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The algebraic method (AM) suggested by Sun et. al. is developed into a nodal variational AM (VAM) to offset the possible experimental errors by using an energy variational part δE after analyzing the error amplification effect. The VAM is used to study the full vibrational levels {Eυ} and the dissociation energies De for 51Πu7Li2, (6d)1Δg Na2, (7d)1ΔgNa2 and 51∑+ NaK alkali metal diatomic molecular electronic systems. The results reproduce all known experimental vibrational energies, predict correct dissociation energies and all unknown high-lying levels that may not be given if one uses original AM or other numerical methods or experimental methods. These theoretical analyses and results not only show that the VAM is feasible and correct for many diatomic systems, but also provide constructive reference for other numerical calculations or simulations.
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Keywords:
- diatomic molecule /
- vibrational level /
- dissociation energy /
- algebraic method
[1] Zhdanov B V, Ehrenreich T, Knize R J 2005 Opt. Commun. 260 696
[2] Krupke W F, Beach R J, Kanz V K, Payne S A 2003 Opt. Lett. 28 2336
[3] Molenaar P A, van der Straten P, Heideman H G M 1996 Phys. Rev. Lett. 77 1460
[4] Sun W G, Hou S L, Feng H, Ren W Y 2002 J. Mol. Spectrosc. 215 93
[5] Sun W G, Ren W Y, Hou S L 2005 Mol. Phys. 103 2335
[6] Sun W G, Liu X Y, Wang Y J, Zhan Y, Fan Q C 2007 Prog. in Phys. 27 151 (in Chinese) [孙卫国, 刘秀英, 王宇杰, 詹妍, 樊群超 2007 物理学进展 27 151]
[7] Ren W Y, Sun W G 2005 Acta Phys. Sin. 54 594 (in Chinese) [任维义, 孙卫国 2005 54 594]
[8] Sun W G, Fan Q C, Ren W Y 2007 Sci. China Ser. G 50 611
[9] Sun W G, Liu X Y, Wang Y J, Zhan Y, Fan Q C 2008 Front. Phys. China 3 382
[10] Fan Q C, Sun W G 2009 Spectrochi. Acta Part A 72 298
[11] Fan Q C, Sun W G, Hao F 2009 Spectrochi. Acta Part A 74 911
[12] Fan Q C, Feng H, Sun W G 2010 Acta Phys. Sin. 59 203 (in Chinese) [范群超, 冯灏, 孙卫国 2010 59 203]
[13] Liu X Y, Sun W G, Fan Q C 2008 Chin. Phys. B 17 2048
[14] Qu S S, Sun W G, Wang Y J, Fan Q C 2009 Acta Phys. Chim. Sin. 25 13 (in Chinese) [渠双双, 孙卫国, 王宇杰, 樊群超 2009 物理化学学报 25 13]
[15] Tian Y, Feng H, Sun W G 2011 Acta Phys. Sin. 60 023301 (in Chinese) [田寅, 冯灏, 孙卫国 2011 60 023301]
[16] Jedrzejewski-Szmek Z, Grochola A, Jastrzebski W, Kowalczyk P 2007 Chemical Physics Letters 444 229
[17] Nadyak R, Jastrezebski W, Kowalczyk P 2002 Chemical Physics Letters 353 414
[18] Herzeberg G (Translated by WANG D C) 1983 Molecular Spectra and Molecular Structure (I)-Spectra of Diatomic Molecules (Beijing: Science Press) pp307-393 (in Chinese) [赫兹堡著; (王鼎昌译) 1986 分子光谱与分子结构(第一卷)——双原子分子光谱, (北京：科学出版社) 第307-393页]
[19] Pan Y L, Sun D P, Ma L S, D L E, Wang Z G 1995 J. Mol. Spectrosc. 169 534-541
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[1] Zhdanov B V, Ehrenreich T, Knize R J 2005 Opt. Commun. 260 696
[2] Krupke W F, Beach R J, Kanz V K, Payne S A 2003 Opt. Lett. 28 2336
[3] Molenaar P A, van der Straten P, Heideman H G M 1996 Phys. Rev. Lett. 77 1460
[4] Sun W G, Hou S L, Feng H, Ren W Y 2002 J. Mol. Spectrosc. 215 93
[5] Sun W G, Ren W Y, Hou S L 2005 Mol. Phys. 103 2335
[6] Sun W G, Liu X Y, Wang Y J, Zhan Y, Fan Q C 2007 Prog. in Phys. 27 151 (in Chinese) [孙卫国, 刘秀英, 王宇杰, 詹妍, 樊群超 2007 物理学进展 27 151]
[7] Ren W Y, Sun W G 2005 Acta Phys. Sin. 54 594 (in Chinese) [任维义, 孙卫国 2005 54 594]
[8] Sun W G, Fan Q C, Ren W Y 2007 Sci. China Ser. G 50 611
[9] Sun W G, Liu X Y, Wang Y J, Zhan Y, Fan Q C 2008 Front. Phys. China 3 382
[10] Fan Q C, Sun W G 2009 Spectrochi. Acta Part A 72 298
[11] Fan Q C, Sun W G, Hao F 2009 Spectrochi. Acta Part A 74 911
[12] Fan Q C, Feng H, Sun W G 2010 Acta Phys. Sin. 59 203 (in Chinese) [范群超, 冯灏, 孙卫国 2010 59 203]
[13] Liu X Y, Sun W G, Fan Q C 2008 Chin. Phys. B 17 2048
[14] Qu S S, Sun W G, Wang Y J, Fan Q C 2009 Acta Phys. Chim. Sin. 25 13 (in Chinese) [渠双双, 孙卫国, 王宇杰, 樊群超 2009 物理化学学报 25 13]
[15] Tian Y, Feng H, Sun W G 2011 Acta Phys. Sin. 60 023301 (in Chinese) [田寅, 冯灏, 孙卫国 2011 60 023301]
[16] Jedrzejewski-Szmek Z, Grochola A, Jastrzebski W, Kowalczyk P 2007 Chemical Physics Letters 444 229
[17] Nadyak R, Jastrezebski W, Kowalczyk P 2002 Chemical Physics Letters 353 414
[18] Herzeberg G (Translated by WANG D C) 1983 Molecular Spectra and Molecular Structure (I)-Spectra of Diatomic Molecules (Beijing: Science Press) pp307-393 (in Chinese) [赫兹堡著; (王鼎昌译) 1986 分子光谱与分子结构(第一卷)——双原子分子光谱, (北京：科学出版社) 第307-393页]
[19] Pan Y L, Sun D P, Ma L S, D L E, Wang Z G 1995 J. Mol. Spectrosc. 169 534-541
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