Bonding crystal orbital

A second mechanism (the polarization mechanism) arises due to the polarization of the fully occupied (bonding) crystal orbitals formed by the eg. oxygen 2p. and Li 2s atomic orbitals in the presence of a magnetic field. A fully occupied crystal (or molecular) orbital in reality comprises one one-electron orbital occupied by a spin-up electron and a second one-... 

The orbital combinations for p and Py (hereafter abbreviated as x and y, respectively), the p orbitals perpendicular to the chain propagation axis, are of course of the same energy (or degenerate). We see from 19 that s, x, and y give the most bonding crystal orbital when the unit cell (here a single carbon atom) orbitals are all in-phase, i.e., have the same sign. This is the k = 0 (termed r) Bloch function. 

From the analysis of Table 3.2 there is noted how, for example, the atomic orbitals such as s, J and produce, by their arrangement as prescribed by Eq. (3.36), the bonding crystal orbitals in the center of k-zoae (F), and respectively, by their arrangement in the anti-phase as... 

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 polydiacetylene crystals (1-4) most strikingly corroborate these conjectures. Along this line of thought is also shown that this electron-phonon interaction is intimately interwoven with the polymerisation process in these materials and plays a profound role there. We make the conjecture that this occurs through the motion of an unpaired electron in a non-bonding p-orbital dressed with a bending mode and guided by a classical intermolecular mode. Such a polaron type diffusion combined with the theory of non radiative transitions explains the essentials of the spectral characteristics of the materials as well as their polymerisation dynamics. ... 

At the end of Section 10.1 the Mulliken overlap population is mentioned as a quantity related to the bond order. A corresponding quantity for solids was introduced by R. Hoffmann the crystal orbital overlap population (COOP). It is a function that specifies the bond strength in a crystal, all states being taken into account by the Mulliken overlap populations Its calculation requires a powerful computer however, it can... 

Similar shortening of the C-N bond and lengthening of the C=0 bond is found when the structures of acetamide [376, 377], fluoroacetamide [299], and thioacetamide [204] in the hydrogen-bonded crystals are compared with ab-initio molecular orbital calculations for the isolated molecule, as shown in Thble 5.4. 

Figure 29 Crystal orbital overlap population curves for the Mn-Mn bonds (solid line) and Mn-P bonds (dotted line) in the Mn2P22 single layer.

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