Chapter Six - How competitive are expansions in orbital products with explicitly correlated expansions for helium dimer

While majority of current molecular electronic structure calculations use orbital basis sets, for two-electron systems the bases used are always explicitly correlated. The latter bases are also often used for up to four-electrons systems, but its use in direct solutions of Schrödinger's equation becomes prohibitively expensive for six or more electrons (such bases are often used in perturbative or coupled-cluster approaches for much larger systems). Quantitative comparisons of the performance of orbital bases relative to explicitly correlated ones are not available for few-electron systems. We provide such comparisons on the example of the helium dimer nonrelativistic Born–Oppenheimer interaction energies. We use the most accurate such energies (Przybytek et al., 2017, Ref. 42) computed in very large basis sets of explicitly correlated Gaussian (ECG) functions with carefully optimized nonlinear parameters. We have performed analogous calculations up to the full configuration interaction level using the largest currently possible orbital basis sets at each level of theory. We show that the errors of such orbital results are from one to two orders of magnitude larger than the uncertainties of the ECG results. Thus, at the present time the former methodology is not competitive with the latter one for four-electron systems.