Linear Response Theory
This chapter introduces the concept of linear response theory. The response function giving the change in charge density induced by a small change in the potential is derived in terms of the Green function of Chapter 1. These concepts lead to an expression for the error in the Harris–Foulkes functional due to neglect of complete self-consistency, which is shown to be second order in the error in the model input charge density. Linear response in jellium — the uniform gas of electrons — is explored in detail, including the response to non-local potentials. This is background for deriving pairwise potentials in simple metals in Chapter 6. The incorporation of exchange and correlation in the response function is described, whereby pairwise potential models in simple metals can contain more physics than the local density approximation or generalized gradient approximations used in fully self-consistent density functional theory.
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