A orbitals

Figure Bl.6.11 Electron transmission spectrum of 1,3-cyclohexadiene presented as the derivative of transmitted electron current as a fiinction of the incident electron energy [17]. The prominent resonances correspond to electron capture into the two unoccupied, antibonding a -orbitals. The negative ion state is sufficiently long lived that discrete vibronic components can be resolved.

A simple example would be in a study of a diatomic molecule that in a Hartree-Fock calculation has a bonded cr orbital as the highest occupied MO (HOMO) and a a lowest unoccupied MO (LUMO). A CASSCF calculation would then use the two a electrons and set up four CSFs with single and double excitations from the HOMO into the a orbital. This allows the bond dissociation to be described correctly, with different amounts of the neutral atoms, ion pair, and bonded pair controlled by the Cl coefficients, with the optimal shapes of the orbitals also being found. For more complicated systems... 

Notice that the total number of a orbitals arising from the interaction of the 2s and 2p orbitals is equal to the number of aos that take part in their formation. Notice also that this is true regardless of whether one thinks of the interactions involving bare 2s and 2p... 

Hamiltonian contains (fe2/2me r ) 32/3y2 whereas the potential energy part is independent of Y, the energies of the moleeular orbitals depend on the square of the m quantum number. Thus, pairs of orbitals with m= 1 are energetieally degenerate pairs with m= 2 are degenerate, and so on. The absolute value of m, whieh is what the energy depends on, is ealled the X quantum number. Moleeular orbitals with = 0 are ealled a orbitals those with = 1 are 7i orbitals and those with = 2 are 5 orbitals. 

Another example of reduced symmetry is provided by the changes that occur as H2O fragments into OH and H. The a bonding orbitals (ai and b2) and in-plane lone pair (ai) and the a antibonding (ai and b2) of H2O become a orbitals (see the Figure below) the out-of-plane bi lone pair orbital becomes a" (in Appendix IV of Electronic Spectra and Electronic Structure of Polyatomic Molecules, G. Herzberg, Van Nostrand Reinhold Co., New York, N.Y. (1966) tables are given which allow one to determine how particular... 

Energies of the bonding a and antibonding a orbitals as funetions of interfragment distanee Re denotes a distanee near the equilibrium bond length for XY. 

In the heteronuelear ease, the Sx and Sy orbitals still eombine to form a bonding a and an antibonding a orbital, although these orbitals no longer belong to g and u symmetry. The energies of these orbitals, for R values ranging from near Rg to R °o, are depleted below. 

The energy "gap" between the a and a orbitals at R = depends on the eleetronegativity differenee between the groups X and Y. If this gap is small, it is expeeted that the behavior of this (slightly) heteronuelear system should approaeh that of the homonuelear X2 and Y2 systems. Sueh similarities are demonstrated in the next seetion. 

As R oo, the CSF energies (i H are more diffieult to "intuit" beeause the a and a orbitals beeome degenerate (in the homonuelear ease) or nearly so. To pursue this point and arrive at an energy ordering for the CSFs that is appropriate to the R region, it is useful to express eaeh of the above CSFs in terms of the atomie orbitals Sx and Sy that eomprise a and a. To do so, the ECAO-MO expressions for a and a. ... 

Figure 7.4 Russell-Saunders coupling of (a) orbital angular momenta li and I2, (b) spin angular momenta Sj and 2 and (c) total orbital and total spin angular momenta, L and S, of sip and a d electron...

MO calculations at the 6-3IG level have been done on both acrolein and aminoethylene. The resulting MOs were used to calculate charge distributions. Figure 1.26 gives the 7t-electron densities calculated for butadiene, acrolein, and aminoethylene. Inclusion of the hydrogen and a orbitals leads to overall charges as shown. These charge distributions result from a polarization which is counter to the n polarization. 

STO-3G calculations find the corresponding transition state to be more stable than other possible conformations by several kilocalories per raole. The origin of the preference for this transition-state conformation is believed to be a stabilization of the C=0 LUMO by the a orbital of the perpendicularly oriented substituent. 

Front-side approach is disfavored both because the density of the a orbital is less in the region between the carbon and the leaving group and because front-side approach would involve both a bonding and an antibonding interaction with the tr orbital since it has a nodal surface between the atoms. 

The preferred alignment of orbitals for a 1,2-hydride or 1,2-alkyl shift involves coplanarity of the p orbital at the carbocation ion center and the a orbital of the migrating group. 

The pA of 1,3-dithiane is 36.5 (Cs" ion pair in THF). The value for 2-phenyl-1,3-dithiane is 30.5. There are several factors which can contribute to the anion-stabilizing effect of sulfur substituents. Bond dipole effects contribute but carmot be the dominant factor because oxygen substituents do not have a comparable stabilizing effect. Polarizability of sulfur can also stabilize the carbanion. Delocalization can be described as involving 3d orbitals on sulfur or hyperconjugation with the a orbital of the C—S bond. MO calculations favor the latter interpretation. An experimental study of the rates of deprotonation of phenylthionitromethane indicates that sulfur polarizability is a major factor. Whatever the structural basis is, there is no question that thio substituents enhance... 

The cyclobutene-butadiene interconversion can serve as an example of the reasoning employed in construction of an orbital correlation diagram. For this reaction, the four n orbitals of butadiene are converted smoothly into the two n and two a orbitals of the ground state of cyclobutene. The analysis is done as shown in Fig. 11.3. The n orbitals of butadiene are ip2, 3, and ij/. For cyclobutene, the four orbitals are a, iz, a, and n. Each of the orbitals is classified with respect to the symmetiy elements that are maintained in the course of the transformation. The relevant symmetry features depend on the structure of the reacting system. The most common elements of symmetiy to be considered are planes of symmetiy and rotation axes. An orbital is classified as symmetric (5) if it is unchanged by reflection in a plane of symmetiy or by rotation about an axis of symmetiy. If the orbital changes sign (phase) at each lobe as a result of the symmetry operation, it is called antisymmetric (A). Proper MOs must be either symmetric or antisymmetric. If an orbital is not sufficiently symmetric to be either S or A, it must be adapted by eombination with other orbitals to meet this requirement. 

An orbital correlation diagram can be constructed by examining the symmetry of the reactant and product orbitals with respect to this plane. The orbitals are classified by symmetry with respect to this plane in Fig. 11.9. For the reactants ethylene and butadiene, the classifications are the same as for the consideration of electrocyclic reactions on p. 610. An additional feature must be taken into account in the case of cyclohexene. The cyclohexene orbitals tr, t72. < i> and are called symmetry-adapted orbitals. We might be inclined to think of the a and a orbitals as localized between specific pairs of carbon... 

The sp hybrid state of nitrogen is just like that of carbon except nitrogen has one more electron. Each N—H bond in NH3 involves overlap of an sp hybrid orbital of N with a orbital of hydrogen. The unshared pair of NH3 occupies an sp orbital. 

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