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

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.