Molecular orbitals LUMO

Frontier orbitals (Section 30.1) The highest occupied (HOMO) and lowest unoccupied (LUMO) molecular orbitals. 

Fig. 4 Schematic representation of (1) the energy of electron donor (D) or electron acceptor (A) units (regardless as to whether molecules or electrodes), (2) the HOMO and LUMO molecular orbitals, and (3) the energy gap AE between D/A and the molecular orbitals, (a) AE is changed by changing the electronic structure of the molecular bridge, (b) AE is changed by changing the energy levels of the donor or acceptor units...

Figure 6.23 HOMO and LUMO molecular orbitals for the [AuAg(C6H5)2]4 model system.

FIGURE 9. HOMO-LUMO molecular orbitals for the model [Au2(C6H5)2Ag2]2. 

Different practical procedures for computing r) have been proposed, that range from the computation of the difference between the energy values of the highest occupied (HOMO) and the lowest unoccupied (LUMO) molecular orbitals [8,9], to the atom in molecules based models [10, 11], to the charge sensitivity analysis [12, 13], to the use of Slater transition state theory [14], to the Janak s extension of DFT for fractional occupancies [15, 16]. Recently, Neshev and Mineva have proposed a scheme for the construction of the internally resolved hardness tensor in... 

Other fundamental characteristics of heteroaromatic systems are their electron-donor and electron-acceptor properties. The energies of the highest occupied (HOMO) and the lowest unoccupied (LUMO) molecular orbitals (the frontier orbitals) can serve as measures of such properties. Pyridine-like heteroatoms lower the energies of all the MOs and compounds containing heteroatoms of this type can be expected to show more -acceptor and less r-donor character. In accord with this expectation (Table 2), -acceptor properties of azines decrease in the sequence l,2,4>5-tetrazine > pyrazine > pyridazine > pyrimidine > pyridine. 

The solid state properties of the linear chain compounds are substantially determined by the electronic structure of the molecular [Pt(CN)4]2 units. An ab initio calculation of the electronic structure of the [Pt(CN)4]2 complex including all 132 electrons or at least the 48 valence electrons does not exist as yet. Concerning the optical spectroscopy, however, mainly the highest occupied (HOMO) and the lowest unoccupied (LUMO) molecular orbitals are of interest. Thus, the number of electrons and states, which have to be considered, is restricted drastically compared to the full problem. The method usually applied to the approximative determination of the relevant states and their electronic structures is the molecular-orbital ligand field theory mostly using empirical fitting data50,31). 

The decrease in bond lengths in (Ar—P=C=0)2 may be due to the reduced covalent radius of the sp2 ring carbon compared to the sp3-hybridized C atom. The dimerization of the phosphaketenes extensively corresponds to analogous reactions of ketoketenes (142, 142a). The small difference of energies between HOMO and LUMO molecular orbitals in the case of the unsubstituted phosphaketene explains the... 

Chang and coworkers, using extended Huckel MO calculations provided an explanation for the easier oxidations and harder reductions as the porphyrin macrocycle is progressively reduced [93]. The calculated energy levels for the highest occupied (HOMO) and lowest unoccupied (LUMO) molecular orbitals of porphine, chlorin, iBC and BC complexes of Zn(II) are shown in Fig. 7. As the... 

Let us take the example of the cycloaddition of two ethylene molecules when they bind together, forming the cyclobutane. The frontier orbitals of (he ground-state ethylene molecule are the doubly occupied tt (HOMO) and the empty n (LUMO) molecular orbitals. 

Elastic resonant tunneling and/or through bond tunneling has also become a central theme in the interpretation and theoretical development of STM imaging of molecules adsorbed on metal surfaces [2, 3, 39, 44, 45], Numerous images of molecules adsorbed on metallic surfaces display a likeness to the shape of the highest occupied (HOMO) and lowest unoccupied (LUMO) molecular orbitals of... 

Figure 2c shows the electronic structure of graphene described by a simple tight-binding Hamiltonian the electronic wavefunctions from different atoms overlap. However, such an overlap between the Pz(it) orbital and the Px and Py orbitals is zero by symmetry. Thus, the Pz electrons form the 71 band, and they can be treated independently from the other valence electrons. The two sub-lattices lead to the formation of two bands, n and Jt, which intersect at the corners of the Brillouin zone. This yields the conical energy spectrum (Dirac cone, inset in Fig. 2c) near the points K and K, which are called Dirac points. The bottom cone (equivalent to the HOMO molecular orbital) is fully occupied, while the top cone (equivalent to the LUMO molecular orbital) is empty. The Fermi level Ep is chosen as the zero-energy reference and lies at the Dirac point. Consequently, graphene is a special semimetal or zero-band-gap semicondutor, whose intrinsic Fermi surface is reduced to the six points at the corners of the two-dimensional Brillouin zone. 

PROBLEM 12.59 Here are two reactions of allyl systems that are related to the Diels-Alder reaction. Use a HOMO-LUMO molecular orbital analysis to show why reaction a succeeds whereas reaction b fails. 

Because molecular orbitals must recognize the symmetry of a molecule, a symmetry operation must either preserve the value of the wavefunction or simply change the sign of the wavefunction. The wavefunction therefore provides a basis for a representation of the molecule s point group. Inspection of the HOMO and LUMO molecular orbitals of ethylene (Fig. 4.6) shows that the HOMO transforms as the irreducible representation and z in the D2h point group (Table 4.2), whereas the LUMO transforms as Bj,g and yz. 

Fig. 4.17 Components of the transition matrix element of the gradient operator for excitation of ethylene. (A, B) Contour plots of the amplitudes of the HOMO and LUMO molecular orbitals in the yz plane. The C=C double bond lies on the y axis. (C, E) The derivatives of with respect to y and z, respectively. (D, F) The products of these derivatives with The y and...

We extend our considerations of the micro-environment imposed by the protein to the thesis that axial ligands, hydrogen bonds and neighboring residues of photo synthetic chromophores help to define a scaffolding that in turn controls the conformations of the molecules. Theoretical calculations indicate that conformational variations would shift the highest occupied (HOMO) and lowest unoccupied (LUMO) molecular orbitals of (B)Chls and thereby modulate their redox and light-absorption properties [17,32]. We consider here the evidence for and the consequences of such conformational differences in (B)Chls, and test our conclusions with a series of synthetic porphyrins that are significantly puckered. 

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