Of low symmetry

Pemberton J E, Bryant M A, Sobooinski R L and Joa S L 1992 A simple method for determination of orientation of adsorbed organios of low symmetry using surfaoe-enhanoed Raman soattering J. Rhys. Chem. 96 3776-82... 

Most complexes showing spin-state transitions are in fact of low symmetry. In order to describe their electronic structure it is convenient to employ term symbols appropriate to cubic symmetry and this practice will be followed below. The most common transition-metal ions for which spin-state transitions have been observed are Fe " (3d ), Fe " (3d ) and Co (3d ), a minor role being played by Co " (3d ), Mn " (3d ), as well as Cr " and Mn " (3d ). The relevant ground states for an octahedral disposition of the ligands are LS Ui,(t ,) and HS r2,(t ,e ) for iron(II), LS and HS Ai,(t, e ) for... 

Although symmetry considerations often permit g- and hyperfine matrix principal axes to be non-coincident, there are relatively few cases of such noncoincidence reported in the literature. Most of the examples discussed by Pilbrow and Lowrey in their 1980 review36 cite cases of transition metal ions doped into a host lattice at sites of low symmetry. This is not to say that matrix axis non-coincidence is rare but that the effects have only rarely been recognized. 

Excited states formed by light absorption are governed by (dipole) selection rules. Two selection rules derive from parity and spin considerations. Atoms and molecules with a center of symmetry must have wavefunctions that are either symmetric (g) or antisymmetric (u). Since the dipole moment operator is of odd parity, allowed transitions must relate states of different parity thus, u—g is allowed, but not u—u or g—g. Similarly, allowed transitions must connect states of the same multiplicity—that is, singlet—singlet, triplet-triplet, and so on. The parity selection rule is strictly obeyed for atoms and molecules of high symmetry. In molecules of low symmetry, it tends to break down gradually however,... 

The AOM has been used to parameterise the ligand field in detailed analyses of magnetic properties in non-cubic complexes. It may also be used to obtain the ground state wave function in systems of low symmetry where d-orbital mixing is important the mixing coefficients can be obtained from the off-diagonal elements of the AOM matrix in terms of parameters, whose magnitudes can be found from the d-d spectrum. 

Horrocks (155,156) has developed a somewhat similar comprehensive approach to the optical and magnetic properties of low-symmetry complexes, using a weak-field model. This has been applied to the CoCl4 ion in Cs2CoCl4 and Cs3CoCls. 

The dependence of lifetime on temperature in the range above RT shows an activation energy in the order of 10-25 meV [Bu3, Ool]. This was proposed to be a consequence of the exchange splitting of the exciton between the singlet and the triplet state. While at RT both states are populated, only the lower triplet state is populated at temperatures below 20 K. However, it has been shown that even for crystallites of low symmetry the calculated values of the exchange splitting are too low compared with experimental observations [De3]. Calculations of the radiative lifetime of the triplet exciton that take into account spin-orbit interactions are reported to be consistent with experimental results [Nal]. 

This E site energy in the exponential of Eq. 28 may be replaced with the perturbed site energies in the interacting system (E + E yfi) to include environmentally induced diagonal perturbations, but this has no consequence at all to the instanton analysis and the derivation of Eq. 30. In treatments of low symmetry molecular systems donor and acceptor site energies may be differentially perturbed, which means that one is not properly at the exact transition state with respect to electrostatic interactions in the medium. However the Monte Carlo path simulation will automatically signal the condition of excessive imbalance by a tendency of the instanton to slide to one end of the chain if the product of p and this site energy imbalance is not sufficiently small. 

For ions in crystals of high symmetry, as in the case of our reference octahedral ABe center, the correction factor is Eioc/Eo = (n + 2)/3 (Fox, 2001), where n is the refractive index of the medium. Although this correction factor is not strictly valid for centers of low symmetry, it is often used even for these centers. Thus, assuming this local field correction and inserting numerical values for the different physical constants, expression (5.21) becomes... 

The molecular ion will be of low symmetry and have an odd electron. It will have as many low-lying excited electronic states as necessary to form essentially a continuum. Radiationless transitions then will result in transfer of electronic energy into vibrational energy at times comparable to the periods of nuclear vibrations. 

For atoms in sites of low symmetry, the EFG tensor must be diagonalized to obtain its principal components V y. Since the tensor as defined by Eq. (8.9) is traceless, two values will define all three principal elements. They are commonly chosen as V 33, the principal component with the largest magnitude, and the asymmetry parameter t] = V 22 — V n / V 33, which has the range 0 < q < 1. 

The remaining exceptions concern the lanthanide series, where samarium at room temperature has a particular hexagonal structure and especially the lower actinides uranium, neptunium, and plutonium. Here the departure from simple symmetry is particularly pronounced. Comparing these three elements with other metals having partly filled inner shells (transition elements and lanthanides), U, Pu, Np have the lowest symmetry at room temperature, normal pressure. This particular crystallographic character is the reason why Pearson did not succeed to fit the alpha forms of U, Pu, and Np, as well as gamma-Pu into his comprehensive classification of metallic structures and treated them as idiosyncratic structures . Recent theoretical considerations reveal that the appearance of low symmetries in the actinide series is intimately linked to the behaviour of the 5f electrons. 

Narrow absorption lines can be observed in the liquid state only when the relaxation processes do not produce small values for Tv Thus the resonance of Ti(H20)6+ is not seen because the octahedral symmetry gives orbital states close to the ground state and this in turn leads to short 7Vs and hence broad absorption lines. When fluoride ions are added to produce a complex of low symmetry (23) in which there are no excited states close to the ground state, the ESR spectrum is observed as a narrow line. 

Many of the fast chemical reactions discussed in the preceding sections involve at least one reactant which is of low symmetry. The reactions of the solvated electron with nitrate, naphthalene or pyrene are instances where the oxidant has a mirror plane (in the molecular plane) in the accepting orbital. Hence, reaction of the solvated electron with such a scavenger when both are contained in this plane should be slower than in other configurations. Similarly, the contact quenching of fluorescence from naphthalene or 1,2-benzanthracene by carbon tetrabromide [7], or... 

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