Home

Citation: Dongju Zhang, Xinyi Cai, Qisheng Song. 直链和单环共轭多烯本征行列式递推公式及本征能级的推导[J]. University Chemistry, ;2022, 37(7): 211006. doi: 10.3866/PKU.DXHX202110068 shu

直链和单环共轭多烯本征行列式递推公式及本征能级的推导

School of Chemistry and Chemical Engineering, Shandong University, Jinan 250100, China

Received Date: 22 October 2021

休克尔(Hückel)分子轨道法是描述共轭体系π电子运动的近似模型，《结构化学》教科书中通常直接给出其本征行列式和其本征能级的递推公式，缺乏推导过程。本文用数学归纳法推导了直链和单环共轭多烯本征多项的递推公式，给出了对应本征能级的通式、特点和规律，适于未掌握群论和图论等数学工具的学生学习使用。
- Conjugated polyenes,
- Eigendeterminants,
- Recurrence formula,
- Eigenenergy levels
1. [1]
2. [2]
3. [3]
4. [4]
5. [5]
6. [6]
7. [7]
8. [8]
9. [9]
10. [10]
11. [11]
1. [1]
  Zhixin Zhou , Ran Chen , Yuanjian Zhang , Songqin Liu , Yanfei Shen . 分析化学课程本硕一体化的全英文教学改革. University Chemistry, 2025, 40(6): 64-70. doi: 10.12461/PKU.DXHX202407093
2. [2]
  Shui Hu , Houjin Li , Zhenming Zang , Lianyun Li , Rong Lai . Integration of Science and Education Promotes the Construction of Undergraduate-to-Master’s Integration Experimental Courses: A Case Study on the Extraction, Separation and Identification of Artemisinin from Artemisia annua. University Chemistry, 2024, 39(4): 314-321. doi: 10.3866/PKU.DXHX202310063
3. [3]
  Lijun Huo , Mingcun Wang , Tianyi Zhao , Mingjie Liu . Exploration of Undergraduate and Graduate Integrated Teaching in Polymer Chemistry with Aerospace Characteristics. University Chemistry, 2024, 39(6): 103-111. doi: 10.3866/PKU.DXHX202312059
4. [4]
  Jiaqi Chen , Shuwei Chen , Suocai Ren , Yue Sun , Chunhui Luan , Xu Wu . Exploring the People-Centered Safety Construction Model in Basic Chemistry Laboratories: A Case Study in Analytical Chemistry Laboratories. University Chemistry, 2024, 39(7): 264-271. doi: 10.3866/PKU.DXHX202311009
5. [5]
  Yanan Fan , Jingjing Huang . Interactive Electronic Courseware Facilitates the Development of Integrated Undergraduate-Graduate Instrumental Analysis Laboratory Courses: A Case Study of UV-Vis Spectroscopy Analysis Experiment. University Chemistry, 2025, 40(10): 282-287. doi: 10.12461/PKU.DXHX202411009
6. [6]
  Cunling Ye , Xitong Zhao , Hongfang Wang , Zhike Wang . A Formula for the Calculation of Complex Concentrations Arising from Side Reactions and Its Applications. University Chemistry, 2024, 39(4): 382-386. doi: 10.3866/PKU.DXHX202310043
7. [7]
  Ruming Yuan , Laiying Zhang , Xiaoming Xu , Pingping Wu , Gang Fu . Application of Mathematica in Visualizing Physical Chemistry Formulas. University Chemistry, 2024, 39(8): 375-382. doi: 10.3866/PKU.DXHX202401030
8. [8]
  Tiejun Su . The Construction and Application of the Calculation Formula for Endpoint Error in Precipitation Titration: A Case Study of the Mohr Method. University Chemistry, 2024, 39(11): 384-387. doi: 10.12461/PKU.DXHX202402039
9. [9]
  Fengmei Wang , Xin Zhang , Hong Yan , Xiangyu Xu , Guirong Wang . Inverted 'Π' Graphic Memory Method for Thermodynamic Basic Equations and the Application in Teaching Practice. University Chemistry, 2025, 40(11): 369-375. doi: 10.12461/PKU.DXHX202412087
10. [10]
  Hongyi Zhang , Zhihong Shi , Zhijun Zhang . A New Strategy for “De-formulized” Calculation of Dynamic Buffer Capacity in Analytical Chemistry Education. University Chemistry, 2024, 39(3): 390-394. doi: 10.3866/PKU.DXHX202309030
11. [11]
  Ran HUO , Zhaohui ZHANG , Xi SU , Long CHEN . Research progress on multivariate two dimensional conjugated metal organic frameworks. Chinese Journal of Inorganic Chemistry, 2024, 40(11): 2063-2074. doi: 10.11862/CJIC.20240195
12. [12]
  Junjie Zhang , Chaochao Dong , Jinke Li , Jiawen Guo , Yingxin Shui , Yue Wang , Xinhua Duan . 共轭聚合物探针的设计及其对藻蓝蛋白的智能检测. University Chemistry, 2026, 41(5): 285-293. doi: 10.12461/PKU.DXHX202509114
13. [13]
  Xiyuan Su , Zhenlin Hu , Ye Fan , Xianyuan Liu , Xianyong Lu . Change as You Want: Multi-Responsive Superhydrophobic Intelligent Actuation Material. University Chemistry, 2024, 39(5): 228-237. doi: 10.3866/PKU.DXHX202311059
14. [14]
  Zongpei Zhang , Yanyang Li , Yanan Si , Kai Li , Shuangquan Zang . Developing a Chemistry Experiment Center Employing a Multifaceted Approach to Serve High-Quality Laboratory Education. University Chemistry, 2024, 39(7): 13-19. doi: 10.12461/PKU.DXHX202404041
15. [15]
  Ruilin Han , Xiaoqi Yan . Comparison of Multiple Function Methods for Fitting Surface Tension and Concentration Curves. University Chemistry, 2024, 39(7): 381-385. doi: 10.3866/PKU.DXHX202311023
16. [16]
  Xingyuan Lu , Yutao Yao , Junjing Gu , Peifeng Su . Energy Decomposition Analysis and Its Application in the Many-Body Effect of Water Clusters. University Chemistry, 2025, 40(3): 100-107. doi: 10.12461/PKU.DXHX202405074
17. [17]
  Weijie Yang , Mansheng Chen , Chen Xu , Fujian Xu . Hydroxyl-Rich Polycations: Innovative Materials Empowering Life and Health. University Chemistry, 2025, 40(9): 332-343. doi: 10.12461/PKU.DXHX202410072
18. [18]
  Yixian Zhou , Xiaodong Shen , Lina Zhu . Polycyclic Aromatic Hydrocarbons (PAHs) as Environmental Pollutants: Recent Advances in Adsorptive Removal Technologies. University Chemistry, 2026, 41(4): 239-249. doi: 10.12461/PKU.DXHX202502084
19. [19]
  Yunting Shang , Yue Dai , Jianxin Zhang , Nan Zhu , Yan Su . Something about RGO (Reduced Graphene Oxide). University Chemistry, 2024, 39(9): 273-278. doi: 10.3866/PKU.DXHX202306050
20. [20]
  Anbang Du , Yuanfan Wang , Zhihong Wei , Dongxu Zhang , Li Li , Weiqing Yang , Qianlu Sun , Lili Zhao , Weigao Xu , Yuxi Tian . Photothermal Microscopy of Graphene Flakes with Different Thicknesses. Acta Physico-Chimica Sinica, 2024, 40(5): 2304027-0. doi: 10.3866/PKU.WHXB202304027

Get Citation

PDF

XML

Metrics

PDF Downloads(3)
Abstract views(1703)
HTML views(218)

通讯作者: 陈斌, bchen63@163.com

1.
沈阳化工大学材料科学与工程学院沈阳 110142

Address：Zhongguancun North First Street 2,100190 Beijing, PR China Tel: +86-010-82449177-888

DownLoad: Full-Size Img PowerPoint

Return