Computational Magnetism

In many cases, one can introduce a local moment in spite of the itinerancy of the electrons. This is because of the two time scales in the problem. The first one is the time scale given by the electron hopping. This determines the instantaneous moment on a site, which fluctuates rapidly. The other time scale is that of the expectation value of the moment at the site. This is a much slower time scale, and makes it possible to introduce a local moment variable [89]. This is usually called the adiabatic principle. 

For a deeper discussion of the subject, I refer to a book by Yosida [127] and, for itinerant magnetism and general solid state physics with any relation to magnetism, a book by Kiibler [128]. 

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Luo, J. B. and Yang, M. C., Surface Modification of Computer Magnetic Head, Sino-German Symposium on Micro Systems and Nano Technology, 7-9 Sept., Braunschweig, Germany, 2001. 

The magnetic field is independent of the choice of the gauge origin. So too are the computed magnetic properties if the wave function used is exact. Regrettably, we are not often afforded the opportunity to work with exact wave functions. For HF wave functions, one can also achieve independence of the gauge by using an infinite basis set, but that is hardly a practical option either. 

Figure 13 Computed magnetic moments for an octahedral NiAs chromophore. Full lines refer to 305 K, broken lines to 155 K, and dotted lines to 5 K. (a) The effect of varying e (e =0cm-1) (b) the effect of varying ex/ea (e = 3000 cm-1) (c) the effect of varying (see text e = 3000 cm, e = 0 cm-1)...

The discovery of high-temperature superconductors is surely one of the most exciting scientific developments in the last 20 years. It has stimulated an enormous amount of research in chemistry, physics, and materials science that could some day lead to a world of superfast computers, magnetically levitated trains, and power lines that carry electric current without loss of energy. 

Fig. 2. Variations of the computed magnetic anisotropies Ax with respect to the distortion of a cube toward (a) elongated and compressed tetragonal prisms, (b) a tetragonal antiprism and (c) a dodecahedron (adapted from Mironov...

Table 68 The heat of combustion and the computed magnetic susceptibiiity anisotropies (cgs)...

According to both the computed magnetic susceptibility anisotropies and relative energies, the benzo[. ]thiophenes lie between the benzo[ ]pyrroles and benzo[. ]furans the benzo[r]thiophene should be more stable than the benzo[r]furan benzo[ ]thiophene should be the more stable isomer. 

We will not concern ourselves here with the attempt to discern a true definition of aromaticity, nor with the largely unproductive " desire to rank-order relative aromaticity. Rather, we will focus on how computational chemistry has been used to help define two of the criteria of aromaticity. We will discuss how to compute the stabilization energy of an aromatic species and then how we can compute magnetic properties that can be related to aromaticity. We will then conclude with a discussion of how these measures have been employed to investigate the nature of annulenes and the MiUs-Nixon effect. 

Maintain a system for tracking the locations where electronic records are stored (hard drives on mainframes and personal computers, magnetic tapes, disks, CDs and other media). This system is required to enable timely retrieval of electronic data. 

Figure 8. Experimental (solid line with solid circles, ) and computed magnetic susceptibility curves (the inset expands the low temperature region). The computed curves are for model spaces 2mbb (+), 3mbb ( ), 4mbb (A), 2mbb-(mbb) (x), and model 2mbb with a scaling factor 1.1 ( ), which reproduces best the experimental curve.

Measured as the shortest O O distance between the ONCNO groups. The threshold distance comes from increasing by 1.0 A the largest ONCNO ONCNO distance, for which a non-negligible computed magnetic / interaction was found in another nitronyl nitroxide radical (KAXHAS). 

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