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## Homework Statement

i) Write down an expression for the LJ cohesive energy of a molecule consisting of four atoms lying on the corners of a square of side

*a*.

ii) Deduce the equilibrium value of the nearest-neighbour separation,

*a*, assuming the molecule retains its square shape

iii) What other configuration could the molecule adopt that would lower its LJ energy further?

Relevant equation:

U[itex]_{tot}[/itex]=2N[itex]\epsilon[/itex][A[itex]_{12}[/itex]([itex]\frac{σ}{a}[/itex])[itex]^{12}[/itex]-A[itex]_{6}[/itex]([itex]\frac{σ}{a}[/itex][itex])^{6}[/itex]]

## The Attempt at a Solution

I have done parts i) and ii). It is part iii) that I am stuck on. Because bcc, hcp and fcc all have higher N, number of atoms per unit cell, and higher values of A[itex]_{12}[/itex], making the cohesive energy higher - this is the case, isn't it? So what other configuration could the molecule adopt?