HOMO, LUMO also

HOMO and LUMO, also known as Frontier orbitals, are important in interpreting results of a calculation (see Frontier Molecular Orbitals on page 141). You can use these molecular orbitals to compute the lowest excited electronic singlet state of molecules and the ground states of radicals. 

Calculations for Ceo in the LDA approximation [62, 60] yield a narrow band (- 0.4 0.6 eV bandwidth) solid, with a HOMO-LUMO-derived direct band gap of - 1.5 eV at the X point of the fee Brillouin zone. The narrow energy bands and the molecular nature of the electronic structure of fullerenes are indicative of a highly correlated electron system. Since the HOMO and LUMO levels both have the same odd parity, electric dipole transitions between these levels are symmetry forbidden in the free Ceo moleeule. In the crystalline solid, transitions between the direct bandgap states at the T and X points in the cubic Brillouin zone arc also forbidden, but are allowed at the lower symmetry points in the Brillouin zone. The allowed electric dipole... 

For C70, molecular orbital calculations [60] reveal a large number of closely-spaced orbitals both above and below the HOMO-LUMO gap [60]. The large number of orbitals makes it difficult to assign particular groups of transitions to structure observed in the solution spectra of C70. UV-visible solution spectra for higher fullerenes (C n = 76,78,82,84,90,96) have also been reported [37, 39, 72]. 

The numerical value of hardness obtained by MNDO-level calculations correlates with the stability of aromatic compounds. The correlation can be extended to a wider range of compounds, including heterocyclic compounds, when hardness is determined experimentally on the basis of molar reffactivity. The relatively large HOMO-LUMO gap also indicates the absence of relatively high-energy, reactive electrons, in agreement with the reduced reactivity of aromatic compounds toward electrophilic reagents. 

When both the 1,3-dipoIe and the dipolarophile are unsymmetrical, there are two possible orientations for addition. Both steric and electronic factors play a role in determining the regioselectivity of the addition. The most generally satisfactory interpretation of the regiochemistry of dipolar cycloadditions is based on frontier orbital concepts. As with the Diels-Alder reaction, the most favorable orientation is that which involves complementary interaction between the frontier orbitals of the 1,3-dipole and the dipolarophile. Although most dipolar cycloadditions are of the type in which the LUMO of the dipolarophile interacts with the HOMO of the 1,3-dipole, there are a significant number of systems in which the relationship is reversed. There are also some in which the two possible HOMO-LUMO interactions are of comparable magnitude. 

Consideration of the HOMO-LUMO interactions also indicates that the [2n + 2ti] additions would be allowed photochemically. The HOMO in this case is the excited alkene 71 orbital. The LUMO is the ti of the ground-state alkene, and a bonding interaction is present between the carbons where new bonds must be formed ... 

These concepts play an important role in the Hard and Soft Acid and Base (HSAB) principle, which states that hard acids prefer to react with hard bases, and vice versa. By means of Koopmann s theorem (Section 3.4) the hardness is related to the HOMO-LUMO energy difference, i.e. a small gap indicates a soft molecule. From second-order perturbation theory it also follows that a small gap between occupied and unoccupied orbitals will give a large contribution to the polarizability (Section 10.6), i.e. softness is a measure of how easily the electron density can be distorted by external fields, for example those generated by another molecule. In terms of the perturbation equation (15.1), a hard-hard interaction is primarily charge controlled, while a soft-soft interaction is orbital controlled. Both FMO and HSAB theories may be considered as being limiting cases of chemical reactivity described by the Fukui ftinction. 

Selective, trisilver, cryophotochemical transformations have also been observed that involve HOMO-LUMO visible excitation (420-440 nm, depending on the matrix support) (151). A typical series of optical traces that depict the outcome of Ags/Kr, 423-nm excitation at 10-12 K is illustrated in Fig. 16. These data show that Agj absorptions at 423/ 247 nm may be selectively photoannihilated simultaneously with the... 

The pole strength profiles obtained in the outer valence region of the 1,3-trans butadiene, 1,3,5-trans hexatriene and 1,3,5,7-trans octatetraene compounds relate also typically to that found (10) with low-gap hydrogen chains. They nicely reflect the competition for intensity between the main and the correlation i.e. satellite) bands in that region. In both cases, the less energetic (HOMO LUMO (10,12)... 

At the turn of this century it was realized that carrier generation was also possible between the HOMO and LUMO band even in neutral single-component materials assuming that there was a small HOMO-LUMO gap and conduction paths have been associated with the presence of large transverse intermolecular interactions. The most relevant examples of single-component molecular conductors are the mononuclear M(dithiolate)2 (M = Co, Ni, Cu, Au) complexes with... 

Figure 3. Charge distributions in the S, and S, slates of the 2-3 and 3-4 perp forms (0=90°) of BMPC, as obtained by single configuration (ground state SCF and [HOMO,LUMO]) wavefunctions. Only the overall charge is reported for the methyl substituents. The global net charges of the perpendicular subunits, emphasizing localization of the charge, are also indicated.

AMI semi-empirical and B3LYP/6-31G(d)/AMl density functional theory (DFT) computational studies were performed with the purpose of determining which variously substituted 1,3,4-oxadiazoles would participate in Diels-Alder reactions as dienes and under what conditions. Also, bond orders for 1,3,4-oxadiazole and its 2,5-diacetyl, 2,5-dimethyl, 2,5-di(trifluoromethyl), and 2,5-di(methoxycarbonyl) derivatives were calculated <1998JMT153>. The AMI method was also used to evaluate the electronic properties of 2,5-bis[5-(4,5,6,7-tetrahydrobenzo[A thien-2-yl)thien-2-yl]-l,3,4-oxadiazole 8. The experimentally determined redox potentials were compared with the calculated highest occupied molecular orbital/lowest unoccupied molecular orbital (HOMO/LUMO) energies. The performance of the available parameters from AMI was verified with other semi-empirical calculations (PM3, MNDO) as well as by ab initio methods <1998CEJ2211>. 

Compared with the conducting anion radical salts of metal complexes, the number of molecular conductors based on cationic metal complexes is still limited. Donor type complexes M(dddt)2 (M = Ni, Pd, Pt Fig. 1) are the most studied system. The M(dddt)2 molecule is a metal complex analogue of the organic donor BEDTTTF. Formally, the central C=C bond of BEDT-TTF is substituted by a metal ion. The HOMO and LUMO of the M(dddt)2 molecule are very similar in orbital character to those of the M(dmit)2 molecule. In addition, the HOMO of the M(dddt)2 molecule is also very similar to that of BEDT-TTF. More than ten cation radical salts of M(dddt)2 with a cation (monovalent) anion ratio of 2 1 or 3 2 are reported [7]. A few of them exhibit metallic behavior down to low temperatures. The HOMO-LUMO band inversion can also occur in the donor system depending on the degree of dimerization. In contrast to the acceptor system, however, the HOMO-LUMO band inversion in the donor system leads a LUMO band with the one-dimensional character to the conduction band. 

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