Douglas-Kroll first-order

The chapter consists of two parts. In the first part I discuss some aspects of relativistic theory, the accuracy of the infinite order two-component relativistic lOTC method and its advantage over the infinite order Douglas-Kroll-Hess (DKHn) theory, in the proper description of the molecular spectroscopic parameters. Spin-free and spin dependent atomic mean filed (AMFI) theory is presented. Additionally, the accuracy of the relevant potential energy curves is discussed as well. In the second part I show the role of the QED corrections and that they are necessary for the correct description of the spectroscopic properties of atoms for the X-ray spectra. Some examples of the molecular QED calculations will be discussed here as well. 

We can classify the Douglas-Kroll expansion in terms of the leading power of c as well as in terms of V. The off-diagonal operator in the zeroth order (free-particle Foldy-Wouthuysen) expansion is Its elimination in the first Douglas-Kroll... 

The second-order one-electron Douglas-Kroll Hamiltonian has found wide application in quantum chemistry programs through approximations that are discussed in the next two sections. Although it is a considerable improvement on the first-order Hamiltonian, for some heavy elements the error is significant. Hamiltonians through fifth order have been derived by Nakajima and Hirao (2000). The third-order Hamiltonian is given by... 

The first parenthesis contains the first-order term from the free-particle Foldy-Wouthuysen transformation, and the second parenthesis contains the second-order Douglas-Kroll term. Both A and Ep are spin-free, so the spin-dependence comes from the transformations involving 1 2, which was defined as... 

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. 

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