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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
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)
Chinese Physics, 2007, 16 (10):
2962-2967.
DOI: 10.1088/1009-1963/16/10/024
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 $J=0$.
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