The Linear Response Function. - Vrije Universiteit Brussel

2.3 An Orbital based approach• Single Slater determinant ( say KS-DFT)• Second order perturbation theory V=• Closed shell, spin restricted calculations• Frozen core∆E ~ ε -ε•i→a a i( )χ r,r' =4N 2∞∑ ∑i( )∑δv r( ) ( ) ( ) ( )φ r φ r φ r' φ r'* *i a a iε -εi=1 a=N 2+1 i ai∗(P.W.Ayers,Faraday Discussions,135, 161, 2007)φi: occupied orbitals φa: unoccupied orbitals εi,εa: orbital energiesExact( δρ( r) δvKS( r' ))N∗Zeroth order approximation to the linear response kernel forthe interacting systemPag.6-1-2012 19