Planar unsaturated molecules

This factorization amounts to the statement thatEq. (2.25) breaks down into two separate linear systems, one for the determination of a orbitals, and the other for n orbitals. In the Hartree-Fock scheme, self-consistent field equations (SCF equations 2.25) have as solutions symmetry-adapted functions (i.e. in the case of planar unsaturated molecules symmetric or antisymmetric functions with respect ot the molecular plane), at least for closed-shell ground states iM8,20,2i) ... 

E. Hiickel introduced a simple quantum mechanical model for the description of the electronic structure of planar unsaturated molecules with the bonding connectivity as input. This model has been widely used. Although today s computing power and quantum chemistry software available for all chemists have made the assumptions of the Hiickel model unnecessarily simplistic, the model is still used to make estimates of molecular energies and has established itself as a useful teaching tool. 

Propagator or Green s function methods are employed in this chapter to analyze the many-electron problem in planar unsaturated molecules as treated within the Pariser-Parr-Pople (PPP) model. A derivation of the model in many-electron theory serves to demonstrate the nature of the approximations involved. Applications are presented for the case of weakly interacting atoms. A decoupling procedure for Green s functions proposed by the authors is shown capable of yielding a correct description of this case. 

For planar unsaturated and aromatic molecules, many MO calculations have been made by treating the a and n electrons separately. It is assumed that the o orbitals can be treated as localized bonds and the calculations involve only the tt electrons. The first such calculations were made by Hiickel such calculations are often called Hiickel molecular orbital (HMO) calculations Because electron-electron repulsions are either neglected or averaged out in the HMO method, another approach, the self-consistent field (SCF), or Hartree-Fock (HF), method, was devised. Although these methods give many useful results for planar unsaturated and aromatic molecules, they are often unsuccessful for other molecules it would obviously be better if all electrons, both a and it, could be included in the calculations. The development of modem computers has now made this possible. Many such calculations have been made" using a number of methods, among them an extension of the Hiickel method (EHMO) and the application of the SCF method to all valence electrons. ... 

A number of X-ray crystal structures of complexes with coordinated heteroalkenes have been reported, unambiguously confirming the rp coordination of the unsaturated molecules with one exception (vide infra). Structural features of the most relevant complexes are shown in Table 11. TTie inner coordination about the nickel(O) atom is nearly planar, as already found in alkene complexes. The tj2 coordination of the 0=0 group has been determined in the three complexes (33)-(35). 

For planar unsaturated and aromatic molecules, many molecular-orbital calculations (MO calculations) have been made by treating the a and n electrons separately. It is assumed that the a orbitals can be treated as localized bonds and the... 

Another possibility is to compute V(r) at a distance removed from a molecule (in its equilibrium geometry), e.g., in a plane above the approximate molecular plane, if any. We have found that unsaturated molecules bearing electron-withdrawing substituents sometimes have planar buildups of positive potential above and below certain bonds, e.g., C—NO2, and/or cyclic portions of the molecules. We have shown that these can serve as initial sites... 

A general, unsaturated molecule is a planar, or near-planar, system for the moment we shall consider it to be exactly planar. In this very special situation, molecular orbitals describing the molecule as a whole will inevitably divide themselves into two fundamentally different types. These types are distinguished by symmetry—those which are symmetric and those which are... 

We shall use the allyl radical to illustrate how one can treat planar unsaturated organic molecules using multiconfigurational methods. Some properties of the groimd state will be studied and, in addition, the electronic spectrum. The system has acmally been used as a example in a course given at the Department of Theoretical Chemistry in Lund called Quantum Chemistry at Work and a number of students have performed the calculations. We shall use their results. Some of them were recently published [69]. 

Hie canonical MOs of a planar unsaturated organic molecule can be divided into molecular plane is +1 or -1, respectively (Section 15.10). The earliest semiempirical methods for planar conjugated organic compounds (Sections 16.2-16.4) treated the tt electrons separately from the cr electrons. Coulson stated that the justification for the ct-tt separability approximation lies in the different symmetry of the cr and tt orbitals and in the greater polarizability of the tt electrons, which makes them more susceptible to perturbations such as those occurring in chemical reactions. 

Complexes of Platinum(0) with Olefins and Related Molecules. In the period of this Report the geometries of ten complexes of bis(triphenylphosphine)-platinum(O) with unsaturated molecules, such as olefins, acetylenes, and dioxygen, have been described. In these complexes the metal co-ordination is trigonal planar, one site heing occupied by a more or less symmetrically co-ordinated multiple bond, as in (71). A selection of distances and angles... 

Alkenes are unsaturated molecules and they are important compounds in many synthetic pathways because of their readiness to undergo addition reactions. The structure of alkenes makes these molecules particularly susceptible to electrophilic attack. Each carbon atom involved in the carbon-carbon double bond makes three O bonds with bond angles of 120°, so the region immediately around the double bond is planar. The remaining shared pair of electrons which complete the double bond between the two carbon atoms are contained in a molecular orbital that lies above and below this plane, forming a localized n bond above and... 

For larger molecules we usually do not observe vibrationally structured bands (Figs. 19,21, and 22). The number of possible vibrations that can be excited in the final ion state increases rapidly with the size of the system, and the superposition of the different vibrational excitations leads to more or less continuous bands. For these unstructured bands the VIP is attributed to the band maximum. Some bands show vibrational fine structure even for larger molecules (Figs. 3 and 22). In planar unsaturated compounds, for example, an ionization from the Jt system usually couples to skeletal modes that lie near 1400 cm resulting in a well-developed vibrational structure. However, for the same molecules the bands that result from ionizations from CH a bonds are mostly broad and unstructured. 

The most common stereoselective syntheses involve the formation and cleavage of cyclopentane and cyclohexane derivatives or their unsaturated analogues. The target molecule (aff-cts)-2-methyl-l,4-cyclohexanediol has all of its substituents on the same side of the ring. Such a compound can be obtained by catalytic hydrogenation of a planar cyclic precursor. Methyl-l,4-benzoquinone is an ideal choice (p-toluquinone M. Nakazaki, 1966). 

The chemistry of propylene is characterized both by the double bond and by the aHyUc hydrogen atoms. Propylene is the smallest stable unsaturated hydrocarbon molecule that exhibits low order symmetry, ie, only reflection along the main plane. This loss of symmetry, which implies the possibiUty of different types of chemical reactions, is also responsible for the existence of the propylene dipole moment of 0.35 D. Carbon atoms 1 and 2 have trigonal planar geometry identical to that of ethylene. Generally, these carbons are not free to rotate, because of the double bond. Carbon atom 3 is tetrahedral, like methane, and is free to rotate. The hydrogen atoms attached to this carbon are aUyflc. 

The K conjugate molecules usually have planar geometries and no difference between the two faces above and below the molecular plane. When substitutions break the symmetry with respect to the plane, n orbitals mix a orbitals orthogonal prior to the substitution. Rehybridization occurs and the unsaturated bonds have... 

An X-ray structure analysis of 74 (R=C4Hg) revealed that the unsaturated portion of the molecule was planar, with the angles between adjacent acetylenic bonds deviating by 13 -15° from 180°, the value for a strain-free molecule. Since the connection of the alkyne moieties to the aromatic rings was only shifted slightly (2-3°), distortion of the acetylene linkages appears as the major source of instability in these macrocycles. 

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