The Linear Response Function. - Vrije Universiteit Brussel

2.2 Direct evaluation of the second orderfunctional derivativeA first step: the numerical approach• direct evaluation of the second order functional derivative( )χ r,r'2⎛ δ E ⎞= ⎜δv( r) δv( r' ) ⎟⎝⎠N• methodology in line with the first order case( )f r( )⎛ ∂ρ r ⎞ ⎛ δµ ⎞= ⎜ ⎟ = ∂N⎜ δv r ⎟( )⎝ ⎠v⎝ ⎠Nfukui functionf( 2 )( r)( )⎛ ∂f r ⎞ ⎛ δη⎞= ⎜ ⎟ = ∂N⎜ δv r ⎟( )⎝ ⎠v⎝ ⎠Ndual descriptorP.W Ayers, F. De Proft, A. Borgoo, P. Geerlings, JCP, 126, 224107, 2007.N. Sablon, F. De Proft, P.W. Ayers, P. Geerlings, JCP, 126, 224108, 2007.Pag.6-1-2012 13