The Linear Response Function. - Vrije Universiteit Brussel

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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
? Visualisation /interpretation of this six dimensional kernel• Condensation to an atom-condensed linear response matrixχAB• multi-center numerical integration scheme using Becke’s “fuzzy” Voronoi polyhedra( )χ = χ r,r' drdr'AB∫ ∫vAvBM.Torrent Sucarrat, P. Salvador, P. Geerlings, M.Solá,J.Comp.Chem. 28, 574, 2007Pag.6-1-2012 17
Page 1 and 2: The Linear Response Function.Paul G
Page 3 and 4: 1. Introduction : Chemical Concepts
Page 5 and 6: Conceptual DFT (R.G. Parr, W. Yang,
Page 7 and 8: Identification of two first derivat
Page 9 and 10: What about third order derivatives?
Page 11 and 12: What about the remaining second ord
Page 13 and 14: 2.2 Direct evaluation of the second
Page 15: An example H 2 COFukui function f +
Page 19 and 20: 2.3 An Orbital based approach• Si
Page 21 and 22: H 2 OPresent methodO H1 H2O -1.76H
Page 23 and 24: 2.4 Inductive and mesomeric effects
Page 25 and 26: Substituted benzenes vs cyclohexane
Page 27 and 28: 2.5 The linear response function as
Page 29 and 30: Pag.6-1-2012 29• typical benzene-
Page 31 and 32: An application: inorganic ringsPag.
Page 33 and 34: Valence Bond StructuresX= NH, O, PH
Page 35 and 36: Related cases• Boroxine• s-trip
Page 37 and 38: 4. Conclusions• Conceptual DFT of
Page 39 and 40: A Comment on “the nearsightedness

The Linear Response Function. - Vrije Universiteit Brussel

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