Swiss Light Source (SLS)

The apparatus described in section 2.2 at the Swiss Light Source is used to study the photoionization behavior and dissociation rates of energy selected ions for various thermodynamic calculations. Like at the ALS, data is collected over a range of photon energies above the ionization energy of the species in question. After ionization the electrons are accelerated towards the detector and will arrive at its center if they have no excess kinetic energy. On the other hand, if they have excess kinetic energy, they will reach the outer ring of the detector or blocked by the mask. This procedure will provide an image like the one shown in Figure 3-8 below.

Figure 3-8. A typical image of the detection of electrons from the PEPICO instrument. White corresponds to the highest count and blue is the lowest.

Using the i2_{PEPICO program v1.5.2,}25 _{an area defined as “circle” is used to count all of the coincidences}

that are within the center of the mask and correspond to the zero kinetic energy electrons. Next, an area is defined as “ring” will average the number of counts around the center to determine the average number of hot electrons that reach the detector. The subtraction of the ring counts from the center counts will provide the TPES as described in section 3.3. Figure 3-9 shows this process pictorially. With the use of delay lines (see section 2.2.4.2), it is possible to relate each electron count to the complementary fragmentation incident. This will supply a time-of-flight mass spectrum (TOF-MS) as shown in Figure 3-10.

48

Figure 3-9. Images showing the process of subtracting hot electrons from the zero kinetic energy electrons to provide the TPES.

Figure 3-10. A time-of-flight mass spectrum obtained after subtracting the hot electrons from the zero kinetic energy electrons. The x-axis it the time-of-flight (μs) and the y-axis is counts (a.u.)

Once a TOF-MS is obtained and the time-of-flights of all ions and fragments are known, the TOF- MS can be integrated at each photon energy to obtain the counts for all ions and fragments. Then, the fractional abundance of each ion or fragment can be plotted against the photon energy. This in known as a breakdown diagram (Figure 3-11).

49

Figure 3-11. An experimentally obtained breakdown diagram showing the change in relative abundance of the parent ion (red circles) with respect to the first daughter ion (green circles).

A set of vibrational frequencies for the cationic and neutral parent, and transition states to products should be obtained through ab initio or density functional methods. In addition, the rotational constants of the neutral parent must also be found to calculate the internal energy distribution using the Boltzmann formula below.26 _{In this equation ρ(E) is the classical density of states function for rotational motions at an energy}

E, kB is the Boltzmann constant, and T is the temperature. 𝑃(𝐸) = 𝜌(𝐸)𝑒−𝐸/𝑘𝐵𝑇

∫ 𝜌(𝐸)𝑒₀∞ −𝐸/𝑘𝐵𝑇 (3.15)

This information can then be used in the MiniPEPICO program v189f26 _{to fit the experimental data using}

the RRKM theory describe in section 3.6.

In the cases with a “slow” first dissociation (rates between 103_–107 _s-1_{) an asymmetric peak will be}

observed in the TOF-MS. This is caused by only a limited percentage of the ions having enough excess energy to dissociate immediately. When this happens, the asymmetric peak must also be modeled as it contains rate information. This process is also performed in the MiniPEPICO program and a successful fit

50

is shown in Figure 3-12.26 _{The rest of the dissociations will happen at a slower rate due to the loss of}

translational momentum and the broadening of the daughter ions internal energy distribution (Figure 3-13) so the TOF peaks do not need to be fit.26

Figure 3-12. A successful modeling of a TOF distribution of a daughter ion to obtain the dissociation rate information.26

Figure 3-13. Experimentally determined internal energy distributions of a parent ion (P(C2H5)3+ compared

to the broadening of the daughter cation (HP(C2H5)2+) and the neutral daughter ion (C2H4 + translational

51

Once all dissociations have been successfully modeled, the curve should appear similar to Figure 3-14.26 _{With this information it is possible to extrapolate the 0 K appearance energies of the ions. The 0 K}

appearance energy (AE) of the first dissociation can easily be found as the photon energy where all of the parent ions dissociate. The first example is a fast dissociation (rates above 107 _s-1_),26 _{as shown in Figure 3-}

11. In this case, the 0 K AE is found when the ratio of parent ions to daughter ions reaches zero. The ratio can be found through equation 3.16. Here, Pi is the normalized internal energy at a specific photon energy

and E0 – IE is the difference between the photon energy that the parent ion signal vanishes (E0) and the

ionization energy of the neutral parent molecule (IE).

𝐵𝐷(ℎ𝜈) = ∫₀𝐸0−𝐼𝐸𝑃𝑖(𝑒, ℎ𝜈)d𝐸 (3.16)

In Figure 3-11, this occurs at 10.37 eV, which will be shown in chapter 6. Appearance energies for ions that form through a slow dissociation (rates between 103 _{and 10}7 _s-1₎26 _{can be found through a similar}

method, but with an additional term to account for ions that do not dissociate within the timescale of the experiment and have an internal energy exceeding the dissociation barrier (i.e. the ions are detected before they dissociate). This additional term is shown in equation 3.17 where τmax is the probability that the ion

does not dissociate before detection and k(E) is the internal energy-dependent rate constant.26

𝐵𝐷(ℎ𝜈) = ∫₀𝐸0−𝐼𝐸𝑃𝑖(𝑒, ℎ𝜈)d𝐸+ ∫_𝐸+∞_0−𝐼𝐸𝑃𝑖(𝑒, ℎ𝜈) ∙ exp (−𝑘(𝐸) ∙ 𝜏max)d𝐸 (3.17)

For competing (parallel) dissociations of species i compared to all other species j, the 0 K appearance energy of i can be calculated using equation 3.18. The term 𝑘_𝑖(𝐸) ∑ 𝑘⁄ _{𝑗 𝑗}(𝐸) is the branching ratio at a specific ion internal energy. 𝐵𝐷𝑖(ℎ𝜈) = ∫ 𝑃𝑖(𝑒, ℎ𝜈) ∙_{∑ 𝑘}𝑘𝑖(𝐸) 𝑗(𝐸) 𝑗 (1 − exp(− ∑ 𝑘𝑗 𝑗(𝐸) ∙ 𝜏max)) d𝐸 +∞ 𝐸0−𝐼𝐸 (3.18)

The MiniPEPICO program contains a downhill simplex algorithm to fit these values, or they can be manually adjusted to obtain the best fit.26 _{Using these appearance energies and ionization energies it is}

possible to obtain very precise measurements of bond dissociation energies.26 _{Also, with the breakdown}

52

s-1_.26 _{Rates faster than this could not be observed in our experiments and slower rates cannot be discerned}

from competing processes, such as radiative decay. Therefore, they will not be discussed.

Figure 3-14. A modeled breakdown diagram that is used to extrapolate 0 K appearance energies, bond dissociation energies, and dissociation rates.26

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3.8 References

1. Wardle, B., Principles and Applications of Photochemistry. Wiley: Manchester, UK, 2009. 2. Foresman, J. B.; Frisch, A., Exploring Chemistry with Electronic Strucutre Methods. Gaussian, Inc: Pittsburgh, PA, 1993.

3. Atkins, P.; Paula, J. D., Physical Chemistry. 6 ed.; W.H. Freeman: New York, 2006; p 1139. 4. Sztáray, B.; Baer, T., Suppression of Hot Electrons in Threshold Photoelectron Photoion Coincidence Spectroscopy Using Velocity Focusing Optics. Rev. Sci. Instrum. 2003,74 (8), 3763.

5. Taatjes, C. A.; Hansen, N.; Osborn, D. L.; Kohse-Höinghaus, K., "Imaging" Combustion Chemistry Via Multiplexed Synchrotron-Photoionization Mass Spectrometry. Phys. Chem. Chem. Phys. 2008,10, 20- 34.

6. Yang, B.; Wang, J.; Cool, T. A.; Hansen, N.; Skeen, S.; Osborn, D. L., Absolute Photoionization Cross-Sections of Some Combustion Intermediates. Int. J. Mass Spectrom. 2011.

7. Wang, J.; Yang, B.; Cool, T. A.; Hansen, N.; Kasper, T., Near-Threshold Absolute Photoionization Cross-Sections of Some Reaction Intermediates in Combustion. Int. J. Mass Spectrom. 2008,269 (3), 210- 220.

8. Savee, J. D.; Soorkia, S.; Welz, O.; Selby, T. M.; Taatjes, C. A.; Osborn, D. L., Absolute Photoionization Cross-Section of the Propargyl Radical. J. Chem. Phys. 2012,136 (13), 134307.

9. Welz, O.; Zádor, J.; Savee, J. D.; Ng, M. Y.; Meloni, G.; Fernandes, R. X.; Sheps, L.; Simmons, B. A.; Lee, T. S.; Osborn, D. L.; Taatjes, C. A., Low-Temperature Combustion Chemistry of Biofuels: Pathways in the Initial Low-Temperature (550 K-750 K) Oxidation Chemistry of Isopentanol. Phys. Chem. Chem. Phys. 2012,14 (9), 3112-3127.

10. Osborn, D. L.; Zou, P.; Johnsen, H.; Hayden, C. C.; Taatjes, C. A.; Knyazev, V. D.; North, S. W.; Peterka, D. S.; Ahmed, M.; Leone, S. R., The Multiplexed Chemical Kinetic Photoionization Mass Spectrometer: A New Approach to Isomer-Resolved Chemical Kinetics. Rev. Sci. Instrum. 2008, 79, 104103.

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11. Frisch, M. J.; Trucks, G. W.; Schlegel, H. B.; Scuseria, G. E.; Robb, M. A.; Cheeseman, J. R.; Scalmani, G.; Barone, V.; Mennucci, B.; Petersson, G. A.; Nakatsuji, H.; Caricato, M.; Li, X.; Hratchian, H. P.; Izmaylov, A. F.; Bloino, J.; Zheng, G.; Sonnenberg, J. L.; Hada, M.; Ehara, M.; Toyota, K.; Fukuda, R.; Hasegawa, J.; Ishida, M.; Nakajima, T.; Honda, Y.; Kitao, O.; Nakai, H.; Vreven, T.; J. A. Montgomery, J.; Peralta, J. E.; Ogliaro, F.; Bearpark, M.; Heyd, J. J.; Brothers, E.; Kudin, K. N.; Staroverov, V. N.; Kobayashi, R.; Normand, J.; Raghavachari, K.; Rendell, A.; Burant, J. C.; Iyengar, S. S.; Tomasi, J.; Cossi, M.; Rega, N.; Millam, J. M.; Klene, M.; Knox, J. E.; Cross, J. B.; Bakken, V.; Adamo, C.; Jaramillo, J.; Gomperts, R.; Stratmann, R. E.; Yazyev, O.; Austin, A. J.; Cammi, R.; Pomelli, C.; Ochterski, J. W.; Martin, R. L.; Morokuma, K.; Zakrzewski, V. G.; Voth, G. A.; Salvador, P.; Dannenberg, J. J.; Dapprich, S.; Daniels, A. D.; Farkas, Ö.; Foresman, J. B.; Ortiz, J. V.; Cioslowski, J.; Fox, D. J. Gaussian 09, Revision A.1, Gaussian, Inc.: Wallingford, CT, 2009.

12. Dennington, R.; Keith, T.; Millam, J., Gaussview. 5 ed.; SemiChem Inc.: Shawnee Mission KS, 2009.

13. Becke, A. D., Density-Functional Thermochemistry. Iii. The Role of Exact Exchange. The Journal of Chemical Physics 1993,98 (7), 5648.

14. Becke, A. D., Density-Functional Thermochemistry. I. The Effect of the Exchange-Only Gradient Correction. The Journal of Chemical Physics 1992,96 (3), 2155.

15. Becke, A. D., Density-Functional Thermochemistry. Ii. The Effect of the Perdew–Wang Generalized-Gradient Correlation Correction. The Journal of Chemical Physics 1992,97 (12), 9173. 16. Lee, C.; Yang, W.; Parr, R. G., Development of the Colle-Salvetti Correlation-Energy Formula into a Functional of the Electron Density. Physical Review B 1988,37 (2), 785-789.

17. Becke, A. D., Density-Functional Exchange-Energy Approximation with Correct Asymptotic Behavior. Physical Review A 1988,38 (6), 3098-3100.

18. Krishnan, R.; Binkley, J. S.; Seeger, R.; Pople, J. A., Self-Consistent Molecular Orbital Methods. Xx. A Basis Set for Correlated Wave Functions. The Journal of Chemical Physics 1980,72 (1), 650.

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19. Montgomery, J. A.; Frisch, M. J.; Ochterski, J. W.; Petersson, G. A., A Complete Basis Set Model Chemistry. Vi. Use of Density Functional Geometries and Frequencies. The Journal of Chemical Physics

1999,110 (6), 2822.

20. Montgomery, J. A.; Frisch, M. J.; Ochterski, J. W.; Petersson, G. A., A Complete Basis Set Model Chemistry. Vii. Use of the Minimum Population Localization Method. The Journal of Chemical Physics

2000,112 (15), 6532.

21. Baer, T.; Hase, W. L., Unimolecular Reaction Dynamics: Theory and Experiments. Oxford University Press: New York, NY, 1996.

22. Hinshelwood, C. N., On the Theory of Unimolecular Reactions. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 1926,113 (763), 230-233.

23. Paul Scherrer Institut - Swiss Light Source. http://www.psi.ch/sls/swiss-light-source.

24. Zádor, J.; Taatjes, C. A.; Fernandes, R. X., Kinetics of Elementary Reactions in Low-Temperature Autoignition Chemistry. Prog. Energy Combust. Sci. 2011,37 (4), 371-421.

25. Bodi, A.; Hemberger, P.; Gerber, T.; Sztaray, B., A New Double Imaging Velocity Focusing Coincidence Experiment: I2_{pepico. Rev. Sci. Instrum. 2012,83 (8), 083105.}

26. Sztáray, B.; Bodi, A.; Baer, T., Modeling Unimolecular Reactions in Photoelectron Photoion Coincidence Experiments. J. Mass Spectrom. 2010,45 (11), 1233-45.

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Chapter 4

Absolute Photoionization Cross-Sections of Selected Furanic and Lactonic Potential Biofuels 4.1 Abstract

Absolute photoionization cross sections of the molecules γ-butyrolactone (GBL), γ-valerolactone (GVL), α-angelicalactone (AAL), and γ-methylene-γ-butyrolactone (GMGB), including partial ionization cross sections for dissociative ionization, are measured. The experiments are carried out using photoionization mass spectrometry (PIMS) at the Advanced Light Source, and an orthogonal extraction time-of-flight spectrometer is used for mass analysis. Photoionization of furan, 2-methyl furan (2-MF), and 2,5-dimethyl furan (2,5-DMF) is also investigated to confirm the accuracy of our measurements, which show a good agreement of the absolute partial photoionization cross sections with literature values. CBS- QB3 calculations of adiabatic ionization energies (AIE) and appearance energies (AE) agree well with the experimental results.