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

doi:10.1088/1009-1963/16/10/024

Abstract

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_{e}

, the dissociation energy

D_{e}

and the harmonic frequency

ω_{e}

for the

X^{1} Σ_{g}^{+}

state of sodium dimer in a number of basis sets. The conclusion is gained that the best

R_{e}

,

D_{e}

and

ω_{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_{e}

,

D_{0}

,

R_{e}

,

ω_{e}

,

ω_{e} χ_{e}

,

α_{e}

and

B_{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_{υ} H_{υ}

,

L_{υ}

,

M_{υ}

,

N_{υ}

and

O_{υ})

are reported for the first time for the first 31 vibrational states when

J = 0

.

Keywords: dissociation energy vibrational level turning point centrifugal distortion constant

Received: 31 December 2006
Revised: 01 January 2007
Accepted manuscript online:

PACS:	33.20.Tp	(Vibrational analysis)
	31.15.E-
	31.50.-x	(Potential energy surfaces)
	33.15.Fm	(Bond strengths, dissociation energies)
	33.15.Mt	(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

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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

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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