Accurate explicitly correlated wave functions for two electrons in a square

An explicitly correlated linear-r(12) variational method is developed for a system of two electrons confined to a two-dimensional square well with infinite walls. The wave function is written as an expansion in products of non-negative integer powers of the relative and center-of-mass electronic coordinates and powers of r(12) restricted to 0 and 1. This form indirectly includes higher powers of the interelectronic distance and exhibits a much faster convergence than a similar expansion without r(12)-dependent terms. The method is implemented using high-precision floating-point arithmetic. Ground-state total energies are reported with at least 12 accurate significant figures for squares with sides from 1 to 50 bohrs. The method can be used "as is" for excited states and for two-dimensional rectangular wells. We also show that wave functions for two electrons in a square and in a rectangle have a higher symmetry than can be accounted for by the point group of the system.