Residual angular momentum

Free atoms are spherically symmetrical, which implies conservation of their angular momenta. Quantum-mechanically this means that both Lz and L2 are constants of the motion when V = V(r). The special direction, denoted Z, only becomes meaningful in an orienting field. During a chemical reaction such as the formation of a homonuclear diatomic molecule, which occurs on collisional activation, a local held is induced along the axis of approach. Polarization also happens in reactions between radicals, in which case it is directed along the principal symmetry axes of the activated reactants. When two radicals interact they do so by anti-parallel line-up of their symmetry axes, which ensures that any residual angular momentum is optimally quenched. The proposed sequence of events is conveniently demonstrated by consideration of the interactions between simple hydrocarbon molecules. 

Each carbon atom has residual angular momentum which can be quenched in a Kekule configuration, provided that all atoms are in the xy-plane, as shown in figure 9. 

There are no steric restrictions that militate against the formation of planar (CHjs. However, by the same principle that stabilizes benzene, (CH)5 should have an unpaired spin and residual angular momentum of h along z, because of the odd number of pxy- electrons. In order to quench the angular momentum one p2-electron could transfer to pxy and to pair the odd spin, the molecule may accept an extra electron. The most efficient solution would be accepting an electron with angular momentum, e.g. by photochemical electron transfer. This may account for the ease whereby (CH) sandwiches... 

Derivative work, based on this analysis, erroneously assumes degeneracy of the linear combinations when defining a set of orthogonal real orbitals . There is no theoretical basis in the seminal paper to justify this assumption. However, what is clearly implied is that the orbital moment on each carbon atom is directed perpendicular to the molecular plane. The molecular angular momentum is therefore quenched vectorially only for this planar arrangement of the molecule. Torsional distortion which creates residual angular momentum therefore requires work, the true basis of a barrier to rotation. 

Two kinds of environmental interactions are commonly important in the ESR spectrum of a free radical (i) To the extent that the unpaired electron has residual, or unquenched, orbital angular momentum, the total magnetic moment is different from the spin-only moment (either larger or smaller,... 

It is known from experience that only chiral molecules have the ability to rotate the plane of polarization. This observation suggests that molecular chirality is a manifestation of residual orbital angular momentum, and vice versa. When an achiral molecule is placed in a magnetic field the molecular magnetic vectors are aligned in the diection of the field and not along the local molecular symmetry directions. The molecule therefore acquires a... 

Reacting fragments align themselves so as to quench any residual orbital angular momentum in projection. 

It would be desirable to identify the residual donors in GaAs from the transition involving an exclton bound to the first non-rigid-rotational state. The terminal state consists of the excited state (n = 2) of the electron on the donor. The observation of different residual donor species from this transition is made possible by performing the experiment in a magnetic field. The magnetic field produces two effects (a) It separates out states with different orbital angular momentum and (b) it compresses the wave function which sharpens the lines and separates the donors. 

The precise nature of the magic Rydberg states is still a matter of controversy. It seems likely that they are states of high angular momentum, since otherwise their lifetimes (which scale as n5 rather than n3) would not be high enough. If so, then photoexcitation alone would not allow them to be reached, and it is likely that collisions with atoms of the residual vacuum play some role in populating them. 

A choice of basis set implies a partitioning of the Hamiltonian, H = Hel -I- Hso + Tn(R) + Hrot, into two parts a part, H ° which is fully diagonal in the selected basis set, and a residual part, H(1b The basis sets associated with the various Hund s cases reflect different choices of the parts of H that are included in fP°). Although in principle the eigenvalues of H are unaffected by the choice of basis, as long as this basis set forms a complete set of functions, one basis set is usually more convenient to use or better suited than the others for a particular problem. Convenience is a function of both the nature of the computational method and the relative sizes of electronic, spin-orbit, vibrational, and rotational energies. The angular momentum basis sets, from which Hund s cases (a)-(e) bases derive, are... 

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