The recursion method and expectation values

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Abstract
The recursion method has been of use in many localised orbital calculations of the electronic structures of imperfect solids. However, most such calculations have been of local densities of states and there have been few attempts to extend or generalise the method. The authors show how the method can be used to calculate expectation values and response functions in general and so extend the possible range of applications considerably. The techniques described are efficient in that only one tridiagonalisation of the Hamiltonian is needed for each expectation value or response function.