Bonds mirror-symmetric

Ethylene, the first member of the series, is already familiar. Two adjacent p orbitals interacting will yield a bonding orbital, symmetric with respect to reflection in the mirror plane lying midway between the two carbons and perpendicular to the C—C axis, and an antibonding orbital antisymmetric with respect to that mirror plane. Figure 10.18 illustrates the interaction and the resulting orbitals. 

Based on some interesting reactions in certain inorganic crystalline compounds, Kohlschutter [9,10] proposed that the nature and properties of the products obtained take place on the surface or within the solid state. Indeed, he coined the term topochemistry for such reactions in the solid state. However, systematic investigations of photoinduced reactions in crystals began from 1964 onward by Schmidt and Cohen [11], Their studies on the 2tt + 2tt photoreaction of cinnamic acid derivatives in the crystalline state and correlation with the molecular organization in these crystals led to what are now known as Topochemical Principles. The most important conclusions reached by them are as follows (1) The necessary conditions for the reactions to take place are that the reactive double bonds are parallel to one another and the center-to-center distance be within 4.1 A (2) there is one-to-one correspondence between the stereochemistry of the photoproduct and the symmetry relationship between the reactants. The centrosymmet-ric relationship (called the a-form) leads to centrosymmetric cyclobutane (anti-HT), whereas the mirror symmetric arrangements (called the (5-form) produce mirror symmetric dimer (yy -HH). 

The molecular structure of 2,2 -bithiophene has been determined by gas electron diffraction in 1958 [4], and by gas diffraction combined with ab initio calculations in 1993 [5], Both works conclude that in the gas phase the molecule is twisted around the 2,2 -bond, and occurs in at least two conformations. Whereas the early work assumes the individual monomers to be internally mirror symmetric, the recent work allows for an asymmetric thiophene ring, and the parameters obtained by the latter, shown in Figure 1(b) are therefore considered the more reliable. The molecule is clearly conjugate, as determined by the alternating bond lengths 1,363-1.452-1,370-1.456-1,370-1.452-... 

When a molecule is symmetric, it is often convenient to start the numbering with atoms lying on a rotation axis or in a symmetry plane. If there are no real atoms on a rotation axis or in a mirror plane, dummy atoms can be useful for defining the symmetry element. Consider for example the cyclopropenyl system which has symmetry. Without dummy atoms one of the C-C bond lengths will be given in terms of the two other C-C distances and the C-C-C angle, and it will be complicated to force the three C-C bonds to be identical. By introducing two dummy atoms to define the C3 axis, this becomes easy. 

Fig. 7.10 When the H-O-C-O torsions in dihydroxymethane, CH2(OH)2, are 180° and form a planar backbone (structure on the left), the H-C-0 angles (110.9°), C-H (1.086 A), O-H (0.963 A), and C-0 bond lengths (1.425 A) are identical, the molecule has a mirror plane, and the carbon atom is symmetric. In contrast, when one of the O-H bonds is rotated out of the plane, equivalent bond lengths and angles are different (1.078 A and 1.085 A, for C-H 1.438 A and 1.417 A for C-O 0.963 A and 0.965 A for O-H and 111.9° and 109.4° for H-O-C). Thus, in the structure on the right, the carbon atom is asymmetric with four different substituents. (All values from Schafer et al. 1984G).

Rh (172)]. These species merit comparison to the rhenium- and manganese-dicopper species 158 and 159, which have molecular mirror symmetry and a V-shaped trimetal unit that lacks a Cu-Cu bond. Although 171 and 172 appear symmetric in solution on the NMR time scale due to fluxional processes, in the solid state the two copper centers are clearly inequivalent and a Cu-Cu bond is present. The metal triangle is supported by two B-H Cu linkages, one to each Cu center, involving p- and y-B H vertexes in the M -bound CBBBBEi belt. 

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