A -New Approach to Solve the Secular Equation

S. Gnanasekaran. R. D. Rajan and S. Sampath Krishnan

Department of Physics, College of Engineering. Anna University, Madras-25 India.

ABSTRACT:

A new approach is given for solving the secular equation | G F — λ E | = 0 applicable for any n-th order vibrational problem. A suitable method which gives expression for off- diagonal elements is chosen (Isotani's) and applied to reduce the secular equation to a system of n non-linear equation in n unknowns (Fij). Newton-Raphson method is used to solve this system of equations and a new technique i s introduced here to determine the values of function and derivatives involved by proper utilization of the symmetry found in them. This is illustrated in three types of pyramidal molecules Gel 13 x. GclhXY and GclbXYZ which contain two 3 x 3,4 X 4 and 5x5 vibrational problems.

KEYWORDS:

Approach; Equation; Newton-Raphson

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Copy the following to cite this article: Gnanasekaran S, Rajan R. D, Krishnan S. S. A -New Approach to Solve the Secular Equation. Orient J Chem 1993;9(1).

Copy the following to cite this URL: Gnanasekaran S, Rajan R. D, Krishnan S. S. A -New Approach to Solve the Secular Equation. Orient J Chem 1993;9(1). Available from: http://www.orientjchem.org/?p=38337