Antibonding crystal orbital

Conversely, the most antibonding crystal orbital, 20, has the unit cell orbitals all out-of-phase, or, in other words, each second unit cell has a different sign. This is the wave function at the Briiiouin zone edge, traditionaiiy caiied Z. For the (hereafter z) orbitais on the other hand, the reverse is true in both cases its out-of-phase combination in 19 (k = n/a,Z) is most bonding whiie the in-phase one in 20 (k = 0, T) is most antibonding. 

Another question is whether the filled orbitals are of a bonding or antibonding character. This is displayed on a crystal orbital overlap population (COOP) plot as shown in Figure 34.3. Typically, the positive bonding region is plotted to the right of the zero line. 

The "Crystal Orbital Overlap Population" (COOP) [20] shows (Fig. 4) that all levels arising below the Fermi level are a and Jt bonding and the highest energy levels are ct and n antibonding however the specific COOP curves for each Mo-0 distance (Fig. 5) show a... 

The different shift mechanisms may be understood in more detail by considering the effect of the magnetic field on the populations and energies of the different crystal orbitals (Figure 7a). Transfer of electron density via the 90° interaction arises due to a direct delocalization of spin density due to overlap between the half-filled tzg. oxygen jt, and empty Li 2s atomic orbitals (the delocalization mechanism. Figure 7b).This overlap is responsible for the formation of the tzg (antibonding) molecular orbital in a molecule or the tzg crystal orbital (or band) in a solid. No shift occurs for the 180° interaction from this mechanism as the eg orbitals are empty. 

Lithium clusters have been a popular model for the calculation of metal properties because of their low atomic number. Lasarov and Markov (49) used a Hiickel procedure to determine the properties of a 48-atom Li crystal. They found a transition to metal properties with the binding energy per atom approaching 1.8 eV at 30 atoms. The ionization potential approached the bulk value since some electrons occupy antibonding molecular orbitals, as observed for Ag clusters. The calculated properties of the largest cluster were not those of a bulk metal. 

Crystal orbitals are built by combining different Bloch orbitals (which we will henceforth refer to as Bloch sums), which themselves are linear combinations of the atomic orbitals. There is one Bloch sum for every type of valence atomic orbital contributed by each atom in the basis. Thus, the two-carbon atom basis in diamond will produce eight Bloch sums - one for each of the s- and p-atomic orbitals. From these eight Bloch sums, eight COs are obtained, four bonding and four antibonding. For example, a Bloch sum of s atomic orbitals at every site on one of the interlocking FCC sublattices in the diamond structure can combine in a symmetric or antisymmetric fashion with the Bloch sum of s atomic orbitals at every site of the other FCC sublattice. 

In general, semiconductors can have different types of valence band and conduction band structures. These differences can affect the chemical reactivity of the various types of semiconducting solids. For example, in a covalent solid such as Si, the valence and conduction bands can be considered as crystal orbitals that are either bonding or antibonding combinations of hybridized Si atomic orbitals. This situation is closely related to our polyene example, where the valence band consisted of bonding tt-orbitals and the conduction band consisted of antibonding 7r -orbitals. However, in an ionic crystal such as TiOi, the valence band is composed of crystal orbitals that are derived from the filled O 2p orbitals, while the conduction band is composed of crystal orbitals that are... 

The single-crystal ESR spectra of [ 03(00)9(/it3-E)] (E = S or Se), which are isoelectronic with 65 , show definitively that the half-filled orbital has 2fl2 symmetry (in Csv geometry) and is antibonding with respect to the metal-metal bonds 144, 145). Consistent with this, the metal-metal distances of the diamagnetic complexes 65, which do not contain an extra electron in the antibonding M3 orbital, are shorter by 4-9 pm than those of [Co3(CO)9(/i3-E)] 145, 146). 

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