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

Feng Sheng-Qi; Qiu Qing-Chun

doi:10.7498/aps.60.057106

Abstract

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.

Keywords:

Authors and contacts

Feng Sheng-Qi¹,
Qiu Qing-Chun²

(1)Department of Physics and Electronic Engineering, Hanshan Normal University, Chaozhou 521041, China; (2)Department of Physics and Informatics, Medical College, Shantou University, Shantou 515041, China

References

[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

Cited By

[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]	Zhou Nian-Jie, Huang Wei-Qi, Miao Xin-Jian, Wang Gang, Dong Tai-Ge, Huang Zhong-Mei, Yin Jun. Effects of quantum confinement and symmetry on the silicon photonic crystal band gap. Acta Physica Sinica, 2015, 64(6): 064208. doi: 10.7498/aps.64.064208
[2]	Lou Zhi-Mei, Mei Feng-Xiang. The third independent conserved quantity and its symmetry of the two-dimensional anisotropic harmonic oscillator. Acta Physica Sinica, 2012, 61(11): 110201. doi: 10.7498/aps.61.110201
[3]	Zhang Yi, Xue Yun, Ge Wei-Kuan. Symmetries and conserved quantities of the Rosenberg problem. Acta Physica Sinica, 2010, 59(7): 4434-4436. doi: 10.7498/aps.59.4434
[4]	Ding Guang-Tao. Hojman method for construction of Birkhoffian representation and the Birkhoff symmetry. Acta Physica Sinica, 2010, 59(6): 3643-3647. doi: 10.7498/aps.59.3643
[5]	Guo Chang-Xin, Tan Xiao-Liang, Liu Wen-Peng, Yin Shao-Tang, Jiang Hai-He, Xiao Jin, Xia Shang-Da, Zhang Qing-Li, Zhou Wen-Long. Crystal field energy-levels of Nd3+:Gd3Sc2Al3O12 and fitting. Acta Physica Sinica, 2010, 59(10): 7306-7313. doi: 10.7498/aps.59.7306
[6]	Ding Guang-Tao. Effects of gauge transformations on symmetries of Birkhoffian system. Acta Physica Sinica, 2009, 58(11): 7431-7435. doi: 10.7498/aps.58.7431
[7]	Lu Kai, Fang Jian-Hui, Zhang Ming-Jiang, Wang Peng. Noether symmetry and Mei symmetry of discrete holonomic system in phase space. Acta Physica Sinica, 2009, 58(11): 7421-7425. doi: 10.7498/aps.58.7421
[8]	Zhang Yi. Lie symmetries and adiabatic invariants for holonomic systems in event space. Acta Physica Sinica, 2007, 56(6): 3054-3059. doi: 10.7498/aps.56.3054
[9]	Mu Zhong-Fei, Wu Fu-Gen, Zhang Xin, Zhong Hui-Lin. Effect of translation group symmetry on phononic band gaps studied by supercell calculation. Acta Physica Sinica, 2007, 56(8): 4694-4699. doi: 10.7498/aps.56.4694
[10]	Wang Ce, Chen Xiao-Bo, Zhang Chun-Lin, Zhang Yun-Zhi, Chen Luan, Ma Hui, Li Song, Gao Ai-Hua. Optical parameters and energy level splitting of Er3+ in Er3+: GdVO4. Acta Physica Sinica, 2007, 56(10): 6090-6097. doi: 10.7498/aps.56.6090
[11]	Zhang Yi, Fan Cun-Xin, Mei Feng-Xiang. Perturbation of symmetries and Hojman adiabatic invariants for Lagrangian system. Acta Physica Sinica, 2006, 55(7): 3237-3240. doi: 10.7498/aps.55.3237
[12]	Lou Zhi-Mei. Parametric orbit equation and symmetries of classical particle in the field of noncentral force. Acta Physica Sinica, 2005, 54(4): 1460-1463. doi: 10.7498/aps.54.1460
[13]	Zheng Shi-Wang, Fu Jing-Li, Li Xian-Hui. Momentum-dependent symmetries and non-Noether conserved quantities for mechanico-electrical systems. Acta Physica Sinica, 2005, 54(12): 5511-5516. doi: 10.7498/aps.54.5511
[14]	Huang Yong-Chang, Li Xi-Guo. Unification of different integral variational principles. Acta Physica Sinica, 2005, 54(8): 3473-3479. doi: 10.7498/aps.54.3473
[15]	Wu Hui-Bin, Mei Feng-Xiang. Symmetries of Lagrange system subjected to gyroscopic forces. Acta Physica Sinica, 2005, 54(6): 2474-2477. doi: 10.7498/aps.54.2474
[16]	He Li-Ming, Cao Wei, Chen Xue-Qian, Zhu Yun-Xia. Calculation of helium 1D—3D term intervals for　1snd(n=4—11) states. Acta Physica Sinica, 2005, 54(11): 5077-5081. doi: 10.7498/aps.54.5077
[17]	Luo Shao-Kai. Mei symmetry,Noether symmetry and Lie symmetry of Hamiltonian canonical equations in a singular system. Acta Physica Sinica, 2004, 53(1): 5-10. doi: 10.7498/aps.53.5
[18]	Zhang Yi. Effects of non-conservative forces and nonholonomic constraints on Lie symmetrie s of a Hamiltonian system. Acta Physica Sinica, 2003, 52(6): 1326-1331. doi: 10.7498/aps.52.1326
[19]	Zhang Yi. . Acta Physica Sinica, 2002, 51(3): 461-464. doi: 10.7498/aps.51.461
[20]	Zhang Yi. . Acta Physica Sinica, 2002, 51(8): 1666-1670. doi: 10.7498/aps.51.1666

Catalog

Vol. 60, Issue 5 - 2011-03-05

Metrics

Abstract views: 11500
PDF Downloads: 932
Cited By: 0

姓名
邮箱
手机号码
标题
留言内容
验证码

Search

Article

留言板