Fukui - Calculating the Fukui (and condensed Fukui)...

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Calculating the Fukui (and condensed Fukui) function using Spartan Francisco Mendez and Jose L. Gazquez (J. Am. Chem. Soc. 116, 9298(1994)) discuss chemical reactivity in terms of hard-soft acid-base theory. They state "the regions of a molecule where the Fukui function is large are chemically softer than the regions where the fukui function is small, and by invoking the HSAB principle in a local sense, one may establish the behavior of the different sites with respect to hard or soft reagents" They define, using a finite difference approximation, the Fukui function: f + (r) = ρ N+1 (r) - ρ N (r) or nucleophilic attack f - (r) = ρ N (r) - ρ N-1 (r) for electrophilic attack f o (r) = 1/2 ( ρ N+1 (r) - ρ N-1 (r)) for radical attack Where ρ N is the electron density at a point r in space around the molecule. The N corresponds to the number of electrons in the molecule. N+1 corresponds to an anion, with an electron added to the LUMO of the neutral molecule. N-1 correspondinly is the cation with an electron removed from the HOMO of the neutral. All calculations are done at the ground-state geometry. These functions can be condensed to the nuclei by using an atomic charge partitioning scheme, such as Mulliken population analysis: f + Ak = q Ak (N A + 1) - q Ak (N A ) for nucleophilic attack f - Ak = q Ak (N A ) - q Ak (N A - 1) for electrophilic attack f o Ak = 1/2 (q Ak (N A + 1) - q Ak (N A - 1)) for radical attack Where q Ak (N A ) is the Mulliken charge on atom k for N A total electrons. While the user can obtain values for the condensed functions by hand, the difference plotting capabilities of Spartan can be used to obtain 3D grid representations of the Fukui function. Merely run the appropriate calculations of the (N+1), (N) or (N-1) state using the same geometry, and subtract the resulting density volumes. Easy Method
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Fukui - Calculating the Fukui (and condensed Fukui)...

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