Electron bond populations

Table 3.4 Electron bond populations in model complexes cis-C syn-C3H,NdCVAl(CH3)3 + C3H, ...

In each of the B-H-B bridges, only two electrons bond the three atoms together by having the orbitals on the boron atoms simultaneously overlap the hydrogen Is orbital. A bond of this type is known as a two-electron three-center bond. In terms of molecular orbitals, the bonding can be described as the combination of two boron orbitals and one hydrogen orbital to produce three molecular orbitals, of which only the one of lowest energy is populated ... 

Already in the thorium dimer, Th2, we see another pattern. The 7s population is reduced to close to one. The electron is moved to 6d, and a strong quadruple bond is formed, involving three two-electron bonds and two 6d one-electron bonds. We also start to see some population of the 5f orbitals that hybridizes with 6d. 

The strongest bond is formed between the Pa atoms in Pa2. Here the contribution of 6d is maximum, and we see a complete promotion to the atomic state with five unpaired electrons. A quintuple bond is formed with a short bond distance and a bond energy close to 5 eV. The bond contains the (7sag)2(6dnu)4 triple bond plus a 6dag two-electron bond and two 6dhg one-electron bonds. The 5/population is increased to one electron, but we still do not see any molecular orbital dominated by this atomic orbital. They are all used but rather in combination with the 6d orbitals. 

Figure 2b depicts a strong acceptor bond for a Na atom. It is formed from the weak bond depicted in Fig. 2a, for example, as a result of the capture and localization of a free electron, that is, as a result of the transformation of a Na+ ion of the lattice serving as an adsorption center, into a neutral Na atom. We obtain a bond of the same type as in the molecules H2 or Na2. This is a typically homopolar two-electron bond formed by a valence electron of the adsorbed Na atom and an electron of the crystal lattice borrowed from the free electron population. The quantum-mechanical treatment of the problem 2, 8) shows that these two electrons are bound by exchange forces which in the given case are the forces keeping the adsorbed Na atom at the surface and at the same time holding the free electron of the lattice near the adsorbed atom. 

Electron distributions are ascertained by means of a Mulliken population analysis of the ir-electron atomic populations (in the case of complete n-delocalization, each atom in the 67r-electron five-membered ring would have 1.20 7r-electrons associated with it) by determining the spatial extent of the localized orbitals of both the out-of-plane lone pair of the heteroatom and the C=C double bonds as well as through comparing the total electron density plots in planes parallel to the molecular plane. 

Most of the reactivity problems described in Sect. VI C have been treated recently by methods based on the electronic Overlap Population concept as introduced in the Electronic Population analysis of R. S. MuUiken. In fact the studies of the problems of Sect. VI C have established the general usefulness and apphcability of electronic overlap populations as reactivity measures for other excited- and ground-state reactions. The most important advantage of the electronic overlap population method of reactivity analysis is the possibihty provided for relating bond forming reactivity of two initially nonbonded atoms to the strength of their electronic interaction. 

The electronic overlap populations in all three cases were calculated from the one electron Extended Hiickel MO s. For the photocyclizations of 1,2-difuryl ethylenes very similar results were obtained also from minimal basis set ab-initio wavefunctions l The possibility of obtaining useful reactivity analyses from wave-functions which are easily available even for large systems could prove to be an important practical consideration for further applications of this method. The dependence on Sri sj ill (5) ensures that electronic overlap populations show the desirable physical characteristics for their use as reactivity measures strong falling-off with increasing interatomic distance and proper directional dependence. This last point is of particular significance for bond formation in polyenes. Thus for two C 2 p atomic... 

The stability of related isomers towards ring opening in both ground and excited state can be compared using electronic overlap populations of the C4a-C4b bonds. Thus in the ground state for 44 n = 0.7274 while for n = 0.7201 reflecting the greater stability of 44 relative to 45. 

The MO methods have been used to calculate the ir-electronic bond orders in unprotonated cytosine, and the bond lengths have been calculated on the basis of these quantities in the customary way.168a The qualitative agreement (Fig. 2) between the theoretical and experimental values is, in general, good, the best being obtained by means of the simple tt-HMO method. The 77-bond orders or total bond overlap populations calculated by different methods can be found in several papers 1t-HMO calculations on cytosines, see reviews1 140,170-172 n-SC... 

In NiO, the Ni2+ ion contributes eight electrons. Bonding is dominated by population of the bonding, mainly s,p-type, orbitals. The octahedron can be considered a 20 electron complex. Two electrons have to be placed in the bondweakening antibonding dx2 y2 and dz2 orbitals. As a result of Hund s rule, this results in a triplet state. Clearly, a more stable situation exists in octahedrally coordinated Co3+, forming an 18 electron complex. 

The asymmetry parameter in 1,2-disubstituted 5-nitroimidazoles decreases with increasing the substituent size. The n-electron density and N-l bond population is calculated according to the Townes-Dailey theory and described in detail by Dr. Lucken [1408] and Dr. Dolgushin [1409,1410] based on height with lengthening of the substituent on N-l [1411]. 

A molecular orbit lower in energy than any of the atomic orbitals from which it is derived lends stability to a molecule or ion when populated with electron Bonding Pair... 

In contrast to the nice, neat two-center-two-electron bond model, it is not so easy to determine the overall bonding character from MO orbital drawings alone. We need another measure. This comes from the Mulliken overlap population which is a numerical indicator of bonding (positive) and antibonding (negative) character between a pair of atoms within a molecule. For N2 in an approximate calculation the overall overlap populations are +0.68 for the three a filled MOs and +0.54 each for the it MOs. If one considers each it interaction of bond order one then the overall bond order is clearly three. 

When a population analysis is performed for the various wavefunctions used above, for the hydrogen molecule, it is found that the overlap populations are always positive (indicating a flow of electron density into the overlap region between the nuclei) but that the predicted enhancement of the density in the bond region depends on which function is used for example, the MO and VB functions give bond populations... 

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