Home

Citation: Lü Tianxiong, Jiang Yuansheng. HÜCKEL EIGENVALUES OF RECTANGULAR CLUSTERS[J]. Acta Physico-Chimica Sinica, ;1988, 4(04): 393-400. doi: 10.3866/PKU.WHXB19880413 shu

HÜCKEL EIGENVALUES OF RECTANGULAR CLUSTERS

1.
Institute of Theoretical Chemistry; Jilin University; Changchun

Received Date: 15 December 1986
Available Online: 15 August 1988

The Hückel eigenvalues of three-dimensional rectangular clusters of arbitary size are explored on concerning not only the nearest but also those second and third neighboring interactions. For better specifying these interactions, three sets of parameters namely (β_1,β_2,β_3), (η_1,η_2,η_3) and ζ are introduced which can be illustrated schematically by 4_~.
Based on the well-known solution of the linear Hückel chain verned by a tri-dia nal matrix A~((1)) and the commutability between matrices A~((1))'s of equal dimension, we efficently derive the genera solutions for the planar and rectangular clusters respectively which are expressed by Eqs.(11) and (16).
The three-dimensional solution can be reduced to various special cases previously obtained by Messmer~[2] and Bilek & Skala~[3] but that for the face center rectangular lattice is new due to the introduction of parameters (η_1, η_2, η_3). The energy levels spread symmetricaly around α in terms of parameters (β_1, β_2, β_3) and ζ but the antibonding partners would be increased depending on the magnitude of η′s as indicated by 7_~. This means that the second neighbors play a role of destabilization in more or less extent much like the Madelung contribution in ionic crystals. As a consequence, the face-center (fc) lattice would be less favorable than the body-center (bc) one for alkali crystals, which seems really the case that most alkali metals are of be lattice except for lithium which is of either lattice form.
What is the minimum size of a cluster behaving like a crystal? In other words, when does the discrete energy levels change into continuous bands? By dint of the present results, we try to propose a criterion of maximum energy level separation, 0.02 eV that a finite cluster might behave approximately as a crystal. In order to illustrate the estimation, numerical calculation are given in Table 2.
1. [1]
  Yong Shu , Xing Chen , Sai Duan , Rongzhen Liao . How to Determine the Equilibrium Bond Distance of Homonuclear Diatomic Molecules: A Case Study of H₂. University Chemistry, 2024, 39(7): 386-393. doi: 10.3866/PKU.DXHX202310102
2. [2]
  Wei Zhong , Dan Zheng , Yuanxin Ou , Aiyun Meng , Yaorong Su . K原子掺杂高度面间结晶的g-C₃N₄光催化剂及其高效H₂O₂光合成. Acta Physico-Chimica Sinica, 2024, 40(11): 2406005-. doi: 10.3866/PKU.WHXB202406005
3. [3]
  Jiantao Zai , Hongjin Chen , Xiao Wei , Li Zhang , Li Ma , Xuefeng Qian . The Learning-Centered Problem-Oriented Experimental Teaching. University Chemistry, 2024, 39(4): 40-47. doi: 10.3866/PKU.DXHX202309023
4. [4]
  Xia Zhang , Xiaoguang Sang , Jinxia Wang , Hao Meng . Problem-Driven Inorganic Chemistry Course Teaching Practice Integrating Industry,Academia,and Research. University Chemistry, 2024, 39(10): 369-376. doi: 10.12461/PKU.DXHX202310027
5. [5]
  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
6. [6]
  Yongmin Zhang , Shuang Guo , Mingyue Zhu , Menghui Liu , Sinong Li . Design and Improvement of Physicochemical Experiments Based on Problem-Oriented Learning: a Case Study of Liquid Surface Tension Measurement. University Chemistry, 2024, 39(2): 21-27. doi: 10.3866/PKU.DXHX202307026
7. [7]
  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
8. [8]
  Guoxian Zhu , Jing Chen , Rongkai Pan . Enhancing the Teaching Quality of Atomic Structure: Insights and Strategies. University Chemistry, 2024, 39(3): 376-383. doi: 10.3866/PKU.DXHX202305027
9. [9]
  Jin Jia , Shangda Jiang . Is the z Axis Special in Atomic Structure?. University Chemistry, 2024, 39(6): 400-404. doi: 10.12461/PKU.DXHX202403091
10. [10]
  Linhan Tian , Changsheng Lu . Discussion on Sextuple Bonding in Diatomic Motifs of Chromium Family Elements. University Chemistry, 2024, 39(8): 395-402. doi: 10.3866/PKU.DXHX202401056
11. [11]
  Chunmei GUO , Weihan YIN , Jingyi SHI , Jianhang ZHAO , Ying CHEN , Quli FAN . Facile construction and peroxidase-like activity of single-atom platinum nanozyme. Chinese Journal of Inorganic Chemistry, 2024, 40(9): 1633-1639. doi: 10.11862/CJIC.20240162
12. [12]
  Fei Xie , Chengcheng Yuan , Haiyan Tan , Alireza Z. Moshfegh , Bicheng Zhu , Jiaguo Yu . d带中心调控过渡金属单原子负载COF吸附O₂的理论计算研究. Acta Physico-Chimica Sinica, 2024, 40(11): 2407013-. doi: 10.3866/PKU.WHXB202407013
13. [13]
  Haiping Wang . A Streamlined Method for Drawing Lewis Structures Using the Valence State of Outer Atoms. University Chemistry, 2024, 39(8): 383-388. doi: 10.12461/PKU.DXHX202401073
14. [14]
  Mengyao Shi , Kangle Su , Qingming Lu , Bin Zhang , Xiaowen Xu . Determination of Potassium Content in Tobacco Stem Ash by Flame Atomic Absorption Spectroscopy. University Chemistry, 2024, 39(10): 255-260. doi: 10.12461/PKU.DXHX202404105
15. [15]
  Wenliang Wang , Weina Wang , Sufan Wang , Tian Sheng , Tao Zhou , Nan Wei . “Schrödinger Equation – Approximate Models – Core Concepts – Simple Applications”: Constructing a Logical Framework and Knowledge Graph of Atom and Molecule Structures. University Chemistry, 2024, 39(8): 338-343. doi: 10.3866/PKU.DXHX202312084
16. [16]
  Peipei Sun , Jinyuan Zhang , Yanhua Song , Zhao Mo , Zhigang Chen , Hui Xu . 引入内建电场增强光载流子分离以促进H₂的生产. Acta Physico-Chimica Sinica, 2024, 40(11): 2311001-. doi: 10.3866/PKU.WHXB202311001
17. [17]
  Baohua LÜ , Yuzhen LI . Anisotropic photoresponse of two-dimensional layered α-In₂Se₃(2H) ferroelectric materials. Chinese Journal of Inorganic Chemistry, 2024, 40(10): 1911-1918. doi: 10.11862/CJIC.20240105
18. [18]
  Yingran Liang , Fei Wang , Jiabao Sun , Hongtao Zheng , Zhenli Zhu . Construction and Application of a New Experimental Device for Determination of Alkaline Metal Elements by Plasma Atomic Emission Spectrometry Based on Solution Cathode Glow Discharge: An Alternative Approach for Fundamental Teaching Experiments in Emission Spectroscopy. University Chemistry, 2024, 39(5): 380-387. doi: 10.3866/PKU.DXHX202312024
19. [19]
  Xinyu Yin , Haiyang Shi , Yu Wang , Xuefei Wang , Ping Wang , Huogen Yu . Spontaneously Improved Adsorption of H₂O and Its Intermediates on Electron-Deficient Mn^(3+δ)+ for Efficient Photocatalytic H₂O₂ Production. Acta Physico-Chimica Sinica, 2024, 40(10): 2312007-. doi: 10.3866/PKU.WHXB202312007
20. [20]
  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

Get Citation

PDF

XML

Metrics

PDF Downloads(1692)
Abstract views(2464)
HTML views(102)

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