Relativistic coupled cluster method based on Dirac—Coulomb—Breit wavefunctions. Ground state energies of atoms with two to five electrons

Explorations of many-body relativistic wave equations within a one-dimensional model

A one-dimensional analog that reflects many of the features of the many-body Dirac equation is considered. The model can be solved numerically using a convenient finite basis discrete variable representation. Both an (unbound) harmonic oscillator potential and a (bound) inverse Gaussian one-particle potential are discussed for interacting particles. In a second thread in the paper, the mass term is neglected in the model many-body Dirac equation, and it is shown that the original equation, which has 2N coupled components for N particles can then be reduced to 2N decoupled one-component equations, which can be solved “analytically” for arbitrary many particles interacting through central two-body potentials.

The Dirac equation in quantum chemistry: strategies to overcome the current computational problems

A perspective on the use of the relativistic Dirac equation in quantum chemistry is given. It is demonstrated that many of the computational problems that plague the current implementations of the different electronic structure methods can be overcome by utilizing the locality of the small component wave function and density. Possible applications of such new and more efficient formulations are discussed.