Orbital mixing

So far, we have considered primarily interactions between orbitals of identical energy. However, orbitals with similar, but not equal, energies interact if they have appropriate symmetries. We will outline two approaches to analyzing this interaction, one in which the molecular orbitals interact and one in which the atomic orbitals interact directly. 

FIGURE 5-6 Interaction between Molecular Orbitals. Mixing molecular orbitals of the same symmetry results in a greater energy difference between the orbitals. The a orbitals mix strongly the o orbitals differ more in energy and mix weakly. 

Alternatively, we can consider that the four molecular orbitals (MOs) result from combining the four atomic orbitals (two 2s and two 2p ) that have similar energies. The resulting molecular orbitals have the following general form (where a and b identify the two atoms)  

FIGURE 5.7 Energy Levels of the Homonuclear DIatomics of the Second Period. 

The molecular orbital description of Hc2 predicts two electrons in a bonding orbital and two in an antibonding orbital, with a bond order of zero—in other words, no bond. This is what is observed experimentally. The noble gas He has no significant tendency to form diatomic molecules and, like the other noble gases, exists in the form of free atoms. He2 has been detected only in very low-pressure and low-temperature molecular beams. It has an extremely low binding energy, approximately 0.01 J/mol for comparison, H2 has a bond energy of 436 kJ/mol. 

Be2 has the same number of antibonding and bonding elections and consequently a bond order of zero. Hence, like He2, Be2 is an unstable species.  

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The interaction between the three cr localized orbitals is slightly more complex. As we have just shown, it is proper to start by combining orbitals of same energy (the crCIf2 pair), and then to interact the new combinations with the remaining orbitals. The procedure is simple here because, by symmetry, only the in-phase combination of the crCH2 group orbitals mixes with the acc bond orbital (see Fig. 17). The reader will notice that the acc orbital has been placed,... 

The construction of the acc molecular orbitals is solved in exactly the same manner each acc bond orbital has a positive overlap with its two neighbors via this overlap, the bond orbitals mix and form three typical combinations (see Fig. 25). A glance at... 

Keywords Chemical orbital theory. Electron delocalization. Frontier orbital. Orbital amplitude, Orbital energy, Orbital interaction. Orbital mixing rule, Orbital phase, Orbital phase continuity, Orbital phase environment. Orbital synunetry, Reactivity, Selectivity... 

The orbital mixing rules are described in detail and shown to be powerful for understanding and designing selective reactions in Chapter Orbital Mixing Rules and applied in chapter ji-Facial Selectivities of Diels-Alder reactions . 

Keywords Orbital mixing. Orbital amplitude. Orbital phase. Orbital polarization. Orbital deformation, Regioselectivity, Stereoselectivity, n Facial selectivity... 

The K conjugate molecules usually have planar geometries and no difference between the two faces above and below the molecular plane. When substitutions break the symmetry with respect to the plane, n orbitals mix a orbitals orthogonal prior to the substitution. Rehybridization occurs and the unsaturated bonds have... 

Orthogonal orbitals and ( ) are mixed with each other by nearby electric charges [3]. Electrostatic orbital mixing rules state ... 

According to the frontier orbital theory, a bond preferentially forms between the atoms with the largest frontier orbital amplitudes (Sect. 3.4 in the Chapter Elements of a Chemical Orbital Theory by Inagaki in this volume). This is applicable for the regioselectivities of Diels-Alder reactions [15]. The orbital mixing rules are shown here to be useful to understand and design the regioselectivities. 

The orbital mixing rules are applied to the polarization of 7t of ethene by a C=0 group on the assumption that is lowered below The 7t orbital has mix in phase and the low lying tc orbital mix out of phase with (Scheme 16). As a result, the phase relation between t( and n is fixed. The amplitude is larger on C than on C and the carbonyl carbon. 

Scheme 3b). The it orbital of ethene has a low-lying bonding orbital mix out of phase, and the low-lying n orbital mix out of phase with (7, . The relations are placed where the strongest interactions occur, or between (7, and the p orbital on the closer carbon (C ) in rand 7t. The phase relation of tt with ris uniquely determined. The signs of p orbitals in n and r are the same on and opposite on Cj. Thep amplitnde increases on and decreases on Cj. It follows that the LUMO of propene has large amplitude on C. ...

Orbital Mixing in Benzenes Substituted with an Electron Donating Group... 

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