差分收敛法对双原子分子高J值转动谱线的预言

江永红; 孙卫国; 张燚; 付佳; 樊群超

doi:10.7498/aps.65.070202

摘要

为了更精确地预言转动量子数J 100时双原子分子R支和Q支的振转跃迁谱线, 本文在考虑了转动能级展开式中高阶小项Hv的前提下重新推导出能更好地预言R支和Q支跃迁谱线的物理解析公式. 另一方面, 通过对差分收敛法计算过程的细致分析, 从物理误差的角度提出了一个在没有实验数据作为参照时仍然能有效收敛的重要物理判据. 应用这些新公式和新判据对TiF和CO分子R支振转跃迁谱线和TiF分子Q支振转跃迁谱线进行了研究. 结果表明: 包含高阶小项Hv的新公式的预言结果精度比原有不含Hv的公式的结果提高了一个数量级; 新判据的使用能更有效地减小预言谱线的可能误差, 提高预言结果精度. 最后通过与最小二乘法计算结果的对比, 进一步说明新公式和新判据在预言R支和Q支振转跃迁谱线数据方面的有效性和准确性.

关键词:

Abstract

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.

Keywords:

作者及机构信息

1.
国防科学技术大学理学院, 长沙 410073;

2.
四川大学原子与分子物理研究所, 成都 610065;

3.
西华大学物理与化学学院, 先进计算研究中心, 成都 610039;

4.
国防科学技术大学光电科学与工程学院, 长沙 410073

通信作者: 孙卫国, wgsun@scu.edu.cn

基金项目: 国家自然科学基金(批准号: 11074204, 11174236, 11204244)和教育部基金(批准号: 20100181110085) 资助的课题.

Authors and contacts

1.
College of Science, National University of Defense Technology, Changsha 410073, China;

2.
Institute of Atomic and Molecular Physics, Sichuan University, Chengdu 610065, China;

3.
Research Center for Advanced Computation, School of Physics and Chemistry, Xihua University, Chengdu 610039, China;

4.
College of OptoElectronic Science and Engineering, National University of Defense Technology, Changsha 410073, China

Corresponding author: Sun Wei-Guo, wgsun@scu.edu.cn

Funds: Project supported by the National Natural Science Foundation of China (Grant Nos. 11074204, 11174236, 11204244) and the Foundation of Ministry of Education of China (Grant No. 20100181110085).

参考文献

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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
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[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
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[13]	Larkin P J 2011 IR and Raman Spectroscopy: Principles and Spectral Interpretation (Holland: Elsevier) pp149-172
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[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 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 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 62 233301]

施引文献

[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 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 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 62 233301]

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