Highest occupied molecular orbital and LUMO

The HOMO (highest occupied molecular orbital) and LUMO (lowest unoccupied MO) levels for hydrogen donors used in coal liquefaction are not yet well known, but the principles involved can be illustrated with the group transfer reaction between molecular hydrogen, a (4n+2)e donor with n=0, and naphthalene, a (4m)e acceptor with m=l ... 

Table 1 Calculation of some molecular-based descriptors for BOA, DIMBOA and MBOA. Physicochemical descriptor like logP (partition coefficient between octanol and water) constitutional descriptors like the number of a specified atoms or bonds (number of carbons, hydrogens, oxygens, nitrogens, single and aromatic bonds, the total number of atoms and bonds) and molecular weight quantum-mechanical descriptors like HOMO (Highest Occupied Molecular Orbital) and LUMO (Lowest Unoccupied Molecular Orbital).

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. 

In Chapter 4 we talked about the HOMO (highest occupied molecular orbital) and LUMO (lowest unoccupied molecular orbital) of organic molecules. CH3 (like all radicals) has an orbital containing one electron, which we call a Singly Occupied Molecular Orbital (SOMO). 

Table I shows that the band gap, the energy difference between HOMO (highest occupied molecular orbitals) and LUMO (lowest unoccupied molecular orbitals) levels, decreases monotonically with the increase in network dimension. This decrease is caused by the delocalization of skeleton a electrons, which form both band edges. As is well known, eigenvalues of delocalized wave functions confined to a potential well are determined by the well size and potential-barrier heights. When delocalized wave functions are confined to a smaller area, the HOMO level moves downward and the LUMO level moves upwards, which results in the increase in band gap energy. This quantum size effect is given by...

The Woodward-Hoffmann rules can be rationalized by examining the properties of the frontier MOs of the reactants, i.e., the HOMOs (highest occupied molecular orbitals) and LUMOs (lowest unoccupied molecular orbitals) of the reactants. In order to understand pericyclic reactions, then, you need to be able to construct the MOs of a polyene system from the constituent p orbitals. 

HOMO is the Highest Occupied Molecular Orbital, and LUMO is the Lowest Unoccupied... 

Figure 2.18. Electron affinities of Aui 7g. Predicted shell closings at 8, 20, 34, and 58 are o bserved L The gradual increase in electron affinity, and also the decrease in ionization potential can be nnderstood electrostatically. When a conductive sphere increases in size, the charge can be better accommodated because it can distribute over a larger surface. The low electron affinities are found at the shell closure values, because the empty orbitals have a high energy with respect to the occupied orbitals. The differences in energy between the odd- and even-number clusters reflect differences in energy between the corresponding HOMO (Highest Occupied Molecular Orbital) and LUMO (Lowest Unoccupied Molecular Orbital).

This means that the tunnehng current is proportional to the local density of states (LDOS) of the sample at the center of the sphere (tip) and therefore, a constant current image reflects the LDOS of the sample. This demonstrates that an STM image does not display the mere topography of a sample surface. Instead, the electronic properties of the surface play an important role—which holds especially true for molecules adsorbed onto a surface. The electronic states of the molecules (HOMO, highest occupied molecular orbital and LUMO, lowest unoccupied molecular orbital) mix with those of the substrate surface, but modified by molecule-substrate interactions. Therefore, depending on the substrate site and material, an image of the molecules is obtained. 

In principle, molecules can be either passive or active electronic components, either singly or in parallel as a one-molecule-thick monolayer array. This may lead to electronic devices with dimensions of 1-3 nm. Unimolecular electronics (UE) or molecular electronics sensu stricto, or molecular-scale electronics evolved from studies of organic crystalline metals, superconductors, and conducting polymers the idea is to exploit the electronic energy levels of a single molecule, and most importantly its HOMO (highest occupied molecular orbital) and LUMO (lowest unoccupied molecular orbital), which can be tuned, or modified by incorporation of electron-donating... 

TABLE 4.15 The Training (Calibration) and Test (Marked With Asterisk - to be chosen) Compounds Studied Along Their HOMA (Harmonic Oscillator Model of Aromatic) Index (Mosquera et al., 2007 Ciesielski et al., 2009) and of Associated Computed (Hypercube, 2002 (Semiempirical, AMI, Polak-Ribier optimization procedure)) Structural First, Second, and Third Order HOMO (Highest Occupied Molecular Orbital) and LUMO (Lowest Unoccupied Molecular Orbital) Reactivity Indices (Tarko Putz, 2010)... 

---