Chang-Pelissier-Durand

ZORA zeroth-order regular approximation, also known as CPD (for Chang-Pelissier-Durand)... 

CPD=Chang - Pelissier- Durand DCB = Dirac - Coulomb -Breit DHF = Dirac-Hartree-Fock DK = Douglas-Kroll FORA = first-order regular approximation MVD = mass-velocity-Darwin term QED = quantum electrodynamics ZORA = zero-order regular approximation. 

As shown by Chang, Pelissier and Durand (CPD) [41] a regular expansion, however, can be deduced by isolating the Coulomb singularity by infinite summations. Let us rewrite the equation (38), when z — 0... 

If we wish to incorporate some level of relativistic effects into the zeroth-order Hamiltonian, we cannot start from Pauli perturbation theory or direct perturbation theory. But can we find an alternative expansion that contains relativistic corrections and is valid for all r that is, can we derive a regular expansion that is convergent for all reasonable values of the parameters The expansion we consider in this chapter has roots in the work by Chang, Pelissier, and Durand (1986) and HeuUy et al. (1986), which was developed further by van Lenthe et al. (1993, 1994). These last authors coined the term regular approximation because of the properties of the expansion. 

In the development of the Pauli Hamiltonian in section 17.1, truncation of the power series expansion of the inverse operator after the first term yielded the nonrelativistic Hamiltonian. In (18.1), the zeroth-order term is the Hamiltonian first developed by Chang, Pelissier, and Durand (1986), often referred to as the CPD Hamiltonian. The name given by van Lenthe et al. is the zeroth-order regular approximation, ZORA, which we will adopt here. The zeroth-order Hamiltonian is... 

A more promising route is to look for a perturbation parameter which permits a regular expansion for all values of the momentum. Chang, Pelissier, and Durand (CPD) have found a corresponding perturbation series, and the Amsterdam group " has developed it further. It makes use of... 

Chang, C., Pelissier, M. and Durand, P. (1986) Regular Two-Component Pauli-Like Effective Hamiltonians in... 

Chang, Ch., Pelissier, M., and Durand, Ph. (1986). Regular two-component Pauli-like effective Hamiltonians in Dirac theory. Phys. Scr., 34, 394-404. 

Faegri Jr K et al. 2007 Introduction to relativistic quantum chemistry. Oxford University Press. Chang C, Pelissier M and Durand P 1986 Regular two-component panh-hke effective hamil-tonians in dirac theory. Physica Scripta 34(5), 394. 

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