Home

Citation: Guisheng Wu, Meng Hu, Dongsen Mao. Deriving the Matrix Representation of Molecular Point Groups Using the Product of Symmetric Operation Matrix Representation[J]. University Chemistry, ;2024, 39(1): 309-313. doi: 10.3866/PKU.DXHX202305062 shu

Deriving the Matrix Representation of Molecular Point Groups Using the Product of Symmetric Operation Matrix Representation

School of Chemical and Environmental Engineering, Shanghai Institute of Technology, Shanghai 201418, China

Corresponding author: Dongsen Mao, dsmao@sit.edu.cn
Received Date: 19 May 2023

Based on matrix multiplication, the third symmetric operation, which is equivalent to the product of different symmetric operations, was deduced in this paper. Furthermore, it was proposed how the group containing different symmetric elements can be derived from the direct product of its subgroups. At the same time, the new symmetric elements can be derived from the multiplication of its group elements.
- Symmetric operation,
- Symmetric elements,
- The direct product of a group,
- Symmetric operation multiplication
1. [1]
2. [2]
3. [3]
4. [4]
  Atkins, P.; Paula, J. D. Physical Chemistry, 9th ed.; Oxford University Press: New York, NY, USA, 2010.
5. [5]
1. [1]
  Hong Lu , Yidie Zhai , Xingxing Cheng , Yujia Gao , Qing Wei , Hao Wei . Advancements and Expansions in the Proline-Catalyzed Asymmetric Aldol Reaction. University Chemistry, 2024, 39(5): 154-162. doi: 10.3866/PKU.DXHX202310074
2. [2]
  Xincan Zhou , Xueyao Wang , Xiaokang Chen , Di Lan , Yuting Gao , Xiaoxia Wang , Daohao Li , Shuchao Zhang , Lijie Zhang , Guanglei Wu . Charge redistribution on Pd mediated by electronically asymmetric carbon for boosting ethanol oxidation. Acta Physico-Chimica Sinica, 2026, 42(7): 100287-0. doi: 10.1016/j.actphy.2026.100287
3. [3]
  Ke QIAO , Yanlin LI , Shengli HUANG , Guoyu YANG . Advancements in asymmetric catalysis employing chiral iridium (ruthenium) complexes. Chinese Journal of Inorganic Chemistry, 2024, 40(11): 2091-2104. doi: 10.11862/CJIC.20240265
4. [4]
  Guanghui SUI , Yanyan CHENG . Application of rice husk-based activated carbon-loaded MgO composite for symmetric supercapacitors. Chinese Journal of Inorganic Chemistry, 2025, 41(3): 521-530. doi: 10.11862/CJIC.20240221
5. [5]
  Weina Wang , Lixia Feng , Fengyi Liu , Wenliang Wang . Computational Chemistry Experiments in Facilitating the Study of Organic Reaction Mechanism: A Case Study of Electrophilic Addition of HCl to Asymmetric Alkenes. University Chemistry, 2025, 40(3): 206-214. doi: 10.12461/PKU.DXHX202407022
6. [6]
  Dan Liu . 可见光-有机小分子协同催化的不对称自由基反应研究进展. University Chemistry, 2025, 40(6): 118-128. doi: 10.12461/PKU.DXHX202408101
7. [7]
  Dengke Ma . Application of Integrating Fundamental Knowledge and Cutting-Edge Developments in the Teaching of Organic Synthesis: Taking the Asymmetric Meinwald Rearrangement as an Example. University Chemistry, 2026, 41(4): 67-74. doi: 10.12461/PKU.DXHX202502112
8. [8]
  Shaohua Wu , Jianfeng Yan , Chunfa Xu , Yuanming Li , Kai Yang , Caixia Lin . Construction of the synthetic chemistry experiment course under the Chemistry “101 Plan”: instructional design and implementation of the L-proline-catalyzed asymmetric aldol condensation reaction experiment. University Chemistry, 2026, 41(6): 152-159. doi: 10.12461/PKU.DXHX202511100
9. [9]
  Qianwen Han , Tenglong Zhu , Qiuqiu Lü , Mahong Yu , Qin Zhong . Performance and Electrochemical Asymmetry Optimization of Hydrogen Electrode Supported Reversible Solid Oxide Cell. Acta Physico-Chimica Sinica, 2025, 41(1): 100005-0. doi: 10.3866/PKU.WHXB202309037
10. [10]
  Kai Hu , Haiyan Liu , Chi Huang , Faqiong Zhao , Yanping Ren , Xiuyun Wang , Juanjuan Song , Yongxian Fan , Dongcheng Liu , Xiuqiong Zeng , Wan Li , Wenwei Zhang , Mei Shi , Min Hu , Weihong Li , Xiaohang Qiu , Yong Fan , Jianrong Zhang , Shuyong Zhang . Suggestions on Operating Specifications for Gas Generation, Purification, and Collection. University Chemistry, 2026, 41(3): 99-109. doi: 10.12461/PKU.DXHX202507038
11. [11]
  Ying Xiong , Guangao Yu , Lin Wu , Qingwen Liu , Houjin Li , Shuanglian Cai , Zhanxiang Liu , Xingwen Sun , Yuan Zheng , Jie Han , Xin Du , Chengshan Yuan , Qihan Zhang , Jianrong Zhang , Shuyong Zhang . Basic Operations and Specification Suggestions for Determination of Physical Constants of Organic Compounds. University Chemistry, 2025, 40(5): 106-121. doi: 10.12461/PKU.DXHX202503079
12. [12]
  Yuahua Weng , Chanzi Ruan , Xiaohang Qiu , Yiru Wang , Juanjuan Song , Yongxian Fan , Dongcheng Liu , Yanping Ren , Xiuqiong Zeng , Faqiong Zhao , Mei Shi , Min Hu , Wan Li , Xiuyun Wang , Wenwei Zhang , Weihong Li , Yong Fan , Jianrong Zhang , Shuyong Zhang . Specifications, Storage, and Suggestions on Handling of Chemical Reagents. University Chemistry, 2026, 41(3): 67-76. doi: 10.12461/PKU.DXHX202507040
13. [13]
  Qiong Ding , Haiyan Liu , Yuwen Liu , Min Xie , Ying Yang , Xiaojun Wu , Kai Hu . Exploration and practice of fundamental operation instruction in basic chemistry experiments. University Chemistry, 2026, 41(6): 160-165. doi: 10.12461/PKU.DXHX202508082
14. [14]
  Houjin Li , Zhanxiang Liu , Yuan Zheng , Shuanglian Cai , Jie Han , Ying Xiong , Xingwen Sun , Chengshan Yuan , Guangao Yu , Qingwen Liu , Lin Wu , Qihan Zhang , Xin Du , Jianrong Zhang , Shuyong Zhang . Exploration and Practice of the Construction of the Basic Operation Standard of Organic Chemistry Experiment Based in Virtual Teaching Research. University Chemistry, 2025, 40(5): 230-237. doi: 10.12461/PKU.DXHX202502064
15. [15]
  Faqiong Zhao , Xiuqiong Zeng , Kai Hu , Haiyan Liu , Yanping Ren , Wan Li , Wenwei Zhang , Juanjuan Song , Yongxian Fan , Dongcheng Liu , Mei Shi , Min Hu , Xiuyun Wang , Weihong Li , Xiaohang Qiu , Yong Fan , Jianrong Zhang , Shuyong Zhang . Suggestions on Operation Specifications for Drying of Chemical Substances and Use of Air-Blast Drying Ovens, Vacuum Drying Ovens and Freeze Dryers. University Chemistry, 2026, 41(3): 110-121. doi: 10.12461/PKU.DXHX202507033
16. [16]
  Yiru Wang , Chanzi Ruan , Juanjuan Song , Yongxian Fan , Dongcheng Liu , Yanping Ren , Xiuqiong Zeng , Faqiong Zhao , Wenwei Zhang , Mei Shi , Min Hu , Wan Li , Xiuyun Wang , Weihong Li , Xiaohang Qiu , Yong Fan , Jianrong Zhang , Shuyong Zhang . Solid-Liquid Separation and Suggestions on the Operation Standards (I): Decantation and Centrifugation with Centrifuge Operation. University Chemistry, 2026, 41(3): 122-129. doi: 10.12461/PKU.DXHX202507037
17. [17]
  Yiru Wang , Zhiqiang Dong , Juanjuan Song , Yongxian Fan , Dongcheng Liu , Yanping Ren , Xiuqiong Zeng , Faqiong Zhao , Wenwei Zhang , Mei Shi , Min Hu , Wan Li , Xiuyun Wang , Weihong Li , Xiaohang Qiu , Yong Fan , Jianrong Zhang , Shuyong Zhang . Solid-Liquid Separation and Suggestions on the Operation Standards (II): Gravity Filtration and Vacuum Filtration with Vacuum Pump Operation. University Chemistry, 2026, 41(3): 130-142. doi: 10.12461/PKU.DXHX202507042
18. [18]
  Cai Sun , Shoutian Zheng , Yaofeng Yuan . Experimental case study on crystal structure refinement using non-spherical atomic models. University Chemistry, 2026, 41(6): 449-456. doi: 10.12461/PKU.DXHX202504038
19. [19]
  Faqiong Zhao , Xiaohang Qiu , Yanping Ren , Juanjuan Song , Dongcheng Liu , Xiuqiong Zeng , Wenwei Zhang , Mei Shi , Min Hu , Wan Li , Yongxian Fan , Yiru Wang , Xiuyun Wang , Weihong Li , Yong Fan , Jianrong Zhang , Shuyong Zhang . The Use of pH Indicator Papers and pH Meters. University Chemistry, 2025, 40(5): 32-39. doi: 10.12461/PKU.DXHX202503099
20. [20]
  Xiuqiong Zeng , Jiqing Cai , Yanping Ren , Faqiong Zhao , Wenwei Zhang , Yongxian Fan , Wan Li , Houjin Li , Min Hu , Mei Shi , Kai Hu , Yiru Wang , Yong Fan , Xiuyun Wang , Weihong Li , Xiaohang Qiu , Juanjuan Song , Dongcheng Liu , Jianrong Zhang , Shuyong Zhang . Suggestions on Common Laboratory Apparatus and Their Cleaning and Drying. University Chemistry, 2026, 41(3): 87-98. doi: 10.12461/PKU.DXHX202507044

Get Citation

PDF

XML

Metrics

PDF Downloads(5)
Abstract views(1543)
HTML views(247)

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