Orbital conservation

Cyclooctatetraene (COT) —> Semibullvalene (SB) Photorearrangement. Irradiation of COT yields semibullvalene [97], in spite of the fact that this photochemical reaction is forbidden by orbital conservation mles. The Longuet-Higgins loop for this system actually predicts that this should happen, although the reaction is phase preserving. (Fig. 42). This is another example of type C loop (Fig. 11). Only six of the eight electrons re-pair as COT transforms to SB. The reaction is made possible by the fact that COT valence isomerization, a phase-inverting reaction (four electron-pair Hiickel system), takes place simultaneously. One expects to produce in the reaction a COT isomer, that can be detected solely by proper substitution. 

Since the virtual orbitals conserve the nature of the fundamental VB structures, the entire VBCI wave function can be rewritten in a compact form,... 

Figure 1. Schematic diagram showing the densities of orbitals conserving the prescribed subsystem density (panel A) and overall density (panel B), which are used in the constrained search constructions of Eqs. (25) and (23), respectively.

The concept of orbital conservation (Chapter 5) requires that when molecular orbitals are formed from two atoms, each interacting pair of atomic orbitals (such as 2s) gives rise to two molecular orbitals (0-2 and 0-2 ). When n atoms are used, the same approach results in n molecular orbitals. In the case of solids, n is very large—Avogadro s number for a mole of atoms. If the atoms were all in a one-dimensional row, the lowest energy orbital would... 

Wlien the atom-atom or atom-molecule interaction is spherically symmetric in the chaimel vector R, i.e. V(r, R) = V(/-,R), then the orbital / and rotational j angular momenta are each conserved tln-oughout the collision so that an i-partial wave decomposition of the translational wavefiinctions for each value of j is possible. The translational wave is decomposed according to... 

The main drawback of the chister-m-chister methods is that the embedding operators are derived from a wavefunction that does not reflect the proper periodicity of the crystal a two-dimensionally infinite wavefiinction/density with a proper band structure would be preferable. Indeed, Rosch and co-workers pointed out recently a series of problems with such chister-m-chister embedding approaches. These include the lack of marked improvement of the results over finite clusters of the same size, problems with the orbital space partitioning such that charge conservation is violated, spurious mixing of virtual orbitals into the density matrix [170], the inlierent delocalized nature of metallic orbitals [171], etc. 

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. 

For Woodward-Hoffm an allowed thermal reactions (such as the con rotatory ring opening of cyclobulan e), orbital symmetry is conserved and there is no change in orbital occupancy. Hven though bonds are made and broken, you can use the RHFwave fun etion. 

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. 

Woodward, R.B. and Hoffmann, R. Conservation of Orbital Symmetry Verlag Chemie, Weinheim, ERG, 1970. 

R. B. Woodward and R. Hoffmann, The Conservation of Orbital Symmety, Academic Press, Inc., New York, 1970. 

The key to understanding the mechanism of the concerted pericyclic reactions was the recognition by Woodward and Hoffmann that the pathways of such reactions were determined by the symmetry properties of the orbitals that were directly involved. Their recognition that the symmetry of each participating orbital must be conserved during the... 

Cycloaddition involves the combination of two molecules in such a way that a new ring is formed. The principles of conservation of orbital symmetry also apply to concerted cycloaddition reactions and to the reverse, concerted fragmentation of one molecule into two or more smaller components (cycloreversion). The most important cycloaddition reaction from the point of view of synthesis is the Diels-Alder reaction. This reaction has been the object of extensive theoretical and mechanistic study, as well as synthetic application. The Diels-Alder reaction is the addition of an alkene to a diene to form a cyclohexene. It is called a [47t + 27c]-cycloaddition reaction because four tc electrons from the diene and the two n electrons from the alkene (which is called the dienophile) are directly involved in the bonding change. For most systems, the reactivity pattern, regioselectivity, and stereoselectivity are consistent with describing the reaction as a concerted process. In particular, the reaction is a stereospecific syn (suprafacial) addition with respect to both the alkene and the diene. This stereospecificity has been demonstrated with many substituted dienes and alkenes and also holds for the simplest possible example of the reaction, that of ethylene with butadiene ... 

Which of the following reactions are allowed according to the orbital symmetry conservation rules Explain,... 

For the discussion of the rearrangements in section III only stepwise reaction sequences will be considered. We must note, however, that many of these transformations may just as well result from concerted processes in accordance with the rules for orbital symmetry conservation,... 

The density fitting functions may or may not be the same as those used in expanding the orbitals. The fitting constants a are chosen so that the Coulomb energy arising from the difference between the exact and fitted densities is minimized, subject to the constraint of charge conservation. The J integrals then become... 

---