Molecular symmetry plane

Recognize molecular symmetry planes and axes. Even approximate, or local symmetry elements may be useful. One should not step back just because, formally, the molecule has no symmetry elements. A methyl and an ethyl substituent, or chlorine and bromine substituent, can be equated. Substituents that disrupt the molecular symmetry but have trivial electronic requirements may be deleted. 

Fig. 7.9 In the a-helical conformation of the model dipeptide N-acetyl N -methyl glycineamide (left), the C-H bond lengths and H-C-X angles at the a-carbon are different (1.081 A and 1.078 A for C-H and 109.3° and 109.7° for H-C-N). Thus, the a-carbon is asymmetric. In contrast, in the C5 conformation of N-acetyl N -methyl glycineamide (right), bonds and angles at C(a) are identical, there is a molecular symmetry plane, and the a-carbon is symmetric. (All values from Schafer et al. 1984.)...

Next consider Sx and S2 axes. Since the only kind of reflection that sends the momental ellipsoid into an equivalent configuration is one in a plane containing two principal axes, a molecular symmetry plane contains two of the principal axes and is perpendicular to the third. A molecular center of symmetry coincides with the center of mass, which is the point of intersection of the three principal axes. 

The symmetry requirements severely restrict the possible forms of the normal vibrations. Thus for a nondegenerate mode, nuclei lying in a molecular symmetry plane can only vibrate in this plane or perpendicular to it, while nuclei lying on an axis of symmetry can only vibrate along the axis or perpendicular to it. Symmetry can frequently be used to deduce the qualitative appearance of the normal modes, without solving the vibrational secular equation.1... 

Fig. 11 Relative size and orientation of dipole moment vectors of the ground state black) and the excited states JMLCT (bJA ), 3IL (b3A"), and 3MLCT (a3A") of [Re(Etpy)(CO)3(bpy)]+, projected onto the optimized ground-state molecular structure. Dipole moment vectors originate in the center of charge calculated using Mulliken population analysis. They lie in the molecular symmetry plane. (Calculated by TD-DFT G03/PBE0/vacuum at the optimized ground state geometry.) Reproduced with permission from [76]...

Like in the past, most of the data on the QEC effect involve this class of the metal hydrides. The NMR formalism used in the description of the coherent and stochastic dynamics in the trihydrides is a phenomenological generalization of that describing the two-particle case. In consistence with the spirit of the semiclassical AB theory, the dynamics in the two two-particle subsystems (of which either engages the nucleus in the centre) are assumed to be independent. In the trihydrides, the central hydride atom lies in the molecular symmetry plane such that the three hydride nuclei form an A2B system. Therefore, the pertinent line shape equation has the form... 

I.r. and Raman spectra have also been reported and assigned for CsH5BeBH4 and CsHsBeBD4. The hydrogen bridge structure is definitely (3), and, in contrast to Be(BH4)2, this is found in the gaseous, liquid, and solid states. The BeH2B plane and the Q molecular symmetry plane are coincident. 

Atoms have complete spherical synnnetry, and the angidar momentum states can be considered as different synnnetry classes of that spherical symmetry. The nuclear framework of a molecule has a much lower synnnetry. Synnnetry operations for the molecule are transfonnations such as rotations about an axis, reflection in a plane, or inversion tlnough a point at the centre of the molecule, which leave the molecule in an equivalent configuration. Every molecule has one such operation, the identity operation, which just leaves the molecule alone. Many molecules have one or more additional operations. The set of operations for a molecule fonn a mathematical group, and the methods of group theory provide a way to classify electronic and vibrational states according to whatever symmetry does exist. That classification leads to selection rules for transitions between those states. A complete discussion of the methods is beyond the scope of this chapter, but we will consider a few illustrative examples. Additional details will also be found in section A 1.4 on molecular symmetry. 

We now consider planar molecules. The electronic wave function is expressed with respect to molecule-fixed axes, which we can take to be the abc principal axes of ineitia, namely, by taking the coordinates (x,y,z) in Figure 1 coincided with the principal axes a,b,c). In order to detemiine the parity of the molecule through inversions in SF, we first rotate all the electrons and nuclei by 180° about the c axis (which is peipendicular to the molecular plane) and then reflect all the electrons in the molecular ab plane. The net effect is the inversion of all particles in SF. The first step has no effect on both the electronic and nuclear molecule-fixed coordinates, and has no effect on the electronic wave functions. The second step is a reflection of electronic spatial coordinates in the molecular plane. Note that such a plane is a symmetry plane and the eigenvalues of the corresponding operator then detemiine the parity of the electronic wave function. 

This geometry possesses three important elements of symmetry, the molecular plane and two planes that bisect the molecule. All MOs must be either symmetric or antisymmetric with respect to each of these symmetry planes. With the axes defined as in the diagram above, the orbitals arising from carbon 2p have a node in the molecular plane. These are the familiar n and n orbitals. 

The remaining AOs are the four H 1, two C 1, and four C 2p orbitals. All lie in the molecular plane. Only two combinations of the C 2s and H U orbitals meet the molecular symmetry requirements. One of these, nearest-neighbor atoms. No other combination corresponds to the symmetry of the ethylene molecule. 

Let us now apply these results to the ethylene molecule (Fig. 14), for which we attempt to build the bonding molecular orbitals. Clearly there are three symmetry planes. Two of these are of special interest... 

In molecules with little or no symmetry, it may still be possible to recognize the main localized-orbital component of certain molecular orbitals. It is then convenient to adopt the label of this localized type as the label of the molecular orbital, even though the molecular symmetry does not coincide with the local symmetry. For instance, in methylenimine again, the 5A orbital is clearly built out of the in-plane 7rc 2 group orbital, with a small NH component. We therefore label the orbital t CU2, although the molecule does not have a vertical symmetry plane. Similarly, the orbitals 7A and 8A of propylene are labeled 7TqH3, tt CU2 (111.49).a Other examples where the local symmetry is sufficiently preserved and only weakly perturbed by the molecular environment are hydrazine (111.34) and methylamine (III.31). In some cases we have omitted the label as no unambiguous classification is possible. 

Figure 16, Relation between symmetry in (a) the single space and (b) the double space of a system whose molecular symmetry group has a a plane in the single space, and is isomorphic with C2v in the double space.

Conformational populations of cyanomethylphosphine oxides (136) have been estimated from dipole moments and indicate a preference for the tra/15-conformation. The moments of the o-, m- and p-chloro- and tolyl-derivatives of triaryl phosphites (137, Y = ) and triaryl phosphates (137 Y = O) indicate that the oxygen atom in the latter series causes the aryl rings to rotate further away from a position in which their planes all meet along the molecular symmetry axis. Conformational studies have also been carried out on the dioxaphosphorinanes. The moments of the isomeric series (138a) and (138b) were in the ranges 3.7—4.2 and 5.4—5.5 D respectively. ... 

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