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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, 戴启润, 施德恒, 刘玉芳
2007 (10):
2962-2967.
doi: 10.1088/1009-1963/16/10/024
摘要
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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 $J=0$.
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