In this paper we apply a similar detailed analysis to various examples of the deactivation of highly vibrationally excited azulene, which has become a benchmark system for investigations of CET.

Type: Goal | Advantage: None | Novelty: None | ConceptID: Goa1

37
Time-resolved ultraviolet absorption has been applied in several studies.

Type: Background | Advantage: None | Novelty: None | ConceptID: Bac3

38
The first experiments reported an almost energy independent 〈ΔE〉 for all bath gases, with the exception of excess energies below roughly 10 000 cm–1.7

Type: Background | Advantage: None | Novelty: None | ConceptID: Bac3

39
Subsequently these studies were extended to other excitation energies.11,12

Type: Background | Advantage: None | Novelty: None | ConceptID: Bac3

40
In contrast to the early study, an almost linear energy dependence of the first moment of energy transfer was found, though a leveling-off at the highest energies (about 50 000 cm–1) could not be ruled out.

Type: Background | Advantage: None | Novelty: None | ConceptID: Bac3

41
The most recent measurements, carried out at temperatures ≥373 K for excitation energies <20 000 cm–1, show the highest signal-to-noise ratio obtained so far in an azulene UVA experiment.13

Type: Background | Advantage: None | Novelty: None | ConceptID: Bac3

42
An almost linear energy dependence of 〈ΔE〉 was found over the whole energy range for all colliders, sometimes with substantial deviations from the earlier UVA data.

Type: Background | Advantage: None | Novelty: None | ConceptID: Bac3

43
In addition, a variety of measurements employing time-resolved IR fluorescence exists.6,14–16

Type: Background | Advantage: None | Novelty: None | ConceptID: Bac4

44
These data were later reanalyzed with an adjusted calibration curve.

Type: Background | Advantage: None | Novelty: None | ConceptID: Bac4

45
This resulted in a substantial change of the original 〈ΔE〉 values by 30–50%, depending on the bath gas.17

Type: Background | Advantage: None | Novelty: None | ConceptID: Bac4

46
We show that the deviations of all measurements in Figs. 1 and 2 from the KCSI curves can be removed within very narrow error limits, with the origins of the apparent deviations identified in agreement with experimental parameters originally given or very reasonable estimates of them.

Type: Result | Advantage: None | Novelty: None | ConceptID: Res5

47
It will become clear that the sometimes puzzlingly large differences can be traced back to two main effects: (1) contamination of the available data sets by – at first sight – small amounts of self-collisions and (2) uncertainties of the calibration curves needed for converting the raw UV absorption and IR fluorescence data.

Type: Conclusion | Advantage: None | Novelty: None | ConceptID: Con2

48
By proper accounting for these two effects, we can show that all older measurements for azulene and toluene are in fact in complete agreement with the KCSI benchmark data.

Type: Conclusion | Advantage: None | Novelty: None | ConceptID: Con2

49
Disagreements reported on CET for related systems are also highly likely due to self-collision and calibration issues.

Type: Conclusion | Advantage: None | Novelty: None | ConceptID: Con3

Evaluation of available data and their simulation

50
The primary quantity obtained from UVA and IRF experiments is 〈〈ΔE(〈E〉)〉〉, which corresponds to a 〈ΔE(E)〉 “bulk averaged” over the normalized vibrational distribution g(E) in the ground electronic state with average energy 〈E〉: 〈〈ΔE(〈E〉)〉〉 = ∫∞0g〈E〉(E′)〈ΔE(E′)〉dE′

Type: Model | Advantage: None | Novelty: None | ConceptID: Mod1

51
Differences between microcanonical and the respective bulk averaged values of the first moments are however small, as long as one is sufficiently far away from thermal equilibrium.9

Type: Model | Advantage: None | Novelty: None | ConceptID: Mod1

52
In the discussion of the first moment results, we will therefore only apply the notation 〈ΔE〉 for both quantities.

Type: Model | Advantage: None | Novelty: None | ConceptID: Mod1

53
Comparisons for the bath gases argon and CO2 can be found in Figs. 1 and 2.

Type: Observation | Advantage: None | Novelty: None | ConceptID: Obs1

54
A similar plot for the helium case was already shown in Fig. 22 of ref. 8, which also contains the Lennard-Jones collision numbers required for converting the CET rate constants into the respective moments.

Type: Result | Advantage: None | Novelty: None | ConceptID: Res6

UVA experiments

55
The first CET experiments on azulene employing the UV absorption technique were carried out by Hippler et al.7

Type: Background | Advantage: None | Novelty: None | ConceptID: Bac5

56
An almost energy independent 〈ΔE〉 was found for all bath gases, except for energies smaller than roughly 10 000 cm–1, where eventually 〈〈ΔE〉〉 = 0 has to be fulfilled in thermal equilibrium (〈E〉thermal = 979 cm–1 for azulene).

Type: Background | Advantage: None | Novelty: None | ConceptID: Bac5

57
Later, these experiments were extended to low11 and high excitation energies.12

Type: Background | Advantage: None | Novelty: None | ConceptID: Bac5

58
It is immediately clear from Figs. 1 and 2 and also Fig. 22 of ref. 8 that the older UVA data lie considerably higher than the KCSI values over wide energy ranges.

Type: Result | Advantage: None | Novelty: None | ConceptID: Res7

59
Very recently, new high quality UVA results have been obtained for temperatures ≥373 K and excitation energies <20 000 cm–1.13

Type: Background | Advantage: None | Novelty: None | ConceptID: Bac6

60
The UVA decay curves showing exceptionally low noise were almost monoexponential, which results in a linear energy dependence of 〈ΔE〉 over the whole energy range, due to the fact that the calibration curve in this energy region is practically linear (Fig. 3).18

Type: Background | Advantage: None | Novelty: None | ConceptID: Bac6

61
For a direct comparison with the KCSI results of ref. 8 we calculated time-dependent UVA profiles from the KCSI data via: ε(t) = ∫∞0g(E,t)ε(〈E〉)dEi.e. a convolution of the g(E,t) distributions from a KCSI master equation analysis with a given UVA calibration curve ε(〈E〉) was used to reconstruct ε(t).

Type: Method | Advantage: None | Novelty: New | ConceptID: Met6

62
Such profiles can be directly confronted with the experimental UVA traces.

Type: Method | Advantage: None | Novelty: New | ConceptID: Met6

63
All UVA measurements for azulene rely on the empirical calibration data shown in Fig. 3.

Type: Method | Advantage: None | Novelty: New | ConceptID: Met6

64
The relationship between the absorption coefficient ε and the average internal energy 〈E〉 of the azulene molecules was established from thermal experiments in heated gas cells (open circles) or shocktubes (filled circles) and measurements after laser excitation (open squares).

Type: Observation | Advantage: None | Novelty: None | ConceptID: Obs2

65
For energies below 25 000 cm–1 the calibration curve is practically linear and can be well represented by the solid line in Fig. 3 using the expression:13

Type: Result | Advantage: None | Novelty: None | ConceptID: Res8

66
At higher energies, the calibration curve levels off and there is experimental evidence that it stays constant at least up to roughly 50 000 cm–1.12

Type: Result | Advantage: None | Novelty: None | ConceptID: Res9

67
To describe this behavior we modified the calibration curve given in ref. 19 by a factor of 2.2 to obtain agreement with the experimental points:

Type: Method | Advantage: None | Novelty: New | ConceptID: Met7

68
Above 31 790 cm–1, a constant value of ε = 17 650 l mol–1 cm–1 was assumed, so that the experimentally observed “saturation behavior” of the absorption coefficient is correctly described (dashed line in Fig. 3).

Type: Method | Advantage: None | Novelty: New | ConceptID: Met7

69
Fig. 4 shows a comparison of the most recent UVA data13 for the colliders helium, argon and CO2 with our master equation fits employing the P(E′,E) data from Table IV of .ref. 8

Type: Observation | Advantage: None | Novelty: None | ConceptID: Obs3

70
Note that the UVA data were recorded at slightly elevated temperatures (T = 373 K) so our fits had to be rescaled by the ratio of the respective KCSI and UVA Lennard-Jones collision numbers.

Type: Method | Advantage: None | Novelty: New | ConceptID: Met8

71
The overall fit to the UVA traces is very good.

Type: Result | Advantage: None | Novelty: None | ConceptID: Res10

72
Despite this, there are still visible deviations in the first moment plots, see, e.g., Fig. 2 (and especially also Fig. 22 of .ref. 8)

Type: Result | Advantage: None | Novelty: None | ConceptID: Res10

73
In Fig. 4(a), the decay of the helium UVA signal is slightly faster than in the KCSI fit.

Type: Observation | Advantage: None | Novelty: None | ConceptID: Obs4

74
In Fig. 4(c), the very slight differences in the decay of the experimental and simulated UVA signals for CO2 result in the different slopes of the energy dependence of 〈ΔE〉 in Fig. 2.

Type: Result | Advantage: None | Novelty: None | ConceptID: Res11

75
These deviations might be either due to a slight temperature dependence of the energy transfer or remaining uncertainties in the UVA calibration curve, as demonstrated in our earlier study.9

Type: Conclusion | Advantage: None | Novelty: None | ConceptID: Con4

76
The minor differences for helium can probably be explained by a small contamination of efficient azulene self-collisions in the UVA experiments.

Type: Conclusion | Advantage: None | Novelty: None | ConceptID: Con5

77
Note that the experimental UVA (and IRF) traces are most susceptible to self-collision effects in the case of inefficient colliders.

Type: Conclusion | Advantage: None | Novelty: None | ConceptID: Con5

78
At this point we would like to comment on the clear deviations of 〈ΔE〉 found in older UVA measurements.

Type: Background | Advantage: None | Novelty: None | ConceptID: Bac7

79
The argon data of Hippler and Troe in Fig. 1 exceed the KCSI values considerably, as it is also found for other colliders.

Type: Observation | Advantage: None | Novelty: None | ConceptID: Obs5

80
The even larger discrepancy for helium as a collider is documented as Fig. 22 in .ref. 8

Type: Observation | Advantage: None | Novelty: None | ConceptID: Obs6

81
In Fig. 5(a) the UVA trace for azulene* + argon is shown,11 which decays clearly faster than the simulated fit (dashed curve) using the KCSI parameters from Table IV of ref. 8 employing eqn. (3) as calibration curve.13

Type: Observation | Advantage: None | Novelty: None | ConceptID: Obs7

82
As in the helium case,8 the argon data seem to be contaminated by a visible amount of azulene self-collisions.

Type: Result | Advantage: None | Novelty: None | ConceptID: Res12

83
Such a contribution of collisions with a second bath gas partner in the mixture can be modeled by adding a second term to our general P(E′,E) expression with a parametric exponent in the argument [eqn. (11) in ref. 9]:

Type: Model | Advantage: None | Novelty: None | ConceptID: Mod2

84
For the parameters C0, C1 and Y1 we use the optimized values from the KCSI analysis.8

Type: Model | Advantage: None | Novelty: None | ConceptID: Mod2

85
The experimental conditions given in ref. 11 [P(azulene)/Ptotal = 0.6%] suggest a value x = 6 × 10–3 as a reasonable estimate for the contribution of efficient azulene self-collisions.

Type: Result | Advantage: None | Novelty: None | ConceptID: Res13

86
From the 〈ΔE〉 data in ref. 17 one can extrapolate that the behavior of azulene as collision partner should be very close to that of CHT.

Type: Result | Advantage: None | Novelty: None | ConceptID: Res13

87
We therefore approximated the azulene parameters B0, B1 and Y2 in the small second term of eqn. (5) by using the CHT values from Table IV of .ref. 8

Type: Model | Advantage: None | Novelty: None | ConceptID: Mod3

88
The resulting simulation in Fig. 5(a) now shows good agreement with the original experimental trace.

Type: Result | Advantage: None | Novelty: None | ConceptID: Res14

89
Thus, it is strongly suggested that the UVA trace is contaminated by azulene self-collisions, which have not been considered in the extraction of the UVA 〈ΔE〉 values in .ref. 11

Type: Conclusion | Advantage: None | Novelty: None | ConceptID: Con6

90
Fig. 5(b) shows another set of UVA measurements for azulene deactivation by the collider argon from Damm et al.12

Type: Observation | Advantage: None | Novelty: None | ConceptID: Obs8

91
Two sets of data are available for excitation at 193 and 248 nm.

Type: Observation | Advantage: None | Novelty: None | ConceptID: Obs8

92
The 248 nm curve was shifted so that the decay of both curves coincide.

Type: Method | Advantage: None | Novelty: New | ConceptID: Met9

93
Such a behavior is expected, because the UVA calibration curve appears to be essentially flat for energies above 30 000 cm–1 (Fig. 3).

Type: Result | Advantage: None | Novelty: None | ConceptID: Res15

94
Therefore the signal at 193 nm excitation shows an additional constant portion at early times before showing the same decay as the 248 nm signal.

Type: Result | Advantage: None | Novelty: None | ConceptID: Res15

95
Again we tried to fit the UVA traces using our KCSI parameters, but this time employing eqn. (4) (with the aforementioned constant extension at high energies), which should be valid up to excess energies around 50 000 cm–1.

Type: Model | Advantage: None | Novelty: None | ConceptID: Mod4

96
The results are also included in Fig. 5(b) (dashed and dotted curves).

Type: Observation | Advantage: None | Novelty: None | ConceptID: Obs9

97
While the early part of the traces are very well reproduced, there are deviations at longer times.

Type: Result | Advantage: None | Novelty: None | ConceptID: Res16

98
The UVA traces decay faster.

Type: Observation | Advantage: None | Novelty: None | ConceptID: Obs10

99
This is consistent with the slightly higher –〈ΔE〉 at lower energies already seen in Fig. 1.

Type: Result | Advantage: None | Novelty: None | ConceptID: Res17

100
Again, an influence of self-collisions is very likely.

Type: Conclusion | Advantage: None | Novelty: None | ConceptID: Con7

101
In these UVA measurements the self-collision contributions were smaller [P(azulene)/Ptotal = 0.12%].

Type: Result | Advantage: None | Novelty: None | ConceptID: Res18

102
Nevertheless, including a second term in our P(E′,E) to account for this (x = 1.2 × 10–3 and CHT parameters for azulene as above) leads to a simulation with better agreement (solid line).

Type: Result | Advantage: None | Novelty: None | ConceptID: Res19

103
One can therefore conclude that the existing body of UVA data is in full agreement with the KCSI results, and the differences observed are due to self-collisions in the older measurements and possibly remaining uncertainties in the UVA calibration curve.

Type: Conclusion | Advantage: None | Novelty: None | ConceptID: Con8

104
The issue of calibration curves was already discussed at length in our earlier publication for toluene, where the seemingly very large discrepancies between the UVA and KCSI results could be quantitatively traced back to small uncertainties in the high energy portion of the UVA calibration curve9.

Type: Background | Advantage: None | Novelty: None | ConceptID: Bac8

IRF experiments

105
An extended set of time-resolved IR fluorescence measurements for azulene was obtained by Barker and co-workers.6,14

Type: Background | Advantage: None | Novelty: None | ConceptID: Bac9

106
These data were later reanalyzed by the same group employing an “improved calibration curve”.

Type: Background | Advantage: None | Novelty: None | ConceptID: Bac9

107
Their reevaluation changed the original 〈ΔE〉 by up to 50% and yielded values at the energies 〈E〉 = 13 943 and 24 023 cm–1.17

Type: Background | Advantage: None | Novelty: None | ConceptID: Bac9

108
The results for argon and CO2 of refs. 14 and 17 are included in Figs. 1 and 2 as dotted curves, including a linear interpolation for the reevaluated curve.

Type: Observation | Advantage: None | Novelty: None | ConceptID: Obs11

109
Similar to the KCSI results, the IRF measurements predict a linear energy dependence of 〈ΔE〉.

Type: Result | Advantage: None | Novelty: None | ConceptID: Res20

110
However, the IRF –〈ΔE〉 curves are much higher than the corresponding one from KCSI.

Type: Result | Advantage: None | Novelty: None | ConceptID: Res20

111
To analyze these differences, we again take the “direct” approach by comparing our master equation results with the IRF trace for azulene + argon given in .ref. 14

Type: Method | Advantage: None | Novelty: New | ConceptID: Met10

112
This is done in Fig. 6.

Type: Method | Advantage: None | Novelty: New | ConceptID: Met10

113
Experimental calibration points and a calculated calibration curve relating the IRF emission intensity and the energy E of the azulene molecules were given in refs. 17 and 20.

Type: Background | Advantage: None | Novelty: None | ConceptID: Bac10

114
For our simulations we fitted the calibration curve by a fifth order polynomial:

Type: Model | Advantage: None | Novelty: None | ConceptID: Mod5

115
The time-dependent IRF simulations employing KCSI g(E,t) can then be obtained via: I(t) = ∫∞0g(E,t)I(E)dE

Type: Model | Advantage: None | Novelty: None | ConceptID: Mod5

116
Note that in the IRF experiments the fraction of azulene molecules was roughly 10%, and therefore much higher than in the UVA measurements discussed above.

Type: Method | Advantage: None | Novelty: New | ConceptID: Met11

117
For that reason, measurements at different argon partial pressures together with a “linear mixing rule” approach had to be applied in ref. 14 to extract values for pure argon conditions.

Type: Method | Advantage: None | Novelty: New | ConceptID: Met11

118
Not surprisingly, our KCSI master equation fit in Fig. 6 using eqn. (5) and the argon parameters from ref. 8 decays much slower (dashed line).

Type: Observation | Advantage: None | Novelty: None | ConceptID: Obs12

119
However – like for the UVA data in the preceeding section – perfect agreement is obtained when taking contributions of azulene-azulene collisions into account (solid line).

Type: Result | Advantage: None | Novelty: None | ConceptID: Res21

120
One can only speculate, why we obtain agreement between the IRF signal and our master equation simulation in Fig. 6, when at the same time in Fig. 1 the 〈ΔE〉 curves taken from refs. 14 and 17 show strong deviations.

Type: Result | Advantage: None | Novelty: None | ConceptID: Res22

121
One possible explanation might be that the “linear mixing rule” procedure employed in ref. 14 for different azulene/argon mixing ratios introduces considerable uncertainties when extrapolating to pure argon conditions, greatly affecting the accuracy of the 〈ΔE〉 curves.

Type: Conclusion | Advantage: None | Novelty: None | ConceptID: Con9

Conclusions

122
We have demonstrated that the body of considerably varying data on 〈ΔE〉 in azulene reported in the literature is in an astonishing complete agreement with the more recent “self-calibrating” KCSI data8 if reanalyzed properly.

Type: Result | Advantage: None | Novelty: None | ConceptID: Res23

123
Analogous findings have been reported earlier for the CET of toluene.9

Type: Background | Advantage: None | Novelty: None | ConceptID: Bac11

124
Together this indicates that a recommended preference of the precision 〈ΔE〉 data from KCSI marks a decisive step in defining strict, low error boundary conditions for the application in chemical reaction kinetics.

Type: Conclusion | Advantage: None | Novelty: None | ConceptID: Con10

125
Deviations and spread in reported 〈ΔE〉 values from UVA and IRF reported in earlier studies (see Figs. 1 and 2 and ref. 8) are most probably due to the following two systematic errors in the UVA and IRF experiments, namely (1) contributions of efficient azulene self-collisions which were not correctly accounted for and (2) unavoidable uncertainties in the UVA and IRF calibration curves.

Type: Conclusion | Advantage: None | Novelty: None | ConceptID: Con11

126
The second point can have drastic effects, as we have already shown in detail for toluene in .ref. 9

Type: Conclusion | Advantage: None | Novelty: None | ConceptID: Con11

127
We believe that similar deviations between the results of different CET methods for other systems are mainly due to the same two effects.

Type: Conclusion | Advantage: None | Novelty: None | ConceptID: Con11

128
The following advice for using large molecule CET data for kinetic applications can therefore be given: If available, KCSI data should be used, as they have the highest accuracy and can be – like in the azulene case presented here and in ref. 8 – independent of any external calibration.

Type: Conclusion | Advantage: None | Novelty: None | ConceptID: Con12

129
Simply taking an average of several available measurements from different sources cannot be recommended in the light of the above discussion.

Type: Conclusion | Advantage: None | Novelty: None | ConceptID: Con12

130
Experiments using high partial pressures of the parent molecule should be checked for the contribution of self-collisions, and corrected accordingly.

Type: Conclusion | Advantage: None | Novelty: None | ConceptID: Con12

131
If possible, one should also assess the accuracy of the calibration curves used, as this can introduce a substantial source of error.

Type: Conclusion | Advantage: None | Novelty: None | ConceptID: Con12