Pseudo-selection rules

Problem 4.2. The only normal mode displayed in the IRAS spectrum from W(IOO)—H is the vibration normal to the surface. The intensity of fhe spectral lines corresponding to the other two vibrations parallel to the metal surface are suppressed because of fhe pseudo-selection rule. 

Pseudo-selection rules Attenuation of spectral lines of molecules adsorbed on metal surfaces which correspond to vibrational modes accompanied by the atomic displacements parallel to the surface. 

The first coordination sphere of acido-pentamine [Cr(NH3)5X]2+ complexes has C4v symmetry and this leads to a tetragonal resolution of the 2Eg state into 2At and 1Bl components. The classical ligand field model predicts that these components will be virtually degenerate. This is based on a combination of pseudo-spherical and quasi-spin selection rules of the shell and will be discussed later on in Sect. 5.2. At present we welcome this example of a pseudo-degeneracy as another opportunity to observe fine details of the interelectronic repulsion interaction which have the proper anisotropy to induce a splitting of the 2Eg term. 

In a d-only approximation a further selection rule can be invoked, based on pseudo-angular momenta. This requires a comparison between the actions of the pseudo and true angular momentum operators in the basis of the real... 

Quasi-Spin and Pseudo-Cylindrical Selection Rules... 

Low-symmetry LF operators are time-even one-electron operators that are non-totally symmetric in orbit space. They thus have quasi-spin K = 1, implying that the only allowed matrix elements are between 2P and 2D (Cf. Eq. 28). Interestingly in complexes with a trigonal or tetragonal symmetry axis a further selection rule based on the angular momentum theory of the shell is retained. Indeed in such complexes two -orbitals will remain degenerate. This indicates that the intra-t2g part of the LF hamiltonian has pseudo-cylindrical D h symmetry. As a result the 2S+1L terms are resolved into pseudo-cylindrical 2S+1 A levels (/l = 0,1,..., L ). It is convenient to orient the z axis of quantization along the principal axis of revolution. In this way each A level comprises the ML = A components of the L manifold. In a pseudo-cylindrical field only levels with equal A are allowed to interact, in accordance with the pseudo-cylindrical selection rule ... 

Simple examples of these effects were discussed in Section IV as limiting cases of the pseudo-Jahn Teller and pseudo-Renner-Teller effects. There it was shown that instead of using the adiabatic approximation, we should, in the interest of convenience, adopt a diabatic approximation in which the electronic degeneracy is maintained in zeroth order. The splitting can then simply be ascribed to adiabatic coupling proportional to Q, (or Qf, etc.) or to Qf (or Qf, etc.) between the two electronic components that remain degenerate at Q, = 0. The selection rule for pseudo-Jahn Teller coupling is thus <0° 0 or, iff denotes representation, T , x F,- x F 3-4,. 

The general principles for the construction of the vibronic Hamiltonian and the symmetry selection rules are the same as indicated above and discussed in more detail in Chapter 7. The previous distinction between trigonal and tetragonal point groups does not play a role, and the first-order coupling is always accomplished by doubly degenerate (e) vibrational modes. In an analogous notation as in Eq. (3), the Hamiltonian for the linear (E + A) (g) e pseudo-Jahn-Teller effect is found to... 

Such assignments are in error, however, even though one of them is based on a normal-co-ordinate calculation, and are quite unable, with or without a contribution of pseudo-rotation, to reproduce the measured heat capacity. The most accurate values of the measured thermodynamic properties require, for agreement within 0.1%, that /, = 10.59 x 10 gem a small contribution of anharmonicity was treated by equations (15). A subsequent molecular vibrational analysis led to some revision of the vibrational assignment, but excellent agreement with the measured heat capacity values is still obtained from it-provided the contribution of pseudo-rotation is included. The details of the selection rules for cyclopentane have been discussed. ... 

A high-resolution Raman investigation of cyclopentane provided no positive evidence for pseudo-rotation, but a later i.r. investigation provided such evidence in the form of a series of regular and well-pronounced Q branches in the methylene deformation vibration at 1460 cm. From equation (33), with the selection rule An = 1, the pseudo-rotation levels will give rise to absorptions at wavenumbers... 

For completeness the phonon modulation of the spin-orbit coupling should also be mentioned as a possible source of spin-lattice relaxation. However, the spin-orbit coupling is weak in polymers that contain only light atoms. Furthermore, in ideal 1-D systems this relaxation route is forbidden by time reversal and inversion symmetry. It was suggested by Soda et al. [19] that in pseudo-one-dimensional systems this selection rule can be overcome by interchain hopping, in which case the relaxation rate becomes proportional to the inverse interchain transfer integral /x ... 

The intensities of the majority of the f-f transitions vary only within a factor of 2-3 from host matrix to host matrix, but some transitions are much more host dependent. These transitions are called hypersensitive transitions. These induced electric dipole transitions obey the selection rules for electric quadrupole transitions and are therefore sometimes called pseudo-quadrupole transitions. In sect. 8, we will discuss hypersensitivity in detail. The dependence of the Qx intensity parameters on the host matrix is the subject of sect. 9. Two-photon spectra (sect. 10) and vibronic transitions (sect. 11) are discussed briefly. On the other hand, chiroptical methods will not be considered. Since the color of the lanthanide ions is related to the spectral intensities of f-f transitions, we want to give attention to the phenomenon of color (sect. 12). Finally, the intensities of actinide ions are reviewed (sect. 13). 

The electric quadrupole transition arises from a displacement of charge that has a quadrupolar nature. An electric quadrupole consists of four point charges with overall zero charge and zero dipole moment. It may be pictured as two dipoles arranged so that their dipole moments cancel. An electric quadrupole has even parity. Electric quadrupole transitions are much weaker than magnetic dipole and induced electric dipole transitions. At this moment no experimental evidence exists for the occurrence of quadrupole transitions in lanthanide spectra, although some authors have claimed the existence of such transitions (e.g. Chrysochoos and Evers 1973). However, the so-called hypersensitive transitions (see sect. 8) are eonsidered as pseudo-quadrupole transitions, because these transitions obey the selection rules of quadrupole transitions. 

The intensities of the induced electric dipole transitions in lanthanide ions are not much affected by the environment. The dipole strength of a particular transition of a lanthanide ion in different matrices will not vary more than a factor two or three. However, a few transitions are very sensitive to the environment, and these are usually more intense for a complexed lanthanide ion than for the lanthanide ion in aqueous solution. The intensity increases up to a factor 200 (Gruen and DeKock 1966, Gruen et al. 1967). Only in a few cases has a lower intensity than in the aqueous solution been reported for these transitions (e.g. Krupke 1966). Jorgensen and Judd (1964) have called such transitions hypersensitive transitions. They noted that all known hypersensitive transitions obey the selection rules A5 = 0, AI 2 and jAJj 2. These selection rules are the same as the selection rules of a pure quadrupole transition, but calculations have revealed that the intensities of hypersensitive transitions are several orders of magnitude too large for these transitions to have a quadrupole character. Therefore, hypersensitive transitions have been called also pseudo-quadrupole transitions. No quadrupole transitions have been observed for lanthanide ions, although Chrysochoos and Evers (1973) stated that the intensity of the hypersensitive transitions D2 Fq (in the absorption spectrum) and Do Fi (in the luminescence spectrum) of Eu " are mainly quadrupolar in nature. 

The symmetry argument is rigorously valid only if there is a real center of symmetry, which requires that opposite substituents be identical. However, even if they are not identical but their electrical behavior is nearly the same, selection rules often apply rather well. For example, in fran -R CH = CHR", the substituents can be almost any alkyl groups and the C=C stretch will be weak or missing. It matters very little that one substituent might be ethyl and the other n-hexyl, for example. The molecule can be regarded as possessing a pseudo center of symmetry as far as the C=C stretch is concerned. 

Critics of the MZA data who argue that various forms of bias (placement, rearing by relatives rather than random placement, etc.) probably lead to serious overestimates of genetic influence seldom address both the MZA and URT data sets simultaneously (Dorfman, 1995 Fancher, 1995). Since URTs live in the same home and are matched on far more variables than MZA twins, the whole array of commonly cited biases in MZA studies is brought into question. I used to call this kind of selective reporting pseudo-analysis (Bouchard, 1982) until I discovered it already had a name. It is called the Neglected Aspect Fallacy (Castell, 1935) and it violates Carnap s Total Evidence Rule (1950). 

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