No-pair Dirac-Coulomb-Breit Hamiltonian

Y. Ishikawa, K. Koc. Relativistic many-body perturbation theory based on the no-pair Dirac-Coulomb-Breit Hamiltonian Relativistic correlation energies for the noble-gas sequence through Rn (Z=86), the group-llB atoms through Hg, and the ions of Ne isoelectronic sequence. Phys. Rev. A, 50(6) (1994) 4733-4742. 

E. Eliav, U. Kaldor, Y. Ishikawa. Relativistic Coupled Cluster Theory Based on the No-Pair Dirac-Coulomb-Breit Hamiltonian Relativistic Pair Corrdation Energies of the Xe Atom. Int. J. Quantum Chem. Quantum Chem. Symp., 28 (1994) 205-214. 

The relativistic no-pair Dirac-Coulomb-Breit Hamiltonian... 

The no-virtual-pair Dirac-Coulomb-Breit Hamiltonian, correct to second order in the fine-structure constant a, provides the framework for four-component methods, the most accurate approximations in electronic structure calculations for heavy atomie and molecular systems, ineluding aetinides. Electron correlation is taken into aeeount by the powerful coupled eluster approaeh. The density of states in actinide systems necessitates simultaneous treatment of large manifolds, best achieved by Fock-space coupled eluster to avoid intruder states, which destroy the convergence of the CC iterations, while still treating a large number of states simultaneously, intermediate Hamiltonian sehemes are employed. 

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. 

A full relativistic theory for coupling tensors within the polarization propagator approach at the RPA level was presented as a generalization of the nonrelativistic theory. Relativistic calculations using the PP formalism have three requirements, namely (i) all operators representing perturbations must be given in relativistic form (ii) the zeroth-order Hamiltonian must be the Dirac-Coulomb-Breit Hamiltonian, /foBC, or some approximation to it and (iii) the electronic states must be relativistic spin-orbitals within the particle-hole or normal ordered representation. Aucar and Oddershede used the particle-hole Dirac-Coulomb-Breit Hamiltonian in the no-pair approach as a starting point, Eq. (18),... 

Since the relativistic many-body Hamiltonian cannot be expressed in closed potential form, which means it is unbound, projection one- and two-electron operators are used to solve this problem [39], The operator projects onto the space spanned by the positive-energy spectrum of the Dirac-Fock-Coulomb (DFC) operator. In this form, the no-pair Hamiltonian [40] is restricted then to contributions from the positive-energy spectrum and puts Coulomb and Breit interactions on the same footing in the SCF calculations. 

Having defined our starting point, the second quantized no-pair Hamiltonian, we may now take a closer look at the relations between the matrix elements. For future convenience we will also change the notation of these matrix elements slightly. Due to hermiticity of the Dirac Hamiltonian and the Coulomb-Breit operator we have... 

An overview of the salient features of the relativistic many-body perturbation theory is given here concentrating on those features which differ from the familiar non-relativistic formulation and to its relation with quantum electrodynamics. Three aspects of the relativistic many-body perturbation theory are considered in more detail below the representation of the Dirac spectrum in the algebraic approximation is discussed the non-additivity of relativistic and electron correlation effects is considered and the use of the Dirac-Hartree-Fock-Coulomb-Breit reference Hamiltonian demonstrated effects which go beyond the no virtual pair approximation and the contribution made by the negative energy states are discussed. 

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