Douglas infinite-order

Abstract In this chapter 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 and the potential energy curves. Spin-free and spin dependent atomic mean filed (AMFI) two-component theories are presented. The importance of the quanmm electrodynamics (QED) corrections and their role in the correct description of the spectroscopic properties of many-electron atoms for the X-ray spectra is discussed as well. Some examples of the molecular QED calculations will be discussed here as well. 

The above idea was the basis of the BSS method formulated by Barysz and Sadlej [8]. The BSS method has its roots in the historically earlier Douglas-Kroll-Hess (DKH2 and DKH3) [9, 10] approximation. In the BSS approximation the fine struc-tme constant a is the pertmbative parameters and it differs from the DKH method where the potential V is nsed as the pertmbation. Formally the BSS and DKH methods are of the infinite order in a or V. However, the necessity to define the analytical form of the R operator and the Hamiltonian in each step of the iteration, makes the accmacy of both methods limited to the lowest order in a or V. 

This Hamiltonian can then be used variationally in quantum chemical calculations, since because of its derivation no negative energy states can occur. It should be anticipated that this Hamiltonian is conceptually equivalent to the infinite-order Douglas-Kroll-Hess Hamiltonian to be discussed in section 12.3, because both schemes do not apply any expansion in 1/c. Also the expressions for Ep and Ap are strictly evaluated in closed form within both approaches. However, whereas Douglas-Kroll-Hess theory yields analytic exressions for each order in V, the infinite-order two-component method summarizes all powers of V in the final matrix representation of/+. 

D. K dziera, M. Barysz, A. J. Sadlej. Expectation values in spin-averaged Douglas-KroU and Infinite-order relativistic methods. Struct. Chem., 15(5) (2004) 369-377. 

J. Seine, M. Hada. Magnetic shielding constants calculated by the infinite-order Douglas-KroU-Hess method with electron-electron relativistic corrections. /. Chem. Phys., 132 (2010) 174105. 

Scalar relativistic corrections at the levels of Douglas-Kroll, ZORA, and the infinite-order relativistic approximation (lORA) (Dyall and van Lenthe 1999). 

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