Spin orbitals generalized normal ordering

A full relativistic theory for coupling tensors within the polarization propagator approach at the RPA level was presented as a generalization of the nonrelativistic theory. Relativistic calculations using the PP formalism have three requirements, namely (i) all operators representing perturbations must be given in relativistic form (ii) the zeroth-order Hamiltonian must be the Dirac-Coulomb-Breit Hamiltonian, /foBC, or some approximation to it and (iii) the electronic states must be relativistic spin-orbitals within the particle-hole or normal ordered representation. Aucar and Oddershede used the particle-hole Dirac-Coulomb-Breit Hamiltonian in the no-pair approach as a starting point, Eq. (18),... 

Special attention has been given to the lifetimes of Li autoionization states. There are two types of states that are metastable against autoionization (i) those that cannot decay because of spin conservation, e.g., the state Li(ls2s2p) P, which was studied in detail by Feldman and Novik and (ii) those that cannot decay because of parity conservation, e.g., the state s2p ) P and generally all the doubly excited states with even parity and odd total orbital angular momentum (or vice versa). Whereas typical lifetimes of the normal Li autoionization states are between 10 and 10 sec, the Li(ls2s2p) P lives for t = 5.1 psec and the Li(ls2p ) P has a lifetime in the order of 5.10"" sec. " The main decay... 

An inspection of the experimental data for normal paramagnets shows that deviations from the spin-only formula mostly towards higher values are frequently found. In fact, the amount to which the orbital contribution is quenched depends on the electron configuration and on the symmetry of the particular compound. The structural implications of these observations have been widely used in the past and the results are discussed in various magnetochemical publications [6, 25] and standard coordination chemistry textbooks. It has been found that, in general, the application of ligand field theory is often very useful in order to understand the magnetic behaviour of transition metal complexes. In this respect, we refer to the texts listed in the reference section I.I.8.2. 

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