Interactions filled with unfilled

The standard method of explaining how such molecules can be stable is to invoke the interactions of filled p or hybrid orbitals on the ligands with an empty d orbital on the central element. Like any interaction of filled with unfilled orbitals, interactions with empty d orbitals are bound to be stabilising, but d orbitals are too high in energy relative to the p orbitals for their interaction to have any significant effect. 

Nevertheless, frontier orbital theory, for all that it works, does not explain why the barrier to forbidden reactions is so high. Perturbation theory uses the sum of all filled-with-filled and filled-with-unfilled interactions (Chapter 3), with the frontier orbitals making only one contribution to this sum. Frontier orbital interactions cannot explain why, whenever it has been measured, the transition structure for the forbidden pathway is as much as 40 kJ mol 1 or more above that for the allowed pathway. Frontier orbital theory is much better at dealing with small differences in reactivity. We shall return later in this chapter to frontier orbital theory to explain the much weaker elements of selectivity, like the effect of substituents on the rates and regioselectivity, and the endo rule, but we must look for something better to explain why pericyclic reactions conform to the Woodward-Hoffmann rules with such dedication. 

In this section we shall determine the effect of nonbonded interactions on the physical properties of related molecules. As our model compounds we will utilize difluoroethylene, a molecule having substituents bearing only lone pairs and dicyano-ethylene, a molecule bearing substituents with both filled and unfilled MO s. In particular, we focus on the three possible isomers of a disubstituted ethylene ie. the 1,1, trans-1,2- and cis- 1,2-isomers. The three possible isomers are shown below. 

An example of the effectiveness of this equation is given by an aqueous HEUR gel made up of a polymer with Mn = 20 x 103 Daltons at a concentration of 30kgm-3 filled with a poly(styrene) latex with a particle diameter of 0.2 pm at q> = 0.2. The unfilled gel had a network modulus of 0.4 kPa, whilst the modulus of the filled gel was 0.7 kPa. Equation (2.68) predicts a value of 0.728 kPa. The poly(styrene) particles act as a non-interactive filler because the surface is strongly hydrophobic as it consists mainly of benzene rings and adsorbs a monolayer of HEUR via the hydrophobic groups, resulting in a poly(ethylene oxide) coating that does not interact with the HEUR network. This latter point was... 

Figure 15. Canonical molecular orbital energy levels for [Rh(PH3)2(formamide)]+, showing the filled and unfilled orbitals with the woner symmetry to interact with C C jc and it-orbitals, seen on the right. Scale markings are in eV. All calculations were done at the B3LYP/LANL2DZ level.

CCI2 possesses both a high-energy filled molecular orbital in the o plane and a low-energy unfilled molecular orbital perpendicular to that plane (see discussion in the previous chapter). To interact optimally with the n electrons of an olefin, the carbene must orient itself in the following manner,... 

Molecular orbitals are characterized by energies and amplitudes expressing the distribution of electron density over the nuclear framework (1-3). In the linear combination of atomic orbital (LCAO) approximation, the latter are expressed in terms of AO coefficients which in turn can be processed using the Mulliken approach into atomic and overlap populations. These in turn are related to relative charge distribution and atom-atom bonding interactions. Although in principle all occupied MOs are required to describe an observable molecular property, in fact certain aspects of structure and reactivity correlate rather well with the nature of selected filled and unfilled MOs. In particular, the properties of the highest occupied MO (HOMO) and lowest unoccupied MO (LUMO) permit the rationalization of trends in structural and reaction properties (28). A qualitative predictor of stability or, alternatively, a predictor of electron... 

We cannot, then, expect this approach to understanding chemical reactivity to explain everything. Most attempts to check the validity of frontier orbital theory computationally indicate that the sum of all the interactions of the filled with the unfilled orbitals swamp the contribution from the frontier orbitals alone. Even though the frontier orbitals make a weighted contribution to the third term of the Salem-Klopman equation, they do not account quantitatively for the many features of chemical reactions for which they seem to provide such an uncannily compelling explanation. Organic chemists, with a theory that they can handle easily, have fallen on frontier orbital theory with relief, and comfort themselves with the suspicion that something deep in the patterns of molecular orbitals must be reflected in the frontier orbitals in some disproportionate way. 

The interactions which do have an important energy-lowering effect are the combinations of filled orbitals with unfilled ones. Thus, in Fig. 2-18 and Fig. 2-19, we have such combinations, and in each case we see that the energylowering in the bonding combination is the usual one, and that the rise in energy of the antibonding combination is without effect on the actual energy of the system, because there are no electrons to go into that orbital. 

The soft-soft interaction of filled with empty orbitals is the major interaction in the transition state because there is little hard-hard attraction. In an unsubstituted system two soft-soft interactions stabilize the transition state The filled tl)2 molecular orbital of the diene interacts with the unfilled jt of the dienophile also the empty ips of the diene interacts with the filled Jt of the dienophile. Figure 12.19 gives the interaction diagram. 

If the dienophile has a substituent that extends its pi system, the best transition state for the reaction maximizes overlap between the two pi systems. To achieve this greater degree of interaction the dienophile must place the substituent underneath the diene, endo. The Diels-Alder reaction of two dienes has such a transition state with an additional interaction between the unfilled diene i )3 MO and the filled diene tl)2 MO (Fig. 12.20). 

Complexes with n Bonding. If the ligands have n orbitals, filled or unfilled, it is necessary to consider their interactions with the T2gd orbitals,... 

In terms of the quantum-well picture, a small particle of, e.g., an alkali metal, can be regarded in many respects as a giant atom (or molecule). The electrons are confined by the outer surface of the particle, which presents an approximately spherical potential, similar therefore to the spherically symmetric Coulombic potential in the atom arising from the electron-nucleus electrostatic interaction. Thus, the building-up principle of electrons in such a cluster is quite similar to that underlying the periodic system of the elements, with the characteristic shell-structure for the electrons. Indeed, large differences in reactivity have been observed for clusters with filled or unfilled electron shells An attractive feature of clusters in this respect is, evidently, that the number of electrons (atoms) per cluster can surpass by orders of magnitude the number of elements in the periodic system. 

Even when a transition metal is coordinatively saturated, either filled or unfilled d-orbitals of suitable energy and orientation are available, which may interact with orbitals at the /S-position on the ligand. The existence of such interactions has been established by spectral studies (25). In the systems where the /8-position on the ligand is unsaturated, metal d-orbitals of suitable symmetry may be found that can weakly overlap with the vr-orbitals of the /8-substituent. If the /8-position is saturated, metal c/-orbitals may overlap with either an empty sp lobe of the /8-carbon or one of the sp carbon-substituent orbitals. These interactions are summarized in Fig. 9. 

The progress in the oxidation of LDPE modified with maleic anhydride and alumina proceeds somewhat similar at various doses, because oxygen diffusion is hindered by filler nanoparticles [102]. The noticeable difference between pristine and modified LDPE consists of the presence of maleic anhydride, which interacts with molecular chains due to the electronegativity of oxygen atoms. The same radiation dose affects differently the dielectric behavior of the nanocomposites depending on the filler content. The dose of 50 kGy applied on LDPE-g-AM filled with 5 wt% nano-Al203 leads to a relative permittivity smaller than unfilled LDPE. y-Radiation can lead to a decrease in the dielectric losses of LDPE AI2O3 nanocomposites for properly chosen combination dose-fiUer content. 

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