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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 ...
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 ...
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
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]
The maleic anhydride is an electron-withdrawing species that makes the dieneophile electron deficient, forcing the regular Diels–Alder reaction. Thus, only the reaction between the HOMO of cyclopentadiene and the LUMO of maleic anhydride is allowed.
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 ...
In cases where the ligand has low energy LUMO, such orbitals also participate in the bonding. The metal–ligand bond can be further stabilised by a formal donation of electron density back to the ligand in a process known as back-bonding. In this case a filled, central-atom-based orbital donates density into the LUMO of the (coordinated) ligand.
σ bonding from electrons in CO's HOMO to metal center d-orbital. π backbonding from electrons in metal center d-orbital to CO's LUMO. The electrons are partially transferred from a d-orbital of the metal to anti-bonding molecular orbitals of CO (and its analogs). This electron-transfer strengthens the metal–C bond and weakens the C–O bond.