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The accuracies of the predicted R-branch and Q-branch transitional lines of rovibrational diatomic systems for rotational states of J 100 are improved by using new analytical formulae and an improved difference converging method (DCM) in this study. The new formulae include the contributions from a higher-order energy term Hv. The improved DCM method includes a new physical converging criterion that is particularly useful in predicting unknown transitional lines. These improvements are used to study the transitional lines of the R-branch of the TiF and CO molecules and the Q-branch of the TiF molecule. The results show that the accuracies of the R-branch and Q-branch rotational lines are about one order of magnitude better than the results obtained using previous formulae; the new physical converging criterion can efficiently reduce the possible errors in the spectrum computations; the theoretical rotational lines obtained using the improved DCM method are much better than those obtained using the least-squares method.
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Keywords:
- diatomic molecule /
- transitional lines /
- difference method /
- error analysis
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[2] Xu K Z 2011 Higher Atomic and Molecular Physics (Beijing: Science Press) pp35-87 (in Chinese) [徐克尊 2011 高等原子分子物理学(第二版) (北京: 科学出版社) 第35-87页]
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[4] Li S Y, Guo F M, Wang J, Yang Y J, Jing M X 2015 Chin. Phy. B 24 104205
[5] Zhu L F, Tian H C, Liu Y W, Kang X, Liu G X 2015 Chin. Phy. B 24 043101
[6] Douglass K O, Keske J C, Rees F S, Welch K, Yoo H S, Pate B H, Lemov I, Suenram R D 2003 Chem. Phys. Lett. 376 548
[7] Zhang S H, Zhen J F, Zhang Q, Chen Y 2008 J. Mol. Spectrosc. 252 77
[8] Staanum P, Pashov A, Knockel H, Tiemann E 2007 Phys. Rev. A 75 04251
[9] Yang X H, Ben J W, Li L, Chen Y Q 2008 J. Quant. Spectrosc. Radiat. Transfer. 109 468
[10] Saksena M D, Deo M N, Sunanda K, Behere S H, Londhe C T 2008 J. Mol. Spectrosc. 247 47
[11] O'Brien L C, Borchert B A, Farquhar A, Shaji S, O'Brien J J, Field R W 2008 J. Mol. Spectrosc. 252 136
[12] Le Ru E C, Etchegoin P G 2008 Principles of Surface-Enhanced Raman Spectroscopy (Holland: Elsevier) pp102-121
[13] Larkin P J 2011 IR and Raman Spectroscopy: Principles and Spectral Interpretation (Holland: Elsevier) pp149-172
[14] Li A M, Wei J Z 2003 Atomic Absorption and Atomic Fluorescence Spectrometry (Beijing: Science Press) pp49-56 [李安模, 魏继中 2003 原子吸收及原子荧光光谱分析(北京: 科学出版社) 第49-56页]
[15] Levine I 2011 Quantum Chemistry (Shanghai: Xing Jie Book Publishing Corporation) pp91-115 [Iran. Levine 2011 量子化学(第六版) (上海: 兴界图书出版公司)第91-115页]
[16] Xu G X, Li L M, Wang D M 2001 The Principle of Quantum Mechanics and ab initio Method (Volume 2) (Beijing: Science Press) pp173-198 [徐光宪, 黎乐民, 王德民 2001 量子化学基本原理和从头计算法(中册)(北京: 科学出版社) 第173-198页]
[17] Wu Z K, Tang A Q 1999 The Monograph on Molecular Spectroscopy (Jinan: Shandong Science and Technology Press) pp138-142 [吴征铠, 唐敖庆 1999 分子光谱学专论 (济南: 山东科学技术出版社) 第138-142页]
[18] Hokenberg P, Kohn W 1964 Phys. Rev. B 136 864
[19] Humphreys J E 1972 Introduction to Lie Algebras and Representation Theory (German: Springer) pp41-45
[20] Wang Y Q, Chen D Y, Xia Y Q, Fan R W, Lu F M 2010 Chin. Phys. B 19 023203
[21] Ortakaya S 2013 Chin. Phys. B 22 070303
[22] Sun W G, Fan Q C, Li H D, Feng H 2011 Spectrochi. Acta Part A 79 35
[23] Li H D, Sun W G, Fan Q C, Feng H 2011 Spectrochi. Acta Part A 83 136
[24] Li H D, Sun W G, Fan Q C, Feng H 2012 Acta Phys. Sin. 61 093301 (in Chinese) [李会东, 孙卫国, 樊群超, 冯灏 2012 物理学报 61 093301]
[25] Fu J, Sun W G, Li H D, Fan Q C, Zhang Y, Feng H 2012 Spectrochi. Acta Part A 91 244
[26] Wang Q, Sun W G, Fan Q C 2013 Spectrochi. Acta Part A 114 51
[27] Jiang Y H, Sun W G, Fan Q C, Zhang Y, Fu J, Li H D, Feng H 2013 Acta Phys. Sin. 62 213301 (in Chinese) [江永红, 孙卫国, 樊群超, 张燚, 付佳, 李会东, 冯灏 2013 物理学报 62 213301]
[28] Jiang Y H, Sun W G, Zhang Y, Fu J, Fan Q C, Li H D, Feng H 2016 Spectrochi. Acta Part A 153 87
[29] Imajo T, Kobayashi Y, Nakashima Y, Tanaka K, Tanaka T 2005 J. Mol. Spectrosc. 230 139
[30] Mishra A P, Shetty B J, Kshirsagar R J 2005 J. Mol. Spectrosc. 232 296
[31] Fu J, Fan Q C, Sun W G, Hu S, Jiang Y H 2013 Acta Phys. Sin. 62 233301 (in Chinese) [付佳, 樊群超, 孙卫国, 胡石, 江永红 2013 物理学报 62 233301]
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[1] Herzeberg G (translated by Wang D C) 1983 Molecular Spectra and Molecular Strecture (I): Spectra of Diatomic Molecules (Beijing: Science Press) pp15-38 (in Chinese) [赫兹伯格G 著(王鼎昌 译) 1983分子光谱与分子结构(第一卷)(北京: 科学出版社) 第15-38页]
[2] Xu K Z 2011 Higher Atomic and Molecular Physics (Beijing: Science Press) pp35-87 (in Chinese) [徐克尊 2011 高等原子分子物理学(第二版) (北京: 科学出版社) 第35-87页]
[3] Zhu Z H, Yu H G 1997 The Molecular Structure and Molecular Potential Energy Function (Beijing: Science Press) pp54-66 (in Chinese) [朱正和, 俞华根 1997 分子结构与分子势能函数(北京: 科学出版社) 第54-66页]
[4] Li S Y, Guo F M, Wang J, Yang Y J, Jing M X 2015 Chin. Phy. B 24 104205
[5] Zhu L F, Tian H C, Liu Y W, Kang X, Liu G X 2015 Chin. Phy. B 24 043101
[6] Douglass K O, Keske J C, Rees F S, Welch K, Yoo H S, Pate B H, Lemov I, Suenram R D 2003 Chem. Phys. Lett. 376 548
[7] Zhang S H, Zhen J F, Zhang Q, Chen Y 2008 J. Mol. Spectrosc. 252 77
[8] Staanum P, Pashov A, Knockel H, Tiemann E 2007 Phys. Rev. A 75 04251
[9] Yang X H, Ben J W, Li L, Chen Y Q 2008 J. Quant. Spectrosc. Radiat. Transfer. 109 468
[10] Saksena M D, Deo M N, Sunanda K, Behere S H, Londhe C T 2008 J. Mol. Spectrosc. 247 47
[11] O'Brien L C, Borchert B A, Farquhar A, Shaji S, O'Brien J J, Field R W 2008 J. Mol. Spectrosc. 252 136
[12] Le Ru E C, Etchegoin P G 2008 Principles of Surface-Enhanced Raman Spectroscopy (Holland: Elsevier) pp102-121
[13] Larkin P J 2011 IR and Raman Spectroscopy: Principles and Spectral Interpretation (Holland: Elsevier) pp149-172
[14] Li A M, Wei J Z 2003 Atomic Absorption and Atomic Fluorescence Spectrometry (Beijing: Science Press) pp49-56 [李安模, 魏继中 2003 原子吸收及原子荧光光谱分析(北京: 科学出版社) 第49-56页]
[15] Levine I 2011 Quantum Chemistry (Shanghai: Xing Jie Book Publishing Corporation) pp91-115 [Iran. Levine 2011 量子化学(第六版) (上海: 兴界图书出版公司)第91-115页]
[16] Xu G X, Li L M, Wang D M 2001 The Principle of Quantum Mechanics and ab initio Method (Volume 2) (Beijing: Science Press) pp173-198 [徐光宪, 黎乐民, 王德民 2001 量子化学基本原理和从头计算法(中册)(北京: 科学出版社) 第173-198页]
[17] Wu Z K, Tang A Q 1999 The Monograph on Molecular Spectroscopy (Jinan: Shandong Science and Technology Press) pp138-142 [吴征铠, 唐敖庆 1999 分子光谱学专论 (济南: 山东科学技术出版社) 第138-142页]
[18] Hokenberg P, Kohn W 1964 Phys. Rev. B 136 864
[19] Humphreys J E 1972 Introduction to Lie Algebras and Representation Theory (German: Springer) pp41-45
[20] Wang Y Q, Chen D Y, Xia Y Q, Fan R W, Lu F M 2010 Chin. Phys. B 19 023203
[21] Ortakaya S 2013 Chin. Phys. B 22 070303
[22] Sun W G, Fan Q C, Li H D, Feng H 2011 Spectrochi. Acta Part A 79 35
[23] Li H D, Sun W G, Fan Q C, Feng H 2011 Spectrochi. Acta Part A 83 136
[24] Li H D, Sun W G, Fan Q C, Feng H 2012 Acta Phys. Sin. 61 093301 (in Chinese) [李会东, 孙卫国, 樊群超, 冯灏 2012 物理学报 61 093301]
[25] Fu J, Sun W G, Li H D, Fan Q C, Zhang Y, Feng H 2012 Spectrochi. Acta Part A 91 244
[26] Wang Q, Sun W G, Fan Q C 2013 Spectrochi. Acta Part A 114 51
[27] Jiang Y H, Sun W G, Fan Q C, Zhang Y, Fu J, Li H D, Feng H 2013 Acta Phys. Sin. 62 213301 (in Chinese) [江永红, 孙卫国, 樊群超, 张燚, 付佳, 李会东, 冯灏 2013 物理学报 62 213301]
[28] Jiang Y H, Sun W G, Zhang Y, Fu J, Fan Q C, Li H D, Feng H 2016 Spectrochi. Acta Part A 153 87
[29] Imajo T, Kobayashi Y, Nakashima Y, Tanaka K, Tanaka T 2005 J. Mol. Spectrosc. 230 139
[30] Mishra A P, Shetty B J, Kshirsagar R J 2005 J. Mol. Spectrosc. 232 296
[31] Fu J, Fan Q C, Sun W G, Hu S, Jiang Y H 2013 Acta Phys. Sin. 62 233301 (in Chinese) [付佳, 樊群超, 孙卫国, 胡石, 江永红 2013 物理学报 62 233301]
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