Magnetic dipole Moment operator

In Equation (6) ge is the electronic g tensor, yn is the nuclear g factor (dimensionless), fln is the nuclear magneton in erg/G (or J/T), In is the nuclear spin angular momentum operator, An is the electron-nuclear hyperfine tensor in Hz, and Qn (non-zero for fn > 1) is the quadrupole interaction tensor in Hz. The first two terms in the Hamiltonian are the electron and nuclear Zeeman interactions, respectively the third term is the electron-nuclear hyperfine interaction and the last term is the nuclear quadrupole interaction. For the usual systems with an odd number of unpaired electrons, the transition moment is finite only for a magnetic dipole moment operator oriented perpendicular to the static magnetic field direction. In an ESR resonator in which the sample is placed, the microwave magnetic field must be therefore perpendicular to the external static magnetic field. The selection rules for the electron spin transitions are given in Equation (7)... 

In terms of transition matrix elements of the electric and magnetic dipole moment operators, the transition dipole moments are... 

Thus suppose we had included the interaction of the radiation s magnetic field B with the atomic or molecular electrons and nuclei. The Hamiltonian for this interaction is [Equation (1.268)] -B , where p is the magnetic dipole-moment operator for the system. This gives additional terms in cm that are proportional to... 

The relation between the spherical components AJ0( ) of a general tensor A of rank 2 and the cartesian components A, ( ) are given in Appendix 4. Equations (3.36) will form the basis for derivation of selection rules for rotation-internal motion transitions of SRMs presented in the next section. They also may serve for derivation of the transformation properties of the electric and magnetic dipole moment operators referred to the laboratory system (VH G... 

Mk denotes the nuclear magnetic dipole moment operator, obtained by multiplication of the nuclear spin operator IA- by the magnetogiric factor yK. 

The ETDM and MTDM were calculated using the SAC and SAC-CI wave functions, jx and in are electric and magnetic dipole moment operators, respectively. 

Alternatively the 10 x 10 d Hgand field matrix can be diagonalized as a function of (f). The g-values can then be calculated from the lowest Kramers doublet W- using the magnetic dipole moment operator ... 

Table 11. CCSD results for the total Verdet constant at w = 0.11391 a.u. in the case of hydrogen fluoride. Results labeled as Unrelaxed refer to the use of the unrelaxed (one-electron) magnetic dipole moment operator together with the usual magnetic-field independent basis sets. Results labeled Relaxed include additional contributions due to orbital relaxation in the presence of the magnetic field. Results labeled LAO are those obtained when using GIAOs/LAOs ...

I ml j) are the matrix elements of the electric dipole moment and the magnetic dipole moment operators (exclusive of spin) connecting the ground state a with the excited Vj is the frequency of the transition a -> j, and h is Planck s constant. It is implicitly assumed in (41) and (42) that there is only a single state a accessible to the molecules in thermal equilibrium. If, in fact, there is more than one such state, then... 

The electric dipole moment operators are independent of origin, therfore, the vectors R do not appear. The magnetic dipole moment operators do depend on the origin. 

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