Phase, of orbital

The importance of considering the phase of orbitals is that only orbitals of the same phase will overlap, and so result in a bonding situation orbitals of different phase lead to a repulsive, anti-bonding situation. 

Fig. 2.1 (a) The a donation OC metal here, the transition metal d 2 orbital is shown as the acceptor but it could be some mixture of s, and d 2. Note that there is lone-pair a electron density on both 0 and C. That on C is the larger and so has the greater overlap with the empty metal orbital. In this, and all other figures in this chapter, filled orbitals are shaded the phases of orbitals are given explicitly, (b) The % back-donation metal - CO the metal orbital is almost pure d, the CO orbital is an empty antibonding % orbital. Note that for a linear triatomic OCM system there is second, equivalent, interaction to that shown above (it is like that shown but rotated 90 about the OCM axis and so is located above and below the plane of the paper). 

This is an example of a Mobius reaction system—a node along the reaction coordinate is introduced by the placement of a phase inverting orbital. As in the H - - H2 system, a single spin-pair exchange takes place. Thus, the reaction is phase preserving. Mobius reaction systems are quite common when p orbitals (or hybrid orbitals containing p orbitals) participate in the reaction, as further discussed in Section ni.B.2. 

Conservation of orbital symmetry is a general principle that requires orbitals of the same phase (sign) to match up in a chemical reaction. For example, if terminal orbitals are to combine with one another in a cyclixation reaction as in pattern. A, they must rotate in the same dii ection (conrotatory ovei lap). but if they combine according to pattern H. they must rotate in opposite directions (disrotatory). In each case, rotation takes place so that overlap is between lobes of the it orbitals that are of the same sign. 

The electrophilic character of boron is again evident when we consider the oxida tion of organoboranes In the oxidation phase of the hydroboration-oxidation sequence as presented m Figure 6 11 the conjugate base of hydrogen peroxide attacks boron Hydroperoxide ion is formed m an acid-base reaction m step 1 and attacks boron m step 2 The empty 2p orbital of boron makes it electrophilic and permits nucleophilic reagents such as HOO to add to it... 

For the butadiene-cyclobutene interconversion, the transition states for conrotatory and disrotatory interconversion are shown below. The array of orbitals represents the basis set orbitals, i.e., the total set of 2p orbitals involved in the reaction process, not the individual MOs. Each of the orbitals is tc in character, and the phase difference is represented by shading. The tilt at C-1 and C-4 as the butadiene system rotates toward the transition state is different for the disrotatory and conrotatory modes. The dashed line represents the a bond that is being broken (or formed). 

The quote is from the third volume of Henri Poincare s New Methods of Celestial Mechanics, and is a description of his discovery of homoclinic orbits (see below) in the restricted three-body problem. It is also one of the earliest recorded formal observations that very complicated behavior may be found even in seemingly simple classical Hamiltonian systems. Although Hamiltonian (or conservative) chaos often involves fractal-like phase-space structures, the fractal character is of an altogether different kind from that arising in dissipative systems. An important common thread in the analysis of motion in either kind of dynamical system, however, is that of the stability of orbits. 

J. Interactions of two orbitals gives in-phase and out-of-phase combined orbitals... 

The in-phase (out-of-phase) combined orbitals are stabilized (destabilized) and bonding (antibonding)... 

The stabilization of the in-phase combined orbital implies that electrons are more stabilized by the delocalization to the overlap region than by the localization to the interacting orbitals. The relative stability of the out-of-phase combined orbitals has been reported in a few papers [4-6]. 

We have learned the interactions of the same orbitals and chemical bonds between the same atoms. The orbital phase plays a crucial role in the energies and the spacial extensions of the bond orbitals. Here we learn interactions of different orbitals and amplitude of orbitals, using an example of polar bonds between different atoms. 

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