邏輯演繹序列（LODES）串聯質譜法為近期開發的碳水化合物結構鑑定方法，為了準確辨識質譜觀察到的信號，研究各種醣類分子在邏輯演繹序列串聯質譜中的解離反應是必要的。本研究透過量子化學方法計算脫水反應和交叉環裂解等解離途徑，首先透過常見的己醛糖搜尋各種反應路徑，然後研究N-乙酰己糖胺與己糖胺的取代基效應，最後以果糖的研究了解己酮糖的解離反應。
在電子結構方法的選擇上，一開始的己醛糖研究主要以密度泛函B3LYP配合基底函數6-311+G(d,p )的層級進行計算，但是後來注意到B3LYP的計算低估了特定的反應屏障，而二階微擾法MP2的計算較符合實驗的觀察結果，最終會以MP2計算進行研究。在研究過程中，對於計算數據的解釋方法也從一開始的定性解釋法，逐步改進為定量的預測：從僅透過反應屏障判斷最可能的反應途徑，到考慮速率常數在熵效應與溫度的關係函數，最後建立了微觀動力學模型，直接將質譜信號與計算數據進行比較。在果糖解離反應的研究中，反應物和產物的相對濃度符合質譜信號，驗證了微觀動力學模型的正確性，並且透過該模型研究己醛糖，進一步討論僅考慮反應屏障得出的結論是否正確。
在計算結果中發現，如果所有解離反應都在線性結構下發生，則無法區分單醣的兩個變旋異構物（即α異構物和β異構物），因此N-乙酰己糖胺與己糖胺的變旋異構物是無法區分的，因為它們的解離反應在線性結構下進行。而己醛醣和己酮醣可以通過交叉環通道偏好的差異來區分，交叉環裂解通道很可能通過逆醛醇縮合進行，因此，C = O鍵的位置將決定不同的交叉環通道，所以己醛醣偏好荷質比 143交叉環通道，果糖（己酮醣）卻偏好荷質比 113交叉環裂解。

Only very recently, the logically derived sequence (LODES) tandem mass spectrometry (MSn) has been proposed as a potential routine method for the structural identification of carbohydrates. To better understand the molecular processes occurring during a LODES-MSn measurement and to rationalize the different signals shown by sugars, this work uses quantum chemical calculations to study the dissociation reactions, including dehydration and cross-ring reactions. Initial studies in this work focused on aldohexoses and then turned to N-acetylhexosamines (HexNAcs), hexosamines (HexNs), and finally fructose as an example of ketohexoses.
The initial calculations have been carried out at the B3LYP/6-311+G(d,p) level of theory. But later on, it was noticed that MP2/6-311+G(d,p) level calculations are needed to reproduce the experimental observations as B3LYP functional tends to underestimate specific reaction barriers. Aside from the quantum chemical methods, the approach to interpreting the calculated data has also improved during the studies. The earlier studies only compared the reaction barriers to determine the most likely reaction pathways. Then, to account for the entropy effect, the rate constants have been calculated as a function of temperature. Finally, to directly compare the MS signals with computed data, a micro-kinetic model has been set up to study fructose to calculate the relative concentrations of the reactant and product species. Asides from fructose, the micro-kinetic modeling approach has also been applied to the aldoses to check whether one needs to adjust the conclusions made by only considering the reaction barriers.
Regarding computational results, a monosaccharide's two anomers (i.e., α and β) cannot be distinguished if all of the dissociation reactions (i.e., dehydration and cross-ring cleavage) occur in linear forms. Accordingly, both anomers of HexNAcs and HexNs are undistinguishable since their dissociation reactions are likely to happen in linear structures. Aldohexose and ketohexose can be distinguished based on cross-ring channel preference differences. The cross-ring channel is likely to occur via the retro-aldol mechanism. Hence, the position of the C=O bond will determine the dominant cross-ring product. Accordingly, while aldohexose favors the m/z 143 cross-ring channel, fructose (a ketohexose) prefers the m/z 113 cross-ring cleavage.

Table of Contents
Abstract i
摘要 ii
Acknowledgments iii
1 Introduction 1
1.1 Structural identification of carbohydrates 1
1.2 CID-MS and the role of mechanistic study 3
1.3 Different conformations of monosaccharides 5
1.4 Computational approach: from qualitative to quantitative approach 8
2 Methodology 9
2.1 Quantum-mechanical methods: from B3LYP to MP2 level 9
2.2 Local minima and TS optimizations 11
2.3 Transition state search 12
2.3.1 Dehydration in cyclic and linear forms 13
2.3.2 Deamination in hexosamines 14
2.3.3 Cross-ring cleavage 15
2.4 Gas-phase acidity 18
2.5 Reaction barrier height calculation 18
2.6 Rate constant calculation 19
2.6.1 TST rate constant 19
2.6.2 CVT rate constant 20
2.6.3 Accumulated rate constants 24
2.7 Kinetic modeling 27
3 Dissociation reactions of sodiated aldohexoses and hexose derivatives 31
3.1 Introduction 31
3.2 Computational results 36
3.2.1 Differentiation between anomeric configurations in aldohexoses and aldohexose derivatives 37
3.2.2 The preference of the m/z 143 cross-ring over the m/z 113 channel 42
3.2.3 The reliability of B3LYP for different dissociation reactions 47
3.3 Conclusions 49
4 Kinetic modeling of Dissociation Reactions of Sodiated Fructose 49
4.1 Introduction 49
4.2 Computational methods 54
4.2.1 Geometry optimization 54
4.2.2 Kinetic modeling 54
4.3 Results and discussions 55
4.3.1 MP2 calculations on the dehydration and cross-ring cleavage mechanisms 55
4.3.2 Kinetic modeling of the CID process 61
4.4 Conclusions 66
5 Application of kinetic modeling to sodiated aldohexose 68
5.1 Introduction 68
5.2 Methodology 68
5.3 Results 70
5.3.1 MP2 reaction barriers of dissociation reactions in linear forms 70
5.3.2 Kinetic modeling 72
5.4 Conclusions 73
6 Assessment of assumptions in kinetic modeling 75
6.1 Harmonic approximation 75
6.2 The reversible and irreversible reactions 80
6.3 Missing some low-lying TSs 82
7 Conclusions 85
References 88
Appendix 92
A1 Basic concepts of different quantum chemical methods 92
A1.1 Density functional theory 92
A1.1.1 Hohenberg-Kohn Theorem 92
A1.1.2 Kohn-Sham Equations 93
A1.1.3 B3LYP exchange-correlation functional 94
A1.2 DFTB3 95
A1.3 MP2 96
A2. NBO charge on H atoms of different sugar systems 98
A3. Reaction barriers and geometry plots of dissociation reactions of sodiated monosaccharides 102
A4. Rate constants in kinetic modeling 111
A5. Relation between relative concentration, overall rate constant and time 140

References
1. S. M. Hecht (Eds.), Bioorganic chemistry, carbohydrates, Oxford University Press, Bhavnagar, Gujarat, India, 1999, 45–58.
2. G.J. Gerwig, Analysis of Carbohydrates by Nuclear Magnetic Resonance Spectroscopy. In The Art of Carbohydrate Analysis; Springer: Cham, Switzerland, 2021, 273–296.
3. J. A. Prescher and C. R. Bertozzi, Cell, 2006, 126, 851-854.
4. J. Duus, C. H. Gotfredsen and K. Bock, Chem Rev, 2000, 100, 4589-4614.
5. A. R. Neves, W. A. Pool, J. Kok, O. P. Kuipers, and H. Santos, FEMS Microbiology Reviews, 2005, 29, 531-554.
6. W. A. Bubb, Concepts in Magnetic Resonance, 2003, 19A, 1-19.
7. E. J. Cocinero, P. Carcabal, T. D. Vaden, J. P. Simons and B. G. Davis, Nature, 2011, 469, 76-79.
8. E. Wiercigroch, E. Szafraniec, K. Czamara, M. Z. Pacia, K. Majzner, K. Kochan, A. Kaczor, M. Baranska and K. Malek, Spectrochim Acta A Mol Biomol Spectrosc, 2017, 185, 317-335.
9. S. Soderholm, Y. H. Roos, N. Meinander and M. Hotokka, J Raman Spectrosc, 1999, 30, 1009-1018.
10. S. De, S. Dutta and B. Saha, Green Chem, 2011, 13, 2859-2868.
11. E. J. Cocinero, A. Lesarri, P. Ecija, A. Cimas, B. G. Davis, F. J. Basterretxea, J. A. Fernandez and F. Castano, J Am Chem Soc, 2013, 135, 2845-2852.
12. J. L. Alonso, M. A. Lozoya, I. Peña, J. C. López, C. Cabezas, S. Mata and S. Blanco, Chem. Sci., 2014, 5, 515-522.
13. X. Bohigas, R. Amigó and J. Tejada, Food Res. Int., 2008, 41, 104-109.
14. D. J. Harvey, Mass Spectrom Rev, 1999, 18, 349-450.
15. D. J. Harvey, Proteomics, 2001, 1, 311-328.
16. J. Hofmann, H. S. Hahm, P. H. Seeberger and K. Pagel, Nature, 2015, 526, 241.
17. Y. Huang and E. D. Dodds, Anal Chem, 2015, 87, 5664-5668.
18. G. Nagy and N. L. Pohl, Anal Chem, 2015, 87, 4566-4571.
19. J. Hofmann, A. Stuckmann, M. Crispin, D. J. Harvey, K. Pagel and W. B. Struwe, Anal Chem, 2017, 89, 2318-2325.
20. J. Hofmann and K. Pagel, Angew Chem Int Ed Engl, 2017, 56, 8342-8349.
21. C. J. Gray, B. Thomas, R. Upton, L. G. Migas, C. E. Eyers, P. E. Barran and S. L. Flitsch, Biochim Biophys Acta, 2016, 1860, 1688-1709.
22. D. J. Harvey, Mass Spectrom Rev, 2018, 37, 353-491.
23. H. C. Hsu, S. P. Huang, C. Y. Liew, S. T. Tsai and C. K. Ni, Anal Bioanal Chem, 2019, 411, 3241-3255.
24. S. P. Huang, H. C. Hsu, C. Y. Liew, S. T. Tsai and C. K. Ni, Glycoconj J, 2021, 38, 177-189.
25. S. T. Tsai, C. Y. Liew, C. Hsu, S. P. Huang, W. C. Weng, Y. H. Kuo and C. K. Ni, Chembiochem, 2019, 20, 2351-2359.
26. H. C. Hsu, C. Y. Liew, S. P. Huang, S. T. Tsai and C. K. Ni, J Am Soc Mass Spectrom, 2018, 29, 470-480.
27. H. C. Hsu, C. Y. Liew, S. P. Huang, S. T. Tsai and C. K. Ni, Sci Rep, 2018, 8, 5562.
28. C. Y. Liew, C. C. Yen, J. L. Chen, S. T. Tsai, S. Pawar, C. Y. Wu and C. K. Ni, Commun. Chem, 2021, 4.
29. S. T. Tsai and C. K. Ni, J. Chin. Chem. Soc, 2022, 69, 173-183.
30. C.-K. Ni, C. Y. Liew, H.-S. Luo, T.-Y. Yang, A.-T. Hung, B. J. A. Magoling and C. P.-K. Lai, ChemRxiv., 2022., doi: 10.26434/chemrxiv-2022-rhv80.
31. H. T. Huynh, H. T. Phan, P. J. Hsu, J. L. Chen, H. S. Nguan, S. T. Tsai, T. Roongcharoen, C. Y. Liew, C. K. Ni and J. L. Kuo, Phys Chem Chem Phys, 2018, 20, 19614-19624.
32. J. L. Chen, H. S. Nguan, P. J. Hsu, S. T. Tsai, C. Y. Liew, J. L. Kuo, W. P. Hu and C. K. Ni, Phys Chem Chem Phys, 2017, 19, 15454-15462.
33. C. C. Chiu, C. K. Lin and J. L. Kuo, Phys Chem Chem Phys, 2020, 22, 6928-6941.
34. C. C. Chiu, H. T. Huynh, S. T. Tsai, H. Y. Lin, P. J. Hsu, H. T. Phan, A. Karumanthra, H. Thompson, Y. C. Lee, J. L. Kuo and C. K. Ni, J Phys Chem A, 2019, 123, 6683-6700.
35. C. C. Chiu, S. T. Tsai, P. J. Hsu, H. T. Huynh, J. L. Chen, H. T. Phan, S. P. Huang, H. Y. Lin, J. L. Kuo and C. K. Ni, J Phys Chem A, 2019, 123, 3441-3453.
36. H. T. Huynh, S. T. Tsai, P. J. Hsu, A. Biswas, H. T. Phan, J. L. Kuo, C. K. Ni and C. C. Chiu, Phys Chem Chem Phys, 2022, 24, 20856-20866.
37. B. J. Bythell, M. T. Abutokaikah, A. R. Wagoner, S. Guan and J. M. Rabus, J Am Soc Mass Spectrom, 2017, 28, 688-703.
38. J. C. P. Schwarz, Chem. Soc., Chem. Commun. 1973, 14, 505.
39. H. Satoh and S. Manabe, Chem Soc Rev, 2013, 42, 4297-4309.
40. H. Eyring, Chem. Phys., 1935, 3, 107-115.
41. E. Wigner, Trans. Faraday Soc., 1938, 34, 29-41.
42. K. J. Laidler and M. C. King, J Phys Chem-Us, 1983, 87, 2657-2664.
43. D. G. Truhlar, B. C. Garrett and S. J. Klippenstein, J. Phys. Chem., 1996, 100, 12771-12800.
44. D. G. Truhlar and B. C. Garrett, Acc. Chem. Res., 1980, 13, 440-448.
45. A. D. Becke, Chem. Phys., 1993, 98, 1372-1377.
46. C. Lee, W. Yang and R. G. Parr, Phys Rev B Condens Matter, 1988, 37, 785-789.
47. S. H. Vosko, L. Wilk and M. Nusair, Can. J. Phys., 1980, 58, 1200-1211.
48. M. Marianski, A. Supady, T. Ingram, M. Schneider, and C. Baldauf, J. Chem. Theory Comput., 2016, 12, 12, 6157–6168.
49. R. Krishnan, J. S. Binkley, R. Seeger and J. A. Pople, J. Chem. Phys, 1980, 72, 650-654.
50. A. D. McLean and G. S. Chandler, J. Chem. Phys, 1980, 72, 5639-5648.
51. M. J. Frisch, J. A. Pople and J. S. Binkley, J. Chem. Phys, 1984, 80, 3265-3269.
52. C. Møller and M. S. Plesset, Phys. Rev., 1934, 46, 618-622.
53 J. A. Pople, M. Head-Gordon and K. Raghavachari, J. Chem. Phys., 1987, 87, 5968–5975
54 R. O. Ramabhadran and K. Raghavachari, J. Chem. Theory Comput. 2013, 9, 9, 3986– 3994.
55 D. E. Woon, T. H. Dunning J. Chem. Phys. 1993, 98, 1358.
56 R. A. Kendall; T. H. Dunning,; R. J. Harrison, J. Chem. Phys. 1992, 96, 6796
57 T. H. Dunning, J. Chem. Phys., 1989, 90, 1007
58. M. Gaus, Q. Cui and M. Elstner, J Chem Theory Comput, 2012, 7, 931-948.
59. M. Gaus, A. Goez, and M. Elstner, J Chem Theory Comput, 2013, 9, 338-354.
60. M. Kubillus, T. Kubar, M. Gaus, J. Rezac and M. Elstner, J Chem Theory Comput, 2015, 11, 332-342.
61. M. W. Schmidt, K. K. Baldridge, J. A. Boatz, S. T. Elbert, M. S. Gordon, J. H. Jensen, S. Koseki, N. Matsunaga, K. A. Nguyen, S. Su, T. L. Windus, M. Dupuis and J. A. Montgomery, J. Comput. Chem., 1993, 14, 1347-1363.
62. J. J. Stewart, J Mol Model, 2007, 13, 1173-1213.
63. M. J. Frisch, G.W. Trucks, H. B. Schlegel, G. E. Scuseria, M. A. Robb, J. R. Cheeseman, G. Scalmani, V. Barone, G. A. Petersson, H. Nakatsuji, X. Li, M. Caricato, A. Marenich, J. Bloino, B. G. Janesko, R. Gomperts, B. Mennucci, H. P. Hratchian, J. V. Ortiz, A. F. Izmaylov, J. L. Sonnenberg, D. Williams-Young, F. Ding, F. Lipparini, F. Egidi, J. Goings, B. Peng, A. Petrone, T. Henderson, D. Ranasinghe, V. G. Zakrzewski, J. Gao, N. Rega, G. Zheng, W. Liang, M. Hada, M. Ehara, K. Toyota, R. Fukuda, J. Hasegawa, M. Ishida, T. Nakajima, Y. Honda, O. Kitao, H. Nakai, T. Vreven, K. Throssell, J. A. Montgomery, Jr., J. E. Peralta, F. Ogliaro, M. Bearpark, J. J. Heyd, E. Brothers, K. N. Kudin, V. N. Staroverov, T. Keith, R. Kobayashi, J. Normand, K. Raghavachari, A. Rendell, J. C. Burant, S. S. Iyengar, J. Tomasi, M. Cossi, J. M. Millam, M. Klene, C. Adamo, R. Cammi, J. W. Ochterski, R. L. Martin, K. Morokuma, O. Farkas, J. B. Foresman, and D. J. Fox, Gaussian 09, Revision E.01, Gaussian, Inc., Wallingford CT, 2009.
64. C. Y. Peng, P. Y. Ayala, H. B. Schlegel and M. J. Frisch, J. Comput. Chem., 1996, 17, 49-56.
65. B. Spengler, J. W. Dolce and R. J. Cotter, Anal. Chem., 2002, 62, 1731-1737.
66. A. Huyghues-Despointes and V. A. Yaylayan, J. Agric. Food Chem., 1996, 44, 672-681.
67. G. E. Hofmeister, Z. Zhou and J. A. Leary, J. Am. Chem. Soc., 2002, 113, 5964-5970.
68 J.-Y. Salpin and J. Tortajada, Ref. J. Mass Spectrom., 2004, 39, 930–941.
69 G. Yang, C. Zhu and L. Zhou, J Mol Model, 2016, 22, 104.
70 D. G. Costa, A. B. Rocha, W. F. Souza, S. Shirley X. Chiaro and A. A. Leitao, J. Phys. Chem. B, 2011, 115, 3531–3537.
71. D. A. McQuarrie, J. D. Simon, Molecular Thermodynamics, University Science Books: Sausalito, CA, 1999.
72. J. I. Steinfeld, J. S. Francisco and W. L. Hase, Chemical kinetics and dynamics, Prentice Hall Upper Saddle River, NJ, 1999.
73. P. Pechukas and F. J. McLafferty, Chem. Phys., 1973, 58, 1622-1625.
74. R. Kaur and Vikas, J Phys Chem A, 2018, 122, 1926-1937.
75. P. Virtanen, R. Gommers, T. E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S. J. van der Walt, M. Brett, J. Wilson, K. J. Millman, N. Mayorov, A. R. J. Nelson, E. Jones, R. Kern, E. Larson, C. J. Carey, I. Polat, Y. Feng, E. W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E. A. Quintero, C. R. Harris, A. M. Archibald, A. H. Ribeiro, F. Pedregosa, P. van Mulbregt and C. SciPy, Nat Methods, 2020, 17, 261-272.
76. A. C. Hindmarsh, IMACS Transactions on Scientific Computation, 1983, Vol 1., 55-64.
77. L. Petzold, SIAM Journal on Scientific and Statistical Computing, 1983, Vol. 4, 1, 136-148
78. I. Novak, J. Mol. Liq., 2021, 335, 116558.
79. P. C. M. Herve du Penhoat and A. S. Perlin, Carbohydr. Res., 1974, 36, 111-120.
80. D. Horton and Z. Wałaszek, Carbohydr. Res., 1982, 105, 145-153.
81. A. Allerhand and D. Doddrell, J. Am. Chem. Soc., 2002, 93, 2779-2781.
82. S. J. Angyal and G. S. Bethell, Aust. J. Chem., 1976, 29(6) 1249 – 1265.
83. L. Sattler, Adv Carbohyd Chem, 1948, 3, 113-128.
84. P. Zaby, J. Ingenmey, B. Kirchner, S. Grimme, and S. Ehlerta, J. Chem. Phys., 2021, 155, 104101.
85. B. Kirchner, J. Ingenmey, M. v. Domaros and E. Perlt, Molecules, 2022, 27, 1286.
86. S. Grimme, Chem. Eur. J., 2012,18, 9955 – 9964.
87. J.-D. Chai and M. Head-Gordon, Phys. Chem. Chem. Phys., 2-018, 10, 6615–6620.
88. S. Canneaux, F. Bohr and E. Henon, J. Comp. Chem, 2014, 35, 82–93.
89. P-K. Tsou, H.T. Huynh, H.T. Phan and J-L.Kuo, Phys. Chem. Chem. Phys., 2023, 25, 3332–3342.
a1. Hohenberg, P.; Kohn, W. Phys. Rev.,1964, 136, B864.
a2. Kohn, W.; Sham, L. J. Phys. Rev., 1965, 140, A1133.
a3. Aron J. C., Paula M.-S., and Weitao Y., Chem. Rev. 2012, 112, 289–320.
a4. Yu H. S., Li S. L., and Truhlar D. G., J. Chem. Phys., 2016, 145, 130901.
a5. C. Lee, W. Yang, and R. G. Parr, Phys. Rev. B, 1988, 37, No. 2, 785-789.
a6. Becke, A. D. Phys. Rev. A, 1988, 38, 3098-3100.
a7. S. H. Vosko, L. Will and M. Nusair, Can. J. Phys., 1980, 58. 1200.
a8. F. Spiegelman et. al., Advances in Physics: X, 2019, 5, 1, 1710252.
a9. Porezag D, Frauenheim T, Köhler T, et al., Phys Rev B., 1995, 51, 12947–12957.
a10. Seifert G, Porezag D, Frauenheim T., Int J Quantum Chem., 1996, 58, 185–192.
a11. Elstner M, Porezag D, Jungnickel G, et al., Phys Rev B., 1998;58:7260–7268.
a12. Yang Y, Yu H, York D, et al., J Phys Chem A. 2007, 111, 10861–10873.
a13. Møller C, Plesset MS, Phys Rev, 1934, 46:618–622.
a14. Hartree D. R. and Hartree W., R. Soc. Lond. A,1935, 150, 9–33.
a15. J. C. Slater, Phys. Rev., 1951, 81, 385 –390.
a16. Cremer, D., WIREs Comput Mol Sci, 2011, 1, 509–530.
a17. Bartlett RJ, Silver DM., Int J Quantum Chem, 1974, S8,271–276.
a18. Binkley JS, Pople JA, Int J Quantum Chem, 1975, 9, 229–236.