Magnetic dipole moment permanent

Similarly, the interaction with a magnetic field can be written in terms of a magnetic dipole, quadrupole, and other moments. However, the first derivative in the Taylor series expansion, in the presence of magnetic field, is the permanent magnetic dipole moment the second derivative is the magnetizability. For a further study on the electrical and magnetic properties, one can refer to Dykstra [9]. 

PROBLEM 7.3.1. Prove that molecules with permanent electric or magnetic dipole moments must belong to one of the following point groups C , Cnv, or Cs [1]. 

Combining Eq. 9 and Eq. 10, we obtain the following simple expression for first-order properties (e.g., for the permanent electric and magnetic dipole moments) for a fully variational wave function ... 

Having set up the Hamiltonian, we may calculate the first- and second-order properties in the eigenvector representation. For the permanent electric and magnetic dipole moments, we obtain... 

Whereas the permanent electric dipole moment vanishes for molecules belonging to certain points groups (e.g., for all molecules that possess a center of inversion), the permanent magnetic dipole moment vanishes for all closed-shell systems. To see how the vanishing of the magnetic dipole moment comes about, we first note that... 

An atom, molecule, or ion containing one or more unpaired electrons with the same spin has a permanent magnetic dipole moment jU. In the absence of orbital contributions to the moment (see below), the magnitude /jl of this moment is completely determined by the number of unpaired electrons n ... 

Debye in 1912 extended Langevin s procedure to dielectrics, by attributing to the molecules a permanent (natural) electric dipole moment defined as in equation (34), The classical permanent magnetic dipole moment of a molecule is defined as follows (as an axial vector) ... 

Permanent magnetic dipole moments are known for a few molecules, such as Oj, NO, OH, NOj, and some others. -... 

Dipole length formula, 23, S6-Slt Dipole moment, 465. See also Electric dipole moment Magnetic dipole moment excipicx, 282 excited-slate. 47-48. 132 induced.130 permanent, 130-31 Dipole strength, IS8 Dipole velocity formula, 2, 56-57 Direct reaction. See Reaction 1,4-Disilabenzene, 105-7 Disproportionation, 228-29, 380, 390, 433 Disrotatory. See Elecirocyclic reaction ... 

However, particles of ferromagnetics, when sufficiently small, are of single domain character and possess an intrinsic permanent magnetic dipole moment jj. such that... 

Paramagnetic solids are those in which some of the atoms, ions or molecules making up the solid possess a permanent magnetic dipole moment. These dipoles are isolated from one another. The... 

For the sake of simplicity, we will restrict our discussion to the interaction of polar molecules (i.e., of molecules that carry a permanent electric dipole moment) with electric fields. However, we note that the same arguments and principles hold for the interaction of particles with a magnetic dipole moment with magnetic fields. 

The first term in this equation can be evaluated by use of the Boltzmann principle, with the assumption that the substance contains permanent magnetic dipole moments that can orient themselves in the magnetic field. This theoretical treatment was carried out by the French scientist Paul Langevin in 1905. He derived the equation... 

All nuclei that have an odd atomic number (number of protons) or odd mass number (protons + neutrons) possess a permanent magnetic dipole moment, and therefore behave like tiny bar magnets. This is because such neuclei are not perfect spheres, but are either oblate or prolate spheroids. When placed in a magnetic field, such nuclei absorb electromagnetic radiation in the radio-frequency (RF) region of the spectrum. The exact frequency depends upon various factors, but of critical importance to the chemist is the fact that this frequency (known as the frequency of resonance) varies with the chemical environment of the nucleus, and hence each nucleus in a molecule gives a characteristic signal. NMR therefore allows us to see the individual atoms that molecules are made of, and hence, to determine molecular structure. 

Magnetic properties of compounds arc of great importance when atoms or ions with permanent magnetic dipole moment are involved, because they reflect the effects of the crystal environments on the atoms or ions. By analyzing its magnetic behavior we can get information about the structure of the substance. 

Quantum mechanical expressions for the permanent magnetic dipole moment can be derived in exactly the same way as the corresponding formulas for the electric dipole moment, in Section 4.3. We will therefore skip most of the derivations here and only discuss the final equations. There is, however, one interesting difference. 

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