Advantages of Scalar-Relativistic DKH Hamiltonians

The pleasant features of DKH Hamiltonians, which is the basis for their success in relativistic quantum chemistry, are first of all that they can be given in analytic form. Then, they are strictly variationally stable by construction, since the only source of unbounded behavior, i.e., the part of the Dirac Hamiltonian belonging to the small component, is no longer coupled to the electronic Hamiltonian /+. The odd-order DKH Hamiltonians may not be variational, but may overestimate binding energies for electrons in external potentials, but there exists a ground state for every DKH Hamiltonian, and hence no variational collapse can occur. 

The terms scalar-relativistic, spin-free, spin-averaged and one-component all refer to this very same procedure of eliminating all Pauli spin matrices from the Hamiltonian by simple deletion after employment of Dirac s relation. 

But to be more precise, most implementations of the DKH Hamiltonian transform the one-electron terms of the Fock operator / only. Hence, the general scalar potential V is reduced to the complete electron-nucleus potential 

By inspection of the explicit expressions for the even terms given above it appears that all even terms depend only quadratically on the momentum operator rather than on the linear operator p. It is easy to realize that this is not an accidental feature of the six lowest-order terms of the DKH series but a fundamental property of all even terms occurring within any expansion of the 

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