Semiempirical crystals

A semiempirical crystal band structure program, called BZ, is bundled with MOPAC 2000. There is also a utility, referred to as MAKPOL, for generating the input for band structure calculations with BZ. With the use of MAKPOL, the input for band-structure computations is only slightly more complicated than that for molecular calculations. 

To analyze the influence of high hydrostatic pressure on the emission of lanthanide ions, the semiempirical crystal-field approach is used where the total Hamiltonian of the 4f system is given by the sum of a free ion and the crystal-field terms as follows [113]. 

The next, short, chapter reviews different semiempirical crystal-orbital theories [tt-electron CO theories, namely Huckel and Pariser-Parr-Pople theory, as well as all valence electron CO theories with different degrees of neglect of the so-called differential overlap (CNDO, INDO, MINDO, etc.)]. Applications to highly conducting polymers and to periodic biopolymers are also presented. 

After a number of semiempirical crystal-orbital (CO) calculations (extended Hvickel and CNDO/2 CO calculations for further references see Table III of Andre ) Otto et performed the first ab initio band-structure calculations on different fluorinated polyethylenes. The calculations were conducted for all six different polyfluoroethylenes, namely (CFH-CHj), (CF2-CH2), (CFH-CFH),, (CFH-CFH), (CF2-CFH)jt, and (CF2), which can be obtained from polyethylene through fluorine substitution. 

It can be seen from Table 2.6 that the physically most important valence and conduction bands in the later ab initio calculations are much broader (0.435-0.789 and 0.245-0.820 eV, respectively) than those obtained by application of different semiempirical crystal-orbital methods. With the simple PPP-CO approximation, the corresponding values for the highest filled bands are 0.218-0.299 eV and those for the conduction band are about 0.109 eV. Energy-band-structure calculations for the base stacks taking into account the effect of the other valence electrons with the aid of the CNDO/2 CO method give again broader bands (valence bandwidths of 0.136-0.490 eV and conduction band-widths of 0.109-0.245 eV), while the MINDO/2 CO results indicate somewhat less-broad bands (valence bandwidths of 0.027-0.299 eV and conduction bandwidths of 0.027-0.163 eV). For futher details on the semiempirical crystal-orbital calculations see also Chapter 3. 

The preceding methods were applied to a number of periodic polymers with a small unit cell. Many of these calculations used different all-valence electron semiempirical crystal-orbital methods (CNDO/2, — INDO, — MINDO, and MNDO CO methods). At this point we shall discuss only some of the not very numerous ab initio vibrational calculations and also an MNDO CO work on fra/is-polyacetylene (PA), because in this investigation disorder in PA due to soliton and polaron formation was also taken into account. ... 

Any orbital-based scheme can be used for crystal-structure calculations. The trend is toward more accurate methods. Some APW and Green s function methods use empirical parameters, thus edging them toward a semiempirical classification. In order of preference, the commonly used methods are ... 

Although the band model explains well various electronic properties of metal oxides, there are also systems where it fails, presumably because of neglecting electronic correlations within the solid. Therefore, J. B. Good-enough presented alternative criteria derived from the crystal structure, symmetry of orbitals and type of chemical bonding between metal and oxygen. This semiempirical model elucidates and predicts electrical properties of simple oxides and also of more complicated oxidic materials, such as bronzes, spinels, perowskites, etc. 

Similarly, other cycloadducts of nitrile oxides with C6o were synthesized. The cycloadducts were characterized by 13C NMR spectroscopy and high-resolution fast atom bombardment (FAB) mass spectrometry. It should be mentioned that X-ray structure determination of the 3-(9-anthryl)-4,5-dihydroisoxazole derivative of C6o, with CS2 included in the crystals, was achieved at 173 K (255). Cycloaddition of fullerene C60 with the stable 2-(phenylsulfonyl)benzonitrile oxide was also studied (256). Fullerene formed with 2-PhSC>2C6H4CNO 1 1 and 1 2 adducts. The IR, NMR, and mass spectra of the adducts were examined. Di(isopropoxy)phosphorylformonitrile oxide gives mono- and diadducts with C60 (257). Structures of the adducts were studied using a combination of high performance liquid chromatography (HPLC), semiempirical PM3 calculations, and the dipole moments. 

In the crystal the atoms of this molecule are found to be distributed in three planes Hie two tolyl rings are rotated by 24° (trans to Br) and 68° (cis to Br) with respect to the ethylene plane. Semiempirical Huckel molecular orbital (MO)-type calculations give essentially the same angles in the crystal, but predict 35° and 45° for these angles in the Bee molecule. 

The semiempirical models mentioned above allow an estimation of the stability of binary hydrides provided that the rigid band theory can be applied. However, the interaction of hydrogen with the electronic structure of the host metal in some binary hydrides and especially in the ternary hydrides is often more complicated. In many cases, the crystal structure of the host metal and therefore also the electronic structure... 

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