Relativistic ground state of diatomic molecules from the numerical solution of the Dirac equation on parallel computers

The parallel implementation of a variational method for the numerical solution of the time-independent Dirac equation is presented. This is utilized in the calculation of diatomic molecule relativistic wave functions and ground state energy, in the Born-Oppenheimer approximation. Following [1], a functional equation predicting the same spectrum as the Dirac equation is discretized over a set of basis functions. We find that the combination of B-spline basis functions and prolate spheroidal coordinate systems facilitate the vectorization of the technique using domain decomposition. This procedure results in a non-linear eigenvalue problem which is solved by iteration using Brent's method. We validate our methodology by comparing with existing results and show that it yields very accurate ones. We also analyze the parallelization and demonstrate that our implementation has a good scaling performance. Finally, the utilization of this method for laser-matter interaction and other physical applications will be discussed.