The Linear Response Function. - Vrije Universiteit Brussel

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Methodology: evaluation of⎛⎜⎝δQδv[ ]( )⎛ δQ v ⎞Q[ v+w ]-Q[ v ] = ∫⎜w r dr+ο wδv r ⎟⎝ ⎠⎞⎟⎠( ) (2)i i iNperturbation w i (r) (i= 1, ….P)• <strong>Linear</strong> response regime[ ]( )⎛ δQ v⎜⎝ δv r⎞⎟⎠NK∑j=1jj( )= q β r• basis set expansionK∑ ∫[ ] [ ] ( ) ( )Q v+w -Q v = q w r β r dri j i jj=1d=BqChoose P>K → find q via least squares fitting• Perturbationswi-pr = r-R( )ii• Expansion functions • s on p type GTO centered on each center• exponents doubled as compared to primitive setPag.6-1-2012 14
An example H 2 COFukui function f + (r)Nucleophilic attack (including correct angle) at CSCN -Fukui function f - (r)Softest reaction site for an attacking electrophile: ST. Fievez, N. Sablon, F. De Proft, P.W. Ayers, P. Geerlings, J.Chem.<strong>The</strong>or. Comp., 45, 1065, 2008Pag.6-1-2012 15
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: 2.2 Direct evaluation of the second
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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