The complete basis set limits of the correlation energy of diatomic molecules using distributive $s$-Gaussian functions

In this paper possibilities of distributive s-Gaussian functions to estimate the second-order correlation energy (MP2) are investigated to the complete basis set limit. In contrast to standard atom-centered, the proposed bases consist of functions distributed along the molecular axis and off-axis functions. We propose and investigate the possibilities of one of the models for choosing the alignment of such functions. The model is characterized by a set of subsets of off-axis $s$-functions uniformly distributed along circles whose planes are perpendicular to the molecular axis. The function parameters are determined by minimizing the Hartree–Fock energy (for functions located along the molecular axis) and minimizing the Hylleraas functional (for off-axis $s$-functions). The resulting basis sequences, combined with known extrapolation models, are used to predict the MP2 energy in the complete basis set limit. The efficiency of the models is demonstrated by calculating the energy MP2 of simple H$_2$ and LiH molecules.