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Electron density or electronic density is the measure of the probability of an electron being present at an infinitesimal element of space ... And the LUMO map ...
Diagram of the HOMO and LUMO of a molecule. Each circle represents an electron in an orbital; when light of a high enough frequency is absorbed by an electron in the HOMO, it jumps to the LUMO. 3D model of the highest occupied molecular orbital in CO 2 3D model of the lowest unoccupied molecular orbital in CO 2
The Fukui function is named after Kenichi Fukui, who investigated the frontier orbitals described by the function, specifically the HOMO and LUMO. [3] Fukui functions are related in part to the frontier molecular orbital theory (also known as the Fukui theory of reactivity and selection, also developed by Kenichi Fukui) which discusses how nucleophiles attack the HOMO while at the same time ...
A similar theorem (Janak's theorem) exists in density functional theory (DFT) for relating the exact first vertical ionization energy and electron affinity to the HOMO and LUMO energies, although both the derivation and the precise statement differ from that of Koopmans' theorem. [8]
Traditionally, forming bonds are stabilized when they donate electron density from their bonding HOMO into a neighboring antibonding LUMO, not by accepting electron density into their LUMO. To this end, David A. Evans said of Cieplak's proposal: "Structures are stabilized by stabilizing their highest energy filled states.
In either the S N 2 or the E2 pathway, the HOMO of the nucleophile/base will be donating electron density into this LUMO. [8] As the LUMO for CH 3 CH 2 OH 2 + {\displaystyle {\ce {CH3CH2OH2+}}} has bonding character along the C(β)-H bond, putting electrons into this orbital should result in strengthening of this bond, dissuading its ...
To summarize, we are assuming that: (1) the energy of an electron in an isolated C(2p z) orbital is =; (2) the energy of interaction between C(2p z) orbitals on adjacent carbons i and j (i.e., i and j are connected by a σ-bond) is =; (3) orbitals on carbons not joined in this way are assumed not to interact, so = for nonadjacent i and j; and ...
LUMO map (nucleophilic indicator) – Maps of molecular orbitals may also lead to graphical indicators. For example, the LUMO map, wherein the (absolute value) of the lowest-unoccupied molecular orbital (the LUMO) is mapped onto a size surface (again, most commonly the electron density), providing an indication of nucleophilic reactivity.