Orbital angular momentum symmetry

Their symmetry labels can be obtained by vector coupling (see Appendix G) the spin and orbital angular momenta of the two subsystems. The orbital angular momentum coupling... 

With six electrons and six MOs removed from the active space, one is left with 6 electrons in 20 orbitals, a calculation that could be performed easily. Several calculations were thus done with different space and spin symmetry of the wave function. The resulting ground state was found to be a septet state with all six electrons having parallel spin, and the orbital angular momentum was high with A = 11. Spin-orbit calculations showed that the spin and orbital angular momenta combined to form an O = 8 state. The final label of the ground state is thus yOg. 

The GUGA-Cl wavefunctions are spatial and spin symmetry-adapted, thus the projections of total orbital angular momentum and total spin of a hydrogen molecule in a particular electronic state are conserved for all the values of R. Therefore, the term remains constant for an electronic state, and it causes a... 

Figure 1. Cartoon depicting symmetry considerations of the asymptotic wavefunction that influences which potential energy surface is accessed. Representative angular momentum quantum numbers relevant to the process are the total molecular angular momentum exclusive of nuclear spin (f) and the relative orbital angular momentum (/).

The result of this lower symmetry of the environment is the quenching of the orbital angular momentum of the electron the orbital angular momentum is no longer a good quantum number and has an average value of zero. Some contribution of the orbital motion however remains, and this causes a positive or negative deviation of the g-factor from the free spin value of 2.0023. 

It has been pointed out above that two electrons in the Is orbital must have their spins opposed, and hence give rise to the singlet state So, with no spin or orbital angular momentum, and hence with no magnetic moment. Similarly it is found that a completed subshell of electrons, such as six electrons occupying the three 2p orbitals, must have S — 0 and L = 0, corresponding to the Russell-Saunders term symbol lS0 such a completed subshell has spherical symmetry and zero magnetic moment. The application of the Pauli exclusion prin-... 

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... 

In this case the planar complex is diamagnetic and possesses the usual narrow line, high-resolution diamagnetic spectrum. The tetrahedral complex in Td symmetry would possess a 3T ground state. In approximately tetrahedral nickel(II) complexes the orbital angular momentum is incompletely quenched the result is a very short electron spin relaxation time and an NMR spectrum with relatively narrow, paramagnetic shifted resonances. 

---