Magnetic field perturbation method

The GIAO method is used in conjunction with analytical derivative theory in this approach the magnetic field perturbation is treated in an analogous way to the perturbation produced by changes in the nuclear coordinates. In this framework, the components of the nuclear magnetic shielding tensor are obtained as ... 

The k p method provides analytic descriptions on electronic states of CNT. It shows, for example, that the band gap of a semiconducting CNT is inversely proportional to the diameter because of a linear dispersion of the bands. It is suitable also for descriptions of the electronic motion in external perturbations such as electric and magnetic fields. 

Then the (w -f 1) x (m -f 1) eigenvalue matrix can be constructed from (9) and can be solved exactly by direct diagonalization or with the aid of perturbation methods for the eigenvalues with the external magnetic field along any principal axis, (m -f 1) Energy values and therefore m Am, = 1... 

A brief review is given here of the spectroscopic vector model of an atom or ion. In crystal-field theory, the wave function of the isolated ion is taken as the unperturbed state, and the perturbing effect of the electric and magnetic fields is computed. Thus crystal field theory uses the language, nomenclature, and methods employed in the theory of atomic spectra. A complete discussion of these methods can be found in books by Condon and Shortley (5) and by Griffith (/). 

Such second-order molecular properties as spin-spin coupling depend upon distortion of electron clouds by additional external perturbations that is, in the NMR experiment they depend upon the electronic motion induced by an applied magnetic field. Theories for such second-order molecular properties require a study of the change in the molecular-orbital wavefunctions, which may be found by using a perturbation method to describe the effects occurring when a magnetic field is applied.8-1065-67... 

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