Orbital correlation

The Woodward-Hoffmann method [52], which assumes conservation of orbital symmetry, is another variant of the same idea. In it, the emphasis is put on the symmetries of molecular orbitals. Longuet-Higgins and Abramson [53] noted the necessity of state-to-state correlation, rather than the orbital correlation, which is not rigorously justified (see also, [30,44]). However, the orbital symmetry conservation rules appear to be very useful for most themial reactions. 

The In-Phase ( 3s + 3s) Combination of Rydberg Orbitals Correlates to an s-type Orbital of the United Atom... 

Connecting the energy-ordered orbitals of reactants to those ofproducts according to symmetry elements that are preserved throughout the reaction produces an orbital correlation diagram. 

Orbital-correlation diagram for the reaction C2H2 -h C-----> C3H2... 

Figure 1.1. Orbital correlation diagram illustrating the distinction between normal electron demand (leftside) and inverse electron demand (right side) Diels-Alder reactions.

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. 

We have now considered three viewpoints from which thermal electrocyclic processes can be analyzed symmetry characteristics of the frontier orbitals, orbital correlation diagrams, and transition-state aromaticity. All arrive at the same conclusions about stereochemistiy of electrocyclic reactions. Reactions involving 4n + 2 electrons will be disrotatory and involve a Hiickel-type transition state, whereas those involving 4n electrons will be conrotatory and the orbital array will be of the Mobius type. These general principles serve to explain and correlate many specific experimental observations made both before and after the orbital symmetry mles were formulated. We will discuss a few representative examples in the following paragraphs. 

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... 

Fig. 11.10. Orbital correlation diagram for ethylene, butadiene, and cyclohexene orbitals.

When the orbitals have been classified with respect to symmetry, they can be arranged according to energy and the correlation lines can be drawn as in Fig. 11.10. From the orbital correlation diagram, it can be concluded that the thermal concerted cycloadditon reaction between butadiene and ethylene is allowed. All bonding levels of the reactants correlate with product ground-state orbitals. Extension of orbital correlation analysis to cycloaddition reactions involving other numbers of n electrons leads to the conclusion that the suprafacial-suprafacial addition is allowed for systems with 4n + 2 n electrons but forbidden for systems with 4n 7t electrons. 

Fig. 13.2. Orbital correlation for two ground-state ethenes and cyclobutane. The symmetry designations apply, respectively, to the horizontal and vertical planes for two etl lene molecules approachit one another in parallel planes.

Fig. 13.4. Orbital correlation of energy states involved in the photochemical butadiene-to-cyclobutene conversion.

Figure 15.12 Orbital correlation diagram for cyclobutane formation...

Figure 15.21 Orbital correlation diagram for the disrotatoric ring closure of butadiene...

Fig. 6. Orbital correlation diagram for the photoelectron spectra of 1,2-dithietes (the orbital energies given are the negative ionization energies, -/ j in eV).

We will conclude this section on theory with such a case. In Section 8.3 it was shown that the influence of substituents on the rate of dediazoniation of arenediazonium ions can be treated by dual substituent parameter (DSP) methods, and that kinetic evidence is consistent with a side-on addition of N2. We will now discuss these experimental conclusion with the help of schematic orbital correlation diagrams for the diazonium ion, the aryl cation, and the side-on ion-molecule pair (Fig. 8-5, from Zollinger, 1990). We use the same orbital classification as Vincent and Radom (1978) (C2v symmetry). 

SCF-CI calculations were performed at 20 different intemuclear separations, from 1.2 bohr to 4-00. The lowest separate atom states are, B( P,2p) and H( S) therefore, in order to have a homolytic dissociation and three degenerate 2p orbitals on B we have adopted the closed shell Fock hamiltonian with fractional occupation [23] one electron was placed in the 3(t orbital, correlating with H(ls) at infinite separation, and 1/3 each in the 4it and Itr orbitals correlating with B(2p). 

Electron correlations show up in two ways in the measured cross sections. If the initial target state is well described by the independent particle Hartree-Fock approximation, the experimental orbital (6) is the Hartree-Fock orbital. Correlations in the ion can then lead to many transitions for ionisation from this orbital, rather than the expected single transition, the intensities of the lines being proportional to the spectroscopic factors S K... 

More detailed insight into the interaction of NO with the Cu M5 site can be inferred from the simplified Kohn-Sham orbital correlation diagram shown in Figure 2.11. 

Braterman, P. S. Orbital Correlation in the Making and Breaking of Transition Metal-Carbon Bonds. 92, 149-172 (1980). 

Figure 1. Walsh type orbital correlation diagram (EH MO calculations [6]) for transforming linear H3P-Pt-PH3 (D3h) to a bent (C2V) geometry. Only the valence MOs and the relevant metal contributions to the MO wave functions are shown. 

The techniques which can be used for the construction of orbital correlation diagrams are well known 2,5,8,20) an(j neeq not be reviewed... 

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