Electronic spin angular

Figure 1.10 Space quantization of electron spin angular momentum...

The component of the total (orbital plus electron spin) angular momentum along the intemuclear axis is Qfi, shown in Figure 7.16(a), where the quantum number Q is given by... 

The singlet function corresponds to zero total electron spin angular momentum, S = 0 the triplet functions correspond to S = 1. Operating on these functions with the spin Hamiltonian, we get ... 

The quantum number S defines the total electronic spin angular momentum and its allowed values are... 

Most molecules with A>0 obey Hund s case (a). Here, the axial components of electronic orbital angular momentum (Ah) and of electronic spin angular momentum (2fc) combine to give a resultant axial component of total electronic angular momentum (A + 2)fi. The quantum number ft is defined as (Section 1.19)... 

The older literature uses K instead of N.) For the most common case-(b) case, we have A = 0 here N has the possible values 0,1,2,... and represents just rotational angular momentum. The angular momentum N then adds to the electronic spin angular momentum S to give a total angular momentum apart from nuclear spin, which, as usual, is called J. The quantum number J has the possible values [Equation (1.265)]... 

For case (b) coupling, if we first neglect electronic spin angular momentum, then N is analogous to J and A is analogous to /f, so that (5.67) becomes... 

Considering a A2 as part of the electronic energy and adding a term to take account of the electronic spin angular momentum, we get the expression (4.149). The condition J > K becomes N > A [Equation (4.147)]. 

Polyatomic molecules. The same term classifications hold for linear polyatomic molecules as for diatomic molecules. We now consider nonlinear polyatomics. With spin-orbit interaction neglected, the total electronic spin angular momentum operator 5 commutes with //el, and polyatomic-molecule terms are classified according to the multiplicity 25+1. For nonlinear molecules, the electronic orbital angular momentum operators do not commute with HeV The symmetry operators Or, Os,. .. (corresponding to the molecular symmetry operations R, 5,. ..) commute... 

Now the total angular momentum of an electron is the resultant of the orbital angular momentum vector and the electron-spin angular momentum vector- Both of these are quantized, and we can define a new quantum number, j ... 

The dynamic state is defined by the values of certain observables associated with orbilal and spin motions of the electrons and with vibration and rotation of [lie nuclei, and also by symmetry properties of the corresponding stationary-state wave functions. Except when heavy nuclei ate present, the total electron spin angular momentum of a molecule is separately conserved with magnitude Sh. and molecular slates are classified as singlet, doublet, triplet., . according to the value of the multiplicity (25 + I). This is shown by a prefix superscript lo the term symbol, as in atoms. 

Rather than detail these effects here, however, we can illustrate the effects of angular momentum in a simpler case by examining the electronic spin angular momentum S. Experimentally, it is found that all electrons have angular momentum, and the length of the angular momentum vector is always S = a/37 /2. This angular momentum... 

From our present standpoint, we know that the deflection of a silver atom in the Stern-Gerlach experiment is caused by the interaction of its electronic spin angular momentum S with an inhomogeneous magnetic field. The projection of S on the direction of this field, Ms, is quantized. For a silver atom, Ms can take two values +vjh and — h, where h is Planck s constant h over 2ji and adopts a value of 1.054571596 x 10-34 Js in cgi units. 

Figure 7.16 (a) Hund s case (a) and (b) Hund s case (c) coupling of orbital and electron spin angular momenta in a diatomic molecule... 

The isotropic hyperfine coupling observed in e.s.r. spectra of radicals arises from the Fermi-contact interaction between the electronic spin angular... 

Let us assume, in analogy to Eq. (3.20.6), that the conversion factor between the electron spin angular momentum S and the concomitant spin magnetic moment pu is... 

Russell-Saunders (RS) coupling [29] occurs, for light atoms, when the individual electron orbital angular momenta 1/ and electron spin angular momenta ov add, to form "good" (i.e., valid) vectors L = h ar d S = cr,. These two vectors then couple to form... 

Many free radicals in their electronic ground states, and also many excited electronic states of molecules with closed shell ground states, have electronic structures in which both electronic orbital and electronic spin angular momentum is present. The precession of electronic angular momentum, L, around the intemuclear axis in a diatomic molecule usually leads to defined components, A, along the axis, and states with A =0, 1, 2, 3, etc., are called , n, A, , etc., states. In most cases there is also spin angular momentum S, and the electronic state is then labelled 2,s+1 Id, 2,s+1 A, etc. 

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