Carbon symmetry

Carbon symmetry -letraheJnil isp ) C -C bond length 15.4 nm. trigonal planar sp ) C C bond length 14.2 nm interplanar distance 3J.5 nm... 

Zimmerman and Kutateladze calculated spin-orbit coupling in linear l,n-diyl biradicals (n = 3 to 8) at the CASSCF(4,4)/3-21G level with the Breit-Pauli spin-orbit Hamiltonian and analyzed it using natural bond orbitals. For diyls with an even number of carbons, symmetry forces zero SOC, whereas for those with an odd number of carbons the main terms have like signs and add, providing a nonvanishing net SOC. The maximum SOC is found at 90° orientation... 

Sample Preparation method Carbon Symmetry Sbet (mVg) p (cmVg)... 

A molecule is chiral if it cannot be superimposed on its mirror image (or if it does not possess an alternating axis of symmetry) and would exhibit optical activity, i.e. lead to the rotation of the plane of polarization of polarized light. Lactic acid, which has the structure (2 mirror images) shown exhibits molecular chirality. In this the central carbon atom is said to be chiral but strictly it is the environment which is chiral. 

Bukowski R, Sadie] J, Jeziorski B, Jankowski P, Szalewicz K, Kucharski S A, Williams H L and Rice B M 1999 Intermolecular potential of carbon dioxide dimer from symmetry-adapted perturbation theory J. Chem. Phys. 110 3785... 

Similar to the fullerene ground state the singlet and triplet excited state properties of the carbon network are best discussed with respect to the tliree-dimensional symmetry. SurjDrisingly, the singlet excited state gives rise to a low emission fluorescence quantum yield of 1.0 x 10 [143]. Despite the highly constrained carbon network,... 

As in the case of NH4 the charge is distributed over the whole ion. By considering each multiple bond to behave spatially as a single bond we are again able to use Table 2.8 to correctly deduce that the carbonate ion has a trigonal planar symmetry. Structures for other covalently-bonded ions can readily be deduced. 

The methine carbon atom also obtains an EC value of 4 (= 1 -h 1 + 2) in the second iteration. This process is repeated iteratively until the number of different EC values (c) is lower than or equal to the number of EC values in the previous iteration. Then the relaxation procc.ss is terminated. Next, the EC numbers of the previous iteration are taken for a canonical numbering and for the determination of constitutional symmetry (Figure 2-44),... 

The origin of a torsional barrier can be studied best in simple cases like ethane. Here, rotation about the central carbon-carbon bond results in three staggered and three eclipsed stationary points on the potential energy surface, at least when symmetry considerations are not taken into account. Quantum mechanically, the barrier of rotation is explained by anti-bonding interactions between the hydrogens attached to different carbon atoms. These interactions are small when the conformation of ethane is staggered, and reach a maximum value when the molecule approaches an eclipsed geometry. 

As mentioned above, HMO theory is not used much any more except to illustrate the principles involved in MO theory. However, a variation of HMO theory, extended Huckel theory (EHT), was introduced by Roald Hof nann in 1963 [10]. EHT is a one-electron theory just Hke HMO theory. It is, however, three-dimensional. The AOs used now correspond to a minimal basis set (the minimum number of AOs necessary to accommodate the electrons of the neutral atom and retain spherical symmetry) for the valence shell of the element. This means, for instance, for carbon a 2s-, and three 2p-orbitals (2p, 2p, 2p ). Because EHT deals with three-dimensional structures, we need better approximations for the Huckel matrix than... 

Many molecules, such as carbon monoxide, have unique dipole moments. Molecules with a center of inversion, such as carbon dioxide, will have a dipole moment that is zero by symmetry and a unique quadrupole moment. Molecules of Td symmetry, such as methane, have a zero dipole and quadrupole moment and a unique octupole moment. Likewise, molecules of octahedral symmetry will have a unique hexadecapole moment. 

In SCF problems, there are some cases where the wave function must have a lower symmetry than the molecule. This is due to the way that the wave function is constructed from orbitals and basis functions. For example, the carbon monoxide molecule might be computed with a wave function of 41 symmetry even though the molecule has a C-xt symmetry. This is because the orbitals obey C41 constraints. 

Furthermore (f) 1 2 dichloroethene has a center of symmetry located at the mid t point of the carbon-carbon double bond This too tells us the molecule is achiral... 

Let us now examine the Diels-Alder cycloaddition from a molecular orbital perspective Chemical experience such as the observation that the substituents that increase the reac tivity of a dienophile tend to be those that attract electrons suggests that electrons flow from the diene to the dienophile during the reaction Thus the orbitals to be considered are the HOMO of the diene and the LUMO of the dienophile As shown m Figure 10 11 for the case of ethylene and 1 3 butadiene the symmetry properties of the HOMO of the diene and the LUMO of the dienophile permit bond formation between the ends of the diene system and the two carbons of the dienophile double bond because the necessary orbitals overlap m phase with each other Cycloaddition of a diene and an alkene is said to be a symmetry allowed reaction... 

Figure 10 12 shows the interaction between the HOMO of one ethylene molecule and the LUMO of another In particular notice that two of the carbons that are to become ct bonded to each other m the product experience an antibondmg interaction during the cycloaddition process This raises the activation energy for cycloaddition and leads the reaction to be classified as a symmetry forbidden reaction Reaction were it to occur would take place slowly and by a mechanism m which the two new ct bonds are formed m separate steps rather than by way of a concerted process involving a sm gle transition state... 

In this example, the HOMO is plotted one Angstrom above the plane of the molecule. Since it is of n symmetry, it has a node in the plane of the molecule. It shows the site of electrophilic attack at the carbon adjacent to the oxygen atom. This is also the experimentally observed site. The orbital comes from an Extended Hiickel calculation of an MM-t optimized geometry. 

Structures [VIII] and [IX] are not equivalent they would not superimpose if the extended chains were overlaid. The difference has to do with the stereochemical configuration at the asymmetric carbon atom. Note that the asymmetry is more accurately described as pseudoasymmetry, since two sections of chain are bonded to these centers. Except near chain ends, which we ignore for high polymers, these chains provide local symmetry in the neighborhood of the carbon under consideration. The designations D and L or R and S are used to distinguish these structures, even though true asymmetry is absent. 

In the early days following the discovery of chirality it was thought that only molecules of the type CWXYZ, multiply substituted methanes, were important in this respect and it was said that a molecule with an asymmetric carbon atom forms enantiomers. Nowadays, this definition is totally inadequate, for two reasons. The first is that the existence of enantiomers is not confined to molecules with a central carbon atom (it is not even confined to organic molecules), and the second is that, knowing what we do about the various possible elements of symmetry, the phrase asymmetric carbon atom has no real meaning. 

We have seen in Section 4.1.4 that = n and that S2 = i, so we can immediately exclude from chirality any molecule having a plane of symmetry or a centre of inversion. The condition that a chiral molecule may not have a plane of symmetry or a centre of inversion is sufficient in nearly all cases to decide whether a molecule is chiral. We have to go to a rather unusual molecule, such as the tetrafluorospiropentane, shown in Figure 4.8, to find a case where there is no a or i element of symmetry but there is a higher-fold S element. In this molecule the two three-membered carbon rings are mutually perpendicular, and the pairs of fluorine atoms on each end of the molecule are trans to each other. There is an 54 axis, as shown in Figure 4.8, but no a or i element, and therefore the molecule is not chiral. 

Only one exception to the clean production of two monomer molecules from the pyrolysis of dimer has been noted. When a-hydroxydi-Zvxyljlene (9) is subjected to the Gorham process, no polymer is formed, and the 16-carbon aldehyde (10) is the principal product in its stead, isolated in greater than 90% yield. This transformation indicates that, at least in this case, the cleavage of dimer proceeds in stepwise fashion rather than by a concerted process in which both methylene—methylene bonds are broken at the same time. This is consistent with the predictions of Woodward and Hoffmann from orbital symmetry considerations for such [6 + 6] cycloreversion reactions in the ground state (5). 

When additional substituents ate bonded to other ahcycHc carbons, geometric isomers result. Table 2 fists primary (1°), secondary (2°), and tertiary (3°) amine derivatives of cyclohexane and includes CAS Registry Numbers for cis and trans isomers of the 2-, 3-, and 4-methylcyclohexylamines in addition to identification of the isomer mixtures usually sold commercially. For the 1,2- and 1,3-isomers, the racemic mixture of optical isomers is specified ultimate identification by CAS Registry Number is fisted for the (+) and (—) enantiomers of /n t-2-methylcyclohexylamine. The 1,4-isomer has a plane of symmetry and hence no chiral centers and no stereoisomers. The methylcyclohexylamine geometric isomers have different physical properties and are interconvertible by dehydrogenation—hydrogenation through the imine. 

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 benzene ring has a fully symmetrical (Deh) planar hexagonal carbon framework. Heteroatom substitution upsets this symmetry, but except in certain special cases, as for instance the thiabenzenes , the planarity of the ring is preserved. Although it is known... 

Electron-density calculations for quinazoline (which has no symmetry) vary markedly with the method used. The diagram (6) has the same bases as that given for pyrimidine above it will be observed that the 2- and 4-positions in quinazoline are comparable with the corresponding positions in pyrimidine and that the aromatic carbon atoms (C-5-C-8) in quinazoline are roughly comparable with C-5 in pyrimidine (67MI21300). The dipole moment of quinazoline does not appear to have been measured, but that of 2-methylquinazo-line is 2.2 D. 

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