Investigations on spectroscopic parameters, vibrational levels, classical turning points and inertial rotation and centrifugal distortion constants for the X1Σg+ 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 Re, the dissociation energy De and the harmonic frequency ωe for the X1Σg+ state of sodium dimer in a number of basis sets. The conclusion is gained that the best Re, De and ωe 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 De, D0, Re, ωe, ωeχe, αe and Be 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 Schrödinger 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 (Dv Hv, Lv, Mv, Nv and Ov) are reported for the first time for the first 31 vibrational states when J = 0.