Perturbative corrections for molecular relativistic EFG contributions

In molecular property calculations the same mutual interplay of electron correlation, relativity and perturbation operators (e.g. external fields) occurs. For light until medium atoms relativistic contributions were often accounted for by perturbation theory facilitating quasirela-tivistic approximations to the Dirac-Hamiltonian [114-117]. It is well-known that operators like the Breit-Pauli Hamiltonian are plagued by essential singularities and therefore are not to be used in variational procedures. It can therefore be expected that for heavier elements per-turbational inclusion of relativity will eventually become inadequate and that one has to start from a scheme where relativitiy is included from the beginning. Nevertheless very efficient approximations to the Dirac equation in two-component form exist and will be discussed further below in combination with their relevance for EFG calculations. In order to calculate the different contributions to a first-order property as the EFG, Kello and Sadlej devised a multiple perturbation scheme [118] in which a first-order property is expanded as 

This method was then applied to the hydrogen halides in order to estimate relativistic contributions to the EFG. The mass-velocity and Darwin terms were hereby employed as relativistic operators in combination with a many-body correlation treatment. From the results in 

Also in the molecular case perturbation theory helps to clarify individual contributions to the property ax cording to their order [120] but more crucial is the fact that perturbation theory becomes an inadequate means for the proper description of relativistic effects in heavy atoms. Furthermore spin-orbit effects can substantially influence the result and methods using multi-component wave functions incorporating spin-orbit coupling from the beginning are favorable. 

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