Non-planar system

When the IRP is traced, successive points are obtained following the energy gradient. Because there is no external force or torque, the path is irrotational and leaves the center of mass fixed. Sets of points coming from separate geometry optimizations (as in the case of the DC model) introduce the additional problem of their relative orientation. In fact, the distance in MW coordinates between adjacent points is altered by the rotation or translation of their respeetive referenee axes. The problem of translation has the trivial solution of centering the referenee axes at the eenter of mass of the system. On the other hand for non planar systems, the problem of rotations does not have an analytical solution and must be solved by numeiieal minimization of the distanee between sueeessive points as a funetion of the Euler angles of the system [16,24]. 

Thus by several criteria l,4-dihydro-l,4-diazocines without a strongly electron-withdrawing group at the 1,4-positions are aromatic compounds, whereas those with such groups are non-planar systems with localized bonding. Diene character in the latter compounds is seen in the cycloaddition of N- phenyltriazolinedione to give the adducts (234b and c). 

With some exceptions, i.e. non-planar systems, variances in geometry are small within the class of benzenoid (alternant) hydrocarbons and thus can be neglected. Hence the individual representatives of this class of compounds differ only with regard to their molecular topologies. Provided the influence of the non-topological structural characteristics (kind of atoms, geometry, additional electronic interactions that are not referred to in the constitutional formulae) on the physical and chemical properties... 

An intensity enhancement has been observed for /3,y unsaturated carbonyl compounds such as 32, which is due to r-.7r interactions in the non-planar system of reduced symmetry (Labhart and Wagniere, 1959). In the series of polyene aldehydes, of the transition increases with in-... 

The RDF descriptor is interpretable by using simple rule sets, and thus it provides a possibility for conversion of the code back into the corresponding 3D structure. Besides information about interatomic distances in the entire molecule, the RDF code provides further valuable information, e.g., about bond distances, ring types, planar and non-planar systems and atom types. This fact is a most valuable consideration for a computer-assisted code elucidation. 

Ortho-lithiation of an O-protected m-fluorophenol, followed by treatment with phosphorus tribromide and aqueous acid deprotection, has given the phosphino-phenol 18. In the presence of potassium t-butoxide in an aprotic solvent, this is converted into the non-planar system 19, which exhibits pyroelectric properties. An organolithium route to the alkynylphosphine 20 has been developed. The same paper also reports a new route to the lithiated alkynylphosphine 21 and a study of its reactivity towards electrophiles. Diastereoselective lithiation of... 

Other compounds which might be mentioned, because they illustrate applications of the method to distinctly non-planar systems, are the bridged annulenes bicyclo[4,4,l] undecapentaene f 12] and the isomeric[5,3,l] compound [13]. The x-ray structure is known for [12] and the calculated values are in quite good... 

U Annelated derivatives of [10]aimuleiie have been prepared but all of these compounds show n.m.r. spectra typical of non-planar systems, and do not represent delocalized lOre-electron systems V3.74.7S). 

The reactants cannot retain their coplanarity during cycloaddition, but -as M.G. Evans pointed out over half a century ago - the transition state of the Diels-Alder reaction nevertheless reduces to a six-electron problem [26] in which the mobile electrons. .. simulate their behaviour in a benzene molecule [27]. Following this line of reasoning, Dewar [28] extended to non-planar systems, like those illustrated in (b) and (c) of Fig. 1.1, the scope of the familiar Hiickel Rule [29], according to which planar monocyclic molecules with 4N -f 2 mobile electrons have aromatic stability. It follows that [ 4 2]-cycloaddition, which has an aromatic transition state, is allowed, whereas [ 2 2]-cycloaddition is... 

The Hiickel method is a very primitive example of a semi-empirical method in which various integrals are set equal to either a or p and treated as empirical parameters overlap integrals are ignored. The removal of the restriction of the Hiickel method to planar hydrocarbon systems was achieved with the introduction of the extended Hiickel theory (EHT) in about 1963. In heteroatomic non-planar systems (such as d-metal complexes) the separation of orbitals into k and a is no longer appropriate and each type of atom has a different value of Hu (which in Hiickel theory is set equal to a for all atoms). In this approximation, the overlap integrals are not set equal to zero but ue cdculated expKdtly. Furthermore, the Hjk, which in Hiickel theory are set equal to p, in EHT are made proportional to the overlap integral between the orbitals J and K. 

Although in non-planar systems the o/rt symmetry labelling of molecular orbitals (and related electrons) is no longer valid, it is still possible to enhance electron... 

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