基於聲子輔助穿隧(phonon-assisted tunneling)模型，氣味偵測與分子的低能
量激發態相關。本研究基於芳香分子的紅外光譜(IR spectrum)對其做編碼。
由Gaussian計算軟體計算分子的紅外光譜，並考慮體溫造成之熱效應，建構了
芳香分子的頻譜碼。將芳香分子頻譜碼做k-平均演分群法(k-means clustering)，
我們成功將一組芳香分子資料集以氣味分類。這個分類結果輔助了芳香分子低
能量激發態可以編碼氣味的觀點。

The phonon-assisted tunneling (PAT) model suggests that odor detection is
related to the low-energy excitations of odorants. This research codes odorants
based on their IR spectra of odorants, which represent these low-energy excitations.
Starting with the computation of IR spectra using Gaussian software and
considering thermal effects at body temperature, we constructed the spectral codes
of odorants. Using k-means clustering to the spectral codes, we successfully classified
a set of odorants based on their odors. The results support the view that
the low-energy excitations of odorants encodes the information of odors.

Abstract (Chinese)
Abstract
Acknowledgements (Chinese)
Contents
1 Introduction------------------------------------------------1
2 An Overview of Smell Process
2.1 The Smell Process Inside Our Nose-------------------------3
2.2 The PAT Model---------------------------------------------5
3 How We Code Odorants
3.1 What Ways Were Tried to Code Odorants?--------------------9
3.2 Code Odorants as Spectral Codes---------------------------11
4 Techniques for Quantum Chemistry
4.1 Simulate the IR Spectra of Odorants with Gaussian---------13
4.2 The Spectral Coding with Temperature Consideration--------15
5 Odorant Clsutering
5.1 Design of Dataset-----------------------------------------17
5.2 K-Means Clustering----------------------------------------20
5.2.1 The Main Body of K-Means Clustering.....................20
5.2.2 The K-Means++ Improvement...............................21
5.2.3 Index for Evaluating Clustering Quality.................21
5.3 Result of Clustering--------------------------------------23
6 Outlook-----------------------------------------------------25
A Analysis to Other Datasets----------------------------------26
A.1 Results of the K-Means Clustering-------------------------28
A.2 Divisive Hierarchical K-Means Clustering------------------33
A.3 Cluster by the Divisive Hierarchical K-Means Clustering---33
Bibliography--------------------------------------------------35

1. J. C. Brookes, F. Hartoutsiou, A. P. Horsfield, and A. M. Stoneham. Could humans recognize odor by phonon assisted tunneling? Phys. Rev. Lett., 98:038101, Jan 2007. doi: 10.1103/PhysRevLett.98.038101. URL https://link.aps.org/doi/10.1103/PhysRevLett.98.038101.
2. A. David and S. Vassilvitskii. k-means++: The advantages of careful seeding. Proceedings of the eighteenth annual ACM-SIAM symposium on Discrete algorithms, page 1027–1035, 2007.
3. 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. V. 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. J. Bearpark, J. J. Heyd, E. N. Brothers, K. N. Kudin, V. N. Staroverov, T. A. Keith, R. Kobayashi,
J. Normand, K. Raghavachari, A. P. 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˜16 Revision C.01, 2016. Gaussian Inc. Wallingford CT.
4. S. Kim, J. Chen, T. Cheng, A. Gindulyte, J. He, S. He, Q. Li, B. A. Shoemaker, P. A. Thiessen, B. Yu, L. Zaslavsky, J. Zhang, and E. E. Bolton. PubChem 2023 update. Nucleic Acids Research, 51(D1):D1373–D1380, 10 2022. ISSN 0305-1048. doi: 10.1093/nar/gkac956. URL https://doi.org/10.1093/nar/gkac956.
5. S. LAMROUS and M. TAILEB. Divisive hierarchical k-means. In 2006 International Conference on Computational Inteligence for Modelling Control and Automation and International Conference on Intelligent Agents Web Technologies and International Commerce (CIMCA’06), pages 18–18, 2006. doi: 10.1109/CIMCA.2006.89.
6. J. MacQueen. Some methods for classification and analysis of multivariate observations. Proceedings of the 5th Berkeley Symposium on Mathematical Statistics and Probability, pages 281–297, 1967.
7. S. L. Pashkovski, G. Iurilli, D. Brann, D. Chicharro, K. Drummey, K. M. Franks, S. Panzeri, and S. R. Datta. Structure and flexibility in cortical representations of odour space. Nature, 583:253–258, 2020.
8. P. J. Rousseeuw. Silhouettes: A graphical aid to the interpretation and validation of cluster analysis. Journal of Computational and Applied Mathematics, 20:53–65, 1987. ISSN 0377-0427. doi: https://doi.org/10.1016/0377-0427(87) 90125-7. URL https://www.sciencedirect.com/science/article/pii/0377042787901257.
9. The Good Scents Company. The good scents company information system. http://www.thegoodscentscompany.com/, 1980-2021.
10. L. Turin. A spectroscopic mechanism for primary olfactory reception. Chem. Senses., 21(6):773–91, 1996.