Marvin-integrals

Judd, Crosswhite, and Crosswhite (10) added relativistic effects to the scheme by considering the Breit operator and thereby produced effective spin-spin and spin-other-orbit interaction Hamiltonians. The reduced matrix elements may be expressed as a linear combination of the Marvin integrals,... 

Magnetically correlated corrections such as spin-spin and spin-other-oibit interactions are represented by the term Yk o 2 4 kW in the Hamiltonian, where nik are the operators (Judd et al. 1968). The parameters M are also called Marvin-integrals after... 

Figure 2.33. A fragment analysis application developed by AstraZeneca by integrating Fragmenter and Marvin in Spotfire. The application provides integrated views on hit frequencies of the fragments from a library in various targeted compound collection spaces. The structure and hit frequencies for the fragments are displayed in the lower-right corner while the user can interactively click one fragment dot or select a set of fragments. This screenshot is provided by Paul Xie of AstraZeneca...

Crosswhite (23) has used the correlated multiconfiguration Hartree-Fock scheme of Froese-Fisher and Saxena (24) with the approximate relativistic corrections of Cowan and Griffin (25) to calculate the Slater, spin-orbit, and Marvin radial integrals for all of the actinide ions. A comparison of the calculated and effective parameters is shown in Table II. The relatively large differences between calculation and experiment are due to the fact that configuration interaction effects have not been properly included in the calculation. In spite of this fact, the differences vary smoothly and often monotonically across the series. Because the Marvin radial integral M agrees with the experimental value, the calculated ratios M3(HRF)/M (HRF) =0.56 and M4 (HRF)/M° (HRF) =0.38 for all tripositive actinide ions, are used to fix M and M4 in the experimental scheme. 

As fits to the crystal spectra became more detailed, a lack of balance in the theory appeared. The Coulomb interactions within the 4f shell and the effects of configuration interaction to second order can be taken into account by means of the four Slater integrals F (4f, 4f), the three Trees parameters a, J5, y, and the six three-electron parameters T . In contrast to these 13 electrostatic parameters, the spin-orbit interaction, until 1968, was represented by the single parameter This scheme overlooks the terms that arise from the Breit interaction, which was developed on relativistic grounds to account for the fine structures of the multiplets of Hel Isnp (see Bethe and Salpeter 1957). In the non-relativisitc limit parts of the Breit interaction, such as the retardation of the Coulomb interaction and the magnetic interactions that exist between the electrons in virtue of their orbital motions, can be represented by adjustments to the electrostatic parameters. Two terms cannot be absorbed in that way the spin-spin interaction and the spin-other-orbit interaction Marvin (1947) showed that, for the configurations I", ... 

Marvin Sketch is an advanced chemical editor used for drawing stmctures, queries and reactions [20], This tool can be integrated into the portlet by using javascript as follows ... 

Since the ss and the soo interactions are represented by two-electron operators, they comprise, in analogy with the electrostatic interaction, both a direct and an exchange part. For the spin-spin interaction, these parts are described in terms of the radial integrals A/ (n/, n / ), M ln l, nl)-and N nl, n l ) respectively. The definitions of these parameters are given below (Marvin, 1947). 

Instead of integrating over the entire maximum of J" or G", one can obtain the value of J% or simply from the peak value of the respective loss component if the shape of the maximum is specified. For example, a phenomenological theory of Marvin and Oser predicts the relations... 

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