Field limit strong

The approach we have adopted for the d configuration began from the so-called strong-field limit. This is to be contrasted to the weak-field scheme that we describe in Section 3.7. In the strong-field approach, we consider the crystal-field splitting of the d orbitals first, and then recognize the effects of interelectron repulsion. The opposite order is adopted in the weak-field scheme. Before studying this alternative approach, however, we must review a little of the theory of free-ion spectroscopy... 

Of course, in real systems, the relative contributions of Coulomb and crystal-field effects are such as to place chromophores somewhere inbetween the weak-and strong-field limits. In that case, a real Txg F) A2g transition is not a pure two-electron jump, so that some intensity is observed. 

Finally, we must remember that just as a d-d spectrum is not properly described at the strong-field limit - that is, without recognition of interelectron repulsion and the Coulomb operator - neither is a full account of the energies or number of charge-transfer bands provided by the present discussion. Just as a configuration... 

The extension to non-octahedral complexes is possible, but must be carried out with great care The orbitals chosen can be expressed as a linear combination of the usual orbitals for an octahedron, and electron-electron repulsions can then be calculated from those for the octahedral case. It is not necessarily adequate for tetrahedral complexes of the first row transition elements, to use ligand field theory in the strong field limit, even for powerful ligands in V(mesityl)4 the ligand field splitting is only 9250 cm ... 

The rotational quantum numbers of the free linear dipole are j and m (with m S j), and the rotational constant is denoted by B. Analogous to the strong-field limit of the Stark effect, for linear dipoles at small r, one has... 

M. Herman Prof. Troe explicitly referred to the Stark effect in his talk. In the strong-field limit, the Stark effect will mix the j levels. Does his model explicitly take that mixing into account ... 

The solution using Bethe s method of descending symmetry is summarized in Table 7.8. In the strong-field limit the possible electron configurations derived from d2 in the free ion... 

Fig. 25 Effective magnetic moment for nearly-octahedral d2 complexes. Left Figgis theory for the % reference (k = 1, X > 0, A = 1 - strong-field limit) solid line - v = 0 (octahedron) dashed - v = +10 (compressed bipyramid, Aax > 0) dot-dashed - v = -10 (elongated bipyramid, Aax < 0). Right calculation in a complete d1 space for a weak-field V(III) complex on tetragonal distortion with F4(xy) = 5000 cm-1 dashed - compressed bipyramid with F4(z) = 6000 cm-1 solid - octahedron with F4(z) = 5000 cm-1 dot-dashed - elongated bipyramid with F4(z) = 4000 cm-1...

Fig. 3. Correlation diagram of the doublet states relating weak (left) and strong (right) tetragonal perturbations. In the strong field limit the splitting pattern is determined by pseudo-/l quantum numbers. Note the crossing point on the lowest energy curve...

Spin-orbit coupling in conjunction with the trigonal field leads to a zero-field splitting of the 2E levels. In the strong field limit the spin-orbit levels can be obtained by vector addition of cylindrical orbital and spin momenta. Hence the 2IT state will give rise to 2f7 3/2 and 2/7 1/2 components, comprising resp. the 2D 1/2 1) and 2D 1/2 +1) functions. The trigonal symmetries of these functions are as follows ... 

Bandrauk s long-term research interests include the dressed-state representation of molecular spectroscopy. His contributions to the nonperturba-tive treatment of molecular spectroscopy from the weak field to strong field limits have been summarized in two chapters in a book he edited in 1993.286 Bandrauk and his coworkers published the first theoretical demonstration of the use of chirped pulses to effect laser bond breaking in less than a picosecond.287 His other firsts include the first prediction of molecular stabilization in intense laser fields288 and the first complete non-Born-Oppenheimer calculation of dissociative ionization of molecules in intense femtosecond laser pulses.289... 

A. D. Bandrauk, Ed., Dressed State Representation of Molecular Spectroscopy—Molecules in Laser Fields, Dekker, New York, 1993, Chapters 1 and 3. Nonperturbative Treatment of Molecular Spectroscopy from the Weak Field to Strong Field Limits Analytical and Numerical Methodology. 

Figure 4 Anomalous Zeeman effect on a 2P-2S transition (weak field). The strong-field limit is called the Paschen-Back effect. The splitting of the levels is not drawn to scale.

Tables 1 and 2 assume the strong-field limit for configurations of d electrons in ligand fields (16). In Table 1, all ground states have been considered which are likely to occur in tetrahedral and octahedral symmetries. Table 2 was originally intended for D 5 symmetries appropriate to the metallocenes, but it can also be used for Dn where n > 5, and (with some change of notation) for linear symmetries.

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