Karachi University Journal of Science, 2012, 40, 1-4 1
0250-5363/12 © 2012 University of Karachi
Prediction of
e
x
e
from a Four-Parameter Potential Function of Diatomic
Molecules
Zaheer Uddin,
1,2
Intikhab Ulfat
2,3
and Khursheed A. Siddiqui
4
1
Yanbu University College, Yanbu, KSA;
2
Department of Physics, University of Karachi, Karachi, Pakistan;
3
Department of Applied Physics, Chalmers University of Technology, SE-41296 Göteborg, Sweden and
4
King Abdul Aziz
University, KSA
Abstract: The knowledge of potential energy curves of molecules is essential in order to have clear picture of its energy
levels or molecular structure. No analytic potential function for diatomic molecule has been accepted as universal function
for all molecules. The Values of for eighteen molecular states have been predicted from a four-parameter function.
These values are compared with those predicted by eight other potential functions and with observed one.
Keywords: Empirical model, potential function, diatomic molecule, molecular potential function.
INTRODUCTION
The potential energy functions play an important role in
understanding the spectroscopy of diatomic molecules. There
are different ways to construct the potential energy curves
from these functions. When enough spectroscopic data are
not available and quantum mechanical models can not be
used due to the cumbersome procedures, the empirical
functions can be used for a variety of molecules. In these
empirical methods all stable potential energy curves are
fitted to an algebraic expression. These empirical functions
make use of spectroscopic constants which are experimentally
accurately known and are used to construct the potential
curves. The parameters of the empirical potential functions
are determined in terms of the following constants.
In three parameter functions, the constants
e
and
are the unused constants whereas in four parameter functions
the is the unused constant. These unused constants
have been predicted for a number of molecules by a number
of workers [1-7 and references there in].
The present paper aims at predicting
e
x
e
from a four-
parameter empirical potential energy function [1] for
*Address correspondence to this author at the Department of Physics,
University of Karachi, Karachi, Pakistan
nineteen molecular states used by Steel et al. [2]. Their data
are useful in this respect that such a large data for nineteen
molecular states from seven potential functions is not
available elsewhere. The present paper could not be
combined with the paper on potential function [1] because of
the fact that different molecular states and molecular
constants have been used in the two cases. The four-
parameter potential function of Rafi et al. [1] is:
(1)
where
(2)
, is the inter-nuclear distance, a
and b are defined below.
We use the following relation of Varshni [8] for the
prediction of :
(3)
It will be appropriate to define here first:
i. The dissociation energy (D
e
)
(4)
ii. The harmonic force constant (k
e
)
(5)
iii. The Sutherland parameter (¢)
(6)