On the basis set convergence of electron–electron entanglement measures: helium-like systems - Hofer, Thomas S. (Frontiers in Chemistry, 2013)
A systematic investigation of three different electron--electron entanglement measures, namely the von Neumann, the linear and the occupation number entropy at full configuration interaction level has been performed for the four helium-like systems hydride, helium, lithium(I) and beryllium(II) using a large number of different basis sets. The convergence behaviour of the resulting energies and entropies was revealed that the latter do in general not show monotonic convergence upon increase of the one--electron basis. Overall, the three different entanglement measures show good agreement among each other, the largest deviations being observed for small basis sets. The data clearly demonstrates that it is important to consider the nature of the chemical system when investigating entanglement phenomena in the framework of Gaussian type basis sets: while in case of hydride the use of augmentation functions is crucial, the application of core functions greatly improves the accuracy in case of cationic systems such as lithium(I) and beryllium(II). In addition, numerical derivatives of the entanglement measures with respect to the nucleic charge have been determined, which proved to be a very sensitive probe of the convergence leading to qualitatively wrong results if inadequate basis sets are used.