COOP curve

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 orbital interaction which is responsible for the adsorption of molecular oxygen on the Ag(110) surface is mainly between silver dxz and 7t 0-0- The interaction between the silver surface and molecular oxygen leads to a donation of 1.55 electrons into the 7t o o from surface because the Fermi level of the surface is located higher in energy than n oo In Figure 1 is shown the contribution for the adsorbed molecular oxygen in 2 to the total density of states (DOS) and also the Ag-O and 0-0 crystal orbital overlap population (COOP) curves. 

Figure 1. (a) Total DOS for 2. The contribution from molecular oxygen is shown as the shaded area. The dotted line is the integration of the contribution from molecular oxygen, (b) The COOP curves for the 0-0 bond (dotted line) and the Ag-O bond (full line)... 

The DOS curve for 2 splits in three peaks, one at -13 eV and two just above and just below -16 eV. The 0-0 COOP curve shows that the two latter originate from bonding 0-0 and Ag-O orbitals, whereas the former is the antibonding part. From the Ag-O COOP curve it is seen that bonding Ag-O orbitals only are located below the Fermi level. The DOS and COOP curves for 1 and 3 are very similar to those presented in Figure 1. The adsorption geometry 2 could be the one which is observed by NEXAFS (ref. 6). 

Figure 7.5 (Top) Total DOS curve and C-C it orbital projections, C-C, Y-C, and Y-Y COOP curves for YC2 (bottom) Total DOS curve and C-C it orbital projections for Y2C3 and Y2C2Br2. Fermi levels for each compound is noted by the dashed line.

Total DOS and B-C COOP curves for both the superconducting YNi2B2C and YNiBC are illustrated in Figure 7.7. Nonzero N(EF) values are consistent with metallic behavior, and the peak in the DOS near EF for... 

Figure 7.7 Total DOS curves, jt orbital projections, and B-C COOP curves for (top) YNi2B2C and (bottom) YNiBC. The corresponding Fermi levels are indicated by the dashed...

To get a feeling for this quantity, let s think about what a COOP curve for a hydrogen chain looks like. The simple band structure and DOS were given earlier, 26 they are repeated with the COOP curve in 35. 

Note the general characteristics of COOP curves positive regions that are bonding, negative regions that are antibonding. The amplitudes of these curves depend on the number of states in that energy interval, the... 

Figure 19 The orbitals of N2 (left) and a solid state way to plot the DOS and COOP curves for this molecule. The la, and lau orbitals are out of the range of this figure. 

The integral of the COOP curve up to the Fermi level is the total overlap population of the specified bond. This points us to another way of thinking of the DOS and COOP curves. These are the differential versions of electronic occupation and bond order indices in the crystal. The integral of the DOS to the Fermi level gives the total number of electrons the integral of the COOP curve gives the total overlap population, which is not identical to the bond order, but which scales like it. It is the closest a theoretician can get to that ill-defined but fantastically useful, simple concept of a bond order. 

The tuning of electron counts is one of the strategies of the solid state chemists. Elements can be substituted, atoms intercalated, nonstoichiometries enhanced. Oxidation and reduction, in solid state chemistry as in ordinary molecular solution chemistry, are about as characteristic (but experimentally not always trivial) chemical activities as one can conceive. The conclusions we reached for the Pt-Pt chain were simple, easily anticipated. Other cases are guaranteed to be more complicated. The COOP curves allow one, at a glance, to reach conclusions about the local effects on bond length (will bonds be weaker, stronger) upon oxidation or reduction. 

Earlier we showed a band structure for rutile. The corresponding COOP curve for the Ti-O bond (Fig. 21) is extremely simple. Note the bonding in the lower oxygen bands and antibonding in the eg crystal field destabilized orbitals. The t2g band is, as expected, Ti-0 antibonding. 

What would one expect of the COOP curve for bulk Ni As a first approximation, we could generate the COOP curve for each band separately, as in 38a and b. Each band in 37 has a lower Ni-Ni bonding part, an upper Ni-Ni antibonding part. The composite is 38c. The computed COOP curve is in Fig. 23. The expectations of 38c are met reasonably well. 

Another illustration of the utility of COOP curves is provided next by a question of chemisorption site preference. On many surfaces, including... 

The important frontier orbitals of a carbyne, CR, are shown in 41. The C 2p orbitals, the e set, are a particularly attractive acceptor set, certain to be important in any chemistry of this fragment. We could trace its involvement in the three alternative geometries 40 via DOS plots, but instead we choose to show in Fig. 25 the Pt-C COOP curve for one-fold and three-fold adsorption. 

Figure 25 COOP curve for the a-carbon-Pti bond in the one-fold (left) and three-fold (right) geometry of ethylidyne, CCH3, on Pt(lll).

The actual evolution of the DOS and COOP curves allows one to follow this process in detail. For instance, Fig. 38 shows the contribution of the methyl n orbital, the radical lobe, to the total DOS along a hypothetical coupling reaction coordinate. Note the gradual formation of a two-peaked structure. COOP curves show the lower peak is C-C bonding, the upper one C-C antibonding. These are the o and o bonds of the ethane that is being formed. 

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 ... 

The Ni-Ni COOP curve illustrated on the right side of Figure 6.14 reflects the band structure shown on the left side. Each individual band is bonding in its lower part and antibonding in its upper part. The bonding/antibonding character is more pronounced on the more dispersed bands. Flat bands are merely non-bonding at any k point. The COOP curve is the result of all these effects. 

The COOP curve reflects the fact that the lowest parts of the 3s and 3p bands are bonding and their upper parts are antibonding. There are three valence electrons per A1 atom so the band is 3/8 filled with the electrons in COs of Al-Al bonding character. Note that all the bonding levels are occupied whereas all the antibonding ones are empty. This is a mark of stability. There is no band gap at the Fermi level, consistent with the fact that bulk A1 is metallic in character. 

A very simple example of COOP curves are those corresponding to the 1,2 and 1,3 interactions in ideal polyacetylene (87). As discussed in Section 4, all the 1,2 interactions are bonding at the bottom of the lower band (39a) but antibonding at the top of the upper band (39b). The levels at the top of the lower band and bottom of the upper band are essentially nonbonding (40). Thus the COOP curve for the... 

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