Effective spin-orbit

In the 5 d series however it is possible to derive additional information bearing upon the problem of the relative extent of central field and symmetry restricted covalency. For many 5 d complexes reasonable estimates of the effective spin-orbit coupling constant can be derived from the spectra, and thence the relativistic ratio, / (= complex/ gas). When both f) and / are known for a given system, Jorgensen (74) has suggested how estimates of both covalencv contributions may be made. 

We have not as yet however treated the charge-transfer data available for complexes of the 5 d series. For these latter species though the effective spin-orbit coupling constants are often of the order of 3 kK. or more, as compared with only about 1 kK. for Ad systems, and smaller values still for the 3d elements. Consequently, as for the d—d transitions it is often necessary explicitly to consider relativistic effects in the interpretation of charge-transfer spectra, and in particular to make allowance for the changes in spin-orbit contributions which may accompany a given di transition. In fact one of us has shown (18) that these changes are... 

Spin-polarization, metalloporphyrins, effects spin-orbit, 59-71 Structural features, nickel... 

ESR parameters of the complex show its distortion upon entrapment, depending on the geometry of the intrazeolite space. In ZSM-5, the decreased effective spin-orbit coupling constants and molecular orbital coefficients for in-plane n binding are indicative of increased covalency between Cu and en, due to distortion from planarity upon encapsulation. This distortion from planar geometry is confirmed by a red shift in the energy-level diagrams at least for the zeolites with the smaller pores (ZSM-5 Beta). An intensity enhancement of the d-d bands occurs in parallel. 

The structure of isolated R3M+ cations in the gas phase was the subject of several computational studies. Significant difficulties are associated with calculations for molecules containing the heavier elements, particularly Sn and Pb. NMR chemical shift calculations require consideration of relativistic effects (spin-orbit coupling). A discussion of these difficulties and of effective core potentials developed for these calculations is beyond the scope of this review. 

Relativistic effect (spin-orbit-coupling) in L. C. A. O. M. O. approximation... 

When this expression is extended to many-electron systems, two related problems arise. Firstly, what is the effective spin-orbit hamiltonian for the electron in open shells Secondly, what is the potential in which they move For a hydrogen-like atom the field would be written... 

Another method, devised by Cohen et al. to determine oxygen-rate gas collision parameters is to define an effective spin-orbit operator that includes r dependence, Zeff/r3, where the value of Zeff is adjusted to match experimental data (76). Langhoff has compared this technique with all-electron calculations using the full microscopic spin-orbit Hamiltonian for the rare-gas-oxide potential curves and found very good agreement (77). This operator has also been employed in REP calculations on Si (73), UF6 (78), U02+ and Th02 (79), and UF5 (80). The REPs employed in these calculations are based on Cowen-Griffin atomic orbitals, which include the relativistic mass-velocity and Darwin effects but do not include spin-orbit effects. Wadt (73), has made comparisons with calculations on Si by Stevens and Krauss (81), who employed the ab initio REP-based spin-orbit operator of Ermler et al. (35). 

Tj g state yields two different four-fold degenerate Vq states which mix with Eg, and accordingly, Equation 9 yields two distinct coefficients, denoted cj and C2 At the level of first-order perturbation theory, these two states lie at +/2 and 4 2+/3 ith respect to the ground state, where is the effective spin-orbit coupling integral for the Co " 3d orbital (17). 

An even simpler but less well-justified approximation avoids the calculation of the matrix elements of the two-electron part of the operator altogether. Only the matrix elements of the one-electron part of are computed, and in the sum over nuclei a in Equation 3.3, contributions from each atom are not multiplied by Z but by the effective spin-orbit coupling nuclear charge of atom a, which has been optimized empirically to represent the partial compensation of the one-electron part by the two-electron part of the operator. Recommended values of for atoms of main-group and transition metal elements are listed in Table 3.1. This method is generally acceptable in molecules containing heavy atoms but is not very accurate in those composed of light atoms only. 

In 1992 Dmitriev, Khait, Kozlov, Labzowsky, Mitrushenkov, Shtoff and Titov [151] used shape consistent relativistic effective core potentials (RECP) to compute the spin-dependent parity violating contribution to the effective spin-rotation Hamiltonian of the diatomic molecules PbF and HgF. Their procedure involved five steps (see also [32]) i) an atomic Dirac-Hartree-Fock calculation for the metal cation in order to obtain the valence orbitals of Pb and Hg, ii) a construction of the shape consistent RECP, which is divided in a electron spin-independent part (ARECP) and an effective spin-orbit potential (ESOP), iii) a molecular SCF calculation with the ARECP in the minimal basis set consisting of the valence pseudoorbitals of the metal atom as well as the core and valence orbitals of the fluorine atom in order to obtain the lowest and the lowest H molecular state, iv) a diagonalisation of the total molecular Hamiltonian, which... 

Diatomic molecules containing heavy elements are often used as benchmark of relativistic methods because they are small enough to be treated by demanding approaches like four-component methods nevertheless, diatomics with a variety of chemical bonds afford a thorough testing. To illustrate the accuracy of the DKH approach to relativistic DF calculations, we chose Auz and Bi2. Au2 shows predominantly scalar relativistic effects, spin-orbit interaction is not important because bonding is predominantly mediated by the interaction of the... 

Z. S. Romanova, K. Deshayes, P. Piotrowiak, Remote intermolecular heavy-atom effect spin-orbit coupling across the wall of a hemicarcerand, J. Am. Chem. Soc., 2001, 123, 2444-2445. 

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