Htickel systems

We note that it is the Htickel systems with 4N electrons and the Mobius systems with 4N + 2 electrons which have a nonbonding degenerate pair of MO s and thus a facile mode of converting starting excited state to ground state of product. Finally, it should be noted the the Mobius-Huckel method is fully consistent with the Woodward-Hoffmann treatment, both for ground state and for photochemical reactions 40). 

Note that both the [2 - - 2] and [4 + 2] transition states are Htickel systems no matter what basis sets we chose. For example. Fig. 15.9 shows other basis sets we might have chosen. In every case there will be zero or an even number of sign inversions. 

In the Mobius-Htickel approach, diagrams similar to Fig. 18.4 can be drawn for this case. Here too, the disrotatory pathway is a Htickel system and the conrotatory pathway a Mdbius system, but since six electrons are now involved, the thermal reaction follows the Htickel pathway and the photochemical reaction the Mobius pathway. 

Thiirene oxide systems ((30) and (31)) are of particular interest due to their being simultaneously both a potentially nonbenzenoid aromatic (An -f 2)7t and antiaromatic 4 7t Htickel system. 

Common examples of systems often mistaken as being aromatic (because of their alternating double and single bonds) are cyclobutadiene and cyclo-octatetraene (shown in Figure 6-9). In the case of cyclobutadiene, 4n + 2 = 4, giving n = 0.5, while for cyclooctatetraene, 4n + 2 = 8, so that n = 1.5. In these two compounds, n is not an integer, so these systems are anti-aromatic (nonaromatic). Anti-aromatic systems (non-Htickel systems) are less stable than aromatic or normal systems. 

The selection rules for [tt4 + tt2 ] and other cycloaddition reactions can also be derived from consideration of the aromaticity of the TS3 In this approach, the basis set p orbitals are aligned to correspond with the orbital overlaps that occur in the TS. The number of nodes in the array of orbitals is counted. If the number is zero or even, the system is classified as a Htickel system. If the number is odd, it is a Mobius system. Just as was the case for ground state molecules (see p. 716), Htickel systems are stabilized with 4 + 2 electrons, whereas Mobius systems are stabilized with 4n electrons. For the [tt4 + tt2] suprafacial-suprafacial cycloaddition the transition state is aromatic. 

For the cyclobutene-butadiene TS, the conrotatory closure results in a Mobius system, whereas a disrotatory TS gives a Htickel system. The same rules of aromaticity apply as for ground state molecules. A Htickel system is aromatic when it has 4 - -2 electrons. A Mobius system is aromatic when it has 4n electrons. In the case of the cyclobutene-butadiene interconversion, which involves four electrons, it is the conrotatory Mobius TS that is the favored aromatic transition state. 

Basis set orbital analysis of the hexatriene-cyclohexadiene system leads to the conclusion that the disrotatory process will be favored. The basis set orbitals for the conrotatory and disrotatory transition states are shown below. Here, with six electrons involved, it is the disrotatory mode (Htickel system) that gives a stabilized TS. 

Six-Electron Anti-Htickel Systems. C/ -type photochemical reactions in six-electron systems involve anti-Hiickel transition states. Equations (6.58) and (6.59) show two typical examples ... 

HyperChem performs an empirical Hiickel calculation to produce th e MO coefficien ts for a minimal basis set and th en projects th ese coefficien ts to the real basis set used in an cife calculation. Th e projected Htickel guess can be applied to rn olecular system s with an atom ic n um ber less th an or equal to 54 (Xe). 

Perhaps the most notable difference between S-N and N-O compounds is the existence of a wide range of cyclic compounds for the former. As indicated by the examples illustrated below, these range from four- to ten-membered ring systems and include cations and anions as well as neutral systems (1.14-1.18) (Sections 5.2-5.4). Interestingly, the most stable systems conform to the well known Htickel (4n -1- 2) r-electron rule. By using a simple electron-counting procedure (each S atom contributes two electrons and each N atom provides one electron to the r-system in these planar rings) it can be seen that stable entities include species with n = 1, 2 and 3. 

The benzene molecule in its equilibrium configuration is planar. Its symmetry is described by the point group as shown in Fig. 8-l(c). The delocalized n system is represented there by dotted lines. The six pz orbitals contribute to tbe jt system, as simply described by the Htickel approximation. The reduction r, = B2g Hjg E2u can be found as in the previous examples. 

There are no fully conjugated spirophosphorus compounds. Novel classes of spiroaromatic ring systems having a common phosphorus atom in which each ring can exhibit either Mobius or Htickel aromaticity have been proposed, such as 132 and 133 <2002J(P2)1499>. 

Consider initially the cyclopentadienyl ring system. In the Htickel approximation the one-electron energies of the molecular orbitals are related in a very simple way to the ring size and the symmetry of the particular level thus one finds... 

In contrast to the useful conceptual framework provided by the approximate approach just described, the results of more detailed molecular orbital calculations have on the whole been rather disappointing. Thus, although some semi-empirical SCF treatments were attempted, most of the earlier MO calculations for metallocene systems (18, 161, 162, 163, 164,165) suffered from such deficiencies as the neglect of the a-framework, or the use of various one-electron Hamiltonians, for example the various Wolfsberg-Helmholz techniques. Of late, Drago and his coworkers have carried out further Extended Htickel type computations for a wide range of both metallocene and bis-arene species (153, 154), and similar... 

Finally, the distinction between Hiickel and Mobius systems is considered. The above definitions are valid for Htickel-type reactions. For aromatic Mobius-type reations, the reverse holds An ATS is formed when an even number of electron pairs is re-paired. 

The phthalocyanine [1-4] system is structurally derived from the aza-[18]-annulene series, a macrocyclic hetero system comprising 18 conjugated n-electrons. Two well known derivatives of this parent structure, which is commonly referred to as porphine, are the iron(III)complex of hemoglobin and the magnesium complex of chlorophyll. Both satisfy the Htickel and Sondheimer (4n + 2)- electron rule and thus form planar aromatic systems. 

Before discussing mathematical formalism we should stress here that the Kirkwood approximation cannot be used for the modification of the drift terms in the kinetics equations, like it was done in Section 6.3 for elastic interaction of particles, since it is too rough for the Coulomb systems to allow us the correct treatment of the charge screening [75], Therefore, the cut-off of the hierarchy of equations in these terms requires the use of some principally new approach, keeping also in mind that it should be consistent with the level at which the fluctuation spectrum is treated. In the case of joint correlation functions we use here it means that the only acceptable for us is the Debye-Htickel approximation [75], equations (5.1.54), (5.1.55), (5.1.57). 

Obviously, the density description suggests that homoantiaromatic molecules prefer Mobius 4q + 2 electron systems rather than Htickel 4q systems. This is in line with the PMO analyses of Hehre66,69 and Jorgensen72-73 (see Section III.C). 

Htickel s rule states that planar cyclic % systems involving 4n+2 electrons will be unusually stable ( aromatic ), while cyclic 7t systems with 4n electrons will be unstable ( antiaromatic ). 

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