Lowest unfilled molecular orbitals

The lowest unfilled molecular orbitals in the haloalkanes are formed from the out-of-phase overlap of an sp3 hybrid orbital of the carbon atom... 

The determination of the perfect lattice band structure is relatively straightforward. The hole and electron occupy states based respectively upon the highest filled and lowest unfilled molecular orbitals of the parent molecule. The energy levels of these states are broadened into bands by the intermolecular overlap of the molecular orbitals. Knowing the crystal structure and assuming reasonable forms of these orbitals, the band structure may be calculated (Chojnacki, 1968 Le Blanc, 1961, 1962a, b). 

Fig. 1.46 The filled molecular orbitals and the lowest unfilled molecular orbital of methyl...

Fig. 4.19 The filled and lowest unfilled molecular orbitals of methylene...

In view of these results, it follows that the placement of the orbital labelled 4 in Figures 1 and 2 may have to be altered. This orbital may be, in fact, the lowest unfilled molecular orbital in these complexes. We are currently studying the time resolved spectroscopy of the hetero-bischelated complexes between —196° and 0°C to establish the correct placement of the d-d levels. 

The accepted mechanism for this reaction class is an electron transfer from M to the lowest unfilled molecular orbital of Xa as the M and Xa... 

An incorrect dissociation limit is a common failure of SCF MO wavefunctions (as we already noted for H2O). Thus for H2 the SCF MO wavefunction (n ) leads to a dissociation limit which is an equal mixture of atoms and ions because there is no correlation between the two electrons (there is an equal chance of finding the two electrons on the same atom and on different atoms). The addition of a configuration (cTj ), where is the lowest energy unfilled molecular orbital, removes this error, and in the dissociation limit the wavefunction has to be an equal mixture of and Thus a wavefunction that stops at this limit is called an optimum double configuration (ODC) function. 

Another aspect of qualitative application of MO theory is the analysis of interactions of the orbitals in reacting molecules. As molecules approach one another and reaction proceeds, there is a mutual perturbation of the orbitals. This process continues until the reaction is complete and the new produet (or intermediate in a multistep reaction) is formed. PMO theory incorporates the eoneept of frontier orbital control. This concept proposes that the most important interactions will be between a particular pair of orbitals. " These orbitals are the highest filled orbital of one reactant (the HOMO, highest occupied molecular orbital) and the lowest unfilled (LUMO, lowest unoccupied molecular orbital) orbital of the other reactant. The basis for concentrating attention on these two orbitals is that they will be the closest in energy of the interacting orbitals. A basic postulate of PMO... 

There are three cases The original p orbital may have contained two, one, or no electrons. Since the original double bond contributes two electrons, the total number of electrons accommodated by the new orbitals is four, three, or two. A typical example of the first situation is vinyl chloride, CH2—CH—CI. Although the p orbital of the chlorine atom is filled, it still overlaps with the double bond. The four electrons occupy the two molecular orbitals of lowest energies. This is our first example of resonance involving overlap between unfilled orbitals and a filled orbital. Canonical forms for vinyl chloride are... 

Isotope-containing organic compounds as ion radical precursors have important significance for ion radical organic chemistry. The link between the isotopic substitution at the reaction center and the change in the kinetic properties is not so obvious for one-electron transfer. In that case, the highest occupied molecular orbit (MO) of a donor loses one electron. This electron is then shuttled to the lowest unfilled MO of an acceptor. 

Molecular orbitals are characterized by energies and amplitudes expressing the distribution of electron density over the nuclear framework (1-3). In the linear combination of atomic orbital (LCAO) approximation, the latter are expressed in terms of AO coefficients which in turn can be processed using the Mulliken approach into atomic and overlap populations. These in turn are related to relative charge distribution and atom-atom bonding interactions. Although in principle all occupied MOs are required to describe an observable molecular property, in fact certain aspects of structure and reactivity correlate rather well with the nature of selected filled and unfilled MOs. In particular, the properties of the highest occupied MO (HOMO) and lowest unoccupied MO (LUMO) permit the rationalization of trends in structural and reaction properties (28). A qualitative predictor of stability or, alternatively, a predictor of electron... 

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