Dipolar interactions classical

Our aim is that of evaluating the energy of the dipolar interaction between the nuclear and electron magnetic moments from the classical expression (see Eq. 

The dipolar interaction between the electron spin magnetic moments is also similar to the interaction between two nuclear spins. It may therefore be represented by a classical dipolar interaction term, but with the electron spin magnetic moments represented by their quantum mechanical operators ... 

The simplest molecular constant to understand is the nuclear spin dipolar interaction constant, to, which is found to be, within experimental error, that calculated from the classical interaction of two magnetic moments, i.e. gFgHfrwO /47t oc2)(7 3> =o. On the other hand, calculation of scalar electron-coupled spin-spin interaction constants is notoriously difficult, requiring a molecular electronic wave function of the highest quality. The best available calculation for HF quoted by Muenter and Klemperer is one due to O Reilly [96]. 

If the I-S heteronuclear dipolar interactions are weak, e.g. reduced by molecular mobility or spacial remoteness, while the I-I homonuclear dipolar interactions are moderate or strong, then the CP kinetics is likely to follow the classical I-S model. In most cases, it is described by Eq. (2) ... 

We consider a nonlinear optical medium, consisting of polyatomic molecules interacting with a classical external electromagnetic field by a dipolar interaction. The total Hamiltonian of the system is... 

Water H NMRD profiles are often analyzed by using the classical dipolar interaction approach, as first described by Solomon ... 

Since nearest neighbor metal ions in a crystal lattice are usually separated by at least a few Angstroms (very seldom less than 5 A), the interaction between an electron on each metal ion is represented quite well to a first-order approximation by a simple classical dipolar interaction between electrons located at a point on each metal atom. The splitting AH produced by this spin-spin interaction is given by... 

Anisotropic Hyperfine Interaction. The anisotropic component of the hyperfine coupling has two contributions a local anisotropy owing to spin density in p- or type orbitals on the atom of observation, and nonlocal dipolar coupling with spin on other atoms. The first type of interaction is proportioned to the orbital coefficient (squared) of the pid orbiteds. To a first approximation the second term can be considered as a classic point dipolar interaction between the nucleus and the electron spin on a nearby atom. This depends on the total electron spin density at the neighbor (p ), the distance between the spins (r,2), and the orientation of the vector between them with respect to the external magnetic field (denoted by angle 0). In the point dipole approximation,... 

Because NMR deals with radio frequencies where the spontaneous radiation is rather weak, the interaction Hamiltonians can be written in semiciassical form, i.e., the r.f. field can be described by classical quantities such as magnetic field, B. In solid-state NMR, the most important interactions are diemical shift, dipolar, and electric quadrupolar interactions. Dipolar interactions can also be divided into direct... 

Owing to the chemical composition of silica, two nuclei are usually analyzed. They are H, as abundant spin and Si as a rare one. Numerous experiments have been done by cross polarization (CP) between proton and silicon nuclei and magic angle spinning (MAS). As it is a classical method analyzed elsewhere [2], it is not described here in details. It is only necessary to notice that the silicon signal is enhanced if the distance to proton is short enough to provide an efficient dipolar interaction. So this means that the method allows to distinguish the different types of hydroxylated silicon species, but also... 

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