Wood-Boring Hamiltonian

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 

Due to the energy-dependence of the Hamiltonian the Wood-Boring approach leads to nonorthogonal orbitals and has been mainly used in atomic finite difference calculations as an alternative to the more involved Dirac-Hartree-Fock calculations. The relation 

Within the central field approximation one obtains from Eq. 18 for an one-electron atom the following radial equation  

20 can be solved iteratively and yields the same one-particle energies as the corresponding Dirac-equation. The radial functions P K r) correspond to the large components. In the many-electron case the correct nonlocal Hartree-Fock potential is used in Eq. 21, but a local approximation to it in Eqs. 22. Averaging over the relativistic quantum number k leads to a scalar-relativistic scheme. 

The WB approach was used to generate both model potentials as well as pseudopotentials. The DKH method was applied in explicit relativistic calculations together with model potentials and also to provide molecular AE results for calibration studies with various valence-only schemes (cf. below). 

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Including Spin-Orbit Effects through the Wood-Boring Hamiltonian. 

Seijo [120] has performed relativistic ab initio model potential calculations including spin-orbit interaction using the Wood-Boring Hamiltonian. Calculations ere performed for several atoms up to Rn, and several dimer... 

In the Cowan-Griffin-Wood-Boring Hamiltonian, the 7] and operators of Eq. (4) read ... 

Barandiaran Z, Seijo L. The ab initio model potential method. Cowan-Griffin relativistic core potentials and valence basis sets from Li (Z = 3) to La (Z = 57). Can J Chem. 1992 70 409. Seijo L. Relativistic ab initio model potential calculations including spin-orbit effects trhough the Wood-Boring Hamiltonian. J Chem Phys. 1995 102 8078. 

The formalism described here to derive energy-consistent pseudopotentials can be used for one-, two- and also four-component pseudopotentials at any desired level of relativity (nonrelativistic Schrbdinger, or relativistic Wood-Boring, Douglas-Kroll-Hess, Dirac-Coulomb or Dirac-Coulomb-Breit Hamiltonian implicit or explicit treatment of relativity in the valence shell) and electron correlation (single- or multi-configurational wavefunctions. The freedom... 

Cowan-Griffin-Wood-Boring AIMP molecular Hamiltonian... 

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... 

J. H. Wood, A. M. Boring. Improved PauU Hamiltonian for local-potential problems. Phys. Rev. B, 18(6) (1978) 2701-2711. 

Wood JH, Boring AM. Improved Pauh hamiltonian for local-potential prohlems. Phys Rev B. 

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