Rotation square planar molecules

Figure 3.4 showed the proper axes of rotation and planes of symmetry in the square planar molecule XeF4. This has 7)41, symmetry. The 7)4], character table is given in Appendix 3, and the top row of the character table that summarizes the symmetry operations for this point group is as follows ... 

Next we 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 inertia. To achieve inversion of all particles with respect to space-fixed axes, we first rotate all the electrons and nuclei by 180° about the c axis (which is perpendicular to the molecular plane) we then reflect all the electrons in the molecular ab plane. The net effect of these two transformations is the desired space-fixed inversion of all particles. (Compare the corresponding discussion for diatomic molecules in Section 4.7.) The first step rotates the electrons and nuclei together and therefore has no effect on the molecule-fixed coordinates of either the electrons or the nuclei. (The abc axes rotate with the nuclei.) Thus the first step has no effect on tpel. The second step is a reflection of electronic spatial coordinates in the molecular plane this is a symmetry plane and the corresponding operator Oa has the possible eigenvalues +1 and — 1 (since its square is the unit operator). The electronic wave functions of a planar molecule can thus be classified as having... 

For example, in a plane triangular molecule such as BF3, each of the twofold symmetry axes lying in the plane can be carried into coincidence with each of the others by rotations of 27r/3 or 2 x 2nl3, which are symmetry operations. Thus all three twofold axes are said to be equivalent to one another. In a square planar AB4 molecule, there are four twofold axes in the molecular plane. Two of them, C2 and C2, lie along BAB axes, and the other two, C and Ci, bisect BAB angles. Such a molecule also contains four symmetry planes, each of which is perpendicular to the molecular plane and intersects it along one of the twofold axes. Now it is easy to see that C2 may be carried into C2 and vice versa, and that C2 may be carried into C2 and vice versa, by rotations about the fourfold axis and by reflections in the symmetry planes mentioned, but there is no way to carry C2 or C into either CJ or Cn or vice versa. Thus C2 and C2 form one set of equivalent axes, and and C form another. Similarly, two of the symmetry planes are equivalent to each other, but not to either of the other two, which are, however, equivalent to each other. 

In hydrated forms of Cu2+-doped H-, Na-, K- and Cs-rho a small part of the Cu + is octahedrally coordinated to six water molecules and undergoes free rotation at room temperature (6,7). This Cu + is located in the a-cages and has little interaction with the cage walls. The major part of the Cu + is coordinated to two water molecules and to oxygens in the zeolite lattice. This species is most likely either a square-planar complex located at site S3 or less likely a square-based pyramid located at site S2. An interesting feature of zeolite rho is that the nature of the hydrated species is independent of the nature of the cocation. This is quite different from the case in zeolite A where the location and hydration number of the major hydrated species is governed by the type of cocation. 

In some molecules, rotation axes of lower orders than the principal axis may be coincident with the principal axis. For example, in square planar XeF4, the principal axis is a C4 axis but this also coincides with a C2 axis (see Figure 4.4). 

Group theory can be used to determine far more than just the symmetries of the vibrational modes and how many vibrations will be IR- or Raman-active. We have shown how the structure of a molecule determines its symmetry, which in turn determines its vibrational spectrum. The paradigm can also be used in reverse. If the structure is unknown, the number of peaks in the IR (or Raman) spectrum can often be used to determine the molecule s structure where the geometry is not known in advance. For instance, molecules of the type AX4 can be either tetrahedral (Tj) or square planar (D4h). Using the mini-Cartesian axis vectors on each atom in the Tj point group gives the reducible representation Fj f in Table 9.4, which reduces to A, -l- -f2T -F 3T2. Subtraction of the translations (T2) and rotations (T,) leaves the following vibrational modes A -F -F T -F ITj. There are potentially two IR-active peaks (the ITj modes) and four Raman-active peaks (A -f +2T2). I say... 

The nickel dimethylglyoxime type compounds form a related series of compounds with rather marked pressure effects. The structure of these molecules is such that the transition metal ion is in the center of an approximately square planar field of nitrogen ions, Rijf 1.9 A . Godychi and Rundle have further determined that the planar molecules stack one above the other with a rotation of 90 between layers. The nickel ions ahne in a chain have a metal-ion-metal-ion distance of 3.25 A. Thus the crystal field consists of four nitrogen ions approximately in a square planar field and two metal ions perpendicular to the plane, at a somewhat longer distance. 

By manually separating the two sets, dissolving them in water, and measuring their optical rotation, Pasteur found one of the crystalline forms to be the pure salt of (-l-)-tartaric acid and the other to be the levorotatory form. Remarkably, the chirality of the individual molecules in this rare case had given rise to the macroscopic property of chirality in the crystal. He concluded from his observation that the molecules themselves must be chiral. These findings and others led in 1874 to the first proposal, by van t Hoff and Le Bel independently, that saturated carbon has a tetrahedral bonding arrangement and is not, for example, square planar. (Why is the idea of a planar carbon incompatible with that of a stereocenter )... 

In the columns identifying the experimental method, MW stands for any method studying the pure rotational spectrum of a molecule except for rotational Raman spectroscopy marked by the rot. Raman entry. FUR stands for Fourier transform infhired spectroscopy, IR laser for any infiured laser system (diode laser, difference frequency laser or other). LIF indicates laser induced fluorescence usually in the visible or ultraviolet region of the spectrum, joint marks a few selected cases where spectroscopic and diffraction data were used to determine the molecular structure. A method enclosed in parentheses means that the structure has been derived from data that were collected by this method in earlier publications. The type of structure determined is shown by the symbols identifying the various methods discussed in section II. V/ refers to determinations using the Kraitchman/Chutjian expressions or least squares methods fitting only isotopic differences of principal or planar moments (with or without first... 

Brown and Crofts analyzed the microwave spectra of tellurophene for three isotopic constitutions of the molecule (C4H4l30Te, C4H4l28Te, C4H4126Te). The line frequencies, computed from the rotational constants obtained from least-squares fitting of low J transitions agree well with those observed. The constancy of the A rotational constant for the three isotopic species indicates that the tellurium atom is on the a axis. This, with the very small inertial defects, is consistent with a planar molecular structure of C2Ksymmetry. Stark shift measurements correspond to a dipole moment of 0.186 D. 

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