Overlap populations

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. 

COOP (crystal orbital overlap population) a plot analogous to population analysis for band-structure calculations... 

The values are called the net atomic populations and the overlap population. Chemists speak of the charges on atoms in molecules, and Mulliken s second contribution was to propose a method of partitioning the overlap population between contributing atoms. He proposed that the overlap populations be divided equally between participating atoms, so giving the gross atomic populations of... 

An important contribution for the endo selectivity in the carho-Diels-Alder reaction is the second-order orbital interaction [1], However, no bonds are formed in the product for this interaction. For the BF3-catalyzed reaction of acrolein with butadiene the overlap population between Cl and C6 is only 0.018 in the NC-transi-tion state [6], which is substantially smaller than the interaction between C3 and O (0.031). It is also notable that the C3-0 bond distance, 2.588 A, is significant shorter than the C1-C6 bond length (2.96 A), of which the latter is the one formed experimentally. The NC-transition-state structure can also lead to formation of vinyldihydropyran, i.e. a hetero-Diels-Alder reaction has proceeded. The potential energy surface at the NC-transition-state structure is extremely flat and structure NCA (Fig. 8.6) lies on the surface-separating reactants from product [6]. 

Table 1. Relative energies and H. .. C overlap populations for the system of H approaching [Fe(C6H6)(r 5-C6H7)]+ at various (H. .. C = 2.0 A)...

Table 9 shows the PP MO results for this interesting series of highly strained three-membered cyclic molecules. Here a detailed comparison is possible with the best results of an all-electron study, including d functions10 (also reported in Table 9). An analysis of this table reveals how all trends in population analysis, both in charges and overlap populations, are the same in the AE + d and in the simple PP calculations, with very few and very minor exceptions. PP predicts a charge donation to the aliphatic groups, while AE predicts a withdrawal, mainly due to the availability of d orbitals on sulphur, which can allocate extra electronic charge. As outlined in the general notes on population analysis (Section III.D) comparisons should be carried out on a relative basis and,...

FIGURE 18. (a) C—S bond overlap population as a function of molecular geometry (b) the same for the S—O BOP. (c) Total charge on sulphur, and (d), p-part of the charge. The black dots are the values for the S02 molecule itself. 

Bond overlap population 14 Boron compounds, as reducing agents 928, 929... 

Figure 3. Net atomic and overlap populations for the low-spin form of C54.

Fig. 10.2 Crystal Orbital Overlap Population (COOP) and Densities of States (DOS) plots for SrCa2ln2Ce (a) COOP plots of the In-In (solid) and In-Ge (dashed) interactions (b) DOS plots of the total DOS (dotted), ln-5py lone pair (dashed), and ln-5px p-states (solid).

Fig. 18.4 (a) A portion of the orbital splitting for NHj/ZrCli as isolated ions and as a hydrogen-bonded ion pair. The HOMO is indicated by Projected overlap populations (positive values representing... 

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... 

Fig.4- Crystal overlap population of M0O3 (negative part antibonding overlap positive part bonding overlap)...

Table 2 shows that the Mo(l)-On (14) overlap population inereases when the eoordination number of On (14) varies from 1 to 2 whereas between Mo(l)-Oni (10),it decreases when the coordination number varies from 2 to 3 in other words the bonding capacity between oxygen and its nearest neighbours is shared between all bonds. Generally, the Mo-0 overlap populations converge rapidly. 

Table 6c Mo-0 overlap population in the three studied surfaces...

The above relationships between the thiiranes (20) and their dioxides (17) are reminiscent of those between cyclopropane and cyclopropanone. The entire phenomena of the C—C bond lengthening and the concomitant C—S bond shortening in the three-membered ring sulfones and sulfoxides can be accounted for in terms of the sulfur 3d-orbital participation and the variation in the donor-acceptor capacities of the S, SO and S02 . The variations of the calculated valence-state orbital energies, together with the corresponding variations of the C—C overlap populations, can be used to understand the discontinuous variations of the C—C and the C—S bond lengths in the series thiiranes -... 

An example of quantum mechanical schemes is the oldest and most widely used Mulliken population analysis [1], which simply divides the part of the electron density localized between two atoms, the overlap population that identifies a bond, equally between the two atoms of a bond. Alternatively, empirical methods to allocate atomic charges to directly bonded atoms in a reasonable way use appropriate rules which combine the atomic electronegativities with experimental structural information on the bonds linking the atoms of interest. A widely used approach included in many programs is the Gasteiger-Hiickel scheme [1]. 

From the good correspondence between the calculated and experimental --values and hfs s, one may conclude that the MO s, calculated with these values for the empirical parameters, give a fair description for the ground state of Cu(Et2C fc)2. The results of the calculation show that the bonding in Cu(Et2C fc)2 is largely covalent, with overlap populations between copper and sulfur atoms of 0.22 electron unit. 

S12 is the overlap integral between %x and 2. The term 2c1c2Sn is the overlap population it expresses the electronic interaction between the atoms. The contributions cf and c2 can be assigned to the atoms 1 and 2, respectively. 

Equation (10.3) is fulfilled when c2 ss 1 and c 0 in this case the electron is localized essentially at atom 1 and the overlap population is approximately zero. This is the situation of a minor electronic interaction, either because the corresponding orbitals are too far apart or because they differ considerably in energy. Such an electron does not contribute to bonding. 

For yq the overlap population 2clcyS12 is positive, and the electron is bonding for yr2 it is negative, and the electron is antibonding. The sum of the values 2clc2Sl2 of all occupied orbitals of the molecule, the Mulliken overlap population, is a measure of the bond strength or bond order (b.o.) ... 

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