Jahn-Teller effect, second-order

The most recent theoretical study, by Alhrichs and co-workers, deals with the di(phosphino)carbene Id and (phosphino) (phosphonio)carbenes Ie,f.16 The optimized geometry of the di(phosphino)carbene Id is weakly bent (PCP angle 160.5°) and highly unsymmetrical Only one of the phosphorus centers (P1) is in a planar environment, and it is much more closely bonded to the carbenic center than the other one (P1C 1.533 and P2C 1.765 A). The atomic charges (P1 +1.0, C -0.8, P2 +0.6) indicate that the short P bond is a double bond reinforced by Coulombic attraction, while the nature of the molecular orbitals revealed a slight delocalization of the carbene lone pair into the low-lying a (P-N) orbitals of the two phosphino substituents. The distortion from the symmetrical structure can be viewed as a second-order Jahn-Teller effect. 

In the examples predated in the text, the distortions from high symmetry which lead to stabilization of the molecular shapes are those in which the HOMO and LUMO of the highly symmetric molecules both become the completely symmetric representations of the distorted molecules, i.e. a. There is a general rule which deals wi+h this phenomenon in a detailed way called the second-order Jahn-Teller effect but nt they say. anotlv . ... 

As noted previously, the outstanding success of orbital symmetry rules in organic chemistry (75, 242) has led to many attempts to extend these rules to organometallic chemistry and metal-catalyzed processes. These qualitative analyses based on the principle of conservation of orbital symmetry or second-order Jahn-Teller effects have been reviewed extensively (91, 142, 143, 173, 175, 179, 221, 225) and will not be considered in any detail here. 

The preceding three reduced molybdenum clusters indicate that rhomboidal cluster units are common among this kind of oxide, and the Mo-Mo distances in the cluster units are dependent on CVE assignable to the Mo4 units. MO calculations on Mo4 molecular cluster compounds containing 10 CVE and 8 CVE have shown that the 8-electron clusters distort from a second-order Jahn-Teller effect (116). Such a distortion has been observed in the 8-electron W4(OEt)16 (117). 

TL OEt) ]224 with distortions due to M—M bonding. Crystal structure analysis of [W4(OEt)i6] (Figure 22) reveals the presence of two short W—W bonds (2.645 and 2.76 A) and two long bonds of 2.93 A. In this structure, there is a total of five possible W—W interactions, and thus, to form five bonds of order one, ten electrons are required. Only eight metal electrons are available for metal-metal bonding, which leads to the observed distortions. It has been suggested that this distortion results from a novel second order Jahn-Teller effect.225... 

This general feature of both class I and class II behaviour of the copper(II) ion, i.e. the ability to exist in a high symmetry environment against the prediction of both the first- and second-order Jahn-Teller effects, is the best single piece of evidence for the cooperative Jahn-Teller effect and has recently been reviewed.432 It is generally responsible for the whole range of fluxional copper(II) stereochemistries and of the temperature variable ESR spectra of... 

Richard Bader was among the earliest of workers to realize the importance of electron density in providing an understanding of chemistry. Early on he was led to formulate the first symmetry rule governing a chemical reaction in answer to the question of how the electron density changes in response to a motion of the nuclei. This rule, termed the pseudo- or second-order Jahn-Teller effect, provides the theoretical underpinnings of frontier molecular orbital theory and is still widely used in discussions of reaction mechanisms and molecular geometries. 

The second-order Jahn-Teller effect at a single centre, equation (29), leads to three equivalent minima on the lowest surface of the adiabatic potential, with equilibrium distortions (VE and WE are of the same sign),... 

FIGURE 37. A molecular orbital diagram which explains the operation of a second-order Jahn-Teller effect in the pyramidalization of MH3. Reprinted with permission from Reference 57. Copyright (1996) American Chemical Society... 

Another way to rationalize the trans-bent geometries is through an-a mixing model (28,95,145), using the second-order Jahn-Teller effect as... 

The essence of the first or second order Jahn-Teller effect is that a high-symmetry geometry generates a real or near degeneracy, which can be broken with stabilization by a symmetry-lowering deformation. Note a... 

A second-order Jahn-Teller effect leads to a trigonal prismatic structure being preferred for some d° MLe species, such as WMee. This illustrates the role of electronic effects in determining coordination geometry. 

A common feature of the dimers is a folded Ru-E-Ru-E core (E = O, S, or N) with a dihedral angle between the Ru-E-Ru planes of from 110 to 129°. The butterfly geometry observed in these dimeric complexes results from the retro r-overlap of lone electron pairs into empty metal orbitals and a second-order Jahn-Teller effect (see Jahn-Teller Effect) arising from the repulsive interaction of filled metal d-orbitals in a flat (Pih) geometry. This type of geometry is exemplified by fhe crysfallographically characterized complex [()]-/ -cymene)Ru(/x2-2,6-di-isopropylphenylamido-iV,Af)]2 (118).i 3... 

In contrast with first derivatives, second derivatives involve couplings with all states (sums over M in (A.15)) that correspond to a second-order Jahn-Teller effect. Such contributions from higher-lying states (M > 2) do not exist in a pure two-level model (see Sec. 2), but they are part of the actual MCSCF calculation, where the number of eigenstates is equal to the number of CSFs. Limiting the values of M to 0 and 1 leads to ... 

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