2D-block geminals: Guidelines to choose effective excitations

A new family of geminal Ansätze called antisymmetrized product of 2D-block geminals (AP2D-BG) has been introduced recently to solve the electronic Schrödinger equation of molecules. They build on an antisymmetrized product of strongly orthogonal geminals (APSG) while lifting the "strong orthogonality" and "seniority zero" restrictions. The combinatorics to select the excitations which can be added to each geminal of the product grows exponentially with the number of geminals. However, in this study on diatomic molecules, we present simple guidelines to drastically reduce the number of excitations, which are useful to lower the electronic energy in variational calculations. Although different regimes to partition the orbital space into 1D- and 2D-blocks in an optimal way are observed along the potential energy curves (PEC), a simple strategy for choosing the block types associated to the geminals in each 2D-block is found successful in all cases. This makes the method quite practical to use. Moreover, the optimal geminals can be easily related to classical Lewis structures of chemistry. The quality of the PECs is assessed by calculating equilibrium geometries and fundamental frequencies; the improvement with respect to APSG is discussed.