Bonding crystal orbital overlap population

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... 

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... 

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.

It is now clear that the apparatus of densities of states and crystal orbital overlap populations has served to restore to us a frontier orbital or interaction diagram way of thinking about the way molecules bond to surfaces, or the way atoms or clusters bond in three-dimensional extended structures. Whether it is 2t CO with d of Ni(100), or e of CR with some part of the Pt(lll) band, or the Mn and P sublattices in Mn2P22, or the Chevrel phases discussed below, in all of these cases we can describe what happens in terms of local action. The only novel feature so far is that the interacting orbitals in the solid often are not single orbitals localized in energy or space, but bands. 

Ultimately, the treatment of electronic structure in extended systems is no more complicated (nor is it less so) than in discrete molecules. The bridge to local chemical action advocated here is through decompositions of the DOS and the crystal orbital overlap population (COOP) curves. These deal with the fundamental questions Where are the electrons Where can I find the bonds ... 

Finally, we study the atom-atom and orbital-orbital interactions by evaluation of the crystal orbital overlap population (COOP) and the overlap population (OP) corresponding to bonds and atomic orbitals, in order to analyze... 

Hj, is the electron orbital occupation. The BOOP, as defined here within the framework of molecular orbital theory, can be considered the quantum-mechanical equivalent of bond order, in the way it was defined by Pauling [10]. In case the periodicity of the metal molecular orbitals is explicitly considered, the BOOP is equivalent to the crystal orbital overlap population defined by Hoffmann [9]. 

Crystal orbital overlap population the formation of bonds... 

Chemical bonding in several transition metal carbides was theoretically investigated by quasi self consistent augmented-plane-wave (APW) calculations [71-73] and by the extended Hiickel method [74]. These calculation indicated a charge transfer from the early transition metal to the carbon atoms. A crystal orbital overlap population analysis (COOP) revealed strong bonding T—T and T-C... 

ABSTRACT. The concepts of a band Structure, Bloch functions, the wave vector, and densities of states are introduced, making as strong connections as possible to quantum chemical ideas. The number of orbitals in a unit ceH determines the number of bonds, orbital overlap is responsible for the dispersion of the bands and the topology of orbital interactions for the way the bands run. A measure of bond strength in the solid, the Crystal Orbital Overlap Population, is introduced. 

Again, chemical bonding must be considered as predominantly intracluster Z-R bonding and polar R-X bonding. Figure 40 shows crystal orbital overlap populations... 

The formation of C-C chemical bonds in a variety of solids, including some refractory dicarbides, has been considered by Li and Hoffman (1989) and Wijeyesekera and Hoffman (1984) based on EHT (extended Huckel theory) calculations. To our knowledge, these works are the only ones where the band analogues of bond populations, the so-called crystal orbital overlap populations (COOPs) have been calculated for refractory compounds. The most noticeable result is that, in spite of the evident crudeness of the nonself-consistent semiempirical EHT method, the calculations allow us to understand the nature of the phase transition from cubic to hexagonal structure which occurs in the ZrC, NbC, MoC,... series as the VEC increases. The increase of metal-to-metal bonding when going from cubic (NaCl-type) to hexagonal (WC-type) becomes evident. 

A difficulty often associated with the use of overlap populations is that it is not sensible to compare values for different pairs of atoms. A useful tool derived within the DPT scheme is that of the crystal orbital Hamilton population (COHP) analysis [14]. In that case, what is partitioned in bonding, nonbonding, and antibonding contributions for a certain energy window is not the number of electrons (COOP) but the band energy (COH P). Except for the obvious fact that the two kinds of curves show opposite sign behavior, they usually lead to the same qualitative analysis. 

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