DFT Reactivity Descriptors and Catalysis - Vrije Universiteit Brussel
DFT Reactivity Descriptors and Catalysis - Vrije Universiteit Brussel
DFT Reactivity Descriptors and Catalysis - Vrije Universiteit Brussel
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Identification of two first derivatives of E with respect to N <strong>and</strong> v in a <strong>DFT</strong><br />
context → response functions in reactivity theory<br />
E[N,v]<br />
⎛ ∂E ⎞<br />
⎜ ⎟<br />
⎝ ∂N⎠<br />
v(r)<br />
= µ<br />
⎛ δE ⎞<br />
⎜ ⎟<br />
⎝ δv(r) ⎠<br />
N<br />
= ρ(r)<br />
⎛ ∂ 2 E ⎞<br />
⎜<br />
⎝ ∂N 2 ⎟<br />
⎠<br />
v(r)<br />
= η<br />
Chemical hardness<br />
∂ 2 E<br />
∂Nδv(r) = ⎛ δµ ⎞<br />
⎜ ⎟<br />
⎝ δv(r) ⎠<br />
= f(r)<br />
N<br />
⎛<br />
= ∂ρ(r) ⎞<br />
⎜ ⎟<br />
⎝ ∂N ⎠<br />
v<br />
2<br />
⎛ δ E ⎞<br />
⎜<br />
⎟<br />
⎝ δ v( r) δ v( r ') ⎠ N<br />
= χ( r, r ')<br />
Linear response<br />
Function<br />
S = 1 η<br />
Chemical Softness<br />
Fukui function<br />
Pag.<br />
30-9-2008 15
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