The Variational DKH Scheme for Perturbing Potentials

As before, we stick to the one-electron case and leave the generalization to N electrons to the reader. The proper choice of the DKH expansion parameter, V or V(A), for the DKH transformation is a decisive question in the sequential unitary transformation scheme as it produces a series expansion of the block-diagonal operator with each term to be classified according to a well-defined order in the expansion parameter. In the case of a one-step decoupling scheme (for instance, in a purely numerical fashion as suggested by Barysz and Sadlej for the Hamiltonian see section 11.6) all derivations of this section are also valid. 

If the property is incorporated variationally into the four-component Dirac picture (as in section 15.1), the A-dependent energy is the reference value which has to be reproduced by the DKH calculation. In order to evaluate this energy within a two-component framework, the perturbed Hamiltonian 

This one-electron energy e, (A) may be generalized to the many-electron case to yield E (A). According to the basic philosophy of the generalized DKH theory [611], the global unitary transformation U A) is constructed step by step as the product 

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