Distorted coordinates

W. H. Baur, Bond length variation and distorted coordination polyhedra in inorganic crystals. Trans. Am. Crystallogr. Assoc. 6 (1970) 129. 

X-ray structural studies of the diamagnetic anion (406) confirm that the Ir(-I) center is in a distorted coordination geometry intermediate between square planar and tetrahedral, with the P donor atoms in a cis position. The metal-ligand bond distances do not show significant changes among (404), (405), and (406). The Ir1/0 and Ir0/(-1) redox couples are measured at easily accessible potentials and are solvent dependent. 

In many closely related compounds of Cd and Hg with all-oxygen or oxygen dominated coordination spheres, the metals adopt different coordination numbers and geometries—even independent metals in the same structure. As a rule, in the rare isostructural Cd and Hg compounds, Hg possesses the more distorted coordination. 

Figure 3.42 Potential-energy curves for benzene (17), comparing the total energy (-Etotai, solid curve) with the energy of the idealized single Lewis structure dotted curve) along a D3h distortion coordinate AR = R2,3 — R i that lowers the D6h symmetry to cyclohexatriene form.

Figure 3.43 The pi-conjugative non-Lewis energy (l NL(7t)) for benzene (17) along a distortion coordinate (cf. Fig. 3.42). Corresponding values for m-butadiene (2, crosses) are shown for comparison. (The cusp-like behavior arises because Lnl171 is defined with respect to a different idealized Lewis structure on each side of A R = 0.)...

In the X-ray structures of both 3 and 4, the tetrahedral distortion is greater than that found in model A. Since there is an electronic preference for a square planar coordination, the pendant phenyl substituents in 3 and 4 likely result in further steric crowding and therefore in more distorted structures compared to model A. In the QM/MM model B an optimized 0 angle of 30° is found, close to the 34° angle of the X-ray structure. Since the phenyl and trimethyl phenyl groups are accounted for on a steric basis only in model B, the result supports the notion that the severely distorted coordination of the Pd center in 3 is due to a steric effect. 

A model of the ZFS coupling removing the restriction of its constant amplitude and allowing both processes, the stochastic variations of the internal coordinates and the rotational diffusion, to modulate the ZFS interaction was proposed by Westlund and co-workers (13,85,88,91). According to this model, the ZFS interaction provided the coupling between the electron spin variables, the stochastic time-dependent distortion coordinates and the reorientational degrees of freedom by the expression ... 

Wood B. I and Strens R. G. J. (1972). Calculation of crystal field splittings in distorted coordination polyhedra Spectra and thermodynamic properties of minerals. Min. Mag, 38 909-917. 

Although Fe "and Mn " have similar ionic radii, Mn " does not fit as readily into the goethite structure as does Fe " because owing to its four d electrons, Mn " has a tetragonally distorted coordination sphere on an octahedral site Jahn-Tdler effect). 

The curve sketched in Figure 7.6, which is drawn with grossly distorted coordinates to encompass all features, contains several similarities to p-V isotherms. Not all the features... 

The controlled hydrolysis of MC15 or [Ta(OR)5]2 (R = Et, SiMe3) led to polymeric oxo alkoxides. On the other hand the hydrolysis of [NbCl2(OR)3]2 in the presence of bipyridyl led to [NbOCl2(OR)(bipy)] (R = Et, Pr1) adducts. 13 >364>412 An X-ray structure for R = Et showed a distorted coordination octahedron, with the two chlorine atoms trans to each other (Nb=Or 1.71(3) A). The Nb—OR bond is only 0.16 A longer than the Nb=0 oxo bond, and was presumed to have considerable double bond character, which is also consistent with the very open NbOC bond angle of 149°. 

Jahn-Teller effects,13 which are the chemist s analog of electron-phonon coupling mechanisms in molecules, are consequences of the application of perturbation theory. With respect to some distortion coordinate si the total electronic energy for a system may be expressed to second order as... 

Figure 2. Plot of potential energy vs. distortion coordinate for a material with a harmonic potential.

Second-order optical nonlinearities result from introduction of a cubic term in the potential function for the electron, and third-order optical nonlinearities result from introduction of a quartic term (Figure 18). Two important points relate to the symmetry of this perturbation. First, while negative and positive p both give rise to the same potential and therefore the same physical effects (the only difference being the orientation of the coordinate system), a negative y will lead to a different electron potential than will a positive y. Second, the quartic perturbation has mirror symmetry with respect to a distortion coordinate as a result, both centrosymmetric and noncentrosymmetric materials will exhibit third-order optical nonlinearities. If we reconsider equation 23 for the expansion of polarization of a molecule as a function of electric field and assume that the even-order terms are zero (i.e., that the molecule is centrosymmetric), we see that polarization at a given point in space is ... 

For the sake of argument, we will assume that both the it- and the a-energies are quadratic in the distortion coordinate, with respective force constants Ajt and ka.34 This leads to the following expression for the displacement of the ground state (ARgs) relative... 

The interesting observation, unexpected on the basis of limited published data of a tetradentate derivative of L8 249 250 but in full agreement with the MM analysis is that the stabilities do not follow the usual Irving-Williams behavior (Co2+ < Ni2+ < Cu2+ > Zn2+)251 252 but that L4 is zinc(II)-selective. This was interpreted as a combination of the steric effects discussed above, electronic effects (distorted coordination geometries, misdirected valences), which are unimportant for the d10 ion zinc(II), in contrast to copper(II), especially nickel(II) and smaller metal ions such as cobalt(III).78... 

Even though the system is stable in symmetric form, a vibronic part acts in the inner resorts of the electronic structure. Anticipating, the aromaticity can be presented as the situation when the distortion tendency does not overcome the non-vibronic positive harmonic constant maintaining the high symmetry. The lAg ground state have the aspect of in-phase combination of the Kekule resonance structures, whereas the first excited lB2u state results from their out-of-phase mixing. These states are mixed via the b2u distortion coordinate of bond alternation. Additionally... 

In a second step, first results obtained for the JX / /iwg quantity for Cu2+ in cubic oxides [1-6] (MgO and SrO) are shown. This study sheds some light on the occurrence of dynamic vibronic effects in Cu2+-doped MgO [2-4,6], The present methodology can also be applied to systems where the distortion coordinate at equilibrium becomes comparable to interatomic distances. Along this line some results reached for d9 ions in crystal with fluorite structure [2,11] will also briefly discussed. 

It is possible to depict an RC = CR metal binding by several resonance structures including the metallocyclopropane form, — 111 form, and almost noncontributing form with two M = C bonds. It is noted that alkynes are usually nonlinear when coordinated [184e]. An interesting consequence of the distorted coordination geometry is the fact that small cyclic acetylenes, which are unstable as free molecules, are stabilized by coordination to a metal, for example CpTa(Me)2(benzene) or (cycloheptyne)Pt(PPh3)2 [21b]. 

Many ferroelectric materials were found in the past. However, there is a limited number of structures that are adopted by the majority of the commercially important ferroelectric materials. In each of these structures, the ferroelectricity is tied to distortion of the coordination polyhedra of one or more of the cations in the structure. One example is the perovskite structure. Cations that seem to be especially susceptible to forming such distorted polyhedra include Ti, Zr, Nb, Ta, and Hf. All of these ions lie near crossover points between the stability of different electronic orbitals, and so may be likely to form distorted coordination polyhedra [5], Polarizable cations such as Pb and Bi are also common to many ferroelectric materials. In this case, it has been suggested that the lone pair electrons may play an important role in stabilizing ferroelectric structures. Thus the ferroelectric transition temperature and spontaneous distortion of PbTiC>3 is much larger than that of BaTiC>3. 

Figure 6. Bond length deviation plotted against quadrupole splittihg of Fe3+ ions in a variety of distorted coordination sites in minerals.

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