Bond order overlap population

Another useful quantity to calculate is the bond order overlap population ... 

Orbital is a bonding orbital. A bonding orbital will always have a positive bond order overlap population density contribution. This is different for the corresponding density contribution due to orbital... 

Equations (2.114) follow from Eqs.(2.102). p E) and p2(E) are drawn in Fig.(2.23). In section 2.2 we illustrated the use of Eqs.(2.58) for a diatomic molecule. A positive value means a bonding contribution to the bond energy, a n ative value means an antibonding bond weakening contribution. For the infinite closed chain the expression for the bond-order overlap populations becomes ... 

Figure 2.42. Bond-order overlap population density between adatom and endatom, one-dimensional chain (schematic), a weak adsorption limit b surface molecule limit.

Figure 3.22. Bond Order Overlap Population densities of CO with surface metal orbitals on Rh (111). In all plots the Fermi level is indicated by Ep.

Bond order overlap population densities of C with surface metal orbitals on Rh (111). 

Figure 3.59. Ag-0 bond-order overlap population densities of two O3 adsorption geometries.

Indices of interest comprise (total and tt) electron densities (atomic populations), bond orders (overlap populations), and HOMO electron densities, the last ones being of interest for discussions of chemical reactivities. 

The bond order overlap population (BOOP) is defined as the sum of the occupied corresponding OPDOS matrix elements [9] ... 

The OPDOS curves. Figs. 3.4a and b, show that the interaction of the NH3 a2p orbital with the metal d-orbitals changes from attractive (positive) to repulsive (negative) in comparing the values for Tr at increasing orbital energies. The Bond Order Overlap Population (BOOP) between fragment orbitals i and j is defined as... 

Figure 2.24. Bond-order overlap properties of open and closed chains, a total bond-order population as a function of E.

NBO (natural bond order) the name of a set of population analysis techniques NDO (neglect of differential overlap) the fundamental assumption behind many semiempirical methods... 

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]. 

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.) ... 

As a general rule, pi bond orders, pi overlap populations and total pi overlap populations allow a diagnosis of the type of pi interactions which obtain between two AO s. The situation is much more uncertain in the case of sigma AO interactions, and one has to rely upon bond orders and/or overlap populations. 

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