The Linear Response Function. - Vrije Universiteit Brussel

Identification of two first derivatives of E with respect to N and v in a DFTcontext → response functions in reactivity theoryE[N,v]⎛ ∂E ⎞⎜ ⎟⎝ ∂N⎠v(r)ElectronicChemicalPotential= µ= −χElectronegativity⎛ δE⎞⎜ ⎟⎝ δv(r)⎠N= ρ(r)⎛ ∂ 2 E ⎞⎜⎝ ∂N 2 ⎟⎠v(r)= η∂ 2 E∂Nδv(r) = ⎛ δµ ⎞ ⎛⎜ ⎟ = ∂ρ(r) ⎞⎜ ⎟⎝ δv(r) ⎠ ⎝ ∂N ⎠Nv⎛ 2 δE⎞= χ(r, r ')⎜ δv(r) δv(r ') ⎟⎝ ⎠NChemical hardness= f(r)Linear responseFunctionS = 1 ηChemical SoftnessFukui function6-1-2012 Pag.7