The Linear Response Function. - Vrije Universiteit Brussel

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Starting point for DFT perturbative approach to chemical reactivityConsiderE = E[N,v]Atomic, molecular system, perturbed in numberof electrons and/or external potentialdE =⎛ ∂E ⎞⎜ ⎟⎝ ∂N⎠dN +v(r)⎛ δE ⎞∫ ⎜ ⎟⎝ δv(r) ⎠δv(r)drNµidentificationfirst order perturbation theoryρ( r)identificationElectronic Chemical Potential (R.G. Parr et al, J. Chem. Phys., 68, 3801 (1978))= - χ (Iczkowski - Margrave electronegativity)Pag.6-1-2012 6
Identification of two first derivatives of E with respect to N and v in a DFTcontext → response functions in reactivity theoryE[N,v]⎛ ∂E ⎞⎜ ⎟⎝ ∂N⎠v(r)ElectronicChemicalPotential= µ= −χElectronegativity⎛ δE⎞⎜ ⎟⎝ δv(r)⎠N= ρ(r)⎛ ∂ 2 E ⎞⎜⎝ ∂N 2 ⎟⎠v(r)= η∂ 2 E∂Nδv(r) = ⎛ δµ ⎞ ⎛⎜ ⎟ = ∂ρ(r) ⎞⎜ ⎟⎝ δv(r) ⎠ ⎝ ∂N ⎠Nv⎛ 2 δE⎞= χ(r, r ')⎜ δv(r) δv(r ') ⎟⎝ ⎠NChemical hardness= f(r)<strong>Linear</strong> response<strong>Function</strong>S = 1 ηChemical SoftnessFukui function6-1-2012 Pag.7
Page 1 and 2: The Linear Response Function.Paul G
Page 3 and 4: 1. Introduction : Chemical Concepts
Page 5: Conceptual DFT (R.G. Parr, W. Yang,
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 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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