Connection of the vibron model with the modified P€ oschl–Teller potential in configuration space R. Lemus * , R. Bernal Instituto de Ciencias Nucleares, UNAM, A.P. 70-543, Circuito Exterior, C.U., 04510 Mexico, D.F., Mexico Received 18 February 2002 Abstract ThemodifiedP€ oschl–Teller (MPT) potential is analyzed by a realization of its dynamical group in configuration space. The expansions of the coordinate and momentum in terms of the creation and annihilation operators are obtained from thisrealization.AsystemoftwoMPToscillatorsinteractingviaapotentialcouplingbilinearinthecoordinate x isstudied. This analysis allows to establish an exact quantum-mechanical connection between the suð2Þ vibron model and the tra- ditional description of molecular vibrations. It is shown that the suð2Þ vibron model corresponds to taking the dominant Dv ¼1 interaction in an approximate fashion. The energy spectrum for the system of coupled oscillators is compared withboththesuð2Þ vibronmodelandthemoregeneralapproachofconsideringhigher-ordertermsoftheexpansionsinthe algebraic space. In addition, a two oscillator system with an interacting potential in terms of the variables u i ¼ tanhðax i Þ is analyzed. Comparison of the spectrum generated by this system with previous results in the space ðp; xÞ suggests that u is the natural variable to describe the P€ oschl–Teller systems. Ó 2002 Elsevier Science B.V. All rights reserved. 1. Introduction A considerable number of applications regard- ing the vibron model have been published since its appearance in the early eighties [1]. The vibron model, which was originated from the IBM in nuclear physics [2], is characterized by its algebraic structure and does not involve an explicit corre- spondence with the traditional rovibrational de- scription in configuration space. The vibron model was first proposed to describe the rovibrational degrees of freedom of diatomic molecules [3], but later on was generalized to describe linear poly- atomic molecules [4]. Due to its complexity, how- ever, for arbitrary polyatomic molecules a simplified version was required. The one-dimen- sional version of the model, known as the su(2) vibron model, was proposed to describe the vi- brational excitations of polyatomic molecules in a local mode scheme [5,6]. In the framework of this approach the stretching degrees of freedom are represented by Morse oscillators, while the bend- ing modes may be associated either to a Morse or P€ oschl–Teller potentials, as long as isomerization and tunneling effects are not present. A relation between the SU(2) group and the Morse and P€ oschl–Teller systems can be directly established by means of certain coordinate trans- Chemical Physics 283 (2002) 401–417 www.elsevier.com/locate/chemphys * Corresponding author. Fax: +52-5-616-2233. E-mail address: renato@nuclea.unam.mx (R. Lemus). 0301-0104/02/$ - see front matter Ó 2002 Elsevier Science B.V. All rights reserved. PII:S0301-0104(02)00630-4