The Hiickel model for alkali clusters

An alternative to the spherical jellium approximation just described is to use the tried and tested methods of theoretical chemistry, namely the energy variational principle, to determine the most probable geometrical structure for atomic clusters. This is the basis of the Hiickel method, a rough outline of which is as follows. 

We suppose that there is only one delocalised electron per site (an appropriate assumption for an alkali cluster). The Hiickel Hamiltonian for the cluster can then be written as  

The cohesion energy is defined as the difference between the total energy and the energies of the individual atoms, i.e. 

Ecoh can then be minimised for clusters of one-electron atoms by starting from an arrangement with equal binding lengths and exploring all possible geometries. An example is shown in fig. 12.8. 

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