搜索

x

留言板

尊敬的读者、作者、审稿人, 关于本刊的投稿、审稿、编辑和出版的任何问题, 您可以本页添加留言。我们将尽快给您答复。谢谢您的支持!

姓名
邮箱
手机号码
标题
留言内容
验证码

具有D4h对称性构型的C2+4分子的Jahn-Teller效应与能级分裂

冯胜奇 邱庆春

引用本文:
Citation:

具有D4h对称性构型的C2+4分子的Jahn-Teller效应与能级分裂

冯胜奇, 邱庆春

The Jahn-Teller effect and energy-level splitting for C2+4molecules with the D4h symmetry configuration

Feng Sheng-Qi, Qiu Qing-Chun
PDF
导出引用
  • 依据量子理论与配位场理论,利用群论和对称性分析的方法探讨了C2+4分子在具有D4h对称性构型时,E×(b1g+b2g)系统的Jahn-Teller效应中的相关问题.研究了C2+4分子的电子态与声子态的对称性及其活跃声子态,讨论了系统声子间的耦合与CG系数,构建了E×(b1g+b2g
    Based on quantum theory and ligand field theory, the E×(b1g+b2g) Jahn-Teller system for C2+4 molecules with the D4h symmetry configuration was studied in this paper using the methods of group theory and symmetry analysis. The symmetry of electronic states and phonon states for the system were explored, the coupling between phonons and CG coefficients were discussed, and the vibronic Hamiltonian for the E×(b1g+b2g) Jahn-Teller system was constructed. The ground state of the system and its energy were calculated using unitary shift transformation. It was found that there were four minima on the potential energy surface of the system because of the vibronic coupling. No matter which minimum the system is in, the ground energy level of the system is split into two energy levels after the Jahn-Teller distortion and the electronic degeneracy of the system is completely lifted. The Jahn-Teller distortion direction for the system was studied further using group theory. The results show that the distortion direction of the system should be D4h→D2h, and the symmetry of the ground state for C2+4 molecules is B1uunder the group D2h after the Jahn-Teller distortion.
    • 基金项目: 广东省自然科学基金(批准号:34613)资助的课题.
    [1]

    Jahn H A, Teller E 1937 Proc. R. Soc. A 161 220

    [2]

    Bates C A 1978 Phys. Rep. 35 187

    [3]

    Wu J B 1991 Acta Phys. Sin. 40 1474 (in Chinese) [吴建斌 1991 物理学报 40 1474]

    [4]

    Qiu Q C 2004 Acta Phys. Sin. 53 2292 (in Chinese) [邱庆春 2004 物理学报 53 2292]

    [5]

    Zhang S L, Kong H, Cen C, Su J R, Zhu C F 2005 Acta Phys. Sin. 54 4379 (in Chinese) [张士龙、孔 辉、岑 诚、苏金瑞、朱长飞 2005 物理学报 54 4379]

    [6]

    Zhou Y Y 2002 Physica B:Condensed Matter 322 61

    [7]

    Wu J B, Wang Z C 1991 Acta Phys. Sin. 40 1320 (in Chinese) [吴建斌、王志成 1991 物理学报 40 1320]

    [8]

    Yin C H, Zhang L, Zhao J P, Jiao Y, Song N, Ru R P, Yang L 2006 Acta Phys. Sin. 55 6055 (in Chinese) [殷春浩、张 雷、赵纪平、焦 杨、宋 宁、茹瑞鹏、杨 柳 2006 物理学报 55 6055]

    [9]

    Yin C H, Jiao Y, Song N, Ru R P, Yang L, Zhang L 2006 Acta Phys. Sin. 55 5471 (in Chinese) [殷春浩、焦 杨、宋 宁、茹瑞鹏、杨 柳、张 雷 2006 物理学报 55 5471]

    [10]

    Lü H P, Yin C H, Wei X S, Niu Y X, Song N, Ru R P 2007 Acta Phys. Sin. 56 6608 (in Chinese) [吕海萍、殷春浩、魏雪松、钮应喜、宋 宁、茹瑞鹏 2007 物理学报 56 6608]

    [11]

    Wu W B, Huang D J, Huang C M, Hsu C H, Chang C F, Lin H J, Chen C T 2007 J. Magnetism and Magnetic Materials 310 813

    [12]

    Rout G C, Nilima P, Behera S N 2007 Physica B 387 259

    [13]

    Zheng G H, Ma Y Q, Zhu X B, Sun Y P 2007 Solid State Communications 142 217

    [14]

    Wang R, Zhu Z H, Yang C L 2001 Acta Phys. Sin. 50 1675 (in Chinese) [汪 蓉、朱正和、杨传路 2001 物理学报 50 1675]

    [15]

    Huang H, Li Q 2003 Chin. J. At. Mol. Phys. 20 409 (in Chinese) [黄 辉、李 权 2003 原子与分子物理学报 20 409]

    [16]

    Guo J J, Yang J X, Die D, Yu G F, Jiang G 2005 Acta Phys. Sin. 54 3571 (in Chinese) [郭建军、杨继先、迭 东、于桂凤、蒋 刚 2005 物理学报 54 3571]

    [17]

    Shen H X, Cai N L, Wen Y H, Zhu Z Z 2005 Acta Phys. Sin. 54 5362 (in Chinese) [沈汉鑫、蔡娜丽、文玉华、朱梓忠 2005 物理学报 54 5362]

    [18]

    Chen L Z, Wang X C, Wen Y H, Zhu Z Z 2007 Acta Phys. Sin. 56 2920 (in Chinese) [陈鲁倬、王晓春、文玉华、朱梓忠 2007 物理学报 56 2920]

    [19]

    He L H, Zhang P L, Yan Q W 2001 Chin. Phys. 10 853

    [20]

    Shu M M, Cao S X, Gao T, Yuan S J, Kang B J, Yu L M, Zhang J C 2009 Acta Phys. Sin. 58 3309 (in Chinese) [舒苗苗、曹世勋、高 湉、袁淑娟、康保娟、郁黎明、张金仓 2009 物理学报 58 3309]

    [21]

    Lu Y, Li Q A, Di N L, Ma X, Kou Z Q, Luo Z, Cheng Z H 2003 Chin. Phys. 12 789

    [22]

    Qiu Q C, Dunn J L, Bates C A, Abou-Ghantous M, Polinger V Z 2000 Phys. Rev. B 62 16155

    [23]

    Bates C A, Dunn J L 1989 J. Phys.:Condens. Matter 1 2605

    [24]

    Luo X, Martin R M 2005 Phys. Rev. B 72 035212

    [25]

    Sartbaeva A, Wells S A, Thorpe M F 2006 Phys. Rev. Lett. 97 065501

    [26]

    Feng S Q, Fang H, Qiu Q C 2011 Acta Phys. Sin. 60 544 (in Chinese) [冯胜奇、方 海、邱庆春 2011物理学报 60 544]

    [27]

    Bersuker I B, Polinger V Z 1989 Vibronic interactions in molecules and crystals (Berlin:Springer) pp20—23

    [28]

    Landau L D, Lifshitz E M 1981 Quantum mechanics (volume 2) (Beijing:Higher Education Press) pp128—134 (in Chinese)[朗 道、栗弗席茨著,严肃译 1981 量子力学(下册)(北京:高等教育出版社)第128—134页]

    [29]

    Bishop D M 1973 Group Theory and Chemistry (London:Oxford university press) pp151—162

    [30]

    Stevens K W H 1952 Proc. Phys. Soc. A 65 209

    [31]

    Bates C A, Dunn J L, Sigmund E 1987 J. Phys. C:Solid State Phys. 20 1965

    [32]

    Qiu Q C 2003 Acta Phys. Sin. 52 958 (in Chinese) [邱庆春 2003 物理学报 52 958]

    [33]

    Pearson R G 1976 Symmetry Rules for Chemical Reactions:Orbital Topology and Elementary Process (New York:Wiley) pp78—85 (in Chinese) [皮尔逊 R G著,石宝林、封继康、李志如译 1986 化学反应对称规则—轨道拓扑学和基元过程 (北京:科学出版社)第78—85页]

    [34]

    Zhou Y Y 2004 J. Appl. Phys. 95 6870

    [35]

    Zhou Y Y 2008 Z. Naturforsch. 63a 830

    [36]

    Qiu Q C, Dunn J L, Bates C A 2001 Phys. Rev. B 64 075102

    [37]

    Hallam L D, Bates C A, Dunn J L 1992 J. Phys.:Condens. Matter 4 6775

    [38]

    Qiu Q C, Qiao F 2006 Chin. Sci. Bull. 51 2553

  • [1]

    Jahn H A, Teller E 1937 Proc. R. Soc. A 161 220

    [2]

    Bates C A 1978 Phys. Rep. 35 187

    [3]

    Wu J B 1991 Acta Phys. Sin. 40 1474 (in Chinese) [吴建斌 1991 物理学报 40 1474]

    [4]

    Qiu Q C 2004 Acta Phys. Sin. 53 2292 (in Chinese) [邱庆春 2004 物理学报 53 2292]

    [5]

    Zhang S L, Kong H, Cen C, Su J R, Zhu C F 2005 Acta Phys. Sin. 54 4379 (in Chinese) [张士龙、孔 辉、岑 诚、苏金瑞、朱长飞 2005 物理学报 54 4379]

    [6]

    Zhou Y Y 2002 Physica B:Condensed Matter 322 61

    [7]

    Wu J B, Wang Z C 1991 Acta Phys. Sin. 40 1320 (in Chinese) [吴建斌、王志成 1991 物理学报 40 1320]

    [8]

    Yin C H, Zhang L, Zhao J P, Jiao Y, Song N, Ru R P, Yang L 2006 Acta Phys. Sin. 55 6055 (in Chinese) [殷春浩、张 雷、赵纪平、焦 杨、宋 宁、茹瑞鹏、杨 柳 2006 物理学报 55 6055]

    [9]

    Yin C H, Jiao Y, Song N, Ru R P, Yang L, Zhang L 2006 Acta Phys. Sin. 55 5471 (in Chinese) [殷春浩、焦 杨、宋 宁、茹瑞鹏、杨 柳、张 雷 2006 物理学报 55 5471]

    [10]

    Lü H P, Yin C H, Wei X S, Niu Y X, Song N, Ru R P 2007 Acta Phys. Sin. 56 6608 (in Chinese) [吕海萍、殷春浩、魏雪松、钮应喜、宋 宁、茹瑞鹏 2007 物理学报 56 6608]

    [11]

    Wu W B, Huang D J, Huang C M, Hsu C H, Chang C F, Lin H J, Chen C T 2007 J. Magnetism and Magnetic Materials 310 813

    [12]

    Rout G C, Nilima P, Behera S N 2007 Physica B 387 259

    [13]

    Zheng G H, Ma Y Q, Zhu X B, Sun Y P 2007 Solid State Communications 142 217

    [14]

    Wang R, Zhu Z H, Yang C L 2001 Acta Phys. Sin. 50 1675 (in Chinese) [汪 蓉、朱正和、杨传路 2001 物理学报 50 1675]

    [15]

    Huang H, Li Q 2003 Chin. J. At. Mol. Phys. 20 409 (in Chinese) [黄 辉、李 权 2003 原子与分子物理学报 20 409]

    [16]

    Guo J J, Yang J X, Die D, Yu G F, Jiang G 2005 Acta Phys. Sin. 54 3571 (in Chinese) [郭建军、杨继先、迭 东、于桂凤、蒋 刚 2005 物理学报 54 3571]

    [17]

    Shen H X, Cai N L, Wen Y H, Zhu Z Z 2005 Acta Phys. Sin. 54 5362 (in Chinese) [沈汉鑫、蔡娜丽、文玉华、朱梓忠 2005 物理学报 54 5362]

    [18]

    Chen L Z, Wang X C, Wen Y H, Zhu Z Z 2007 Acta Phys. Sin. 56 2920 (in Chinese) [陈鲁倬、王晓春、文玉华、朱梓忠 2007 物理学报 56 2920]

    [19]

    He L H, Zhang P L, Yan Q W 2001 Chin. Phys. 10 853

    [20]

    Shu M M, Cao S X, Gao T, Yuan S J, Kang B J, Yu L M, Zhang J C 2009 Acta Phys. Sin. 58 3309 (in Chinese) [舒苗苗、曹世勋、高 湉、袁淑娟、康保娟、郁黎明、张金仓 2009 物理学报 58 3309]

    [21]

    Lu Y, Li Q A, Di N L, Ma X, Kou Z Q, Luo Z, Cheng Z H 2003 Chin. Phys. 12 789

    [22]

    Qiu Q C, Dunn J L, Bates C A, Abou-Ghantous M, Polinger V Z 2000 Phys. Rev. B 62 16155

    [23]

    Bates C A, Dunn J L 1989 J. Phys.:Condens. Matter 1 2605

    [24]

    Luo X, Martin R M 2005 Phys. Rev. B 72 035212

    [25]

    Sartbaeva A, Wells S A, Thorpe M F 2006 Phys. Rev. Lett. 97 065501

    [26]

    Feng S Q, Fang H, Qiu Q C 2011 Acta Phys. Sin. 60 544 (in Chinese) [冯胜奇、方 海、邱庆春 2011物理学报 60 544]

    [27]

    Bersuker I B, Polinger V Z 1989 Vibronic interactions in molecules and crystals (Berlin:Springer) pp20—23

    [28]

    Landau L D, Lifshitz E M 1981 Quantum mechanics (volume 2) (Beijing:Higher Education Press) pp128—134 (in Chinese)[朗 道、栗弗席茨著,严肃译 1981 量子力学(下册)(北京:高等教育出版社)第128—134页]

    [29]

    Bishop D M 1973 Group Theory and Chemistry (London:Oxford university press) pp151—162

    [30]

    Stevens K W H 1952 Proc. Phys. Soc. A 65 209

    [31]

    Bates C A, Dunn J L, Sigmund E 1987 J. Phys. C:Solid State Phys. 20 1965

    [32]

    Qiu Q C 2003 Acta Phys. Sin. 52 958 (in Chinese) [邱庆春 2003 物理学报 52 958]

    [33]

    Pearson R G 1976 Symmetry Rules for Chemical Reactions:Orbital Topology and Elementary Process (New York:Wiley) pp78—85 (in Chinese) [皮尔逊 R G著,石宝林、封继康、李志如译 1986 化学反应对称规则—轨道拓扑学和基元过程 (北京:科学出版社)第78—85页]

    [34]

    Zhou Y Y 2004 J. Appl. Phys. 95 6870

    [35]

    Zhou Y Y 2008 Z. Naturforsch. 63a 830

    [36]

    Qiu Q C, Dunn J L, Bates C A 2001 Phys. Rev. B 64 075102

    [37]

    Hallam L D, Bates C A, Dunn J L 1992 J. Phys.:Condens. Matter 4 6775

    [38]

    Qiu Q C, Qiao F 2006 Chin. Sci. Bull. 51 2553

  • [1] 周年杰, 黄伟其, 苗信建, 王刚, 董泰阁, 黄忠梅, 尹君. 量子受限效应和对称性效应对硅光子晶体禁带的影响. 物理学报, 2015, 64(6): 064208. doi: 10.7498/aps.64.064208
    [2] 楼智美, 梅凤翔. 二维各向异性谐振子的第三个独立守恒量及其对称性. 物理学报, 2012, 61(11): 110201. doi: 10.7498/aps.61.110201
    [3] 丁光涛. 构造Birkhoff表示的Hojman方法与Birkhoff对称性. 物理学报, 2010, 59(6): 3643-3647. doi: 10.7498/aps.59.3643
    [4] 葛伟宽, 张毅, 薛纭. Rosenberg问题的对称性与守恒量. 物理学报, 2010, 59(7): 4434-4436. doi: 10.7498/aps.59.4434
    [5] 肖进, 张庆礼, 周文龙, 谭晓靓, 刘文鹏, 殷绍唐, 江海河, 夏上达, 郭常新. Nd3+:Gd3Sc2Al3O12 晶场能级及拟合. 物理学报, 2010, 59(10): 7306-7313. doi: 10.7498/aps.59.7306
    [6] 丁光涛. 规范变换对Birkhoff系统对称性的影响. 物理学报, 2009, 58(11): 7431-7435. doi: 10.7498/aps.58.7431
    [7] 路凯, 方建会, 张明江, 王鹏. 相空间中离散完整系统的Noether对称性和Mei对称性. 物理学报, 2009, 58(11): 7421-7425. doi: 10.7498/aps.58.7421
    [8] 张 毅. 事件空间中完整系统的Lie对称性与绝热不变量. 物理学报, 2007, 56(6): 3054-3059. doi: 10.7498/aps.56.3054
    [9] 牟中飞, 吴福根, 张 欣, 钟会林. 超元胞方法研究平移群对称性对声子带隙的影响. 物理学报, 2007, 56(8): 4694-4699. doi: 10.7498/aps.56.4694
    [10] 王 策, 陈晓波, 张春林, 张蕴芝, 陈 鸾, 马 辉, 李 崧, 高爱华. Er3+:GdVO4中Er3+离子的光谱参数计算和晶场中能级分裂的讨论. 物理学报, 2007, 56(10): 6090-6097. doi: 10.7498/aps.56.6090
    [11] 张 毅, 范存新, 梅凤翔. Lagrange系统对称性的摄动与Hojman型绝热不变量. 物理学报, 2006, 55(7): 3237-3240. doi: 10.7498/aps.55.3237
    [12] 楼智美. 非中心力场中经典粒子的轨道参数方程与对称性. 物理学报, 2005, 54(4): 1460-1463. doi: 10.7498/aps.54.1460
    [13] 郑世旺, 傅景礼, 李显辉. 机电动力系统的动量依赖对称性和非Noether守恒量. 物理学报, 2005, 54(12): 5511-5516. doi: 10.7498/aps.54.5511
    [14] 黄永畅, 李希国. 不同积分变分原理的统一. 物理学报, 2005, 54(8): 3473-3479. doi: 10.7498/aps.54.3473
    [15] 吴惠彬, 梅凤翔. Lagrange系统在施加陀螺力后的对称性. 物理学报, 2005, 54(6): 2474-2477. doi: 10.7498/aps.54.2474
    [16] 贺黎明, 曹 伟, 陈学谦, 朱云霞. 氦原子1snd(n=4—11)组态下1D—3D谱项分裂值的计算. 物理学报, 2005, 54(11): 5077-5081. doi: 10.7498/aps.54.5077
    [17] 罗绍凯. 奇异系统Hamilton正则方程的Mei对称性、Noether对称性和Lie对称性. 物理学报, 2004, 53(1): 5-10. doi: 10.7498/aps.53.5
    [18] 张 毅, 梅凤翔. 广义经典力学系统对称性的摄动与绝热不变量. 物理学报, 2003, 52(10): 2368-2372. doi: 10.7498/aps.52.2368
    [19] 张毅. 单面约束Birkhoff系统对称性的摄动与绝热不变量. 物理学报, 2002, 51(8): 1666-1670. doi: 10.7498/aps.51.1666
    [20] 张毅. Birkhoff系统的一类Lie对称性守恒量. 物理学报, 2002, 51(3): 461-464. doi: 10.7498/aps.51.461
计量
  • 文章访问数:  9593
  • PDF下载量:  903
  • 被引次数: 0
出版历程
  • 收稿日期:  2010-06-27
  • 修回日期:  2010-08-27
  • 刊出日期:  2011-05-15

/

返回文章
返回