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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.
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Keywords:
- C2+4 molecules /
- symmetry /
- energy level splitting /
- Jahn-Teller distortion
[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 40 1474]
[4] Qiu Q C 2004 Acta Phys. Sin. 53 2292 (in Chinese) [邱庆春 2004 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 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 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 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 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 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 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 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 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 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 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 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 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 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
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[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 40 1474]
[4] Qiu Q C 2004 Acta Phys. Sin. 53 2292 (in Chinese) [邱庆春 2004 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 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 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 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 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 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 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 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 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 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 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 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 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 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
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