**61**, 341-348 (2011)

https://doi.org/10.1140/epjd/e2010-10058-6

## A new algorithm for the evaluation of equilibrium inter nuclear bond distance of heteronuclear diatomic molecules based on the hardness equalization principle

Department of Chemistry, University of Kalyani, 741235 Kalyani, India

Corresponding author: ^{a}
dcghosh1@rediffmail.com

Received:
29
January
2010

Revised:
9
April
2010

Published online:
14
January
2011

In this report, we have derived a formula for evaluating the equilibrium
inter nuclear bond distances of heteronuclear diatomics relying upon the
concept of hardness equalization principle. We have relied upon the fact
that the hardness, like the electronegativity, is a qualitative property and
since there is much commonality in the basic philosophy of the origin and
the operational significance of these two fundamental descriptors – the
electronegativity and the hardness, there should be a physical process of
hardness equalization similar to the electronegativity equalization.
Starting from the radial dependent formula of computing hardness of atoms
suggested by us and relying upon the hypothesis of hardness equalization
principle, we have derived an algorithm for computing the equilibrium inter
nuclear bond distance of hetero nuclear diatomics as
*R*_{AB}(Å) *≈* *C*(14.4/), where (eV)
is the molecular hardness, *C* is the constant depends on the fundamental
nature of hardness e.g. the bond type, steric factor etc. The optimized value
of *C* is 0.95. We have invoked the algorithm stated above to compute the
equilibrium inter nuclear bond lengths of as many as four different sets of
compounds with widely divergent chemico-physical properties. In order to
explore the efficaciousness of the formula derived in the present work, we
have performed a validity test by comparing the theoretically evaluated bond
distances vis-à-vis their corresponding spectroscopic counterparts. The
comparative study reveals the surprising results that in majority of cases,
the theoretical bond distances just superimpose upon the experimental bond
distances. Thus, it is transparent that the hardness equalization principle
is justifiably a physical process during the formation of molecule.

*© EDP Sciences, Società Italiana di Fisica, Springer-Verlag, 2011*