Dirac-Coulomb Hamiltonian/method

The At2 species and other species containing At atom have brought the attention mainly for testing the rehabiUty of relativistic quantum mechanical methods [9, 28, 29, 92, 96, 97]. It came out notably that SOC strongly affects the properties of the closed-sheU At2 species. Spectroscopic constants calculated at CCSD(T) level using either the 4c Dirac-Coulomb Hamiltonian or an X2C Hamiltonian [9, 98], are presented in Table 20.1. 

The most straightforward method for electronic structure calculation of heavy-atom molecules is solution of the eigenvalue problem using the Dirac-Coulomb (DC) or Dirac-Coulomb-Breit (DCB) Hamiltonians [4f, 42, 43] when some approximation for the four-component wave function is chosen. 

The incorporation of electron correlation effects in a relativistic framework is considered. Three post Hartree-Fock methods are outlined after an introduction that defines the second quantized Dirac-Coulomb-Breit Hamiltonian in the no-pair approximation. Aspects that are considered are the approximations possible within the 4-component framework and the relation of these to other relativistic methods. The possibility of employing Kramers restricted algorithms in the Configuration Interaction and the Coupled Cluster methods are discussed to provide a link to non-relativistic methods and implementations thereof. It is shown how molecular symmetry can be used to make computations more efficient. 

We will start by reviewing some basic relativistic theory to introduce the notation and concepts used. The rest of the chapter is devoted to the three major post-DHF methods that are currently available for the Dirac-Coulomb-Breit Hamiltonian. All formulas will be given in atomic units. 

The DCB CCSD method is based on the Dirac-Coulomb-Breit Hamiltonian... 

An improved basis set with 36s32p24d22fl0g7h6i uncontracted Gaussian-type orbitals was used and all 119 electrons were correlated, leading to a better estimate of the electron affinity within the Dirac-Coulomb-Breit Hamiltonian, 0.064(2) eV [102]. Since the method for calculating the QED corrections [101] is based on the one-electron orbital picture, the 8s orbital of El 18 was extracted from the correlated wave function by... 

Abstract Variational methods can determine a wide range of atomic properties for bound states of simple as well as complex atomic systems. Even for relatively light atoms, relativistic effects may be important. In this chapter we review systematic, large-scale variational procedures that include relativistic effects through either the Breit-Pauli Hamiltonian or the Dirac-Coulomb-Breit Hamiltonian but where correlation is the main source of uncertainty. Correlation is included in a series of calculations of increasing size for which results can be monitored and accuracy estimated. Examples are presented and further developments mentioned. 

The most advanced relativistic approach in relativistic calculations of X-ray spectra, is most likely that based on the Dirac-Coulomb-Breit Hamiltonian and quantum electrodynamic contributions accounted for. In addition, one should also carry out the corresponding correlated-level calculation within these relativistic formalism. To illustrate the role and size of relativistic and QED corrections the core and valence ionisation potentials and excitation energies of noble gases are shown. The relativistic fOTC CASSCE/CASPT2 method together with the restricted active space... 

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