中国物理B ›› 2007, Vol. 16 ›› Issue (10): 2962-2967.doi: 10.1088/1009-1963/16/10/024

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Investigations on spectroscopic parameters, vibrational levels, classical turning points and inertial rotation and centrifugal distortion constants for the X1∑+g state of sodium dimer

余本海1, 戴启润2, 施德恒3, 刘玉芳4   

  1. (1)College of Physics and Electronic Engineering, Xinyang Normal University, Xinyang 464000, China; (2)College of Physics and Electronic Engineering, Xinyang Normal University, Xinyang 464000, China; (3)College of Physics and Electronic Engineering, Xinyang Normal University, Xinyang 464000, China;College of Physics and Information Engineering, Henan Normal University, Xinxiang 453007, China; (4)College of Physics and Information Engineering, Henan Normal University, Xinxiang 453007, China
  • 收稿日期:2006-12-31 修回日期:2007-01-01 出版日期:2007-10-08 发布日期:2007-10-08
  • 基金资助:
    Project supported by the National Natural Science Foundation of China (Grant No~10574039), the Henan Innovation for University Prominent Research Talents (Grant No~2006KYCX002) and the Natural Science Foundation of Henan Province (Grant Nos~2006140008 and

Investigations on spectroscopic parameters, vibrational levels, classical turning points and inertial rotation and centrifugal distortion constants for the X1∑+g state of sodium dimer

Yu Ben-Hai(余本海)a)†, Dai Qi-Run(戴启润)a), Shi De-Heng(施德恒)a) b), and Liu Yu-Fang(刘玉芳)b)   

  1. a College of Physics and Electronic Engineering, Xinyang Normal University, Xinyang 464000, China; b College of Physics and Information Engineering, Henan Normal University, Xinxiang 453007, China
  • Received:2006-12-31 Revised:2007-01-01 Online:2007-10-08 Published:2007-10-08
  • Supported by:
    Project supported by the National Natural Science Foundation of China (Grant No~10574039), the Henan Innovation for University Prominent Research Talents (Grant No~2006KYCX002) and the Natural Science Foundation of Henan Province (Grant Nos~2006140008 and

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摘要： The density functional theory (B3LYP, B3P86) and the quadratic configuration-interaction method including single and double substitutions (QCISD(T), QCISD) presented in Gaussian03 program package are employed to calculate the equilibrium internuclear distance $R_{\rm e}$, the dissociation energy $D_{\rm e }$ and the harmonic frequency $\omega _{\rm e}$ for the $X{}^{1}\Sigma^{ + }_{\rm g}$ state of sodium dimer in a number of basis sets. The conclusion is gained that the best $R_{\rm e}$, $D_{\rm e}$ and $\omega _{\rm e}$ results can be attained at the QCISD/6-311G(3df,3pd) level of theory. The potential energy curve at this level of theory for this state is obtained over a wide internuclear separation range from 0.16 to 2.0~nm and is fitted to the analytic Murrell--Sorbie function. The spectroscopic parameters $D_{\rm e}$, $D_{0}$, $R_{\rm e}$, $\omega _{\rm e}$, $\omega _{\rm e}\chi _{\rm e}$, $\alpha _{\rm e}$ and $B_{\rm e}$ are calculated to be 0.7219~eV, 0.7135~eV, 0.31813~nm, 151.63~cm$^{ - 1}$, 0.7288~cm$^{ - 1}$, 0.000729~cm$^{ - 1}$ and 0.1449~cm$^{ - 1}$, respectively, which are in good agreement with the measurements. With the potential obtained at the QCISD/6-311G(3df,3pd) level of theory, a total of 63 vibrational states is found when $J=0$ by solving the radial Schr\"{o}dinger equation of nuclear motion. The vibrational level, corresponding classical turning point and inertial rotation constant are computed for each vibrational state. The centrifugal distortion constants ($D_{\upsilon }\, H_{\upsilon }$, $L_{\upsilon }$, $M_{\upsilon }$, $N_{\upsilon }$ and $O_{\upsilon })$ are reported for the first time for the first 31 vibrational states when $J=0$.

关键词: dissociation energy, vibrational level, turning point, centrifugal distortion constant

Abstract: The density functional theory (B3LYP, B3P86) and the quadratic configuration-interaction method including single and double substitutions (QCISD(T), QCISD) presented in Gaussian03 program package are employed to calculate the equilibrium internuclear distance $R_{\rm e}$, the dissociation energy $D_{\rm e }$ and the harmonic frequency $\omega _{\rm e}$ for the $X{}^{1}\Sigma^{ + }_{\rm g}$ state of sodium dimer in a number of basis sets. The conclusion is gained that the best $R_{\rm e}$, $D_{\rm e}$ and $\omega _{\rm e}$ results can be attained at the QCISD/6-311G(3df, 3pd) level of theory. The potential energy curve at this level of theory for this state is obtained over a wide internuclear separation range from 0.16 to 2.0 nm and is fitted to the analytic Murrell--Sorbie function. The spectroscopic parameters $D_{\rm e}$, $D_{0}$, $R_{\rm e}$, $\omega _{\rm e}$, $\omega _{\rm e}\chi _{\rm e}$, $\alpha _{\rm e}$ and $B_{\rm e}$ are calculated to be 0.7219 eV, 0.7135 eV, 0.31813 nm, 151.63 cm$^{ - 1}$, 0.7288 cm$^{ - 1}$, 0.000729 cm$^{ - 1}$ and 0.1449 cm$^{ - 1}$, respectively, which are in good agreement with the measurements. With the potential obtained at the QCISD/6-311G(3df,3pd) level of theory, a total of 63 vibrational states is found when $J=0$ by solving the radial Schr?dinger equation of nuclear motion. The vibrational level, corresponding classical turning point and inertial rotation constant are computed for each vibrational state. The centrifugal distortion constants ($D_{\upsilon } H_{\upsilon }$, $L_{\upsilon }$, $M_{\upsilon }$, $N_{\upsilon }$ and $O_{\upsilon })$ are reported for the first time for the first 31 vibrational states when $J=0$.

Key words: dissociation energy, vibrational level, turning point, centrifugal distortion constant

中图分类号:  (Vibrational analysis)

  • 33.20.Tp
31.50.-x (Potential energy surfaces) 33.15.Fm (Bond strengths, dissociation energies) 33.15.Mt (Rotation, vibration, and vibration-rotation constants)