Lowest energy unoccupied molecular orbital

HOMO A [OMO 1 A,umo A.UMO+1 AHf QC Energy of the highest occupied molecular orbital Energy of the second highest occupied molecular orbital Energy of the lowest unoccupied molecular orbital Energy of the second lowest unoccupied molecular orbital Heat of formation Dipole moment... 

QSAR methods can be divided into several categories dependent on the nature of descriptors chosen. In classical one-dimensional (ID) and two-dimensional (2D) QSAR analyses, scalar, indicator, or topological variables are examples of descriptors used to explain differences in the dependent variables. 3D-QSAR involves the usage of descriptors dependent on the configuration, conformation, and shape of the molecules under consideration. These descriptors can range from volume or surface descriptors to HOMO (highest occupied molecular orbital) and LUMO (lowest unoccupied molecular orbital) energy values obtained from quantum mechanics (QM) calculations. 

The presence of an aroyl fragment in azomethine ylides obtained from opening of three-membered rings in the case of dipolarophiles with high LUMO (lowest unoccupied molecular orbital) energy or in the absence of an external dipolarophile can lead to the possibility of such unusual reactions as intramolecular 1,3-dipolar cycloaddition [80]. Examples of such reactions are the thermal isomerization of aroyl aziridines 63 into a pyrrole derivative 64 [81, 82] or into 2,5-diphenyloxazole 65 (in the presence of diphenyliodonium iodide) [83] (Scheme 1.16). 

LSwdin population analysis -> charge descriptors (O atomic charge) lowest unoccupied molecular orbital -> quantum-chemical descriptors lowest unoccupied molecular orbital energy -> quantum-chemical descriptors LUMO electron density on the ath atom -> charge descriptors (O net orbital charge)... 

With the progress in the chemical calculation of the molecule, analyses with HOMO/LUMO (highest occupied molecular orbital/lowest unoccupied molecular orbital) energy, absolute hardness/absolute electron negativity, and research into these new and old descriptors have been reported recently. Furthermore, new methods with neural network computers, as well as multiregression analysis, cluster analysis, and major component analysis have been applied to investigate the relationship between the property and function of the molecule and of each descriptor. 

Lovasz-Pelikan index spectral indices (0 eigenvalues of the adjacency matrix) LOVIs = LOcal Vertex Invariants local invariants Lowdin population analysis quantum-chemical descriptors Lowest-Observed-Effect Level biological activity indices (0 toxicological indices) lowest unoccupied molecular orbital quantum-chemical descriptors lowest unoccupied molecular orbital energy quantum-chemical descriptors LUDI energy function scoring functions Lu index —> hyper-Wiener-type indices... 

LUMO Lowest unoccupied molecular orbital energy... 

The first example of catal34ic asymmetric functionalization of arenes under metal-fi ee conditions was documented by MacMillan and coworkers in 2002 under aminocatalysis regime [1]. The combination of chiral imidazoUdinone 38a with enals 37 resulted into the formation of covalent aggregates (i.e., iminium ion 39) featuring a lower LUMO (lowest unoccupied molecular orbital) energy with respect to the alde-hydic precursor. Therefore, the chirally modified electrophile 39 can enter the catal3dic cycle characterized by a diastereoselective nucleophilic attack of electron-rich benzenes followed by the restoring of the catalytically active secondary amine via hydrolysis of the immonium salt 40 (Scheme 5.12). 

The key feature of iminium-ion activation is the lowering of the LUMO (lowest unoccupied molecular orbital) energy, whereby an increased reactivity of the unsaturated system towards nucleophilic addition is obtained. To better understand the mechanism and kinetics of the iminium-ion formation, several experimental studies and calculations have been performed. Often the reactions are accelerated by the addition of Bronsted acid co-catalysts, which presumably assist the initial condensation. This indicates that the condensation is the rate-determining step in these reactions. In a recent study by Mayr [10], the elec-trophiUcity of different iminium ions obtained from various aminocatalysts and cinnamaldehyde was investigated experimentally (Figure 2.2). 

---