ORIENTAL JOURNAL OF CHEMISTRY www.orientjchem.org An International Open Free Access, Peer Reviewed Research Journal ISSN: 0970-020 X CODEN: OJCHEG 2016, Vol. 32, No. (3): Pg. 1717-1719 Vibrational Frequencies of PH 3 and NF 3 : Lie Algebraic Method J. VIJAYASEKHAR 1 *, K. SRINIVASA RAO 2 and B. V. S. N. HARI PRASAD 3 1 Department of Mathematics, GITAM University, Hyderabad, India. 2 Department of ECE, K L University, Vaddeswaram, Andhra Pradesh, India. 3 Department of Mathematics, Dhanekula Institute of Engg.& Technology,Vijayawada, India. *Corresponding author E-mail: vijayjaliparthi@gmail.com http://dx.doi.org/10.13005/ojc/320352 (Received: May 30, 2016; Accepted: June 17, 2016) ABSTRACT The subject field of vibrational frequencies of polyatomic molecules is an interesting and innovative work in the field of molecular spectroscopy. In this paper we are concerned with the vibrational frequencies of Phosphine (PH3) and Nitrogen triflouride (NF3) using Lie algebraic method. Keywords: Vibrational spectra, Lie algebraic method. INTRODUCTION In the last part of the 19th century, Marius Sophus Lie proposed Lie algebras. Nevertheless, these methods have been useful in the study of the problems in the beginning portion of the 20th century, after the evaluation of quantum mechanics 1,2 . Iachello (1981) presented Lie algebraic method (vibron model) for the study of vibrational spectra of molecules. This method is based on the second quantization of the Schrodinger wave equation with a 3- Dimensional Morse potential function and is described as ro-vibration spectra of diatomic molecules. Considerable attention has been given to determining vibration spectra of molecules. Therefore the study of molecular spectroscopy is fundamental to understanding both experimental and theoretical approaches. There are two general methods which are used to describe molecular vibrations. In the classical approach, the molecular Hamiltonian is parameterized in terms of internal coordinates and the potential energy function is represented in terms of force field constants by spectroscopic data. Although diatomic molecules have very accurate information on force fields, but not in the case of polyatomic molecules. The molecular rotation-vibration spectrum is provided by the Dunham expansion. It is a series of expansion of energy levels of rotational (J) and vibrational (v) quantum numbers. The constant coefficients y ij are