Unstable orbital

If C is an orbit, we call it orbitaJly stable if, given e > 0, there is 7) > 0 such that if B is a representative point following a neighboring trajectory, and B is at a distance i) from C at time t0, then B remains within a distance e from 0 for t > t0. If no such rj exists, O is orbitally unstable... 

Certain mathematical-physical considerations and the subsequent fitting of f (p T) allow us to conclude that the coexistence envelope diameter point (pd(T), pa(T)) is an (orbitally unstable) improper node, i.e. that all solution paths leaving (pD(T), pequilibrium points (pG(T), p (T)), (pD(T), P (T)), and (pL(T), Pa(T)) converge to the critical point (1, 1). This multiple equilibrium point is an orbitally stable, but structurally (topologically) unstable, multiple node. The parameter T thus can be considered as a bifurcation parameter, and T = 1 as a bifurcation value of dynamic System 3. 

For molecules with an even number of electrons, the spin function has only single-valued representations just as the spatial wave function. For these molecules, any degenerate spin-orbit state is unstable in the symmetric conformation since there is always a nontotally symmetric normal coordinate along which the potential energy depends linearly. For example, for an - state of a C3 molecule, the spin function has species da and E that upon... 

We can consider the hydroboration step as though it involved borane (BH3) It sim phfies our mechanistic analysis and is at variance with reality only m matters of detail Borane is electrophilic it has a vacant 2p orbital and can accept a pair of electrons into that orbital The source of this electron pair is the rr bond of an alkene It is believed as shown m Figure 6 10 for the example of the hydroboration of 1 methylcyclopentene that the first step produces an unstable intermediate called a tt complex In this rr com plex boron and the two carbon atoms of the double bond are joined by a three center two electron bond by which we mean that three atoms share two electrons Three center two electron bonds are frequently encountered m boron chemistry The tt complex is formed by a transfer of electron density from the tt orbital of the alkene to the 2p orbital... 

The phenyl cation is an extremely unstable cation, as is reflected by the high hydride affinity shown in Table 5.2. In this case, the ring geometry opposes rehybridization so the vacant orbital retains sp character. Because the empty orbital is in the nodal plane of the ring, it receives no stabilization firom the n electrons. 

In Fig. 9.1, orbitals below the dashed reference line are bonding orbitals when they are filled, the molecule is stabilized. The orbitals that fall on the reference line are nonbonding placing electrons in these orbitals has no effect on the total bonding energy of the molecule. The orbitals above the reference line are antibonding the presence of electrons in these orbitals destabilizes the molecule. The dramatic difference in properties of cyclobutadiene (extremely unstable) and benzene (very stable) is explicable in terms of... 

Protonation of the anion [SN2] by acetic acid in diethyl ether produces the thermally unstable sulfur diimide S(NH)2. Like all sulfur diimides, the parent compound S(NH)2 can exist as three isomers (Scheme 5.5). Ab initio molecular orbital calculations indicate that the (cis,cis) configuration is somewhat more stable than the (cis,trans) isomer, while the (trans,trans) isomer is expected to possess considerably higher energy. The alternative syn,anti or E,Z nomenclatures may also be used to describe these isomers. The structures of organic derivatives S(NR)2 (R = alkyl, aryl) are discussed in Section 10.4.2. 

CH3 (carbonium ions) Unstable reaction intermediates with 1 vacant orbital ... 

Among the diatomic molecules of the second period elements are three familiar ones, N2,02, and F2. The molecules Li2, B2, and C2 are less common but have been observed and studied in the gas phase. In contrast, the molecules Be2 and Ne2 are either highly unstable or nonexistent. Let us see what molecular orbital theory predicts about the structure and stability of these molecules. We start by considering how the atomic orbitals containing the valence electrons (2s and 2p) are used to form molecular orbitals. 

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