Accurate studies of dissociation energies and vibrational energies on alkali metals

doi:10.1088/1674-1056/17/6/019

中国物理B ›› 2008, Vol. 17 ›› Issue (6): 2048-2061.doi: 10.1088/1674-1056/17/6/019

Accurate studies of dissociation energies and vibrational energies on alkali metals

刘秀英, 孙卫国, 樊群超

Institute of Physics, Sichuan University, Chengdu 610065, China

收稿日期:2007-09-13 修回日期:2007-10-18 出版日期:2008-06-20 发布日期:2008-06-20
基金资助:
Project supported by the National Natural Science Foundation of China (Grant No 10774105) and the Science Foundation of the Chinese Educational Ministry.

Accurate studies of dissociation energies and vibrational energies on alkali metals

Liu Xiu-Ying(刘秀英), Sun Wei-Guo(孙卫国)^†, and Fan Qun-Chao(樊群超)

Institute of Physics, Sichuan University, Chengdu 610065, China

Received:2007-09-13 Revised:2007-10-18 Online:2008-06-20 Published:2008-06-20
Supported by:
Project supported by the National Natural Science Foundation of China (Grant No 10774105) and the Science Foundation of the Chinese Educational Ministry.

摘要/Abstract

摘要： This paper studies full vibrational spectra {\{}$E_\upsilon ${\}} and molecular dissociation energies $D_\e$ by using conventional least-squares (LS) fitting and an algebraic method (AM) proposed recently for 10 diatomic electronic states of ${ }^7$Li$_2 $, Na$_2$, NaK and NaLi molecules based on some known experimental vibrational energies in a subset [$E_\upsilon ^{\exp t} $] respectively. Studies show that: (1) although both the full AM spectrum {\{}$E_\upsilon ^{\rm AM} ${\}} and the LS spectrum {\{}$E_\upsilon ^{\rm LS} ${\}} can reproduce the known experimental energies in [$E_\upsilon ^{\exp t} $], the {\{}$E_\upsilon ^{\rm AM} ${\}} is superior to the {\{}$E_\upsilon ^{\rm LS} ${\}} in that the high-lying AM vibrational energies which may not be available experimentally have better or much better accuracy than those LS counterparts in {\{}$E_\upsilon ^{\rm LS} ${\}}, and so is the AM dissociation energy $D_\e^{\rm AM} $; (2) the main source of the errors in the data obtained by using the LS fitting is that the fitting which is just a pure mathematical process does not use any physical criteria that must be satisfied by the full vibrational spectrum, while the AM method does. This study suggests that when fitting or solving a physical equation using a set of source data, it is important not only to apply a proper mathematical tool, but also to use correct physical criteria which measure the physical properties of the data, kick out those data having bigger errors, and impose conditional convergence on the numerical process.

关键词: least-squares method, algebraic method, vibrational energy, dissociation energy

Abstract: This paper studies full vibrational spectra {$E_\upsilon $} and molecular dissociation energies $D_{\rm e}$ by using conventional least-squares (LS) fitting and an algebraic method (AM) proposed recently for 10 diatomic electronic states of ${ }^7$Li$_2 $, Na$_2$, NaK and NaLi molecules based on some known experimental vibrational energies in a subset [$E_\upsilon ^{\exp t} $] respectively. Studies show that: (1) although both the full AM spectrum {$E_\upsilon ^{\rm AM} $} and the LS spectrum {$E_\upsilon ^{\rm LS} $} can reproduce the known experimental energies in [$E_\upsilon ^{\exp t} $], the {$E_\upsilon ^{\rm AM} $} is superior to the {$E_\upsilon ^{\rm LS} $} in that the high-lying AM vibrational energies which may not be available experimentally have better or much better accuracy than those LS counterparts in {$E_\upsilon ^{\rm LS} $}, and so is the AM dissociation energy $D_{\rm e}^{\rm AM} $; (2) the main source of the errors in the data obtained by using the LS fitting is that the fitting which is just a pure mathematical process does not use any physical criteria that must be satisfied by the full vibrational spectrum, while the AM method does. This study suggests that when fitting or solving a physical equation using a set of source data, it is important not only to apply a proper mathematical tool, but also to use correct physical criteria which measure the physical properties of the data, kick out those data having bigger errors, and impose conditional convergence on the numerical process.

Key words: least-squares method, algebraic method, vibrational energy, dissociation energy

中图分类号: (Bond strengths, dissociation energies)

33.15.Fm

31.15.-p (Calculations and mathematical techniques in atomic and molecular physics) 33.15.Mt (Rotation, vibration, and vibration-rotation constants) 33.20.Tp (Vibrational analysis)

刘秀英, 孙卫国, 樊群超. Accurate studies of dissociation energies and vibrational energies on alkali metals[J]. 中国物理B, 2008, 17(6): 2048-2061.

Liu Xiu-Ying(刘秀英), Sun Wei-Guo(孙卫国), and Fan Qun-Chao(樊群超) . Accurate studies of dissociation energies and vibrational energies on alkali metals[J]. Chin. Phys. B, 2008, 17(6): 2048-2061.

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Accurate studies of dissociation energies and vibrational energies on alkali metals

Accurate studies of dissociation energies and vibrational energies on alkali metals

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