Corrections intermediate coupling

We take as an example the case of plutonium monopnictides PuP, PuAs, PuSb, the susceptibility of which is well fitted by Eq, (17). Results are given in Table 8 while bare data are in agreement with the full J multiplet value ( 1 pP in the intermediate coupling), the corrected value is substantially smaller and points towards a Fg ground state (see Table 8) in agreement with more detailed discussions ... 

We shall not present here complete sets of selection rules for all transitions in question. For these transitions they become much more complex, e.g. already for transition (25.24), the pentagon conditions can occur. Interested readers may find them in [173]. Selection rules differ considerably for the various coupling schemes. They change if we account for the relativistic corrections to the non-relativistic E/c-transition operators. However, all selection rules involving intermediate momenta are more or less approximate. Due to the presence of interaction between coupled momenta a certain intermediate coupling scheme takes place, and these selection rules are violated. 

Pacchioni has recently carried out calculations on the low-lying states of Sn2 and Pb2. This author gives the impression that he is the first to carry out a comparative ab initio Cl calculation on these systems. We would like to clarify this further. First, his calculation starts with the Hafner-Schwarz model potentials in comparison to our relativistic ab initio potentials derived from numerical Dirac-Fock solutions of the atoms. Pacchioni s calculations ignore spin-orbit interaction. Our calculations include spin-orbit interaction in a relativistic Cl scheme in comparison to the non-relativistic Cl of Pacchioni. Thus, he obtains a Z), approximately twice the experimental value which he corrects by a semi-empirical scheme to arrive at a value close to our calculated value with a relativistic Cl. Our calculations have clearly demonstrated the need to carry out an intermediate-coupling Cl calculation for Pbj as a result of large spin-orbit contamination. Calculations without spin-orbit, such as Pacchioni s, have little relationship to the real Pb2 molecule. 

In the intermediate-coupling regime Mott-Wannier excitons are the more appropriate description for large dimerization (J = 0.2), while for the undimerized chain Mott-Hubbard excitons are the correct description. For dimerizations relevant to polyacetylene and polydiacetylene (that is, S ... 

Values of (r" ) are based primarily on theoretical calculations of the 4f wave functions, for example, those of Freeman and Watson (1962) and of Judd (1963). In table 18.5 are listed the values of (/ N /), (r ), and Hfs for the tripositive rare-earth ions. Strictly speaking, correction factors differing from unity by a few percent should be applied to these (/ M /) values [Bleaney (1972)] to take account of intermediate coupling effects which arise from the admixture into the ground state (L, S, J) wave function of states of different L, S, but the same /, by the spin-orbit interaction. A table of these values is included in Bleaney (1972). 

The hyperfine interaction constants A and B had been derived from ABMR measurements for the first four levels of the ground quintet [1]. Combining this method with the triple resonance technique, Biittgenbach et al. have obtained more precise values of the constants for p5 and [6]. These constants, corrected by use of the intermediate-coupling wave functions developed by Trees [7] are given in Table 2/1. From the constants A and B effective radial parameters of magnetic dipole and electric quadrupole interaction for the 4d 5s configuration have been derived [6, 16] (in MHz) ... 

Perturbation methods add all types of corrections (S, D, T, Q etc.) to the reference wave function to a given order (2, 3, 4 etc.). The idea in Coupled Cluster (CC) methods is to include all corrections of a given type to infinite order. The (intermediate normalized) coupled cluster wave function is written as... 

The synthesis of the key intermediate aldehyde 68 is outlined in Schemes 19-21. The two hydroxyls of butyne-l,4-diol (74, Scheme 19), a cheap intermediate in the industrial synthesis of THF, can be protected as 4-methoxybenzyl (PMB) ethers in 94% yield. The triple bond is then m-hydrostannylated with tri-n-butyl-tin hydride and a catalytic amount of Pd(PPh3)2Cl238 to give the vinylstannane 76 in 98 % yield. Note that the stereospecific nature of the m-hydrostannylation absolutely guarantees the correct relative stereochemistry of C-3 and C-4 in the natural product. The other partner for the Stille coupling, vinyl iodide 78, is prepared by... 

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