A novel analytic potential function applied to neutral diatomic molecules and charged lons

Li-Xun Song,Chang-Feng Yu,Chang-Jun Zhu,Qiu-Pin Wang,Chong-Hui Zhang

doi:10.4236/ns.2010.23028

Abstract

In this paper, a new method on constructing analytical potential energy functions is pre-sented, and from this a analytical potential en-ergy function applied to both neutral diatomic molecules and charged diatomic molecular ions is obtained. This potential energy function in-cludes three dimensionless undetermined pa-rameters which can be determined uniquely by solving linear equations with the experimental spectroscopic parameters of molecules. The solutions of the dimensionless undetermined parameters are real numbers rather than com-plex numbers, this ensures that the analytical potential energy function has extensive uni-versality. Finally, the potential energy function is examined with four kinds of diatomic molecules or ions—homonuclear neutral diatomic mole-cule , and , homonuclear charged diatomic molecular ion , and , heter-nuclear neutral diatomic Molecule , and , heternuclear ch- arged diatomic Molecular ion , and ,as a conseque- nce, good results are obtained.

Highlights

Analytical potential energy functions are of great significance in the study of material science, molecular spectrum, reaction dynamics of atoms and molecules, vibrational and rotational energy-level structures of molecules, interactions between laser and matter, photoionization etc. [1,2,3] Due to the importance and extensive applications of the potential energy function, the corresponding research works have been carried on all along [4,5,6]
A cosine function with a phase factor is used as basic potential energy function and, through renormalization to the phase factor, a universal potential energy function applied to four kinds of diatomic molecules or ions — homonuclear neutral diatomic molecules, homonuclear charged diatomic molecular ions, heternuclear neutral diatomic molecules and heternuclear charged diatomic molecular ions is given
According to Eqs.22-24, the corresponding force constants can be obtained by using the experimental spectroscopic parameters above, and substituting these force constants into Eq.19 or Eq.21, the undetermined parameters a, b, c can be calculated by solving the linear equations

Summary

INTRODUCTION

Analytical potential energy functions are of great significance in the study of material science, molecular spectrum, reaction dynamics of atoms and molecules, vibrational and rotational energy-level structures of molecules, interactions between laser and matter, photoionization etc. [1,2,3] Due to the importance and extensive applications of the potential energy function, the corresponding research works have been carried on all along [4,5,6]. Sun Weiguo et al have proposed an energy consistent method (ECM) and constructed a new physically well behaved analytical potential function of a diatomic system called ECM potential [11]. In order to obtain the universal analytical potential function of diatomic molecules and ions, renormalization should be needed for the term 1 2 r 2 in Eq., so as to ensure that the derivatives of each order of the Eq. are continuous and finite at equilibrium distance r. The undetermined parameters a, b, c can be determined with the experimental spectroscopic parameters ( e , e e , e Be ) of diatomic molecules or ions The principle of this method is, according to the relationship between undetermined parameters and force constants, to obtain a, b, c by solving linear equations. In Eqs., the relationships between force constants and spectroscopic parameters are as follows f2 4 2 e2c2

APPLIED EXAMPLES OF THE UNIVERSAL ANALYTICAL POTENTIAL ENERGY FUNCTION

5.CONCLUSIONS