The Linear Response Function. - Vrije Universiteit Brussel

Turning to a second functional derivative2⎛ δ Eχ ( r,r' ) = ⎜⎝ δv r δv r'E[ v+wi ]-2E[ v ] +E[ v-wi ] ~ ( ) ( ) ( )∑( ) ( ) ( )χ r,r' = q β r β rkl( ) ( )kl k l⎞⎟⎠N∫∫χ r,r' w r w r' drdr'ii∑ ∫ ∫[ ] [ ] [ ] ( ) ( ) ( ) ( )E v+w -2E v +E v-w = q β r w r dr β r' w r' dr'i i kl k i l iklperturbationsexpansionskl( )q → χ r,r'Pag.6-1-2012 16