Structural stability an illustrative example

The relative stability of different structures is determined by a delicate balance between competing contributions to the total energy. This is illustrated by the following example in which we examine the stability of four-atom molecules with respect to the ideal linear chain, square, rhombus 

Following our discussion of the dimeric bond centred on eqn (3.46), we will divide up the pair potential into a repulsive and a bonding contribution, namely 

This can be expressed as the ratio of dimensionless logarithmic derivatives, namely 

It follows from eqs (4.2) and (4.3) that the curvature of the potential about equilibrium can be written as 

We will define the degree of normalized hardness of an interatomic potential by 

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