The Linear Response Function. - Vrije Universiteit Brussel

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Until now: focus on first and second order derivates• µ = −χ→ Electronegativity Equalization Principle(EEM) (Sanderson, Mortier, …)• η → S= 1 η→ Chemical Hardness and Softness→ HSAB Principle ( Pearson, Parr)Maximum Hardness Principle ( Pearson)• f ( r)s( r ) =Sf ( r)→ Fukuifunction and local Softness.→ Local reactivity / selectivity (Parr, Yang)P. Geerlings, F. De Proft, W. Langenaeker, Chem. Rev. 103, 1793 (2003)Pag.6-1-2012 8
What about third order derivatives?3⎛ ∂ E ⎞ ⎛ ∂η⎞• ⎜ 3 ⎟ = ⎜ ⎟ : hyperhardness: known to be small⎝ ∂N⎠ ⎝ ∂N⎠vv( )( )3⎛ δ E ⎞ ⎛ δχ r,r' ⎞⎜ =δv( r) δv( r' ) δv( r'' ) ⎟ ⎜ δv r'' ⎟⎝ ⎠ ⎝ ⎠• : awkward …? Importance of mixed “2+1” derivativesNN32⎛ ∂ E ⎞ ⎛ δη⎞ ⎛ ∂ ρ r ⎞•( ) ⎛ ∂f ( r)⎞⎜ Nδv( r) ⎟= ⎜ = ⎜ ⎟ = ⎜ ⎟δv( r)⎟⎝ ⎠ ⎝ ⎠ N N ⎠2 2∂N ⎝ ∂ ⎠ ∂v ⎝vDual descriptorC. Morell, A. Grand, A. Toro-Labbé,J. Phys. Chem. A 109, 205, 2005.3⎛ δ E ⎞ ⎛ ∂χ r, r' ⎞ ⎛ δf r ⎞•Already a large number of applications: one shotrepresentation of nucleophilic and electrophilic regions( ) ( )⎟( )⎜ = ⎜ =∂Nδv ( r) δv( r' ) ⎟ ∂N ⎜ δv r' ⎟⎝ ⎠⎝ ⎠vv ⎝ ⎠NunexploredFukui kernelPolarization effects on Fukui functionMight play a role in describing change in polarizability upon ionization,electron attachment, …P. Geerlings, F. De Proft, PCCP, 10, 3028, 2008.Pag.6-1-2012 9
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: Identification of two first derivat
Page 11 and 12: What about the remaining second ord
Page 13 and 14: 2.2 Direct evaluation of the second
Page 15 and 16: An example H 2 COFukui function f +
Page 17 and 18: ? Visualisation /interpretation of
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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