Point group determination

B. E Buxton, J. A. Eades, J. A. Steeds, and G. M. Rackham. PhiL Trans. R. Soc. A. 281, 171, 1976. This paper oudined point group determination for the first time, but the major conclusions are also summarized in Williams op. cit.). 

In an opposite way, if we are able to identify the diffraction group from experimental diffraction patterns, then, we can obtain the point group. This is the basis of the point group determination. To reach this aim, two experimental methods are available a method proposed by Buxton et al. [3] and a multi-beam method proposed by Tanaka et. al. [4]. 

The MO (molecular orbitals) of a polyatomic system are one-electron wave-function k which can be used as a (more or less successful) result for constructing the many-electron k as an anti-symmetrized Slater determinant. However, at the same time the k (usually) forms a preponderant configuration, and it is an important fact67 that the relevant symmetry for the MO may not always be the point-group determined by the equilibrium nuclear positions but may be a higher symmetry. For many years, it was felt that the mathematical result (that a closed-shell Slater determinant contains k which can be arranged in fairly arbitrary new linear combinations by a unitary transformation without modifying k) removed the individual subsistence... 

Number of species for molecular point group determined from Appendix2. 

The combination of point group determination and identification of translation symmetry allows the unique identification of space groups. Both CBED and LACBED techniques can be used for this purpose. 

Structural isomers can have very different point groups. Determine the point groups of 1,4-cyclohexadiene and 1,3-cyclohexadiene, which both have the molecular formula CgHg. 

Fig. 21. Scheme for point group determination in single crystals, based on selected transitions in the ion. 

A D2 <— Fo transition with two peaks in the 0 spectrum and one peak in the It spectrum (2o-i-lJt) is an indication for a C3V or a C3 symmetry. The Dd <— Fq transition will give exclusion (3a-i-2n ) for Csv and (3o-i-3n ) for C3. The point group determination scheme is given in fig. 21. In table 23 the point groups of the rare-earth sites in the most common crystalline host matrices are summarized. 

SymApps converts 2D structures From the ChemWindow drawing program into 3D representations with the help of a modified MM2 force field (see Section 7.2). Besides basic visualization tools such as display styles, perspective views, and light source adjustments, the module additionally provides calculations of bond lengths, angles, etc, Moreover, point groups and character tables can be determined. Animations of spinning movements and symmetry operations can also he created and saved as movie files (. avi). 

Determine the symmetries of the resultant moleeular orbitals in the D3h point group. Draw a qualitative orbital energy diagram using the HMO energies you have ealeulated. 

Molecular point-group symmetry can often be used to determine whether a particular transition s dipole matrix element will vanish and, as a result, the electronic transition will be "forbidden" and thus predicted to have zero intensity. If the direct product of the symmetries of the initial and final electronic states /ei and /ef do not match the symmetry of the electric dipole operator (which has the symmetry of its x, y, and z components these symmetries can be read off the right most column of the character tables given in Appendix E), the matrix element will vanish. 

To illustrate sueh symmetry adaptation, eonsider symmetry adapting the 2s orbital of N and the three Is orbitals of H. We begin by determining how these orbitals transform under the symmetry operations of the C3V point group. The aet of eaeh of the six symmetry operations on the four atomie orbitals ean be denoted as follows ... 

The functions put into the determinant do not need to be individual GTO functions, called Gaussian primitives. They can be a weighted sum of basis functions on the same atom or different atoms. Sums of functions on the same atom are often used to make the calculation run faster, as discussed in Chapter 10. Sums of basis functions on different atoms are used to give the orbital a particular symmetry. For example, a water molecule with symmetry will have orbitals that transform as A, A2, B, B2, which are the irreducible representations of the C2t point group. The resulting orbitals that use functions from multiple atoms are called molecular orbitals. This is done to make the calculation run much faster. Any overlap integral over orbitals of different symmetry does not need to be computed because it is zero by symmetry. 

In Section 4.3.f it was shown that there are 3N — 5 normal vibrations in a linear molecule and 3N — 6 in a non-linear molecule, where N is the number of atoms in the molecule. There is a set of fairly simple rules for determining the number of vibrations belonging to each of the symmetry species of the point group to which the molecule belongs. These rules involve the concept of sets of equivalent nuclei. Nuclei form a set if they can be transformed into one another by any of the symmetry operations of the point group. For example, in the C2 point group there can be, as illustrated in Figure 6.18, four kinds of set ... 

In Table B. 1 in Appendix B are given formulae, analogous to those derived for the C2 point group, for determining the number of normal vibrations belonging to the various symmetry species in all non-degenerate point groups. 

Figure 6 CBED patterns of aluminum oxynitride spinel along the [001] direction. Symmetries in the patterns contributed to the determination of the point group and space group (a) whole pattern showing 1st Laue zone ring and (b) 0th order Laue zone. Both patterns show a fourfold rotation axis and two mirror planes parallel to the axis. (Courtesy of V. P. Dravid)...

We will find an excitation which goes from a totally symmetric representation into a different one as a shortcut for determining the symmetry of each excited state. For benzene s point group, this totally symmetric representation is Ajg. We ll use the wavefunction coefficients section of the excited state output, along with the listing of the molecular orbitals from the population analysis ... 

Determination of carboxy groups. Esterification or polyesterification kinetics is usually followed by this titration which is both easy and accurate. Each sample is dissolved in a solvent or a mixture of solvents (CHCI3, QH /EtOH or MeOH, toluene/EtOH or MeOH...) and then titrated with alcoholic KOH. The end point is determined either with an indicator (in most cases phenolphthalein) or with a pH-meter. An accuracy of about 0.1-1% can generally be achieved. 

Magnetic ordering, 746 Magnetic point groups, 738, 739 international notation, 739 properties of, 740 Schonflies notation, 739 Shubnikov notation, 739 Magnetic point symmetry, determination of, 744... 

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