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)
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
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 $J=0$.
Received: 31 December 2006
Revised: 01 January 2007
Accepted manuscript online:
(Rotation, vibration, and vibration-rotation constants)
Fund: 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
Cite this article:
Yu Ben-Hai(余本海), Dai Qi-Run(戴启润), Shi De-Heng(施德恒), and Liu Yu-Fang(刘玉芳) Investigations on spectroscopic parameters, vibrational levels, classical turning points and inertial rotation and centrifugal distortion constants for the X1∑+g state of sodium dimer 2007 Chinese Physics 16 2962
Altmetric calculates a score based on the online attention an article receives. Each coloured thread in the circle represents a different type of online attention. The number in the centre is the Altmetric score. Social media and mainstream news media are the main sources that calculate the score. Reference managers such as Mendeley are also tracked but do not contribute to the score. Older articles often score higher because they have had more time to get noticed. To account for this, Altmetric has included the context data for other articles of a similar age.