Total Overlap

In all three frontier orbital combinations shown above, the upper orbital components are the same sign, and their overlap is positive. In the two cases on the left, the lower orbital components also lead to positive overlap. Thus, the upper and lower interactions reinforce, and the total frontier orbital interaction is non-zero. Electron movement (chemical reaction) can occur. The right-most case is different. Here the lower orbital components lead to negative overlap (the orbitals have opposite signs at the interacting sites), and the total overlap is zero. No electron movement and no chemical reaction can occur in this case. 

Pff for the cis isomer but also in the greater total overlap population Nf for the cis isomer. The latter quantity is defined as follows ... 

However, INDO calculations have been performed for the cis and trans isomers of l,2-difluoro-l,2-dihydroxyethylene and the results are shown above. As can be seen, the total overlap population is the same in both cases and, hence, the difference in the stabilities of the cis and trans isomers is expected to be very small. 

FIG. 7. Simulated (dotted curves) and experimental (solid curves) voltammograms at 100 mV s at a lONEE (0.079 cm geometric area) in 5 pM TMAFc+ and 0.5 mM sodium nitrate. Simulation assumes the total overlap limiting case (i.e., a macroelectrode with area = 0.079 cm ). 

There is a large, but not total, overlap between the terms condensation polymers and stepwise kinetics and the terms addition (or vinyl) polymers and chain kinetics. In this section we will look at each of these four terms and illustrate the similarities and differences between them. 

Even so, there is no total overlap between the various characteristics of vinyl-chain kinetics and condensation-step kinetics. Following are examples illustrating the lack of adherence to this overlap ... 

Further summation over all AO s centered on k and C gives a total overlap population, n(k, 8)... 

Fig. 11 0 Competition by ligands for Ihe ir bonding d orbilul of a central metal atom. Relative overtop is symbolized by the shaded areas, (a) Equal aod strong tr bonds resulting from equal and good overlap of Ihe two carbon monoxide sr orbitals with the meial J orbital (b) Superior overlap of carbon monoxide t orbital wilh polarized metal d orbiial compared lo poorer overlap between ligand <1 and metal d orbitals. Polarization (mixing of higher energy wave functions) occurs so as to maximize total overlap Recall that the overlap integral includes both spatial and intensive properties Ihe represemation above is a graphic simplification.

In Eq. (8-2) G is the total overlap of the metal orbital with the linear combination of ligand orbitals,... 

The total overlap of a metal orbital and a linear combination of ligand orbitals is called the group overlap G. That is,... 

In most transition metal and organometallic compounds, many modes are displaced. In the case of many displaced normal modes, the total overlap is... 

Each of the displaced modes in the molecule can contribute to the MIME frequency. Each of these modes k has a time dependence whose magnitude is given by eq. 1. The larger the displacement Ak in the kth mode, the sharper the peaks in < The total overlap <<(> (t)> is the product (eq. 10) of the individual modes overlaps and tm will tend to be closest to tk=2n/iok for that mode with the largest Ak. 

In a polyelectronic molecule, it is necessary to sum over all electrons and calculate the total overlap population to obtain a measure of the bond strength. 

In the study of mixtures, differentiation between enantiomers is a two level problem which is somewhat independent of whether the LC system is chiral or conventional. The problems common to both systems are the effects of overlapping bands on the performance of the detectorfs). Overlap can be between chiral-achiral species on the one hand and co-eluted chiral-chiral with achiral on the other. On first thought the chiral-achiral distinction should be relatively easy if a chiroptical detector is used because the achiral compounds will not interfere with the detection measurement. In addition the ability of the chiroptical detector to measure both positive and negative signals makes the confirmation of the enantiomeric structure elementary [3,4], As pointed out earlier, enantiomers co-elute from conventional columns and two detectors in sequence will provide the information to measure the enantiomeric ratio provided the mixture is not racemic. Partial or total overlap of the band for a non-chiral species with the chiral eluate band increases significantly the difficulty in measuring an enantiomeric ratio. In this instance the total absorbance that is measured may include a contribution from the non-chiral species which without correction will lead to an overestimation of the amount of chiral material and an erroneous value for the enantiomeric ratio. Under these circumstances there is no other LC option but to develop a separation that is based upon a chiral system. 

The first criterion to be suggested for the evaluation of the quality of an entire chromatogram was defined as the total overlap by Giddings in 1960 [426]. The definition reads ... 

Table 9. Effective charges (QM, total overlap populations (OP), dipole moments (p), dielectric dipole polarizabilities (a), ionization potentials (IP) and atomization energies (DJ for MO,Cl (M - Tc, Re, and Bh). From [ 1131. ...

Fig. 16. Effective charges (QM) and total overlap populations (OP) for group-4 through 8 halides and oxyhalides obtained as a result of the Mulliken population analysis in the DS-DV and DFT calculations [15,113-114].

The overlap population between S and Pt, which is the nearest to S, is 0.44, which means that this bond is strong. The overlap population between S and the two second-nearest Pt atoms is —0.26, which is a negative value. The overlap population between S and the nine outer Pt atoms is —0.05, which is a small but of negative value. The total overlap population between S and Pt surface is 0.13. 

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