Stevens’ formalism

Stevens formalism turned out to be very powerful, and works easily as long as only the ground 2S+1Lj multiplet ofthe lanthanide ion is considered. As such, it has been widely used in studies on EPR properties of lanthanide-based inorganic systems [6, 22], while it is not well suited for optical spectroscopy. Indeed, when starting to include excited multiplets the Stevens formalism becomes much too involved. This is the reason why a more general formalism, developed by Wybourne [3], is of widespread use in optical studies - naturally dealing with excited multiplets - and... 

Table 1.2 Non-vanishing crystal field terms (Stevens formalism) for common lanthanide point symmetries.

Inspection of Equation 1.23 and consideration of the properties of 3-y and 6-j symbols confirm that only even A--values contribute to crystal field splitting. Further, it indicates that mixing between levels belonging to different / multiplets can only occur if terms with k site symmetry of the lanthanide, in much the same way as discussed above for the Stevens formalism. 

A, comparison between CEF parameters obtained using tensor operators and the commonly used Stevens formalism can be made by a numerical conversion (see table 1). We follow the common convention of writing the tensor parameters as and inverting the indices for the Stevens parameters, B ". Table 1 also contains the conversation factors for a comparison with parameters used by a group at the ETH Zurich. Further details about conversions between various formalisms are available elsewhere (Bleaney and Stevens 1953, Hutchings 1964, Kassman 1970), We stress that care is necessary when comparing parameters obtained by different groups and different techniques. 

Such reductive ring contractions of sulfones are formally similar to two other methods capable of supplanting a sulfur atom by a carbon-carbon double bond the Ramberg-Backlundand Stevens rearrangements. The distinguishing feature of this novel approach to cyclobutenes consists in the resultant higher level of alkyl substitution at the sp -hybridized centers. 

When treating CF parameters in any of the two formalisms, non-specialists often overlook that the coefficients of the expansion of the CF potential (i.e. the values of CF parameters) depend on the choice of the coordinate system, so that conventions for assigning the correct reference framework are required. The conventional choice in which parameters are expressed requires the z-direction to be the principal symmetry axis, while the y-axis is chosen to coincide with a twofold symmetry axis (if present). Finally, the x-axis is perpendicular to both y- and z-axes, in such a way that the three axes form a right-handed coordinate system [31]. For symmetry in which no binary axis perpendicular to principal symmetry axis exists (e.g. C3h, Ctt), y is usually chosen so as to set one of the B kq (in Wybourne s approach) or Aq with q < 0 (in Stevens approach) to zero, thereby reducing the number of terms providing a non-zero imaginary contribution to the matrix elements of the ligand field Hamiltonian. Finally, for even lower symmetry (orthorhombic or monoclinic), the correct choice is such that the ratio of the Stevens parameter is restrained to X = /A (0, 1) and equivalently k =... 

Formally the unperturbed Hamiltonian is equivalent to the Hamiltonian of the hydrogen atom in constant homogenious electric field. Chaotic dynamics of hydrogen atom in constant electric field under the influence of time-periodic field was treated earlier (Berman et. al, 1985 Stevens and Sundaraml987). To treat nonlinear dynamics of this system under the influence of periodic perturbations we need to rewrite (1) in action-angle variables. Action can be found using its standard definition ... 

Tertiary amines can react with electrophilic carbene complexes to yield ammonium ylides which usually undergo Stevens rearrangement (Figure 4.8) leading to products of a formal carbene C-N bond insertion. 

The results show only a modest variation when the van der Waals radii are changed within reasonable bounds (Table 6.2). As the data were not refined with the aspherical atom formalism, the scale of the observed structure factors may be biased, an effect estimated on the basis of other studies (Stevens and Coppens 1975) to correspond to a maximal lowering of the scale by 2%. Values corrected for this effect are listed in the last two columns of Table 6.2. Since neutral TTF and TCNQ have, respectively, 72 and 52 valence electrons, the results imply a charge transfer close to 0.60 e. 

What are the PEGAS proposals for the Stevens rearrangement when a formally similar system... 

Feldman, K. S., Wrobleski, M. L. Alkynyliodonium salts in organic synthesis. Dihydrofuran formation via a formal stevens shift of a carbon substituent within a disubstituted-carbon oxonium ylide. J. Org. Chem. 2000, 65, 8659-8668. 

Hydroxylation of the ring by reactions formally comparable to those carried out by salicylate hydroxylase (White-Stevens et al. 1972), 4-hydroxybenzoate hydroxylase (Howell et al. 1972), or 2,4-dichlorophenol hydroxylase (Beadle and Smith 1982 Perkins et al. 1990). These have been discussed in Section 4.4.1.1. 

Steven D. Johnson is an associate professor of computer science in the Indiana University College of Arts and Sciences. He received a B.A. in mathematics and Russian from Depauw University in 1970, an M.A. in mathematics from Indiana University in 1977, and the Ph.D. in computer science from Indiana University in 1983. His research is in the area of formal methods for system design. He is a member of the IEEE Computer Society, ACM, and IFIP WG 10.5. 

Several years later, Liu and coworkers reported another synthesis of cephalotaxine 172 that relied on a distinct [2,3]-Stevens rearrangement fScheme 1 S.4QL ° Proline derivative 173 was transformed into ammonium ylide 174 in the presence of allyl bromide and K2CO3. This zwitterion rearranged to a-allyl aminoester 175. Hydration of the olefin and reduction of the ester furnished diol 176, which was converted to aminoketone 177 via oxidation and aldol condensation. The assembly of this spirocyclic intermediate represented a formal synthesis of cephalotaxine 172. ... 

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