The Linear Response Function. - Vrije Universiteit Brussel

What about the remaining second order derivativeχ ( r,r' ): linear response functionN( )⎛ 2δ E ⎞ ⎛ δρ r ⎞= =''⎜δv( r) δv( r ) ⎟ ⎜δv( r ) ⎟⎝ ⎠ ⎝ ⎠N• Computationally demanding• ? Chemical Interpretation: six dimensional kernel• ? Condensed VersionFundamental Importance1. Information about propagation of an (external potential) perturbation on position r’throughout the system2. Berkowitz Parr relationship (JCP 88, 2554, 1988)( ) s( r,r ')χ r,r '= − +s( r) s( r' )SSoftness kernelS∫∫s( r)All information⎛ δρ rs( r,r' ) = -⎜⎝ δv r'f(r)( ) ⎞( ) ⎟⎠ µ( )inverted → η r,r'Hardness kernel……Pag.6-1-2012 11