Initializing the cubatures requires the target error threshold that is provided as user input, the number of α groups, and the corresponding α, distances ranges, and integration cutoff values that are associated with a given α group. Provided these inputs, a suitable Gauss-Legendre quadrature and spherical t-design grid are chosen to achieve the target error (ε in Eqs. 3 and 6). As an optimization, the Gauss-Legendre roots and weights are combined with the spherical t-design points resulting in what we refer to as the cubature nodes and weights. This is done to avoid nested loops and accessing multiple arrays. Additionally, constants such as α and z are also pre-incorporated to minimize the number of instructions done later when computing energies and forces.