Wood-Boring equation

The other approach is to use a spin-dependent equation, such as the Dirac-Hartree-Fock or Wood-Boring equation, to obtain spin-dependent pseudopotentials, and take the appropriate averages and differences to obtain a spin-free relativistic pseudopotential and a spin-orbit pseudopotential. The formalism for the latter approach is as follows. 

A straightforward elimination of the small components from the Dirac equation leads to the two-component Wood-Boring (WB) equation [81], which exactly yields the (electronic) eigenvalues of the Dirac Hamiltonian upon iterating the energy-dependent Hamiltonian... 

Elimination of the small component 2a( ) Is ds to a second-order differential equation for the large component Pa( )> the radial Wood-Boring (WB) equation (Wood and Boring... 

The deficiencies of this procedure have been carefully analysed by Boring and Wood [62] who worked with an approximate treatment of the Dirac equations, due to Cowan and Griffith [63]. In this method the spin-orbit operator is omitted from the one-electron Hamiltonian but the mass-velocity... 

If we want to incorporate spin-orbit effects, either subsequent to a spin-free relativistic calculation using this operator or directly as a first step using a modified operator, we must include the previously discarded last term of the large component of the Dirac equation above. For atoms, this was first done by Wood and Boring (1978), who used the operator perturbatively. 

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