Orbital angular frequency

The vector L is so strongly coupled to the electrostatic field and the consequent frequency of precession about the intemuclear axis is so high that the magnitude of L is not defined in other words L is not a good quantum number. Only the component H of the orbital angular momentum along the intemuclear axis is defined, where the quantum number A can take the values... 

The symbol u>, when used to denote a 3c/4e triad (e.g., cuAbc). bond orbital (e.g., u>Ab c) or ligand label (e.g., F ), is unlikely to be confused with other common usages such as angular frequency. Its shape has three points and two connecting arcs to suggest three-center character with two connecting electron pairs. 

The orbital angular momentum possessed by 02(1A,) suggests that this state might exhibit paramagnetic resonance in the gas phase. On the other hand, 02(1E5+) cannot be detected by EPR methods. The energy between Ms levels corresponds to a frequency of v given by... 

In connection with the Jahn-Teller effect the role of A may be well defined. It has been shown that if a dynamic Jahn-Teller effect is operative, very substantial quenching of orbital angular momentum may take place — the Ham effect. In the case of T ground terms, if the dynamic Jahn-Teller frequencies bear the right relationship to spin-orbit coupling and temperature, A may be reduced to values well below 0.5.113119... 

Since the s orbitals do not have orbital magnetic moment, g — ge — 2.0023. A is an eneigy, which in SI units is expressed in joule. Sometimes it is convenient to have it expressed in frequency units, i.e. in hertz or in radians per second, and then we have to divide A by h or by h (ft = h/2n). In magnetic resonance there often is a factor 2jt which complicates life. The frequency which we refer to is the angular frequency or the Larmor precession frequency. Such frequency co is... 

Electron spin quantum component Electron spin quantum number Hyperhne coupling constant Larmor angular frequency Larmor frequency Magnetogyric ratio Nuclear magneton Nuclear spin quantum component Nuclear spin quantum number Orbital quantum number Orbital quantum number component Principal quantum number Quadrupole moment Relaxation time longitudinal transverse Shielding constant... 

Prom these two equations it can easily be seen that the electrons are moving on an orbit in k space which is given by a constant energy surface perpendicular to B. The angular frequency with which the so-called cyclotron orbit is traced is given by the cyclotron frequency Wc = eB/rric, where the cyclotron mass is defined by... 

NMR has become such an invaluable technique for studying the structure of atoms and molecules because nuclei represent ideal noninvasive probes of their electronic environment. If all nuclei of a given species responded at their characteristic Larmor frequencies, NMR might then be useful for chemical analysis, but little else. The real value of NMR to chemistry comes from minute differences in resonance frequencies dependent on details of the electronic structure around a nucleus. The magnetic field induces orbital angular momentum in the electron cloud around a nucleus, thus, in effect, partially shielding the nucleus from the external field B. The actual or local value of the magnetic field at the position of a nucleus is expressed as... 

If eqn. (5) represented the resonance condition for all electrons, one would predict that they would all resonate at the same applied field for a given applied frequency. Consequently, the g factor would always be equal to that of the free electron. However, as well as possessing spin angular momentum, the unpaired electron also possesses electronic orbital angular momentum. The interaction between the two (via spin-orbit coupling) ensures that the electron has an effective magnetic moment different from that of the free electron. Hence, the resonance condition for an unpaired electron in a References pp. 349-352... 

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