Geminal-based high-accuracy quantum mechanics for few-body systems

We elaborate on the variational solution of the Schrödinger and Dirac equations of few-body atomic and molecular systems without relying on the Born-Oppenheimer paradigm [1]. The wavefunction is expanded in terms of parameterized explicitly correlated Gaussians with polynomial prefactors. We developed a simple strategy for the elimination of the translational kinetic energy of the total energy carried out in laboratory-fixed Cartesian coordinates [2]. For semi-classical relativistic calculations we devised a kinetic-balance condition for explicitly correlated basis functions [3]. The resulting form of kinetic balance establishes a relation between all spinor components of an N-fermion system to the non-relativistic limit, which is in accordance with modern exact-decoupling methods. In my talk, I will discuss these developments in the light of spectroscopic results.

[1] E. Matyus, M. Reiher, J. Chem. Phys. 137, 024104 (2012); A. Muolo, E. Matyus, M. Reiher, J. Chem. Phys. (2018) in press.
[2] B. Simmen, E. Matyus, M. Reiher, Mol. Phys. 111, 2086 (2013); A. Muolo, E. Matyus, M. Reiher, J. Chem. Phys. 148, 084112 (2018).
[3] B. Simmen, E. Matyus, M. Reiher, J. Phys. B 48, 245004 (2015).