Orbital polarization scheme

The orbital polarization scheme has been applied to several systems (see references above) where it improved the agreement between theory and experiment. A recent application to americium was reported by Soderlind et al.,[110] who examined structural changes of Am under pressure. The results were consistent with a high-pressure phase with delocalized 5/ electrons and a low-pressure phase with localized and non-bonding 5/ states, a Mott transition. 

The n orbital amplitudes of ethene are identical on both carbons. Unsymmetrical substitutions polarize the n orbital. Electron acceptors or electrophiles attack the carbon with the larger r amplitude. The polarization of frontier orbitals is important for regioselectivities of reactions. Here, mechanism of the n orbital polarization of ethene by methyl substitution [4] is described (Scheme 5). 

Interactions polarize bonds. Trimethylenemethane (TMM) and 2-buten-l,4-diyl (BD) dianions (Scheme 6a, b) are chosen as models for hnear and cross-conjngated dianions. The bond polarization (Scheme 7) is shown to contain cyclic orbital interaction (Scheme 6c) even in non-cyclic conjugation [15]. The orbital phase continnity-discon-tinnity properties (Scheme 6d, e) control the relative thermodynamic stabihties. 

In many complexes, some of the antibonding orbitals in the d block are polarized by mixing, either with a p orbital or with the s orbital of the metal (e.g. see 2-64 and 2-65 for d-p mixing and 2-71 for d-s mixing). The purpose of this appendix is to study the orbital interaction scheme that produces these polarizations in greater detail. 

When an orbital in the d block results simply from the antibonding interaction between a metal d orbital and an orbital of the same symmetry located on the ligands (i) (two-orbital interaction scheme, 2.A1), the d orbital is not polarized. However, polarization does occur if there is a p (or s) orbital on the metal that has the same symmetry as the d and I orbitals, which leads to a three-orbital interaction scheme (2.A2). In this case, while the d and p (or s) orbitals are of course orthogonal (S = 0), since they are located on the same atom, the overlaps between the I orbital on the ligands and each of the metal orbitals are non-zero (Si- and Si-p, 2.A2). 

Although quantum-mechanical calculations have challenged the possible involvement of 2>d orbitals in sulfoxides and sulfones [5-8] this bonding model involving participation of M orbitals at sulfur is reviving again as the result of new basis sets for ab initio calculations [3,9]. It is noted, however, that the role of d functions in hypervalent molecules seems to be to provide additional flexibility for the orbitals to increase their overlap and thereby increase the stabilization of the system (d-orbitals polarization effect) [10], rather than to participate directly in bonding, as depicted in Scheme 3.1. 

A discussion is given of the current decomposition schemes of bond energies and related concepts (exchange (Pauli-)repulsion, polarization, charge transfer). The role of non-orthogonality of fragment orbitals and of kinetic and potential energy for Pauli repulsion and (orbital)polarization is analyzed. 

Perfluoroalkyl groups adjacent to multiple bond systems lower the frontier molecular orbitals (FMOs) Therefore, cycloaddition reactions preferentially occur with electron-rich multiple-bond systems The preference of bis(trifluoromethyl)-substituted hetero-l,3-dienes for polar reacuons makes them excellent model compounds for developing new types of diene reactions deviating from the well documented Diels-Alder scheme (pathway 1) A systematic study of the reactions of diene (1 =2-3=4)-dienophile (5=6) combinations reveals new synthetic possibilities that have not yet been fully exploited as tools for preparative organic cherrustry (equation 25)... 

The electrostatic mixing by the positive charge polarizes rin the same direction (Scheme 12b, cf. Scheme 8a), possibly more significantly than the overlap mixing. The n orbital is the frontier orbital. The proton attacks on C. The regioselectivity is reversed. 

The orbital mixing rules are applied to the polarization of 7t of ethene by a C=0 group on the assumption that is lowered below The 7t orbital has mix in phase and the low lying tc orbital mix out of phase with (Scheme 16). As a result, the phase relation between t( and n is fixed. The amplitude is larger on C than on C and the carbonyl carbon. 

Scheme 17 The polarized frontier orbitals determine the regioselectivity...

Scheme 7 illnstrates the mechanism of the polarization of the n bond. In one path, an electron in the non-bonding orbital a of the anionic center A is transferred to the antibonding orbital r of the double bond TI. The A TI delocalization is... 

For the EAG-snbstimted alkenes, the transition states are non-cycUc E-Il-EAG systems. Polarization of Ft, induced by the delocalization from Ft to EAG and E, determines the regioselectivities. The polarization is analogous to that in the TMM dication (Sect. 2.1.4). The cyclic interaction occurs among the electron-accepting orbital eag ) of the substituent, e, n, and n. The a addition is favored by the orbital phase continuity while the P addition is disfavored by the phase discontinuity (Scheme 16). 

Butanes are chosen as the simplest models for the normal and branched isomers. Both branched and normal isomers contain a C-C bond (2 ) interacting with the terminal C-H bonds (2 and 2 ) (Scheme 26a). The cyclic -aj-a2 -a3 a2- interaction (Scheme 26b) occurs in the polarization of the middle C-C a-bond by the interactions with the antiperiplanar C-H a-bonds. The orbital phase is continuous in the branched isomer and discontinuous in the normal isomer (cf Scheme 4). The branched isomer is more stable. The basic rule of the branching effects on the stability of alkanes is ... 

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