中国物理B ›› 2008, Vol. 17 ›› Issue (8): 2919-2924.doi: 10.1088/1674-1056/17/8/027

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Investigation of analytical potential energy function, harmonic frequency and vibrational levels for the X2∑+ and A2Ⅱ states of CN radical

王建坤, 吴振森   

  1. School of Science, Xidian University, Xi'an 710071, China
  • 收稿日期:2007-10-08 修回日期:2007-12-26 出版日期:2008-08-20 发布日期:2008-08-20
  • 基金资助:
    Project supported by the National Natural Science Foundation of China (Grant No 60771038).

Investigation of analytical potential energy function, harmonic frequency and vibrational levels for the $X^2\varSigma^+$ and $A^2\varPi$ states of CN radical

Wang Jian-Kun(王建坤)† and Wu Zhen-Sen(吴振森)   

  1. School of Science, Xidian University, Xi'an 710071, China
  • Received:2007-10-08 Revised:2007-12-26 Online:2008-08-20 Published:2008-08-20
  • Supported by:
    Project supported by the National Natural Science Foundation of China (Grant No 60771038).

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摘要： This paper calculates the equilibrium structure and the potential energy functions of the ground state ($X^2\Si ^{ + })$ and the low lying excited electronic state ($A^2{\it \Pi}$) of CN radical are calculated by using CASSCF method. The potential energy curves are obtained by a least square fitting to the modified Murrell--Sorbie function. On the basis of physical theory of potential energy function, harmonic frequency ($\omega _{\rm e}$) and other spectroscopic constants ($\omega _{\rm e}\chi _{\rm e}$, $\beta _{\rm e}$ and $\alpha _{\rm e})$ are calculated by employing the Rydberg--Klein--Rees method. The theoretical calculation results are in excellent agreement with the experimental and other complicated theoretical calculation data. In addition, the eigenvalues of vibrational levels have been calculated by solving the radial one-dimensional Schr\"{o}dinger equation of nuclear motion using the algebraic method based on the analytical potential energy function.

关键词: potential energy function, harmonic frequency, vibrational levels, algebraic method

Abstract: This paper calculates the equilibrium structure and the potential energy functions of the ground state ($X^2\varSigma^{ + })$ and the low lying excited electronic state ($A^2{\it \Pi}$) of CN radical are calculated by using CASSCF method. The potential energy curves are obtained by a least square fitting to the modified Murrell--Sorbie function. On the basis of physical theory of potential energy function, harmonic frequency ($\omega _{\rm e}$) and other spectroscopic constants ($\omega _{\rm e}\chi _{\rm e}$, $\beta _{\rm e}$ and $\alpha _{\rm e})$ are calculated by employing the Rydberg--Klein--Rees method. The theoretical calculation results are in excellent agreement with the experimental and other complicated theoretical calculation data. In addition, the eigenvalues of vibrational levels have been calculated by solving the radial one-dimensional Schr\"{o}dinger equation of nuclear motion using the algebraic method based on the analytical potential energy function.

Key words: potential energy function, harmonic frequency, vibrational levels, algebraic method

中图分类号:  (Potential energy surfaces for ground electronic states)

  • 31.50.Bc
31.15.xr (Self-consistent-field methods) 31.50.Df (Potential energy surfaces for excited electronic states) 33.15.Bh (General molecular conformation and symmetry; stereochemistry) 33.15.Mt (Rotation, vibration, and vibration-rotation constants) 33.20.Tp (Vibrational analysis)